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bool 2
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classes | file_name
stringlengths 5
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stringlengths 1
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dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Prims.Tot | val decode32_bounded_integer_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == decode_bounded_integer 3 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b | val decode32_bounded_integer_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == decode_bounded_integer 3 (B32.reveal b)})
let decode32_bounded_integer_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == decode_bounded_integer 3 (B32.reveal b)}) = | false | null | false | be_to_n_3 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.be_to_n_3",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.decode_bounded_integer",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decode32_bounded_integer_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == decode_bounded_integer 3 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.decode32_bounded_integer_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 3
-> y:
LowParse.Spec.BoundedInt.bounded_integer 3
{y == LowParse.Spec.BoundedInt.decode_bounded_integer 3 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 46,
"start_col": 2,
"start_line": 46
} |
Prims.Tot | val bounded_integer_of_le_32_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == bounded_integer_of_le 2 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b | val bounded_integer_of_le_32_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == bounded_integer_of_le 2 (B32.reveal b)})
let bounded_integer_of_le_32_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == bounded_integer_of_le 2 (B32.reveal b)}) = | false | null | false | le_to_n_2 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.le_to_n_2",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.bounded_integer_of_le",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounded_integer_of_le_32_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == bounded_integer_of_le 2 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.bounded_integer_of_le_32_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 2
-> y:
LowParse.Spec.BoundedInt.bounded_integer 2
{y == LowParse.Spec.BoundedInt.bounded_integer_of_le 2 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 142,
"start_col": 2,
"start_line": 142
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3) | let n_to_le_3 = | false | null | false | norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Pervasives.norm",
"Prims.Cons",
"FStar.Pervasives.norm_step",
"FStar.Pervasives.delta_attr",
"Prims.string",
"Prims.Nil",
"FStar.Pervasives.iota",
"FStar.Pervasives.zeta",
"FStar.Pervasives.primops",
"LowParse.SLow.Endianness.n_to_le_t",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.Endianness.Instances.bounded_integer",
"LowParse.SLow.Endianness.mk_n_to_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val n_to_le_3 : LowParse.SLow.Endianness.n_to_le_t (LowParse.Spec.Endianness.Instances.bounded_integer 3) 3 | [] | LowParse.SLow.BoundedInt.n_to_le_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | LowParse.SLow.Endianness.n_to_le_t (LowParse.Spec.Endianness.Instances.bounded_integer 3) 3 | {
"end_col": 112,
"end_line": 220,
"start_col": 16,
"start_line": 220
} |
|
Prims.Tot | val bounded_integer_of_le_32_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == bounded_integer_of_le 3 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b | val bounded_integer_of_le_32_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == bounded_integer_of_le 3 (B32.reveal b)})
let bounded_integer_of_le_32_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == bounded_integer_of_le 3 (B32.reveal b)}) = | false | null | false | le_to_n_3 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.le_to_n_3",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.bounded_integer_of_le",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounded_integer_of_le_32_3 (b: B32.lbytes 3)
: Tot (y: bounded_integer 3 {y == bounded_integer_of_le 3 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.bounded_integer_of_le_32_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 3
-> y:
LowParse.Spec.BoundedInt.bounded_integer 3
{y == LowParse.Spec.BoundedInt.bounded_integer_of_le 3 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 152,
"start_col": 2,
"start_line": 152
} |
Prims.Tot | val parse32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul | val parse32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_4 min max = | false | null | false | parse32_bounded_int32' min max 4ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 16777216 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32 (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 36,
"end_line": 283,
"start_col": 2,
"start_line": 283
} |
Prims.Tot | val bounded_integer_of_le_32_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == bounded_integer_of_le 1 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b | val bounded_integer_of_le_32_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == bounded_integer_of_le 1 (B32.reveal b)})
let bounded_integer_of_le_32_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == bounded_integer_of_le 1 (B32.reveal b)}) = | false | null | false | le_to_n_1 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.le_to_n_1",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.bounded_integer_of_le",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounded_integer_of_le_32_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == bounded_integer_of_le 1 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.bounded_integer_of_le_32_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 1
-> y:
LowParse.Spec.BoundedInt.bounded_integer 1
{y == LowParse.Spec.BoundedInt.bounded_integer_of_le 1 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 132,
"start_col": 2,
"start_line": 132
} |
Prims.Tot | val parse32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul | val parse32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_2 min max = | false | null | false | parse32_bounded_int32' min max 2ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 256 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 65536 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32 (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 36,
"end_line": 275,
"start_col": 2,
"start_line": 275
} |
Prims.Tot | val parse32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul | val parse32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le_1 min max = | false | null | false | parse32_bounded_int32_le' min max 1ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"LowParse.SLow.BoundedInt.parse32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 256 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 39,
"end_line": 344,
"start_col": 2,
"start_line": 344
} |
Prims.Tot | val parse32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul | val parse32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_1 min max = | false | null | false | parse32_bounded_int32' min max 1ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"LowParse.SLow.BoundedInt.parse32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 256 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32 (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 36,
"end_line": 271,
"start_col": 2,
"start_line": 271
} |
Prims.Tot | val bounded_integer_of_le_32 (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == bounded_integer_of_le sz (B32.reveal b)})) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4 | val bounded_integer_of_le_32 (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == bounded_integer_of_le sz (B32.reveal b)}))
let bounded_integer_of_le_32 (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == bounded_integer_of_le sz (B32.reveal b)})) = | false | null | false | match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4 | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"LowParse.Spec.BoundedInt.integer_size",
"LowParse.SLow.BoundedInt.bounded_integer_of_le_32_1",
"LowParse.SLow.BoundedInt.bounded_integer_of_le_32_2",
"LowParse.SLow.BoundedInt.bounded_integer_of_le_32_3",
"LowParse.SLow.BoundedInt.bounded_integer_of_le_32_4",
"FStar.Bytes.lbytes",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.bounded_integer_of_le",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } ) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounded_integer_of_le_32 (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == bounded_integer_of_le sz (B32.reveal b)})) | [] | LowParse.SLow.BoundedInt.bounded_integer_of_le_32 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | sz: LowParse.Spec.BoundedInt.integer_size -> b: FStar.Bytes.lbytes sz
-> y:
LowParse.Spec.BoundedInt.bounded_integer sz
{y == LowParse.Spec.BoundedInt.bounded_integer_of_le sz (FStar.Bytes.reveal b)} | {
"end_col": 35,
"end_line": 174,
"start_col": 2,
"start_line": 170
} |
Prims.Tot | val decode32_bounded_integer (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == decode_bounded_integer sz (B32.reveal b)})
) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4 | val decode32_bounded_integer (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == decode_bounded_integer sz (B32.reveal b)})
)
let decode32_bounded_integer (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == decode_bounded_integer sz (B32.reveal b)})
) = | false | null | false | match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4 | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"LowParse.Spec.BoundedInt.integer_size",
"LowParse.SLow.BoundedInt.decode32_bounded_integer_1",
"LowParse.SLow.BoundedInt.decode32_bounded_integer_2",
"LowParse.SLow.BoundedInt.decode32_bounded_integer_3",
"LowParse.SLow.BoundedInt.decode32_bounded_integer_4",
"FStar.Bytes.lbytes",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.decode_bounded_integer",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } ) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decode32_bounded_integer (sz: integer_size)
: Tot
(b: B32.lbytes sz -> Tot (y: bounded_integer sz {y == decode_bounded_integer sz (B32.reveal b)})
) | [] | LowParse.SLow.BoundedInt.decode32_bounded_integer | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | sz: LowParse.Spec.BoundedInt.integer_size -> b: FStar.Bytes.lbytes sz
-> y:
LowParse.Spec.BoundedInt.bounded_integer sz
{y == LowParse.Spec.BoundedInt.decode_bounded_integer sz (FStar.Bytes.reveal b)} | {
"end_col": 35,
"end_line": 68,
"start_col": 2,
"start_line": 64
} |
Prims.Tot | val parse32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul | val parse32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le_2 min max = | false | null | false | parse32_bounded_int32_le' min max 2ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 256 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 65536 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 39,
"end_line": 348,
"start_col": 2,
"start_line": 348
} |
Prims.Tot | val parse32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul | val parse32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_3 min max = | false | null | false | parse32_bounded_int32' min max 3ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 65536 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 16777216 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32 (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 36,
"end_line": 279,
"start_col": 2,
"start_line": 279
} |
Prims.Tot | val serialize32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le_3
min max
= serialize32_bounded_int32_le' min max 3ul | val serialize32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le_3 min max = | false | null | false | serialize32_bounded_int32_le' min max 3ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul
let serialize32_bounded_int32_le_2
min max
= serialize32_bounded_int32_le' min max 2ul
let serialize32_bounded_int32_le_3 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 65536 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 16777216 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 43,
"end_line": 392,
"start_col": 2,
"start_line": 392
} |
Prims.Tot | val serialize32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul | val serialize32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le_1 min max = | false | null | false | serialize32_bounded_int32_le' min max 1ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 256 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 43,
"end_line": 384,
"start_col": 2,
"start_line": 384
} |
Prims.Tot | val serialize32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (serializer32 (serialize_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le_fixed_size
min32 max32
= serialize32_filter serialize32_u32_le (in_bounds (U32.v min32) (U32.v max32)) | val serialize32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (serializer32 (serialize_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le_fixed_size min32 max32 = | false | null | false | serialize32_filter serialize32_u32_le (in_bounds (U32.v min32) (U32.v max32)) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"LowParse.SLow.Combinators.serialize32_filter",
"LowParse.Spec.Int.parse_u32_kind",
"LowParse.Spec.BoundedInt.parse_u32_le",
"LowParse.Spec.BoundedInt.serialize_u32_le",
"LowParse.SLow.BoundedInt.serialize32_u32_le",
"LowParse.Spec.BoundedInt.in_bounds",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_fixed_size_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le_fixed_size",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le_fixed_size"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul
let serialize32_bounded_int32_le_2
min max
= serialize32_bounded_int32_le' min max 2ul
let serialize32_bounded_int32_le_3
min max
= serialize32_bounded_int32_le' min max 3ul
let serialize32_bounded_int32_le_4
min max
= serialize32_bounded_int32_le' min max 4ul
let parse32_bounded_int32_le_fixed_size
min32 max32
= parse32_filter parse32_u32_le (in_bounds (U32.v min32) (U32.v max32)) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x))
let serialize32_bounded_int32_le_fixed_size | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (serializer32 (serialize_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_fixed_size | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | min32: FStar.UInt32.t -> max32: FStar.UInt32.t{FStar.UInt32.v min32 <= FStar.UInt32.v max32}
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le_fixed_size
(FStar.UInt32.v min32)
(FStar.UInt32.v max32)) | {
"end_col": 79,
"end_line": 404,
"start_col": 2,
"start_line": 404
} |
Prims.Tot | val serialize32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le_2
min max
= serialize32_bounded_int32_le' min max 2ul | val serialize32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le_2 min max = | false | null | false | serialize32_bounded_int32_le' min max 2ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul
let serialize32_bounded_int32_le_2 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 256 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 65536 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 43,
"end_line": 388,
"start_col": 2,
"start_line": 388
} |
Prims.Tot | val serialize32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul | val serialize32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_4 min max = | false | null | false | serialize32_bounded_int32' min max 4ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32",
"LowParse.Spec.BoundedInt.serialize_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 16777216 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32 (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 40,
"end_line": 320,
"start_col": 2,
"start_line": 320
} |
Prims.Tot | val parse32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (parser32 (parse_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le_fixed_size
min32 max32
= parse32_filter parse32_u32_le (in_bounds (U32.v min32) (U32.v max32)) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)) | val parse32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (parser32 (parse_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le_fixed_size min32 max32 = | false | null | false | parse32_filter parse32_u32_le
(in_bounds (U32.v min32) (U32.v max32))
(fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"LowParse.SLow.Combinators.parse32_filter",
"LowParse.Spec.Int.parse_u32_kind",
"LowParse.Spec.BoundedInt.parse_u32_le",
"LowParse.SLow.BoundedInt.parse32_u32_le",
"LowParse.Spec.BoundedInt.in_bounds",
"Prims.op_Negation",
"Prims.op_BarBar",
"FStar.UInt32.lt",
"Prims.bool",
"Prims.eq2",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_fixed_size_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le_fixed_size"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul
let serialize32_bounded_int32_le_2
min max
= serialize32_bounded_int32_le' min max 2ul
let serialize32_bounded_int32_le_3
min max
= serialize32_bounded_int32_le' min max 3ul
let serialize32_bounded_int32_le_4
min max
= serialize32_bounded_int32_le' min max 4ul
let parse32_bounded_int32_le_fixed_size | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le_fixed_size
(min32: U32.t)
(max32: U32.t { U32.v min32 <= U32.v max32 })
: Tot (parser32 (parse_bounded_int32_le_fixed_size (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_fixed_size | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | min32: FStar.UInt32.t -> max32: FStar.UInt32.t{FStar.UInt32.v min32 <= FStar.UInt32.v max32}
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le_fixed_size (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 125,
"end_line": 400,
"start_col": 2,
"start_line": 400
} |
Prims.Tot | val serialize32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul | val serialize32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_2 min max = | false | null | false | serialize32_bounded_int32' min max 2ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32",
"LowParse.Spec.BoundedInt.serialize_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_2
(min32: U32.t)
(max32: U32.t { 256 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 65536 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 256 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 65536 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32 (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 40,
"end_line": 312,
"start_col": 2,
"start_line": 312
} |
Prims.Tot | val serialize32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le_4
min max
= serialize32_bounded_int32_le' min max 4ul | val serialize32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le_4 min max = | false | null | false | serialize32_bounded_int32_le' min max 4ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
#push-options "--z3rlimit 40"
#restart-solver // somehow needed
let serialize32_bounded_int32_le_1
min max
= serialize32_bounded_int32_le' min max 1ul
let serialize32_bounded_int32_le_2
min max
= serialize32_bounded_int32_le' min max 2ul
let serialize32_bounded_int32_le_3
min max
= serialize32_bounded_int32_le' min max 3ul
let serialize32_bounded_int32_le_4 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 16777216 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 43,
"end_line": 396,
"start_col": 2,
"start_line": 396
} |
Prims.Tot | val parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
() | val parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) = | false | null | false | [@@ inline_let ]let sz = U32.v sz32 in
[@@ inline_let ]let min = U32.v min32 in
[@@ inline_let ]let max = U32.v max32 in
parse32_synth ((parse_bounded_integer sz) `parse_filter` (in_bounds min max))
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz)
(in_bounds min max)
(fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
() | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"FStar.UInt.size",
"FStar.UInt32.n",
"LowParse.Spec.BoundedInt.log256'",
"LowParse.SLow.Combinators.parse32_synth",
"LowParse.Spec.Combinators.parse_filter_kind",
"LowParse.Spec.BoundedInt.parse_bounded_integer_kind",
"LowParse.Spec.Combinators.parse_filter_refine",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.BoundedInt.in_bounds",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.Combinators.parse_filter",
"LowParse.Spec.BoundedInt.parse_bounded_integer",
"LowParse.SLow.Combinators.parse32_filter",
"LowParse.SLow.BoundedInt.parse32_bounded_integer",
"Prims.op_Negation",
"Prims.op_BarBar",
"FStar.UInt32.lt",
"Prims.bool",
"FStar.UInt.uint_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.parse_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 }) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32' | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 } ->
sz32:
FStar.UInt32.t{LowParse.Spec.BoundedInt.log256' (FStar.UInt32.v max32) == FStar.UInt32.v sz32}
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32 (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 6,
"end_line": 267,
"start_col": 2,
"start_line": 256
} |
Prims.Tot | val serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
() | val serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) = | false | null | false | [@@ inline_let ]let sz = U32.v sz32 in
[@@ inline_let ]let min = U32.v min32 in
[@@ inline_let ]let max = U32.v max32 in
serialize32_synth ((parse_bounded_integer_le sz) `parse_filter` (in_bounds min max))
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer_le sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
() | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"FStar.UInt.size",
"FStar.UInt32.n",
"LowParse.Spec.BoundedInt.log256'",
"LowParse.SLow.Combinators.serialize32_synth",
"LowParse.Spec.Combinators.parse_filter_kind",
"LowParse.Spec.BoundedInt.parse_bounded_integer_kind",
"LowParse.Spec.Combinators.parse_filter_refine",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.BoundedInt.in_bounds",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.Combinators.parse_filter",
"LowParse.Spec.BoundedInt.parse_bounded_integer_le",
"LowParse.Spec.Combinators.serialize_filter",
"LowParse.Spec.BoundedInt.serialize_bounded_integer_le",
"LowParse.SLow.Combinators.serialize32_filter",
"LowParse.SLow.BoundedInt.serialize32_bounded_integer_le",
"FStar.UInt.uint_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le",
"LowParse.Spec.BoundedInt.serialize_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul
inline_for_extraction
let serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 }) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le' | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 } ->
sz32:
FStar.UInt32.t{LowParse.Spec.BoundedInt.log256' (FStar.UInt32.v max32) == FStar.UInt32.v sz32}
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32_le (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 6,
"end_line": 377,
"start_col": 2,
"start_line": 364
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2) | let n_to_be_2 = | false | null | false | norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Pervasives.norm",
"Prims.Cons",
"FStar.Pervasives.norm_step",
"FStar.Pervasives.delta_attr",
"Prims.string",
"Prims.Nil",
"FStar.Pervasives.iota",
"FStar.Pervasives.zeta",
"FStar.Pervasives.primops",
"LowParse.SLow.Endianness.n_to_be_t",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.Endianness.Instances.bounded_integer",
"LowParse.SLow.Endianness.mk_n_to_be"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val n_to_be_2 : LowParse.SLow.Endianness.n_to_be_t (LowParse.Spec.Endianness.Instances.bounded_integer 2) 2 | [] | LowParse.SLow.BoundedInt.n_to_be_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | LowParse.SLow.Endianness.n_to_be_t (LowParse.Spec.Endianness.Instances.bounded_integer 2) 2 | {
"end_col": 112,
"end_line": 96,
"start_col": 16,
"start_line": 96
} |
|
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4) | let n_to_be_4 = | false | null | false | norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Pervasives.norm",
"Prims.Cons",
"FStar.Pervasives.norm_step",
"FStar.Pervasives.delta_attr",
"Prims.string",
"Prims.Nil",
"FStar.Pervasives.iota",
"FStar.Pervasives.zeta",
"FStar.Pervasives.primops",
"LowParse.SLow.Endianness.n_to_be_t",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.Endianness.Instances.bounded_integer",
"LowParse.SLow.Endianness.mk_n_to_be"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val n_to_be_4 : LowParse.SLow.Endianness.n_to_be_t (LowParse.Spec.Endianness.Instances.bounded_integer 4) 4 | [] | LowParse.SLow.BoundedInt.n_to_be_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | LowParse.SLow.Endianness.n_to_be_t (LowParse.Spec.Endianness.Instances.bounded_integer 4) 4 | {
"end_col": 112,
"end_line": 116,
"start_col": 16,
"start_line": 116
} |
|
Prims.Tot | val decode32_bounded_integer_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == decode_bounded_integer 1 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b | val decode32_bounded_integer_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == decode_bounded_integer 1 (B32.reveal b)})
let decode32_bounded_integer_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == decode_bounded_integer 1 (B32.reveal b)}) = | false | null | false | be_to_n_1 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.be_to_n_1",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.decode_bounded_integer",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decode32_bounded_integer_1 (b: B32.lbytes 1)
: Tot (y: bounded_integer 1 {y == decode_bounded_integer 1 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.decode32_bounded_integer_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 1
-> y:
LowParse.Spec.BoundedInt.bounded_integer 1
{y == LowParse.Spec.BoundedInt.decode_bounded_integer 1 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 26,
"start_col": 2,
"start_line": 26
} |
Prims.Tot | val decode32_bounded_integer_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == decode_bounded_integer 2 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b | val decode32_bounded_integer_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == decode_bounded_integer 2 (B32.reveal b)})
let decode32_bounded_integer_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == decode_bounded_integer 2 (B32.reveal b)}) = | false | null | false | be_to_n_2 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.be_to_n_2",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.decode_bounded_integer",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decode32_bounded_integer_2 (b: B32.lbytes 2)
: Tot (y: bounded_integer 2 {y == decode_bounded_integer 2 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.decode32_bounded_integer_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 2
-> y:
LowParse.Spec.BoundedInt.bounded_integer 2
{y == LowParse.Spec.BoundedInt.decode_bounded_integer 2 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 36,
"start_col": 2,
"start_line": 36
} |
Prims.Tot | val bounded_integer_of_le_32_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == bounded_integer_of_le 4 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b | val bounded_integer_of_le_32_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == bounded_integer_of_le 4 (B32.reveal b)})
let bounded_integer_of_le_32_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == bounded_integer_of_le 4 (B32.reveal b)}) = | false | null | false | le_to_n_4 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.le_to_n_4",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.bounded_integer_of_le",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounded_integer_of_le_32_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == bounded_integer_of_le 4 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.bounded_integer_of_le_32_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 4
-> y:
LowParse.Spec.BoundedInt.bounded_integer 4
{y == LowParse.Spec.BoundedInt.bounded_integer_of_le 4 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 162,
"start_col": 2,
"start_line": 162
} |
Prims.Tot | val decode32_bounded_integer_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == decode_bounded_integer 4 (B32.reveal b)}) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b | val decode32_bounded_integer_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == decode_bounded_integer 4 (B32.reveal b)})
let decode32_bounded_integer_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == decode_bounded_integer 4 (B32.reveal b)}) = | false | null | false | be_to_n_4 b | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Bytes.lbytes",
"LowParse.SLow.BoundedInt.be_to_n_4",
"LowParse.Spec.BoundedInt.bounded_integer",
"Prims.eq2",
"LowParse.Spec.BoundedInt.decode_bounded_integer",
"FStar.Bytes.reveal"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decode32_bounded_integer_4 (b: B32.lbytes 4)
: Tot (y: bounded_integer 4 {y == decode_bounded_integer 4 (B32.reveal b)}) | [] | LowParse.SLow.BoundedInt.decode32_bounded_integer_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | b: FStar.Bytes.lbytes 4
-> y:
LowParse.Spec.BoundedInt.bounded_integer 4
{y == LowParse.Spec.BoundedInt.decode_bounded_integer 4 (FStar.Bytes.reveal b)} | {
"end_col": 13,
"end_line": 56,
"start_col": 2,
"start_line": 56
} |
Prims.Tot | val serialize32_bounded_integer_le_1 : serializer32 (serialize_bounded_integer_le 1) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x | val serialize32_bounded_integer_le_1 : serializer32 (serialize_bounded_integer_le 1)
let serialize32_bounded_integer_le_1 = | false | null | false | fun (x: bounded_integer 1) -> n_to_le_1 x | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.SLow.BoundedInt.n_to_le_1",
"LowParse.SLow.Base.bytes32",
"LowParse.SLow.Base.serializer32_correct",
"LowParse.Spec.BoundedInt.parse_bounded_integer_kind",
"LowParse.Spec.BoundedInt.parse_bounded_integer_le",
"LowParse.Spec.BoundedInt.serialize_bounded_integer_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_integer_le_1 : serializer32 (serialize_bounded_integer_le 1) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_integer_le_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_integer_le 1) | {
"end_col": 13,
"end_line": 209,
"start_col": 39,
"start_line": 208
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2) | let n_to_le_2 = | false | null | false | norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2) | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.Pervasives.norm",
"Prims.Cons",
"FStar.Pervasives.norm_step",
"FStar.Pervasives.delta_attr",
"Prims.string",
"Prims.Nil",
"FStar.Pervasives.iota",
"FStar.Pervasives.zeta",
"FStar.Pervasives.primops",
"LowParse.SLow.Endianness.n_to_le_t",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.Endianness.Instances.bounded_integer",
"LowParse.SLow.Endianness.mk_n_to_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val n_to_le_2 : LowParse.SLow.Endianness.n_to_le_t (LowParse.Spec.Endianness.Instances.bounded_integer 2) 2 | [] | LowParse.SLow.BoundedInt.n_to_le_2 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | LowParse.SLow.Endianness.n_to_le_t (LowParse.Spec.Endianness.Instances.bounded_integer 2) 2 | {
"end_col": 112,
"end_line": 213,
"start_col": 16,
"start_line": 213
} |
|
Prims.Tot | val serialize32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul | val serialize32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_1 min max = | false | null | false | serialize32_bounded_int32' min max 1ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32",
"LowParse.Spec.BoundedInt.serialize_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_1
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 256 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_1 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 256 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32 (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 40,
"end_line": 308,
"start_col": 2,
"start_line": 308
} |
Prims.Tot | val serialize32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul | val serialize32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32_3 min max = | false | null | false | serialize32_bounded_int32' min max 3ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.serialize32_bounded_int32'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32",
"LowParse.Spec.BoundedInt.serialize_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 65536 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 16777216 }
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32 (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 40,
"end_line": 316,
"start_col": 2,
"start_line": 316
} |
Prims.Tot | val parse32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul | val parse32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le_3 min max = | false | null | false | parse32_bounded_int32_le' min max 3ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le_3
(min32: U32.t)
(max32: U32.t { 65536 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 16777216 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_3 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 65536 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 16777216 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 39,
"end_line": 352,
"start_col": 2,
"start_line": 352
} |
Prims.Tot | val parse32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le_4
min max
= parse32_bounded_int32_le' min max 4ul | val parse32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le_4 min max = | false | null | false | parse32_bounded_int32_le' min max 4ul | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"Prims.op_LessThan",
"LowParse.SLow.BoundedInt.parse32_bounded_int32_le'",
"FStar.UInt32.__uint_to_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_le_1
min max
= parse32_bounded_int32_le' min max 1ul
let parse32_bounded_int32_le_2
min max
= parse32_bounded_int32_le' min max 2ul
let parse32_bounded_int32_le_3
min max
= parse32_bounded_int32_le' min max 3ul
let parse32_bounded_int32_le_4 | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le_4
(min32: U32.t)
(max32: U32.t { 16777216 <= U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_4 | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 16777216 <= FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 }
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 39,
"end_line": 356,
"start_col": 2,
"start_line": 356
} |
Prims.Tot | val parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer_le sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
() | val parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32)))
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) = | false | null | false | [@@ inline_let ]let sz = U32.v sz32 in
[@@ inline_let ]let min = U32.v min32 in
[@@ inline_let ]let max = U32.v max32 in
parse32_synth ((parse_bounded_integer_le sz) `parse_filter` (in_bounds min max))
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer_le sz)
(in_bounds min max)
(fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
() | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"FStar.UInt.size",
"FStar.UInt32.n",
"LowParse.Spec.BoundedInt.log256'",
"LowParse.SLow.Combinators.parse32_synth",
"LowParse.Spec.Combinators.parse_filter_kind",
"LowParse.Spec.BoundedInt.parse_bounded_integer_kind",
"LowParse.Spec.Combinators.parse_filter_refine",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.BoundedInt.in_bounds",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.Combinators.parse_filter",
"LowParse.Spec.BoundedInt.parse_bounded_integer_le",
"LowParse.SLow.Combinators.parse32_filter",
"LowParse.SLow.BoundedInt.parse32_bounded_integer_le",
"Prims.op_Negation",
"Prims.op_BarBar",
"FStar.UInt32.lt",
"Prims.bool",
"FStar.UInt.uint_t",
"LowParse.SLow.Base.parser32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.parse_bounded_int32_le"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
()
let serialize32_bounded_int32_1
min max
= serialize32_bounded_int32' min max 1ul
let serialize32_bounded_int32_2
min max
= serialize32_bounded_int32' min max 2ul
let serialize32_bounded_int32_3
min max
= serialize32_bounded_int32' min max 3ul
let serialize32_bounded_int32_4
min max
= serialize32_bounded_int32' min max 4ul
inline_for_extraction
let parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 }) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse32_bounded_int32_le'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (parser32 (parse_bounded_int32_le (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.parse32_bounded_int32_le' | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 } ->
sz32:
FStar.UInt32.t{LowParse.Spec.BoundedInt.log256' (FStar.UInt32.v max32) == FStar.UInt32.v sz32}
-> LowParse.SLow.Base.parser32 (LowParse.Spec.BoundedInt.parse_bounded_int32_le (FStar.UInt32.v min32
)
(FStar.UInt32.v max32)) | {
"end_col": 6,
"end_line": 340,
"start_col": 2,
"start_line": 329
} |
Prims.Tot | val serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Int.Cast",
"short_module": "Cast"
},
{
"abbrev": true,
"full_module": "LowParse.Spec.Endianness.Instances",
"short_module": "EI"
},
{
"abbrev": true,
"full_module": "LowParse.SLow.Endianness",
"short_module": "E"
},
{
"abbrev": true,
"full_module": "FStar.Bytes",
"short_module": "B32"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "Seq"
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.BoundedInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.SLow",
"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
}
] | false | let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
serialize32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
() | val serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32)))
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) = | false | null | false | [@@ inline_let ]let sz = U32.v sz32 in
[@@ inline_let ]let min = U32.v min32 in
[@@ inline_let ]let max = U32.v max32 in
serialize32_synth ((parse_bounded_integer sz) `parse_filter` (in_bounds min max))
(fun x -> (x <: bounded_int32 min max))
_
(serialize32_filter (serialize32_bounded_integer sz) (in_bounds min max))
(fun x -> x)
(fun x -> x)
() | {
"checked_file": "LowParse.SLow.BoundedInt.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Endianness.Instances.fst.checked",
"LowParse.Spec.BoundedInt.fst.checked",
"LowParse.SLow.Endianness.fst.checked",
"LowParse.SLow.Combinators.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.Cast.fst.checked",
"FStar.Bytes.fsti.checked"
],
"interface_file": true,
"source_file": "LowParse.SLow.BoundedInt.fst"
} | [
"total"
] | [
"FStar.UInt32.t",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.UInt32.v",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"FStar.UInt.size",
"FStar.UInt32.n",
"LowParse.Spec.BoundedInt.log256'",
"LowParse.SLow.Combinators.serialize32_synth",
"LowParse.Spec.Combinators.parse_filter_kind",
"LowParse.Spec.BoundedInt.parse_bounded_integer_kind",
"LowParse.Spec.Combinators.parse_filter_refine",
"LowParse.Spec.BoundedInt.bounded_integer",
"LowParse.Spec.BoundedInt.in_bounds",
"LowParse.Spec.BoundedInt.bounded_int32",
"LowParse.Spec.Combinators.parse_filter",
"LowParse.Spec.BoundedInt.parse_bounded_integer",
"LowParse.Spec.Combinators.serialize_filter",
"LowParse.Spec.BoundedInt.serialize_bounded_integer",
"LowParse.SLow.Combinators.serialize32_filter",
"LowParse.SLow.BoundedInt.serialize32_bounded_integer",
"FStar.UInt.uint_t",
"LowParse.SLow.Base.serializer32",
"LowParse.Spec.BoundedInt.parse_bounded_int32_kind",
"LowParse.Spec.BoundedInt.parse_bounded_int32",
"LowParse.Spec.BoundedInt.serialize_bounded_int32"
] | [] | module LowParse.SLow.BoundedInt
open LowParse.SLow.Combinators
#set-options "--split_queries no"
#set-options "--z3rlimit 20"
module Seq = FStar.Seq
module U8 = FStar.UInt8
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module B32 = FStar.Bytes
module E = LowParse.SLow.Endianness
module EI = LowParse.Spec.Endianness.Instances
module Cast = FStar.Int.Cast
friend LowParse.Spec.BoundedInt
inline_for_extraction
noextract
let be_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let decode32_bounded_integer_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == decode_bounded_integer 1 (B32.reveal b) } )
= be_to_n_1 b
inline_for_extraction
noextract
let be_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let decode32_bounded_integer_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == decode_bounded_integer 2 (B32.reveal b) } )
= be_to_n_2 b
inline_for_extraction
noextract
let be_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let decode32_bounded_integer_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == decode_bounded_integer 3 (B32.reveal b) } )
= be_to_n_3 b
inline_for_extraction
noextract
let be_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_be_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let decode32_bounded_integer_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == decode_bounded_integer 4 (B32.reveal b) } )
= be_to_n_4 b
inline_for_extraction
let decode32_bounded_integer
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == decode_bounded_integer sz (B32.reveal b) } )
)
= match sz with
| 1 -> decode32_bounded_integer_1
| 2 -> decode32_bounded_integer_2
| 3 -> decode32_bounded_integer_3
| 4 -> decode32_bounded_integer_4
inline_for_extraction
let parse32_bounded_integer' (sz: integer_size) : Tot (parser32 (parse_bounded_integer sz)) =
[@inline_let]
let _ = decode_bounded_integer_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(decode_bounded_integer sz)
()
(decode32_bounded_integer sz)
let parse32_bounded_integer_1 = parse32_bounded_integer' 1
let parse32_bounded_integer_2 = parse32_bounded_integer' 2
let parse32_bounded_integer_3 = parse32_bounded_integer' 3
let parse32_bounded_integer_4 = parse32_bounded_integer' 4
inline_for_extraction
noextract
let n_to_be_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 1) 1)
inline_for_extraction
let serialize32_bounded_integer_1
: (serializer32 (serialize_bounded_integer 1))
= (fun (input: bounded_integer 1) ->
n_to_be_1 input)
inline_for_extraction
noextract
let n_to_be_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 2) 2)
inline_for_extraction
let serialize32_bounded_integer_2
: (serializer32 (serialize_bounded_integer 2))
= (fun (input: bounded_integer 2) ->
n_to_be_2 input)
inline_for_extraction
noextract
let n_to_be_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 3) 3)
inline_for_extraction
let serialize32_bounded_integer_3
: (serializer32 (serialize_bounded_integer 3))
= (fun (input: bounded_integer 3) ->
n_to_be_3 input)
inline_for_extraction
noextract
let n_to_be_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_be (EI.bounded_integer 4) 4)
inline_for_extraction
let serialize32_bounded_integer_4
: (serializer32 (serialize_bounded_integer 4))
= (fun (input: bounded_integer 4) ->
n_to_be_4 input)
inline_for_extraction
noextract
let le_to_n_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 1) 1)
inline_for_extraction
let bounded_integer_of_le_32_1
(b: B32.lbytes 1)
: Tot (y: bounded_integer 1 { y == bounded_integer_of_le 1 (B32.reveal b) } )
= le_to_n_1 b
inline_for_extraction
noextract
let le_to_n_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 2) 2)
inline_for_extraction
let bounded_integer_of_le_32_2
(b: B32.lbytes 2)
: Tot (y: bounded_integer 2 { y == bounded_integer_of_le 2 (B32.reveal b) } )
= le_to_n_2 b
inline_for_extraction
noextract
let le_to_n_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 3) 3)
inline_for_extraction
let bounded_integer_of_le_32_3
(b: B32.lbytes 3)
: Tot (y: bounded_integer 3 { y == bounded_integer_of_le 3 (B32.reveal b) } )
= le_to_n_3 b
inline_for_extraction
noextract
let le_to_n_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_le_to_n (EI.bounded_integer 4) 4)
inline_for_extraction
let bounded_integer_of_le_32_4
(b: B32.lbytes 4)
: Tot (y: bounded_integer 4 { y == bounded_integer_of_le 4 (B32.reveal b) } )
= le_to_n_4 b
inline_for_extraction
let bounded_integer_of_le_32
(sz: integer_size)
: Tot ((b: B32.lbytes sz) ->
Tot (y: bounded_integer sz { y == bounded_integer_of_le sz (B32.reveal b) } )
)
= match sz with
| 1 -> bounded_integer_of_le_32_1
| 2 -> bounded_integer_of_le_32_2
| 3 -> bounded_integer_of_le_32_3
| 4 -> bounded_integer_of_le_32_4
inline_for_extraction
let parse32_bounded_integer_le' (sz: integer_size) : Tot (parser32 (parse_bounded_integer_le sz)) =
[@inline_let]
let _ = bounded_integer_of_le_injective sz in
make_total_constant_size_parser32 sz (U32.uint_to_t sz)
(bounded_integer_of_le sz)
()
(bounded_integer_of_le_32 sz)
let parse32_bounded_integer_le_1 = parse32_bounded_integer_le' 1
let parse32_bounded_integer_le_2 = parse32_bounded_integer_le' 2
let parse32_bounded_integer_le_3 = parse32_bounded_integer_le' 3
let parse32_bounded_integer_le_4 = parse32_bounded_integer_le' 4
let parse32_u16_le =
parse32_synth'
_
synth_u16_le
parse32_bounded_integer_le_2
()
let parse32_u32_le =
parse32_synth'
_
synth_u32_le
parse32_bounded_integer_le_4
()
inline_for_extraction
noextract
let n_to_le_1 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 1) 1)
let serialize32_bounded_integer_le_1 = fun (x: bounded_integer 1) ->
n_to_le_1 x
inline_for_extraction
noextract
let n_to_le_2 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 2) 2)
let serialize32_bounded_integer_le_2 = fun (x: bounded_integer 2) ->
n_to_le_2 x
inline_for_extraction
noextract
let n_to_le_3 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 3) 3)
let serialize32_bounded_integer_le_3 = fun (x: bounded_integer 3) ->
n_to_le_3 x
inline_for_extraction
noextract
let n_to_le_4 = norm [delta_attr [`%E.must_reduce]; iota; zeta; primops] (E.mk_n_to_le (EI.bounded_integer 4) 4)
let serialize32_bounded_integer_le_4 = fun (x: bounded_integer 4) ->
n_to_le_4 x
let serialize32_u16_le =
serialize32_synth'
_
synth_u16_le
_
serialize32_bounded_integer_le_2
synth_u16_le_recip
()
let serialize32_u32_le =
serialize32_synth'
_
synth_u32_le
_
serialize32_bounded_integer_le_4
synth_u32_le_recip
()
inline_for_extraction
let parse32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 })
: Tot (parser32 (parse_bounded_int32 (U32.v min32) (U32.v max32)))
= [@inline_let]
let sz = U32.v sz32 in
[@inline_let]
let min = U32.v min32 in
[@inline_let]
let max = U32.v max32 in
parse32_synth
(parse_bounded_integer sz `parse_filter` in_bounds min max)
(fun x -> (x <: bounded_int32 min max))
(fun x -> x)
(parse32_filter (parse32_bounded_integer sz) (in_bounds min max) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)))
()
let parse32_bounded_int32_1
min max
= parse32_bounded_int32' min max 1ul
let parse32_bounded_int32_2
min max
= parse32_bounded_int32' min max 2ul
let parse32_bounded_int32_3
min max
= parse32_bounded_int32' min max 3ul
let parse32_bounded_int32_4
min max
= parse32_bounded_int32' min max 4ul
inline_for_extraction
let serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t { 0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296 })
(sz32: U32.t { log256' (U32.v max32) == U32.v sz32 }) | false | false | LowParse.SLow.BoundedInt.fst | {
"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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize32_bounded_int32'
(min32: U32.t)
(max32: U32.t{0 < U32.v max32 /\ U32.v min32 <= U32.v max32 /\ U32.v max32 < 4294967296})
(sz32: U32.t{log256' (U32.v max32) == U32.v sz32})
: Tot (serializer32 (serialize_bounded_int32 (U32.v min32) (U32.v max32))) | [] | LowParse.SLow.BoundedInt.serialize32_bounded_int32' | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
min32: FStar.UInt32.t ->
max32:
FStar.UInt32.t
{ 0 < FStar.UInt32.v max32 /\ FStar.UInt32.v min32 <= FStar.UInt32.v max32 /\
FStar.UInt32.v max32 < 4294967296 } ->
sz32:
FStar.UInt32.t{LowParse.Spec.BoundedInt.log256' (FStar.UInt32.v max32) == FStar.UInt32.v sz32}
-> LowParse.SLow.Base.serializer32 (LowParse.Spec.BoundedInt.serialize_bounded_int32 (FStar.UInt32.v
min32)
(FStar.UInt32.v max32)) | {
"end_col": 6,
"end_line": 304,
"start_col": 2,
"start_line": 291
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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": "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
}
] | false | let valid_stack_slot64 (ptr:int) (h:vale_stack) (t:taint) (stackTaint:memtaint) =
valid_src_stack64 ptr h /\ valid_taint_stack64 ptr t stackTaint | let valid_stack_slot64 (ptr: int) (h: vale_stack) (t: taint) (stackTaint: memtaint) = | false | null | false | valid_src_stack64 ptr h /\ valid_taint_stack64 ptr t stackTaint | {
"checked_file": "Vale.X64.Stack_i.fsti.checked",
"dependencies": [
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Map.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.Stack_i.fsti"
} | [
"total"
] | [
"Prims.int",
"Vale.X64.Stack_i.vale_stack",
"Vale.Arch.HeapTypes_s.taint",
"Vale.X64.Memory.memtaint",
"Prims.l_and",
"Prims.b2t",
"Vale.X64.Stack_i.valid_src_stack64",
"Vale.X64.Stack_i.valid_taint_stack64",
"Prims.logical"
] | [] | module Vale.X64.Stack_i
open FStar.Mul
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.Def.Prop_s
val vale_stack : Type u#0
val valid_src_stack64 (ptr:int) (h:vale_stack) : GTot bool
val load_stack64 (ptr:int) (h:vale_stack) : GTot nat64
val store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : GTot vale_stack
val free_stack64 (start:int) (finish:int) (h:vale_stack) : GTot vale_stack
val valid_src_stack128 (ptr:int) (h:vale_stack) : GTot bool
val load_stack128 (ptr:int) (h:vale_stack) : GTot quad32
val store_stack128 (ptr:int) (v:quad32) (h:vale_stack) : GTot vale_stack
val init_rsp (h:vale_stack) : (n:nat64{n >= 4096})
let modifies_stack (lo_rsp hi_rsp:nat) (h h':vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (load_stack64 addr h') \/ (valid_src_stack64 addr h') }
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\
load_stack64 addr h == load_stack64 addr h'
let valid_src_stack64s (base num_slots:nat) (h:vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h
(* Validity preservation *)
val lemma_store_stack_same_valid64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures valid_src_stack64 i (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_valid64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures valid_src_stack64 ptr (free_stack64 start finish h))
[SMTPat (valid_src_stack64 ptr (free_stack64 start finish h))]
(* Validity update *)
val lemma_store_new_valid64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(valid_src_stack64 ptr (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 ptr (store_stack64 ptr v h))]
(* Classic select/update lemmas *)
val lemma_correct_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(load_stack64 ptr (store_stack64 ptr v h) == v)
[SMTPat (load_stack64 ptr (store_stack64 ptr v h))]
val lemma_frame_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures (load_stack64 i (store_stack64 ptr v h) == load_stack64 i h))
[SMTPat (load_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_load64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures load_stack64 ptr h == load_stack64 ptr (free_stack64 start finish h))
[SMTPat (load_stack64 ptr (free_stack64 start finish h))]
(* Free composition *)
val lemma_compose_free_stack64 (start:int) (inter:int) (finish:int) (h:vale_stack) : Lemma
(requires start <= inter /\ inter <= finish)
(ensures free_stack64 inter finish (free_stack64 start inter h) == free_stack64 start finish h)
[SMTPat (free_stack64 inter finish (free_stack64 start inter h))]
(* Preservation of the initial stack pointer *)
val lemma_same_init_rsp_free_stack64 (start:int) (finish:int) (h:vale_stack) : Lemma
(init_rsp (free_stack64 start finish h) == init_rsp h)
[SMTPat (init_rsp (free_stack64 start finish h))]
val lemma_same_init_rsp_store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(init_rsp (store_stack64 ptr v h) == init_rsp h)
[SMTPat (init_rsp (store_stack64 ptr v h))]
// Taint for the stack
val valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val store_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot memtaint
val lemma_valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack64 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack128 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 16 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack64_reveal (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
(ensures valid_taint_stack64 ptr t stackTaint)
val lemma_correct_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))]
val lemma_frame_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) (i:int) (t':taint) : Lemma
(requires i >= ptr + 8 \/ i + 8 <= ptr)
(ensures valid_taint_stack64 i t' stackTaint == valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))] | false | true | Vale.X64.Stack_i.fsti | {
"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"
} | null | val valid_stack_slot64 : ptr: Prims.int ->
h: Vale.X64.Stack_i.vale_stack ->
t: Vale.Arch.HeapTypes_s.taint ->
stackTaint: Vale.X64.Memory.memtaint
-> Prims.logical | [] | Vale.X64.Stack_i.valid_stack_slot64 | {
"file_name": "vale/code/arch/x64/Vale.X64.Stack_i.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
ptr: Prims.int ->
h: Vale.X64.Stack_i.vale_stack ->
t: Vale.Arch.HeapTypes_s.taint ->
stackTaint: Vale.X64.Memory.memtaint
-> Prims.logical | {
"end_col": 65,
"end_line": 113,
"start_col": 2,
"start_line": 113
} |
|
Prims.Tot | val valid_src_stack64s (base num_slots: nat) (h: vale_stack) : Vale.Def.Prop_s.prop0 | [
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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": "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
}
] | false | let valid_src_stack64s (base num_slots:nat) (h:vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h | val valid_src_stack64s (base num_slots: nat) (h: vale_stack) : Vale.Def.Prop_s.prop0
let valid_src_stack64s (base num_slots: nat) (h: vale_stack) : Vale.Def.Prop_s.prop0 = | false | null | false | forall addr. {:pattern (valid_src_stack64 addr h)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h | {
"checked_file": "Vale.X64.Stack_i.fsti.checked",
"dependencies": [
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Map.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.Stack_i.fsti"
} | [
"total"
] | [
"Prims.nat",
"Vale.X64.Stack_i.vale_stack",
"Prims.l_Forall",
"Prims.int",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.op_Equality",
"Prims.op_Modulus",
"Prims.op_Subtraction",
"Vale.X64.Stack_i.valid_src_stack64",
"Vale.Def.Prop_s.prop0"
] | [] | module Vale.X64.Stack_i
open FStar.Mul
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.Def.Prop_s
val vale_stack : Type u#0
val valid_src_stack64 (ptr:int) (h:vale_stack) : GTot bool
val load_stack64 (ptr:int) (h:vale_stack) : GTot nat64
val store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : GTot vale_stack
val free_stack64 (start:int) (finish:int) (h:vale_stack) : GTot vale_stack
val valid_src_stack128 (ptr:int) (h:vale_stack) : GTot bool
val load_stack128 (ptr:int) (h:vale_stack) : GTot quad32
val store_stack128 (ptr:int) (v:quad32) (h:vale_stack) : GTot vale_stack
val init_rsp (h:vale_stack) : (n:nat64{n >= 4096})
let modifies_stack (lo_rsp hi_rsp:nat) (h h':vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (load_stack64 addr h') \/ (valid_src_stack64 addr h') }
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\
load_stack64 addr h == load_stack64 addr h' | false | true | Vale.X64.Stack_i.fsti | {
"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"
} | null | val valid_src_stack64s (base num_slots: nat) (h: vale_stack) : Vale.Def.Prop_s.prop0 | [] | Vale.X64.Stack_i.valid_src_stack64s | {
"file_name": "vale/code/arch/x64/Vale.X64.Stack_i.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | base: Prims.nat -> num_slots: Prims.nat -> h: Vale.X64.Stack_i.vale_stack -> Vale.Def.Prop_s.prop0 | {
"end_col": 30,
"end_line": 30,
"start_col": 2,
"start_line": 28
} |
Prims.Tot | val modifies_stack (lo_rsp hi_rsp: nat) (h h': vale_stack) : Vale.Def.Prop_s.prop0 | [
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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": "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
}
] | false | let modifies_stack (lo_rsp hi_rsp:nat) (h h':vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (load_stack64 addr h') \/ (valid_src_stack64 addr h') }
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\
load_stack64 addr h == load_stack64 addr h' | val modifies_stack (lo_rsp hi_rsp: nat) (h h': vale_stack) : Vale.Def.Prop_s.prop0
let modifies_stack (lo_rsp hi_rsp: nat) (h h': vale_stack) : Vale.Def.Prop_s.prop0 = | false | null | false | forall addr. {:pattern (load_stack64 addr h')\/(valid_src_stack64 addr h')}
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\ load_stack64 addr h == load_stack64 addr h' | {
"checked_file": "Vale.X64.Stack_i.fsti.checked",
"dependencies": [
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Map.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.Stack_i.fsti"
} | [
"total"
] | [
"Prims.nat",
"Vale.X64.Stack_i.vale_stack",
"Prims.l_Forall",
"Prims.int",
"Prims.l_imp",
"Prims.l_and",
"Prims.b2t",
"Vale.X64.Stack_i.valid_src_stack64",
"Prims.op_BarBar",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"Prims.op_GreaterThanOrEqual",
"Prims.eq2",
"Vale.X64.Memory.nat64",
"Vale.X64.Stack_i.load_stack64",
"Vale.Def.Prop_s.prop0"
] | [] | module Vale.X64.Stack_i
open FStar.Mul
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.Def.Prop_s
val vale_stack : Type u#0
val valid_src_stack64 (ptr:int) (h:vale_stack) : GTot bool
val load_stack64 (ptr:int) (h:vale_stack) : GTot nat64
val store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : GTot vale_stack
val free_stack64 (start:int) (finish:int) (h:vale_stack) : GTot vale_stack
val valid_src_stack128 (ptr:int) (h:vale_stack) : GTot bool
val load_stack128 (ptr:int) (h:vale_stack) : GTot quad32
val store_stack128 (ptr:int) (v:quad32) (h:vale_stack) : GTot vale_stack
val init_rsp (h:vale_stack) : (n:nat64{n >= 4096}) | false | true | Vale.X64.Stack_i.fsti | {
"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"
} | null | val modifies_stack (lo_rsp hi_rsp: nat) (h h': vale_stack) : Vale.Def.Prop_s.prop0 | [] | Vale.X64.Stack_i.modifies_stack | {
"file_name": "vale/code/arch/x64/Vale.X64.Stack_i.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
lo_rsp: Prims.nat ->
hi_rsp: Prims.nat ->
h: Vale.X64.Stack_i.vale_stack ->
h': Vale.X64.Stack_i.vale_stack
-> Vale.Def.Prop_s.prop0 | {
"end_col": 49,
"end_line": 25,
"start_col": 2,
"start_line": 22
} |
Prims.Tot | val modifies_stacktaint (lo_rsp hi_rsp: nat) (h h': memtaint) : Vale.Def.Prop_s.prop0 | [
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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": "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
}
] | false | let modifies_stacktaint (lo_rsp hi_rsp:nat) (h h':memtaint) : Vale.Def.Prop_s.prop0 =
forall addr t. {:pattern (valid_taint_stack64 addr t h') }
(addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_taint_stack64 addr t h == valid_taint_stack64 addr t h' | val modifies_stacktaint (lo_rsp hi_rsp: nat) (h h': memtaint) : Vale.Def.Prop_s.prop0
let modifies_stacktaint (lo_rsp hi_rsp: nat) (h h': memtaint) : Vale.Def.Prop_s.prop0 = | false | null | false | forall addr t. {:pattern (valid_taint_stack64 addr t h')}
(addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_taint_stack64 addr t h == valid_taint_stack64 addr t h' | {
"checked_file": "Vale.X64.Stack_i.fsti.checked",
"dependencies": [
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Map.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.Stack_i.fsti"
} | [
"total"
] | [
"Prims.nat",
"Vale.X64.Memory.memtaint",
"Prims.l_Forall",
"Prims.int",
"Vale.Arch.HeapTypes_s.taint",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_BarBar",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"Prims.op_GreaterThanOrEqual",
"Prims.eq2",
"Vale.Def.Prop_s.prop0",
"Vale.X64.Stack_i.valid_taint_stack64"
] | [] | module Vale.X64.Stack_i
open FStar.Mul
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.Def.Prop_s
val vale_stack : Type u#0
val valid_src_stack64 (ptr:int) (h:vale_stack) : GTot bool
val load_stack64 (ptr:int) (h:vale_stack) : GTot nat64
val store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : GTot vale_stack
val free_stack64 (start:int) (finish:int) (h:vale_stack) : GTot vale_stack
val valid_src_stack128 (ptr:int) (h:vale_stack) : GTot bool
val load_stack128 (ptr:int) (h:vale_stack) : GTot quad32
val store_stack128 (ptr:int) (v:quad32) (h:vale_stack) : GTot vale_stack
val init_rsp (h:vale_stack) : (n:nat64{n >= 4096})
let modifies_stack (lo_rsp hi_rsp:nat) (h h':vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (load_stack64 addr h') \/ (valid_src_stack64 addr h') }
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\
load_stack64 addr h == load_stack64 addr h'
let valid_src_stack64s (base num_slots:nat) (h:vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h
(* Validity preservation *)
val lemma_store_stack_same_valid64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures valid_src_stack64 i (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_valid64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures valid_src_stack64 ptr (free_stack64 start finish h))
[SMTPat (valid_src_stack64 ptr (free_stack64 start finish h))]
(* Validity update *)
val lemma_store_new_valid64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(valid_src_stack64 ptr (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 ptr (store_stack64 ptr v h))]
(* Classic select/update lemmas *)
val lemma_correct_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(load_stack64 ptr (store_stack64 ptr v h) == v)
[SMTPat (load_stack64 ptr (store_stack64 ptr v h))]
val lemma_frame_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures (load_stack64 i (store_stack64 ptr v h) == load_stack64 i h))
[SMTPat (load_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_load64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures load_stack64 ptr h == load_stack64 ptr (free_stack64 start finish h))
[SMTPat (load_stack64 ptr (free_stack64 start finish h))]
(* Free composition *)
val lemma_compose_free_stack64 (start:int) (inter:int) (finish:int) (h:vale_stack) : Lemma
(requires start <= inter /\ inter <= finish)
(ensures free_stack64 inter finish (free_stack64 start inter h) == free_stack64 start finish h)
[SMTPat (free_stack64 inter finish (free_stack64 start inter h))]
(* Preservation of the initial stack pointer *)
val lemma_same_init_rsp_free_stack64 (start:int) (finish:int) (h:vale_stack) : Lemma
(init_rsp (free_stack64 start finish h) == init_rsp h)
[SMTPat (init_rsp (free_stack64 start finish h))]
val lemma_same_init_rsp_store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(init_rsp (store_stack64 ptr v h) == init_rsp h)
[SMTPat (init_rsp (store_stack64 ptr v h))]
// Taint for the stack
val valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val store_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot memtaint
val lemma_valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack64 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack128 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 16 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack64_reveal (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
(ensures valid_taint_stack64 ptr t stackTaint)
val lemma_correct_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))]
val lemma_frame_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) (i:int) (t':taint) : Lemma
(requires i >= ptr + 8 \/ i + 8 <= ptr)
(ensures valid_taint_stack64 i t' stackTaint == valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))]
let valid_stack_slot64 (ptr:int) (h:vale_stack) (t:taint) (stackTaint:memtaint) =
valid_src_stack64 ptr h /\ valid_taint_stack64 ptr t stackTaint
let valid_stack_slot64s (base num_slots:nat) (h:vale_stack) (t:taint) (stackTaint:memtaint) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h) \/ (valid_taint_stack64 addr t stackTaint) \/
(valid_stack_slot64 addr h t stackTaint)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h /\ valid_taint_stack64 addr t stackTaint | false | true | Vale.X64.Stack_i.fsti | {
"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"
} | null | val modifies_stacktaint (lo_rsp hi_rsp: nat) (h h': memtaint) : Vale.Def.Prop_s.prop0 | [] | Vale.X64.Stack_i.modifies_stacktaint | {
"file_name": "vale/code/arch/x64/Vale.X64.Stack_i.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
lo_rsp: Prims.nat ->
hi_rsp: Prims.nat ->
h: Vale.X64.Memory.memtaint ->
h': Vale.X64.Memory.memtaint
-> Vale.Def.Prop_s.prop0 | {
"end_col": 67,
"end_line": 124,
"start_col": 2,
"start_line": 122
} |
Prims.Tot | val valid_stack_slot64s (base num_slots: nat) (h: vale_stack) (t: taint) (stackTaint: memtaint)
: Vale.Def.Prop_s.prop0 | [
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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": "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
}
] | false | let valid_stack_slot64s (base num_slots:nat) (h:vale_stack) (t:taint) (stackTaint:memtaint) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h) \/ (valid_taint_stack64 addr t stackTaint) \/
(valid_stack_slot64 addr h t stackTaint)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h /\ valid_taint_stack64 addr t stackTaint | val valid_stack_slot64s (base num_slots: nat) (h: vale_stack) (t: taint) (stackTaint: memtaint)
: Vale.Def.Prop_s.prop0
let valid_stack_slot64s (base num_slots: nat) (h: vale_stack) (t: taint) (stackTaint: memtaint)
: Vale.Def.Prop_s.prop0 = | false | null | false | forall addr.
{:pattern
(valid_src_stack64 addr h)\/(valid_taint_stack64 addr t stackTaint)\/(valid_stack_slot64 addr
h
t
stackTaint)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h /\ valid_taint_stack64 addr t stackTaint | {
"checked_file": "Vale.X64.Stack_i.fsti.checked",
"dependencies": [
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Map.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.Stack_i.fsti"
} | [
"total"
] | [
"Prims.nat",
"Vale.X64.Stack_i.vale_stack",
"Vale.Arch.HeapTypes_s.taint",
"Vale.X64.Memory.memtaint",
"Prims.l_Forall",
"Prims.int",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThanOrEqual",
"Prims.op_LessThan",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.op_Equality",
"Prims.op_Modulus",
"Prims.op_Subtraction",
"Prims.l_and",
"Vale.X64.Stack_i.valid_src_stack64",
"Vale.X64.Stack_i.valid_taint_stack64",
"Vale.X64.Stack_i.valid_stack_slot64",
"Vale.Def.Prop_s.prop0"
] | [] | module Vale.X64.Stack_i
open FStar.Mul
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.Def.Prop_s
val vale_stack : Type u#0
val valid_src_stack64 (ptr:int) (h:vale_stack) : GTot bool
val load_stack64 (ptr:int) (h:vale_stack) : GTot nat64
val store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : GTot vale_stack
val free_stack64 (start:int) (finish:int) (h:vale_stack) : GTot vale_stack
val valid_src_stack128 (ptr:int) (h:vale_stack) : GTot bool
val load_stack128 (ptr:int) (h:vale_stack) : GTot quad32
val store_stack128 (ptr:int) (v:quad32) (h:vale_stack) : GTot vale_stack
val init_rsp (h:vale_stack) : (n:nat64{n >= 4096})
let modifies_stack (lo_rsp hi_rsp:nat) (h h':vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (load_stack64 addr h') \/ (valid_src_stack64 addr h') }
valid_src_stack64 addr h /\ (addr + 8 <= lo_rsp || addr >= hi_rsp) ==>
valid_src_stack64 addr h' /\
load_stack64 addr h == load_stack64 addr h'
let valid_src_stack64s (base num_slots:nat) (h:vale_stack) : Vale.Def.Prop_s.prop0 =
forall addr . {:pattern (valid_src_stack64 addr h)}
(base <= addr) && (addr < base + num_slots * 8) && (addr - base) % 8 = 0 ==>
valid_src_stack64 addr h
(* Validity preservation *)
val lemma_store_stack_same_valid64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures valid_src_stack64 i (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_valid64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures valid_src_stack64 ptr (free_stack64 start finish h))
[SMTPat (valid_src_stack64 ptr (free_stack64 start finish h))]
(* Validity update *)
val lemma_store_new_valid64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(valid_src_stack64 ptr (store_stack64 ptr v h))
[SMTPat (valid_src_stack64 ptr (store_stack64 ptr v h))]
(* Classic select/update lemmas *)
val lemma_correct_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(load_stack64 ptr (store_stack64 ptr v h) == v)
[SMTPat (load_stack64 ptr (store_stack64 ptr v h))]
val lemma_frame_store_load_stack64 (ptr:int) (v:nat64) (h:vale_stack) (i:int) : Lemma
(requires valid_src_stack64 i h /\
(i >= ptr + 8 \/ i + 8 <= ptr))
(ensures (load_stack64 i (store_stack64 ptr v h) == load_stack64 i h))
[SMTPat (load_stack64 i (store_stack64 ptr v h))]
val lemma_free_stack_same_load64 (start:int) (finish:int) (ptr:int) (h:vale_stack) : Lemma
(requires valid_src_stack64 ptr h /\
(ptr >= finish \/ ptr + 8 <= start))
(ensures load_stack64 ptr h == load_stack64 ptr (free_stack64 start finish h))
[SMTPat (load_stack64 ptr (free_stack64 start finish h))]
(* Free composition *)
val lemma_compose_free_stack64 (start:int) (inter:int) (finish:int) (h:vale_stack) : Lemma
(requires start <= inter /\ inter <= finish)
(ensures free_stack64 inter finish (free_stack64 start inter h) == free_stack64 start finish h)
[SMTPat (free_stack64 inter finish (free_stack64 start inter h))]
(* Preservation of the initial stack pointer *)
val lemma_same_init_rsp_free_stack64 (start:int) (finish:int) (h:vale_stack) : Lemma
(init_rsp (free_stack64 start finish h) == init_rsp h)
[SMTPat (init_rsp (free_stack64 start finish h))]
val lemma_same_init_rsp_store_stack64 (ptr:int) (v:nat64) (h:vale_stack) : Lemma
(init_rsp (store_stack64 ptr v h) == init_rsp h)
[SMTPat (init_rsp (store_stack64 ptr v h))]
// Taint for the stack
val valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot prop0
val store_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : GTot memtaint
val lemma_valid_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack64 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack128 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires valid_taint_stack128 ptr t stackTaint)
(ensures forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 16 ==> Map.sel stackTaint i == t)
val lemma_valid_taint_stack64_reveal (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(requires forall i.{:pattern Map.sel stackTaint i} i >= ptr /\ i < ptr + 8 ==> Map.sel stackTaint i == t)
(ensures valid_taint_stack64 ptr t stackTaint)
val lemma_correct_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) : Lemma
(valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 ptr t (store_taint_stack64 ptr t stackTaint))]
val lemma_frame_store_load_taint_stack64 (ptr:int) (t:taint) (stackTaint:memtaint) (i:int) (t':taint) : Lemma
(requires i >= ptr + 8 \/ i + 8 <= ptr)
(ensures valid_taint_stack64 i t' stackTaint == valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))
[SMTPat (valid_taint_stack64 i t' (store_taint_stack64 ptr t stackTaint))]
let valid_stack_slot64 (ptr:int) (h:vale_stack) (t:taint) (stackTaint:memtaint) =
valid_src_stack64 ptr h /\ valid_taint_stack64 ptr t stackTaint | false | true | Vale.X64.Stack_i.fsti | {
"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"
} | null | val valid_stack_slot64s (base num_slots: nat) (h: vale_stack) (t: taint) (stackTaint: memtaint)
: Vale.Def.Prop_s.prop0 | [] | Vale.X64.Stack_i.valid_stack_slot64s | {
"file_name": "vale/code/arch/x64/Vale.X64.Stack_i.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
base: Prims.nat ->
num_slots: Prims.nat ->
h: Vale.X64.Stack_i.vale_stack ->
t: Vale.Arch.HeapTypes_s.taint ->
stackTaint: Vale.X64.Memory.memtaint
-> Vale.Def.Prop_s.prop0 | {
"end_col": 71,
"end_line": 119,
"start_col": 2,
"start_line": 116
} |
Prims.Tot | val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul) | val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = | false | null | false | (vec_and l (mask26 w), vec_shift_right l 26ul) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"total"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"FStar.Pervasives.Native.Mktuple2",
"Lib.IntVector.vec_and",
"Lib.IntTypes.U64",
"Hacl.Spec.Poly1305.Field32xN.mask26",
"Lib.IntVector.vec_shift_right",
"FStar.UInt32.__uint_to_t",
"FStar.Pervasives.Native.tuple2"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | l: Hacl.Spec.Poly1305.Field32xN.uint64xN w
-> Hacl.Spec.Poly1305.Field32xN.uint64xN w * Hacl.Spec.Poly1305.Field32xN.uint64xN w | {
"end_col": 75,
"end_line": 23,
"start_col": 29,
"start_line": 23
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp) | val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp = | false | null | true | let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Lib.Sequence.eq_intro",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Prims.unit",
"FStar.Classical.forall_intro",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.carry_wide_felem5",
"Lib.Sequence.op_String_Access",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i",
"Hacl.Spec.Poly1305.Field32xN.felem5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | inp: Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
-> FStar.Pervasives.Lemma
(requires Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures
Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_wide_felem5 inp) ==
Hacl.Spec.Poly1305.Field32xN.feval5 inp) | {
"end_col": 34,
"end_line": 469,
"start_col": 41,
"start_line": 466
} |
FStar.Pervasives.Lemma | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () = | false | null | true | assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Prims.unit",
"FStar.Math.Lemmas.modulo_lemma",
"Hacl.Spec.Poly1305.Vec.prime",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Modulus",
"Prims.pow2"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | [] | Hacl.Poly1305.Field32xN.Lemmas1.lemma_prime | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit -> FStar.Pervasives.Lemma (ensures Prims.pow2 130 % Hacl.Spec.Poly1305.Vec.prime = 5) | {
"end_col": 40,
"end_line": 19,
"start_col": 2,
"start_line": 17
} |
FStar.Pervasives.Lemma | val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp) | val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp = | false | null | true | let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Lib.Sequence.eq_intro",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Prims.unit",
"FStar.Classical.forall_intro",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.carry_full_felem5",
"Lib.Sequence.op_String_Access",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i",
"Hacl.Spec.Poly1305.Field32xN.felem5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | inp: Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
-> FStar.Pervasives.Lemma (requires Hacl.Spec.Poly1305.Field32xN.felem_fits5 inp (8, 8, 8, 8, 8))
(ensures
Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 inp) ==
Hacl.Spec.Poly1305.Field32xN.feval5 inp) | {
"end_col": 34,
"end_line": 868,
"start_col": 41,
"start_line": 865
} |
Prims.Tot | val acc_inv_t (#w: lanes) (acc: felem5 w) : Type0 | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1)) | val acc_inv_t (#w: lanes) (acc: felem5 w) : Type0
let acc_inv_t (#w: lanes) (acc: felem5 w) : Type0 = | false | null | false | let o0, o1, o2, o3, o4 = acc in
forall (i: nat).
i < w ==>
(if uint_v (vec_v o0).[ i ] >= pow2 26
then tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\ uint_v (vec_v o0).[ i ] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"total"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims.l_Forall",
"Prims.nat",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.op_GreaterThanOrEqual",
"Lib.IntTypes.uint_v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.uint_t",
"Lib.IntVector.vec_v",
"Prims.pow2",
"Prims.l_and",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.Mktuple5",
"Prims.op_Modulus",
"Prims.bool",
"Prims.logical"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3 | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val acc_inv_t (#w: lanes) (acc: felem5 w) : Type0 | [] | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | acc: Hacl.Spec.Poly1305.Field32xN.felem5 w -> Type0 | {
"end_col": 56,
"end_line": 639,
"start_col": 49,
"start_line": 633
} |
Prims.Tot | val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4') | val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) = | false | null | false | let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
let t1' = vec_add_mod t1 c5 in
(t0', t1', t2, t3', t4') | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"total"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"FStar.Pervasives.Native.Mktuple5",
"Lib.IntVector.vec_t",
"Lib.IntTypes.U64",
"Lib.IntVector.vec_add_mod",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.u64",
"Hacl.Spec.Poly1305.Field32xN.carry26_wide",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_compact | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | inp: Hacl.Spec.Poly1305.Field32xN.felem_wide5 w -> Hacl.Spec.Poly1305.Field32xN.felem5 w | {
"end_col": 26,
"end_line": 83,
"start_col": 55,
"start_line": 60
} |
FStar.Pervasives.Lemma | val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f' | val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' = | false | null | true | let f0, f1, f2, f3, f4 = f in
let f0', f1', f2', f3', f4' = f' in
assert_norm (max26 = pow2 26 - 1);
if
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff ||
v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f' | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims.op_AmpAmp",
"Prims.op_BarBar",
"Prims.op_disEquality",
"Prims.int",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.op_LessThan",
"Prims.op_Equality",
"Lib.IntTypes.range_t",
"Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_0",
"Prims.bool",
"Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_1",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.op_Subtraction",
"Prims.pow2"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f (1, 1, 1, 1, 1)} ->
f': Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = f' in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in
Lib.IntTypes.v f4 = 0x3ffffff && Lib.IntTypes.v f3 = 0x3ffffff &&
Lib.IntTypes.v f2 = 0x3ffffff &&
Lib.IntTypes.v f1 = 0x3ffffff &&
Lib.IntTypes.v f0 >= 0x3fffffb /\
Lib.IntTypes.v f0' = Lib.IntTypes.v f0 - 0x3fffffb &&
Lib.IntTypes.v f1' = Lib.IntTypes.v f1 - 0x3ffffff &&
Lib.IntTypes.v f2' = Lib.IntTypes.v f2 - 0x3ffffff &&
Lib.IntTypes.v f3' = Lib.IntTypes.v f3 - 0x3ffffff &&
Lib.IntTypes.v f4' = Lib.IntTypes.v f4 - 0x3ffffff \/
Lib.IntTypes.v f4 <> 0x3ffffff || Lib.IntTypes.v f3 <> 0x3ffffff ||
Lib.IntTypes.v f2 <> 0x3ffffff ||
Lib.IntTypes.v f1 <> 0x3ffffff ||
Lib.IntTypes.v f0 < 0x3fffffb /\
Lib.IntTypes.v f0' = Lib.IntTypes.v f0 && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 &&
Lib.IntTypes.v f2' = Lib.IntTypes.v f2 &&
Lib.IntTypes.v f3' = Lib.IntTypes.v f3 &&
Lib.IntTypes.v f4' = Lib.IntTypes.v f4)
<:
Type0)
<:
Type0))
(ensures
Hacl.Spec.Poly1305.Field32xN.as_nat5 f' ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 f % Hacl.Spec.Poly1305.Vec.prime) | {
"end_col": 31,
"end_line": 558,
"start_col": 28,
"start_line": 551
} |
FStar.Pervasives.Lemma | val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9) | val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) = | false | null | true | let tmp0, c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1, c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2, c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3, c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4, c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims._assert",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_lemma",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (8, 8, 8, 8, 8)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f0 (Hacl.Spec.Poly1305.Field32xN.zero w) in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp2 c2 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp4 c4 = _ in
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4)
(1, 1, 1, 1, 1) /\ Hacl.Spec.Poly1305.Field32xN.uint64xN_fits c4 9)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 29,
"end_line": 705,
"start_col": 59,
"start_line": 693
} |
FStar.Pervasives.Lemma | val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f | val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f = | false | null | true | let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i: nat{i < w}). uint_v (vec_v l1).[ i ] == uint_v (vec_v f).[ i ]);
assert (forall (i: nat{i < w}). (vec_v l1).[ i ] == (vec_v f).[ i ]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntVector.vecv_extensionality",
"Lib.IntTypes.U64",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Lib.IntVector.vec_v_t",
"Lib.IntVector.vec_v",
"Lib.Sequence.eq_intro",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.SEC",
"Prims.l_Forall",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Lib.Sequence.op_String_Access",
"Prims.int",
"Lib.IntTypes.range",
"Lib.IntTypes.uint_v",
"Lib.Sequence.lseq",
"Lib.Sequence.map2",
"Lib.IntTypes.op_Plus_Dot",
"Hacl.Spec.Poly1305.Field32xN.zero",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero_eq | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Hacl.Spec.Poly1305.Field32xN.uint64xN w
-> FStar.Pervasives.Lemma
(ensures
Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero f ==
Hacl.Spec.Poly1305.Field32xN.carry26_wide f (Hacl.Spec.Poly1305.Field32xN.zero w)) | {
"end_col": 26,
"end_line": 34,
"start_col": 31,
"start_line": 27
} |
FStar.Pervasives.Lemma | val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5)) | val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f = | false | null | true | let f0, f1, f2, f3, f4 = f in
let tmp0, c0 = carry26 f0 (zero w) in
let tmp1, c1 = carry26 f1 c0 in
let tmp2, c2 = carry26 f2 c1 in
let tmp3, c3 = carry26 f3 c2 in
let tmp4, c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_lemma",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.U64",
"Lib.IntTypes.u64",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"Prims.unit",
"Prims._assert",
"Prims.l_and",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma0",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} -> | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (8, 8, 8, 8, 8)}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f)) | {
"end_col": 72,
"end_line": 720,
"start_col": 39,
"start_line": 710
} |
FStar.Pervasives.Lemma | val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime | val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' = | false | null | true | let f0, f1, f2, f3, f4 = f in
let f0', f1', f2', f3', f4' = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <=
pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 +
(pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.modulo_lemma",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.max26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f (1, 1, 1, 1, 1)} ->
f': Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = f' in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in
Lib.IntTypes.v f4 <> 0x3ffffff || Lib.IntTypes.v f3 <> 0x3ffffff ||
Lib.IntTypes.v f2 <> 0x3ffffff ||
Lib.IntTypes.v f1 <> 0x3ffffff ||
Lib.IntTypes.v f0 < 0x3fffffb /\
Lib.IntTypes.v f0' = Lib.IntTypes.v f0 && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 &&
Lib.IntTypes.v f2' = Lib.IntTypes.v f2 &&
Lib.IntTypes.v f3' = Lib.IntTypes.v f3 &&
Lib.IntTypes.v f4' = Lib.IntTypes.v f4)
<:
Type0)
<:
Type0))
(ensures
Hacl.Spec.Poly1305.Field32xN.as_nat5 f' ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 f % Hacl.Spec.Poly1305.Vec.prime) | {
"end_col": 51,
"end_line": 495,
"start_col": 30,
"start_line": 484
} |
FStar.Pervasives.Lemma | val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f | val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f = | false | null | true | carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (8, 8, 8, 8, 8)}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f)
(2, 1, 1, 1, 1) /\
Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f) ==
Hacl.Spec.Poly1305.Field32xN.feval5 f) | {
"end_col": 32,
"end_line": 879,
"start_col": 2,
"start_line": 878
} |
FStar.Pervasives.Lemma | val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i) | val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i = | false | null | true | assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims._assert",
"Prims.eq2",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_s",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"Hacl.Spec.Poly1305.Field32xN.subtract_p5",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"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": 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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_felem5_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (1, 1, 1, 1, 1)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.tup64_fits5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i (Hacl.Spec.Poly1305.Field32xN.subtract_p5
f)
i)
(1, 1, 1, 1, 1) /\
Hacl.Spec.Poly1305.Field32xN.as_nat5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i (Hacl.Spec.Poly1305.Field32xN.subtract_p5
f)
i) ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i f i) %
Hacl.Spec.Poly1305.Vec.prime) | {
"end_col": 66,
"end_line": 608,
"start_col": 2,
"start_line": 608
} |
FStar.Pervasives.Lemma | val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26 | val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i = | false | null | true | let li = (vec_v l).[ i ] in
let cini = (vec_v cin).[ i ] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.pow2_minus",
"Prims.unit",
"FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims._assert",
"Prims.eq2",
"Lib.IntTypes.range_t",
"Lib.IntTypes.mod_mask",
"FStar.UInt32.__uint_to_t",
"Lib.IntTypes.mod_mask_lemma",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.op_Plus_Bang",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.op_Addition",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Subtraction",
"Lib.IntTypes.range",
"Lib.IntTypes.u64",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Lib.IntVector.vec_v",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.uint_t"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w ->
cin: Hacl.Spec.Poly1305.Field32xN.uint64xN w ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(requires
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] <= 2 * Hacl.Spec.Poly1305.Field32xN.max26 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] <=
62 * Hacl.Spec.Poly1305.Field32xN.max26)
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] <= 63 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] * Prims.pow2 26 +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ])
<:
Type0)) | {
"end_col": 36,
"end_line": 909,
"start_col": 37,
"start_line": 897
} |
Prims.Pure | val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4') | val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_s #w f i = | false | null | false | let f0, f1, f2, f3, f4 = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4') | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.uint64",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Subtraction_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.u64",
"Lib.IntTypes.logand_lemma",
"Lib.IntTypes.gte_mask",
"Lib.IntTypes.eq_mask",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_s | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (1, 1, 1, 1, 1)} ->
i: Prims.nat{i < w}
-> Prims.Pure Hacl.Spec.Poly1305.Field32xN.tup64_5 | {
"end_col": 27,
"end_line": 595,
"start_col": 26,
"start_line": 573
} |
FStar.Pervasives.Lemma | val carry_reduce_felem5_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_felem5_lemma #w f =
carry_reduce_felem5_fits_lemma #w f;
carry_full_felem5_eval_lemma f | val carry_reduce_felem5_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_reduce_felem5_lemma #w f = | false | null | true | carry_reduce_felem5_fits_lemma #w f;
carry_full_felem5_eval_lemma f | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
#push-options "--z3rlimit 600"
val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63))
let carry_reduce_felem5_fits_lemma_i0 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 else (uint64xN_v c0).[i] <= 63);
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c1).[i] = 0 else (uint64xN_v c1).[i] <= 63);
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c2).[i] = 0 else (uint64xN_v c2).[i] <= 63);
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c3).[i] = 0 else (uint64xN_v c3).[i] <= 63);
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 /\ (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)
val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i1 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i #w f i =
assert_norm (max26 == pow2 26 - 1);
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_felem5_fits_lemma_i1 #w f i;
FStar.Math.Lemmas.modulo_lemma ((uint64xN_v c4).[i] * 5) (pow2 64);
assert ((uint64xN_v (vec_smul_mod c4 (u64 5))).[i] == (uint64xN_v c4).[i] * 5);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
carry_reduce_felem5_fits_lemma_i0 #w f i;
let res = (tmp0', tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
#pop-options
#push-options "--z3rlimit 100"
val carry_reduce_felem5_fits_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma (felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma #w f =
match w with
| 1 ->
carry_reduce_felem5_fits_lemma_i #w f 0
| 2 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1
| 4 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1;
carry_reduce_felem5_fits_lemma_i #w f 2;
carry_reduce_felem5_fits_lemma_i #w f 3
val carry_reduce_felem5_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_felem5_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t f}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f)
(1, 1, 1, 1, 1) /\
Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f) ==
Hacl.Spec.Poly1305.Field32xN.feval5 f) | {
"end_col": 32,
"end_line": 1033,
"start_col": 2,
"start_line": 1032
} |
FStar.Pervasives.Lemma | val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2 | val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f = | false | null | true | let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Lib.IntVector.vecv_extensionality",
"Lib.IntTypes.U64",
"Prims.unit",
"Lib.Sequence.eq_intro",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.SEC",
"Lib.IntVector.vec_v",
"FStar.Classical.forall_intro",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntTypes.op_Less_Less_Dot",
"FStar.UInt32.__uint_to_t",
"Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five_i",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"Lib.IntVector.vec_shift_left",
"Lib.Sequence.lseq",
"Lib.Sequence.map",
"Lib.IntTypes.mul_mod",
"Lib.IntTypes.mk_int",
"Prims.int",
"Lib.IntTypes.range",
"Lib.IntTypes.v",
"Lib.IntVector.vec_smul_mod"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits f (4096 * Hacl.Spec.Poly1305.Field32xN.max26)}
-> FStar.Pervasives.Lemma
(ensures
Lib.IntVector.vec_smul_mod f (Lib.IntTypes.u64 5) ==
Lib.IntVector.vec_add_mod f (Lib.IntVector.vec_shift_left f 2ul)) | {
"end_col": 27,
"end_line": 55,
"start_col": 28,
"start_line": 50
} |
FStar.Pervasives.Lemma | val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul)) | val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i = | false | null | true | let f = (vec_v f).[ i ] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.v_injective",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntTypes.op_Less_Less_Dot",
"FStar.UInt32.__uint_to_t",
"Prims.unit",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.IntTypes.v",
"Prims.op_Addition",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"Prims.op_Modulus",
"Lib.IntTypes.int_t",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Lib.IntVector.vec_v",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.uint_t"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits f (4096 * Hacl.Spec.Poly1305.Field32xN.max26)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
Lib.IntTypes.u64 5 *. (Lib.IntVector.vec_v f).[ i ] ==
(Lib.IntVector.vec_v f).[ i ] +. ((Lib.IntVector.vec_v f).[ i ] <<. 2ul)) | {
"end_col": 32,
"end_line": 46,
"start_col": 32,
"start_line": 38
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3 | val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp = | false | null | true | let x0, x1, x2, x3, x4 = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_fits_lemma",
"Prims.unit",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26_wide",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_lemma",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero_eq",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_lemma0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ x0 x1 x2 x3 x4 = _ in
let _ = Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero x0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t2 c2 = _ in
let _ = Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero x3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 t3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t3' c6 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t4 c4 = _ in
let t4' = Lib.IntVector.vec_add_mod t4 c6 in
let tmp = t0, t1, t2, t3', t4' in
Hacl.Spec.Poly1305.Field32xN.felem_fits5 tmp (1, 1, 1, 1, 2) /\
Hacl.Spec.Poly1305.Field32xN.felem_fits1 c4 31)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 38,
"end_line": 268,
"start_col": 42,
"start_line": 253
} |
FStar.Pervasives.Lemma | val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1))) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26) | val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i = | false | null | true | let i0, i1, i2, i3, i4 = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[ i ] == (vec_v i0).[ i ] +. (vec_v cin).[ i ]);
assert ((uint64xN_v i0).[ i ] + (uint64xN_v cin).[ i ] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[ i ] + (uint64xN_v cin).[ i ])
(pow2 26) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.euclidean_division_definition",
"Prims.op_Addition",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.op_Subtraction",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.uint_t",
"Lib.IntVector.vec_v",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1))) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1))) | [] | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
acc:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 acc (1, 1, 1, 1, 1)} ->
cin: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin 45} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = acc in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ i0 i1 i2 i3 i4 = _ in
let i0' = Lib.IntVector.vec_add_mod i0 cin in
let acc1 = i0', i1, i2, i3, i4 in
(match (Hacl.Spec.Poly1305.Field32xN.uint64xN_v i0').[ i ] >= Prims.pow2 26 with
| true ->
Hacl.Spec.Poly1305.Field32xN.tup64_fits5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i acc1
i)
(2, 1, 1, 1, 1) /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v i0').[ i ] % Prims.pow2 26 < 47
| _ ->
Hacl.Spec.Poly1305.Field32xN.tup64_fits5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i acc1
i)
(1, 1, 1, 1, 1))
<:
Type0)
<:
Type0)) | {
"end_col": 104,
"end_line": 661,
"start_col": 34,
"start_line": 655
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5)) | val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
let carry_wide_felem5_fits_lemma #w inp = | false | null | true | let x0, x1, x2, x3, x4 = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_lemma",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.U64",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_lemma0",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"Hacl.Spec.Poly1305.Field32xN.carry26_wide",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 200,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | inp: Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
-> FStar.Pervasives.Lemma
(requires Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (Hacl.Spec.Poly1305.Field32xN.carry_wide_felem5 inp
)
(1, 2, 1, 1, 2)) | {
"end_col": 55,
"end_line": 291,
"start_col": 41,
"start_line": 279
} |
FStar.Pervasives.Lemma | val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_felem5_fits_lemma_i1 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i1 #w f i = | false | null | true | let f0, f1, f2, f3, f4 = f in
let tmp0, c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
let tmp1, c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
let tmp2, c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
let tmp3, c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
let tmp4, c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims._assert",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.Mktuple5",
"FStar.Pervasives.Native.tuple5",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_lemma_i",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
#push-options "--z3rlimit 600"
val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63))
let carry_reduce_felem5_fits_lemma_i0 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 else (uint64xN_v c0).[i] <= 63);
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c1).[i] = 0 else (uint64xN_v c1).[i] <= 63);
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c2).[i] = 0 else (uint64xN_v c2).[i] <= 63);
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c3).[i] = 0 else (uint64xN_v c3).[i] <= 63);
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 /\ (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)
val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 600,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t f} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f0 (Hacl.Spec.Poly1305.Field32xN.zero w) in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp2 c2 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp4 c4 = _ in
let res = tmp0, tmp1, tmp2, tmp3, tmp4 in
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v c4).[ i ] <= 63 /\
Hacl.Spec.Poly1305.Field32xN.tup64_fits5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i
res
i)
(1, 1, 1, 1, 1))
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 57,
"end_line": 977,
"start_col": 46,
"start_line": 964
} |
FStar.Pervasives.Lemma | val carry_reduce_felem5_fits_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma (felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_felem5_fits_lemma #w f =
match w with
| 1 ->
carry_reduce_felem5_fits_lemma_i #w f 0
| 2 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1
| 4 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1;
carry_reduce_felem5_fits_lemma_i #w f 2;
carry_reduce_felem5_fits_lemma_i #w f 3 | val carry_reduce_felem5_fits_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma (felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma #w f = | false | null | true | match w with
| 1 -> carry_reduce_felem5_fits_lemma_i #w f 0
| 2 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1
| 4 ->
carry_reduce_felem5_fits_lemma_i #w f 0;
carry_reduce_felem5_fits_lemma_i #w f 1;
carry_reduce_felem5_fits_lemma_i #w f 2;
carry_reduce_felem5_fits_lemma_i #w f 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
#push-options "--z3rlimit 600"
val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63))
let carry_reduce_felem5_fits_lemma_i0 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 else (uint64xN_v c0).[i] <= 63);
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c1).[i] = 0 else (uint64xN_v c1).[i] <= 63);
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c2).[i] = 0 else (uint64xN_v c2).[i] <= 63);
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c3).[i] = 0 else (uint64xN_v c3).[i] <= 63);
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 /\ (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)
val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i1 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i #w f i =
assert_norm (max26 == pow2 26 - 1);
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_felem5_fits_lemma_i1 #w f i;
FStar.Math.Lemmas.modulo_lemma ((uint64xN_v c4).[i] * 5) (pow2 64);
assert ((uint64xN_v (vec_smul_mod c4 (u64 5))).[i] == (uint64xN_v c4).[i] * 5);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
carry_reduce_felem5_fits_lemma_i0 #w f i;
let res = (tmp0', tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
#pop-options
#push-options "--z3rlimit 100"
val carry_reduce_felem5_fits_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma (felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_felem5_fits_lemma:
#w:lanes
-> f:felem5 w{acc_inv_t f} ->
Lemma (felem_fits5 (carry_full_felem5 f) (1, 1, 1, 1, 1)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t f}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 f)
(1, 1, 1, 1, 1)) | {
"end_col": 43,
"end_line": 1021,
"start_col": 2,
"start_line": 1011
} |
FStar.Pervasives.Lemma | val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3 | val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin = | false | null | true | match w with
| 1 -> acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
acc:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 acc (1, 1, 1, 1, 1)} ->
cin: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin 45}
-> FStar.Pervasives.Lemma
(ensures
(let _ = acc in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ i0 i1 i2 i3 i4 = _ in
let i0' = Lib.IntVector.vec_add_mod i0 cin in
Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t (i0', i1, i2, i3, i4))
<:
Type0)) | {
"end_col": 32,
"end_line": 683,
"start_col": 2,
"start_line": 673
} |
FStar.Pervasives.Lemma | val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3 | val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin = | false | null | true | carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 -> carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_lemma_i",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_fits_lemma"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 l m} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (4096 * Hacl.Spec.Poly1305.Field32xN.max26)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
Hacl.Spec.Poly1305.Field32xN.uint64xN_fits l1
((m + 1) * Hacl.Spec.Poly1305.Field32xN.max26) /\
(forall (i: Prims.nat).
i < w ==>
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] * Prims.pow2 26 +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ]))
<:
Type0)) | {
"end_col": 38,
"end_line": 160,
"start_col": 2,
"start_line": 149
} |
FStar.Pervasives.Lemma | val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26) | val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i = | false | null | true | let l = (vec_v l).[ i ] in
let cin = (vec_v cin).[ i ] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.euclidean_division_definition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1",
"Prims._assert",
"Prims.eq2",
"Lib.IntTypes.range_t",
"Lib.IntTypes.mod_mask",
"FStar.UInt32.__uint_to_t",
"Lib.IntTypes.mod_mask_lemma",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.op_Plus_Bang",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.op_Addition",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Subtraction",
"Lib.IntTypes.range",
"Lib.IntTypes.u64",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Lib.IntVector.vec_v",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.uint_t"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 l m} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (4096 * Hacl.Spec.Poly1305.Field32xN.max26)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] <=
(m + 1) * Hacl.Spec.Poly1305.Field32xN.max26 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] * Prims.pow2 26 +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ])
<:
Type0)) | {
"end_col": 66,
"end_line": 109,
"start_col": 40,
"start_line": 97
} |
FStar.Pervasives.Lemma | val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i = | false | null | true | let i0, i1, i2, i3, i4 = inp in
let tmp0, c0 = carry26 i0 (zero w) in
let tmp1, c1 = carry26 i1 c0 in
let tmp2, c2 = carry26 i2 c1 in
let tmp3, c3 = carry26 i3 c2 in
let tmp4, c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let t0, t1, t2, t3, t4 = as_tup64_i tmp i in
let ti0, ti1, ti2, ti3, ti4 = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[ i ] in
let vc1 = (uint64xN_v c1).[ i ] in
let vc2 = (uint64xN_v c2).[ i ] in
let vc3 = (uint64xN_v c3).[ i ] in
let vc4 = (uint64xN_v c4).[ i ] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[ i ] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Prims.op_Modulus",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i0",
"Prims.pow2",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_eval_lemma",
"Hacl.Spec.Poly1305.Field32xN.zero",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.tuple5",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 inp (8, 8, 8, 8, 8)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ i0 i1 i2 i3 i4 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 i0 (Hacl.Spec.Poly1305.Field32xN.zero w) in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 i1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 i2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp2 c2 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 i3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 i4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp4 c4 = _ in
let tmp = tmp0, tmp1, tmp2, tmp3, tmp4 in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i tmp i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let vc4 = (Hacl.Spec.Poly1305.Field32xN.uint64xN_v c4).[ i ] in
(Hacl.Spec.Poly1305.Field32xN.feval5 inp).[ i ] ==
(Lib.IntTypes.v t0 + vc4 * 5 +
Lib.IntTypes.v t1 * Hacl.Spec.Poly1305.Field32xN.pow26 +
Lib.IntTypes.v t2 * Hacl.Spec.Poly1305.Field32xN.pow52 +
Lib.IntTypes.v t3 * Hacl.Spec.Poly1305.Field32xN.pow78 +
Lib.IntTypes.v t4 * Hacl.Spec.Poly1305.Field32xN.pow104) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 89,
"end_line": 822,
"start_col": 46,
"start_line": 792
} |
FStar.Pervasives.Lemma | val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3 | val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f = | false | null | true | match w with
| 1 -> subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_felem5_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0]) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0]) | [] | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_felem5_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f (1, 1, 1, 1, 1)}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_fits5 (Hacl.Spec.Poly1305.Field32xN.subtract_p5 f)
(1, 1, 1, 1, 1) /\
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (Hacl.Spec.Poly1305.Field32xN.subtract_p5 f)).[ 0 ] ==
(Hacl.Spec.Poly1305.Field32xN.feval5 f).[ 0 ]) | {
"end_col": 37,
"end_line": 629,
"start_col": 2,
"start_line": 619
} |
FStar.Pervasives.Lemma | val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26 | val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i = | false | null | true | let l = (vec_v l).[ i ] in
let cin = (vec_v cin).[ i ] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.pow2_minus",
"Prims.unit",
"FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims._assert",
"Prims.eq2",
"Lib.IntTypes.range_t",
"Lib.IntTypes.mod_mask",
"FStar.UInt32.__uint_to_t",
"Lib.IntTypes.mod_mask_lemma",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.op_Plus_Bang",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.op_Addition",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Subtraction",
"Lib.IntTypes.range",
"Lib.IntTypes.u64",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Lib.IntVector.vec_v",
"Lib.Sequence.op_String_Access",
"Lib.IntTypes.uint_t"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
m: Hacl.Spec.Poly1305.Field32xN.scale64 ->
ml: Hacl.Spec.Poly1305.Field32xN.scale32 ->
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 l ml} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (m * Hacl.Spec.Poly1305.Field32xN.max26)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26 /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] < m + ml /\
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] * Prims.pow2 26 +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ])
<:
Type0)) | {
"end_col": 36,
"end_line": 186,
"start_col": 37,
"start_line": 174
} |
FStar.Pervasives.Lemma | val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3 | val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin = | false | null | true | match w with
| 1 -> carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
m: Hacl.Spec.Poly1305.Field32xN.scale64 ->
ml: Hacl.Spec.Poly1305.Field32xN.scale32 ->
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 l ml} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (m * Hacl.Spec.Poly1305.Field32xN.max26)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
Hacl.Spec.Poly1305.Field32xN.felem_fits1 l0 1 /\
Hacl.Spec.Poly1305.Field32xN.uint64xN_fits l1 (m + ml))
<:
Type0)) | {
"end_col": 35,
"end_line": 210,
"start_col": 2,
"start_line": 200
} |
FStar.Pervasives.Lemma | val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3 | val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin = | false | null | true | match w with
| 1 -> carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
m: Hacl.Spec.Poly1305.Field32xN.scale64 ->
ml: Hacl.Spec.Poly1305.Field32xN.scale32 ->
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 l ml} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (m * Hacl.Spec.Poly1305.Field32xN.max26)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
Hacl.Spec.Poly1305.Field32xN.felem_fits1 l0 1 /\
Hacl.Spec.Poly1305.Field32xN.uint64xN_fits l1 (m + ml) /\
(forall (i: Prims.nat).
i < w ==>
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v cin).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l1).[ i ] * Prims.pow2 26 +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v l0).[ i ]))
<:
Type0)) | {
"end_col": 35,
"end_line": 236,
"start_col": 2,
"start_line": 226
} |
FStar.Pervasives.Lemma | val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime | val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' = | false | null | true | let f0, f1, f2, f3, f4 = f in
let f0', f1', f2', f3', f4' = f' in
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc ( == ) {
as_nat5 f' % prime;
( == ) { () }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
( == ) { () }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 +
(v f4 - (pow2 26 - 1)) * pow104) %
prime;
( == ) { (assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 +
v f4 * pow104)
prime
1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
( == ) { () }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.modulo_lemma",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.op_Subtraction",
"Prims.pow2",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"FStar.Math.Lemmas.lemma_mod_sub",
"Prims.op_LessThan"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f (1, 1, 1, 1, 1)} ->
f': Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = f' in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in
Lib.IntTypes.v f4 = 0x3ffffff && Lib.IntTypes.v f3 = 0x3ffffff &&
Lib.IntTypes.v f2 = 0x3ffffff &&
Lib.IntTypes.v f1 = 0x3ffffff &&
Lib.IntTypes.v f0 >= 0x3fffffb /\
Lib.IntTypes.v f0' = Lib.IntTypes.v f0 - 0x3fffffb &&
Lib.IntTypes.v f1' = Lib.IntTypes.v f1 - 0x3ffffff &&
Lib.IntTypes.v f2' = Lib.IntTypes.v f2 - 0x3ffffff &&
Lib.IntTypes.v f3' = Lib.IntTypes.v f3 - 0x3ffffff &&
Lib.IntTypes.v f4' = Lib.IntTypes.v f4 - 0x3ffffff)
<:
Type0)
<:
Type0))
(ensures
Hacl.Spec.Poly1305.Field32xN.as_nat5 f' ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 f % Hacl.Spec.Poly1305.Vec.prime) | {
"end_col": 51,
"end_line": 535,
"start_col": 30,
"start_line": 509
} |
FStar.Pervasives.Lemma | val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3 | val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
let carry26_wide_fits_lemma #w #m l cin = | false | null | true | match w with
| 1 -> carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_fits",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100" | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
l: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 l m} ->
cin:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.uint64xN_fits cin (4096 * Hacl.Spec.Poly1305.Field32xN.max26)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = Hacl.Spec.Poly1305.Field32xN.carry26 l cin in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ l0 l1 = _ in
Hacl.Spec.Poly1305.Field32xN.felem_fits1 l0 1 /\
Hacl.Spec.Poly1305.Field32xN.uint64xN_fits l1
((m + 1) * Hacl.Spec.Poly1305.Field32xN.max26))
<:
Type0)) | {
"end_col": 38,
"end_line": 133,
"start_col": 2,
"start_line": 123
} |
FStar.Pervasives.Lemma | val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_felem5_fits_lemma_i #w f i =
assert_norm (max26 == pow2 26 - 1);
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_felem5_fits_lemma_i1 #w f i;
FStar.Math.Lemmas.modulo_lemma ((uint64xN_v c4).[i] * 5) (pow2 64);
assert ((uint64xN_v (vec_smul_mod c4 (u64 5))).[i] == (uint64xN_v c4).[i] * 5);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
carry_reduce_felem5_fits_lemma_i0 #w f i;
let res = (tmp0', tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i #w f i = | false | null | true | assert_norm (max26 == pow2 26 - 1);
let f0, f1, f2, f3, f4 = f in
let tmp0, c0 = carry26 f0 (zero w) in
let tmp1, c1 = carry26 f1 c0 in
let tmp2, c2 = carry26 f2 c1 in
let tmp3, c3 = carry26 f3 c2 in
let tmp4, c4 = carry26 f4 c3 in
carry_reduce_felem5_fits_lemma_i1 #w f i;
FStar.Math.Lemmas.modulo_lemma ((uint64xN_v c4).[ i ] * 5) (pow2 64);
assert ((uint64xN_v (vec_smul_mod c4 (u64 5))).[ i ] == (uint64xN_v c4).[ i ] * 5);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
carry_reduce_felem5_fits_lemma_i0 #w f i;
let res = (tmp0', tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims._assert",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.Mktuple5",
"FStar.Pervasives.Native.tuple5",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i0",
"Lib.IntVector.vec_t",
"Lib.IntTypes.U64",
"Lib.IntVector.vec_add_mod",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.u64",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"FStar.Mul.op_Star",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.pow2",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i1",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero",
"FStar.Pervasives.assert_norm",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.op_Subtraction"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
#push-options "--z3rlimit 600"
val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63))
let carry_reduce_felem5_fits_lemma_i0 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 else (uint64xN_v c0).[i] <= 63);
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c1).[i] = 0 else (uint64xN_v c1).[i] <= 63);
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c2).[i] = 0 else (uint64xN_v c2).[i] <= 63);
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c3).[i] = 0 else (uint64xN_v c3).[i] <= 63);
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 /\ (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)
val carry_reduce_felem5_fits_lemma_i1:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(uint64xN_v c4).[i] <= 63 /\
tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
let carry_reduce_felem5_fits_lemma_i1 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
assert (tup64_fits5 (as_tup64_i res i) (1, 1, 1, 1, 1))
val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 600,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_felem5_fits_lemma_i:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma (tup64_fits5 (as_tup64_i (carry_full_felem5 f) i) (1, 1, 1, 1, 1)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t f} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.tup64_fits5 (Hacl.Spec.Poly1305.Field32xN.as_tup64_i (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5
f)
i)
(1, 1, 1, 1, 1)) | {
"end_col": 57,
"end_line": 1001,
"start_col": 2,
"start_line": 987
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4 | val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_wide_felem5_eval_lemma_i #w inp i = | false | null | true | let x0, x1, x2, x3, x4 = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[ i ] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[ i ] + (uint64xN_v c4).[ i ] * 5 ==
(uint64xN_v c5).[ i ] * pow2 26 + (uint64xN_v tmp0').[ i ]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[ i ] + (uint64xN_v c5).[ i ]) (pow2 64);
assert ((uint64xN_v tmp1').[ i ] == (uint64xN_v tmp1).[ i ] + (uint64xN_v c5).[ i ]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let o0, o1, o2, o3, o4 = as_tup64_i out i in
let t0, t1, t2, t3, t4 = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[ i ] in
let vc5 = (uint64xN_v c5).[ i ] in
calc ( == ) {
(feval5 out).[ i ];
( == ) { () }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
( == ) { () }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104
) %
prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[ i ] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[ i ] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[ i ] == (feval5 inp).[ i ]);
vec_smul_mod_five c4 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Lib.Sequence.op_String_Access",
"Prims.int",
"Prims.op_Modulus",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Hacl.Spec.Poly1305.Vec.prime",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i1",
"FStar.Math.Lemmas.distributivity_add_left",
"FStar.Calc.calc_finish",
"Prims.op_Subtraction",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.tuple5",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_eval_lemma",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.u64",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_lemma0",
"Hacl.Spec.Poly1305.Field32xN.carry26_wide",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_wide_felem5 inp)).[ i
] ==
(Hacl.Spec.Poly1305.Field32xN.feval5 inp).[ i ]) | {
"end_col": 22,
"end_line": 456,
"start_col": 45,
"start_line": 418
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime) | val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i = | false | null | true | let x0, x1, x2, x3, x4 = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let t0, t1, t2, t3, t4 = as_tup64_i tmp i in
let t0, t1, t2, t3', t4' = as_tup64_i tmp' i in
let xi0, xi1, xi2, xi3, xi4 = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[ i ] in
let vc1 = (uint64xN_v c1).[ i ] in
let vc2 = (uint64xN_v c2).[ i ] in
let vc3 = (uint64xN_v c3).[ i ] in
let vc4 = (uint64xN_v c4).[ i ] in
let vc6 = (uint64xN_v c6).[ i ] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4)
(t0, t1, t2, t3', t4')
vc0
vc1
vc2
vc3
vc4
vc6;
assert ((feval5 inp).[ i ] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Prims.op_Modulus",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i0",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_fits_lemma",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_eval_lemma",
"Hacl.Spec.Poly1305.Field32xN.zero",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero_eq",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.tuple5",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26_wide",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_lemma",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_eval_lemma",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ x0 x1 x2 x3 x4 = _ in
let _ = Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero x0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t2 c2 = _ in
let _ = Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero x3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 t3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t3' c6 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26_wide x4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ t4 c4 = _ in
let t4' = Lib.IntVector.vec_add_mod t4 c6 in
let tmp = t0, t1, t2, t3', t4' in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i tmp i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let vc4 = (Hacl.Spec.Poly1305.Field32xN.uint64xN_v c4).[ i ] in
(Hacl.Spec.Poly1305.Field32xN.feval5 inp).[ i ] ==
(Lib.IntTypes.v t0 + vc4 * 5 +
Lib.IntTypes.v t1 * Hacl.Spec.Poly1305.Field32xN.pow26 +
Lib.IntTypes.v t2 * Hacl.Spec.Poly1305.Field32xN.pow52 +
Lib.IntTypes.v t3 * Hacl.Spec.Poly1305.Field32xN.pow78 +
Lib.IntTypes.v t4 * Hacl.Spec.Poly1305.Field32xN.pow104) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 118,
"end_line": 408,
"start_col": 46,
"start_line": 363
} |
FStar.Pervasives.Lemma | val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime) | val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 = | false | null | true | let t0, t1, t2, t3, t4 = tmp in
let xi0, xi1, xi2, xi3, xi4 = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc ( == ) {
as_nat5 inp % prime;
( == ) { () }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
( == ) { () }
(vc0 * pow2 26 + v t0 + (vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) %
prime;
( == ) { (assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)) }
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
( == ) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.pow2",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.op_Subtraction",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"Hacl.Poly1305.Field32xN.Lemmas1.lemma_prime"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp: Hacl.Spec.Poly1305.Field32xN.tup64_5 ->
tmp: Hacl.Spec.Poly1305.Field32xN.tup64_5 ->
vc0: Prims.nat ->
vc1: Prims.nat ->
vc2: Prims.nat ->
vc3: Prims.nat ->
vc4: Prims.nat ->
vc6: Prims.nat
-> FStar.Pervasives.Lemma
(requires
(let _ = tmp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ xi0 xi1 xi2 xi3 xi4 = _ in
Lib.IntTypes.v xi0 == vc0 * Prims.pow2 26 + Lib.IntTypes.v t0 /\
Lib.IntTypes.v xi1 + vc0 == vc1 * Prims.pow2 26 + Lib.IntTypes.v t1 /\
Lib.IntTypes.v xi2 + vc1 == vc2 * Prims.pow2 26 + Lib.IntTypes.v t2 /\
Lib.IntTypes.v xi3 + vc2 ==
vc3 * Prims.pow2 26 + vc6 * Prims.pow2 26 + Lib.IntTypes.v t3 /\
Lib.IntTypes.v xi4 + vc3 == vc4 * Prims.pow2 26 + Lib.IntTypes.v t4 - vc6)
<:
Type0)
<:
Type0))
(ensures
(let _ = tmp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ _ _ = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 inp % Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v t0 + vc4 * 5 + Lib.IntTypes.v t1 * Hacl.Spec.Poly1305.Field32xN.pow26 +
Lib.IntTypes.v t2 * Hacl.Spec.Poly1305.Field32xN.pow52 +
Lib.IntTypes.v t3 * Hacl.Spec.Poly1305.Field32xN.pow78 +
Lib.IntTypes.v t4 * Hacl.Spec.Poly1305.Field32xN.pow104) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 59,
"end_line": 343,
"start_col": 69,
"start_line": 313
} |
FStar.Pervasives.Lemma | val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime) | val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 = | false | null | true | let t0, t1, t2, t3, t4 = tmp in
let ti0, ti1, ti2, ti3, ti4 = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc ( == ) {
as_nat5 inp % prime;
( == ) { () }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
( == ) { () }
(vc0 * pow2 26 + v t0 + (vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) %
prime;
( == ) { (assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)) }
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
( == ) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.pow2",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.op_Subtraction",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"Hacl.Poly1305.Field32xN.Lemmas1.lemma_prime"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp: Hacl.Spec.Poly1305.Field32xN.tup64_5 ->
tmp: Hacl.Spec.Poly1305.Field32xN.tup64_5 ->
vc0: Prims.nat ->
vc1: Prims.nat ->
vc2: Prims.nat ->
vc3: Prims.nat ->
vc4: Prims.nat
-> FStar.Pervasives.Lemma
(requires
(let _ = tmp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ ti0 ti1 ti2 ti3 ti4 = _ in
Lib.IntTypes.v ti0 == vc0 * Prims.pow2 26 + Lib.IntTypes.v t0 /\
Lib.IntTypes.v ti1 + vc0 == vc1 * Prims.pow2 26 + Lib.IntTypes.v t1 /\
Lib.IntTypes.v ti2 + vc1 == vc2 * Prims.pow2 26 + Lib.IntTypes.v t2 /\
Lib.IntTypes.v ti3 + vc2 == vc3 * Prims.pow2 26 + Lib.IntTypes.v t3 /\
Lib.IntTypes.v ti4 + vc3 == vc4 * Prims.pow2 26 + Lib.IntTypes.v t4)
<:
Type0)
<:
Type0))
(ensures
(let _ = tmp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ t0 t1 t2 t3 t4 = _ in
let _ = inp in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ _ _ = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 inp % Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v t0 + vc4 * 5 + Lib.IntTypes.v t1 * Hacl.Spec.Poly1305.Field32xN.pow26 +
Lib.IntTypes.v t2 * Hacl.Spec.Poly1305.Field32xN.pow52 +
Lib.IntTypes.v t3 * Hacl.Spec.Poly1305.Field32xN.pow78 +
Lib.IntTypes.v t4 * Hacl.Spec.Poly1305.Field32xN.pow104) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 59,
"end_line": 772,
"start_col": 65,
"start_line": 742
} |
FStar.Pervasives.Lemma | val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_reduce_felem5_fits_lemma_i0 #w f i =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 else (uint64xN_v c0).[i] <= 63);
let tmp1,c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c1).[i] = 0 else (uint64xN_v c1).[i] <= 63);
let tmp2,c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c2).[i] = 0 else (uint64xN_v c2).[i] <= 63);
let tmp3,c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c3).[i] = 0 else (uint64xN_v c3).[i] <= 63);
let tmp4,c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[i] = 0 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63);
assert (if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c0).[i] = 0 /\ (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63) | val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63))
let carry_reduce_felem5_fits_lemma_i0 #w f i = | false | null | true | let f0, f1, f2, f3, f4 = f in
let tmp0, c0 = carry26 f0 (zero w) in
carry_reduce_lemma_i f0 (zero w) i;
assert (if (uint64xN_v f0).[ i ] < pow2 26
then (uint64xN_v tmp0).[ i ] < pow2 26
else (uint64xN_v tmp0).[ i ] <= 46);
assert (if (uint64xN_v f0).[ i ] < pow2 26
then (uint64xN_v c0).[ i ] = 0
else (uint64xN_v c0).[ i ] <= 63);
let tmp1, c1 = carry26 f1 c0 in
carry_reduce_lemma_i f1 c0 i;
assert (if (uint64xN_v c0).[ i ] = 0 then (uint64xN_v c1).[ i ] = 0 else (uint64xN_v c1).[ i ] <= 63
);
let tmp2, c2 = carry26 f2 c1 in
carry_reduce_lemma_i f2 c1 i;
assert (if (uint64xN_v c0).[ i ] = 0 then (uint64xN_v c2).[ i ] = 0 else (uint64xN_v c2).[ i ] <= 63
);
let tmp3, c3 = carry26 f3 c2 in
carry_reduce_lemma_i f3 c2 i;
assert (if (uint64xN_v c0).[ i ] = 0 then (uint64xN_v c3).[ i ] = 0 else (uint64xN_v c3).[ i ] <= 63
);
let tmp4, c4 = carry26 f4 c3 in
carry_reduce_lemma_i f4 c3 i;
assert (if (uint64xN_v c0).[ i ] = 0 then (uint64xN_v c4).[ i ] = 0 else (uint64xN_v c4).[ i ] <= 63
);
assert (if (uint64xN_v f0).[ i ] < pow2 26
then (uint64xN_v c0).[ i ] = 0 /\ (uint64xN_v c4).[ i ] = 0
else (uint64xN_v c4).[ i ] <= 63) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Prims._assert",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Prims.pow2",
"Prims.l_and",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"Prims.op_LessThanOrEqual",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_lemma_i",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i])
val carry_full_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_fits5 inp (8, 8, 8, 8, 8))
(ensures feval5 (carry_full_felem5 #w inp) == feval5 inp)
let carry_full_felem5_eval_lemma #w inp =
let o = carry_full_felem5 #w inp in
FStar.Classical.forall_intro (carry_full_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val carry_full_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma
(felem_fits5 (carry_full_felem5 f) (2, 1, 1, 1, 1) /\
feval5 (carry_full_felem5 f) == feval5 f)
let carry_full_felem5_lemma #w f =
carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f
val carry_reduce_lemma_i:
#w:lanes
-> l:uint64xN w
-> cin:uint64xN w
-> i:nat{i < w} ->
Lemma
(requires
(uint64xN_v l).[i] <= 2 * max26 /\
(uint64xN_v cin).[i] <= 62 * max26)
(ensures
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= 63 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry_reduce_lemma_i #w l cin i =
let li = (vec_v l).[i] in
let cini = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v li + v cini) (pow2 64);
let li' = li +! cini in
let li0 = li' &. mask26 in
let li1 = li' >>. 26ul in
mod_mask_lemma li' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v li') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
#push-options "--z3rlimit 600"
val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 600,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_reduce_felem5_fits_lemma_i0:
#w:lanes
-> f:felem5 w{acc_inv_t f}
-> i:nat{i < w} ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
let res = (tmp0, tmp1, tmp2, tmp3, tmp4) in
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v tmp0).[i] < pow2 26 else (uint64xN_v tmp0).[i] <= 46) /\
(if (uint64xN_v f0).[i] < pow2 26 then (uint64xN_v c4).[i] = 0 else (uint64xN_v c4).[i] <= 63)) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i0 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t f} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f0 (Hacl.Spec.Poly1305.Field32xN.zero w) in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp0 c0 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f1 c0 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp1 c1 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f2 c1 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp2 c2 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f3 c2 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp3 c3 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.carry26 f4 c3 in
(let FStar.Pervasives.Native.Mktuple2 #_ #_ tmp4 c4 = _ in
let res = tmp0, tmp1, tmp2, tmp3, tmp4 in
(match (Hacl.Spec.Poly1305.Field32xN.uint64xN_v f0).[ i ] < Prims.pow2 26 with
| true -> (Hacl.Spec.Poly1305.Field32xN.uint64xN_v tmp0).[ i ] < Prims.pow2 26
| _ -> (Hacl.Spec.Poly1305.Field32xN.uint64xN_v tmp0).[ i ] <= 46) /\
(match (Hacl.Spec.Poly1305.Field32xN.uint64xN_v f0).[ i ] < Prims.pow2 26 with
| true -> (Hacl.Spec.Poly1305.Field32xN.uint64xN_v c4).[ i ] = 0
| _ -> (Hacl.Spec.Poly1305.Field32xN.uint64xN_v c4).[ i ] <= 63))
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 130,
"end_line": 946,
"start_col": 46,
"start_line": 928
} |
FStar.Pervasives.Lemma | val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"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
}
] | false | let carry_full_felem5_eval_lemma_i #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[i] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[i] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[i] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[i] == (uint64xN_v tmp0).[i] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[i] == (feval5 inp).[i]) | val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i])
let carry_full_felem5_eval_lemma_i #w inp i = | false | null | true | let i0, i1, i2, i3, i4 = inp in
let tmp0, c0 = carry26 i0 (zero w) in
let tmp1, c1 = carry26 i1 c0 in
let tmp2, c2 = carry26 i2 c1 in
let tmp3, c3 = carry26 i3 c2 in
let tmp4, c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let t0, t1, t2, t3, t4 = as_tup64_i tmp i in
let ti0, ti1, ti2, ti3, ti4 = as_tup64_i inp i in
let vc4 = (uint64xN_v c4).[ i ] in
carry_full_felem5_fits_lemma0 #w inp;
let cin = vec_smul_mod c4 (u64 5) in
assert ((uint64xN_v cin).[ i ] == vc4 * 5);
let tmp0' = vec_add_mod tmp0 cin in
Math.Lemmas.small_mod ((uint64xN_v tmp0).[ i ] + vc4 * 5) (pow2 64);
assert ((uint64xN_v tmp0').[ i ] == (uint64xN_v tmp0).[ i ] + vc4 * 5);
let out = (tmp0', tmp1, tmp2, tmp3, tmp4) in
let o0, o1, o2, o3, o4 = as_tup64_i out i in
assert ((feval5 out).[ i ] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_full_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 out).[ i ] == (feval5 inp).[ i ]) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas1.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Hacl.Spec.Poly1305.Vec.pfelem",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.feval5",
"Lib.Sequence.op_String_Access",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i1",
"Prims.int",
"Prims.op_Modulus",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Hacl.Spec.Poly1305.Vec.prime",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Pervasives.Native.tuple5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"Lib.IntVector.vec_t",
"Lib.IntVector.vec_add_mod",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntVector.vec_v",
"Lib.Sequence.map",
"Lib.IntTypes.mul_mod",
"Lib.IntTypes.mk_int",
"Lib.IntTypes.range",
"Lib.IntVector.vec_smul_mod",
"Lib.IntTypes.u64",
"Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma0",
"FStar.Pervasives.Native.tuple2",
"Hacl.Spec.Poly1305.Field32xN.carry26",
"Hacl.Spec.Poly1305.Field32xN.zero"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas1
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#set-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
noextract
val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w
let carry26_wide_zero #w l = (vec_and l (mask26 w), vec_shift_right l 26ul)
val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w))
let carry26_wide_zero_eq #w f =
let l1 = vec_add_mod f (zero w) in
assert (vec_v l1 == map2 ( +. ) (vec_v f) (vec_v (zero w)));
assert (forall (i:nat{i < w}). uint_v (vec_v l1).[i] == uint_v (vec_v f).[i]);
assert (forall (i:nat{i < w}). (vec_v l1).[i] == (vec_v f).[i]);
eq_intro (vec_v l1) (vec_v f);
assert (vec_v l1 == vec_v f);
vecv_extensionality l1 f
val vec_smul_mod_five_i: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> i:nat{i < w} -> Lemma
(u64 5 *. (vec_v f).[i] == (vec_v f).[i] +. ((vec_v f).[i] <<. 2ul))
let vec_smul_mod_five_i #w f i =
let f = (vec_v f).[i] in
assert (v (f <<. 2ul) == (v f * pow2 2) % pow2 64);
Math.Lemmas.small_mod (v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (v f + v f * pow2 2) (pow2 64);
Math.Lemmas.small_mod (5 * v f) (pow2 64);
assert (5 * v f == v f + v f * 4);
v_injective (u64 5 *. f);
v_injective (f +. (f <<. 2ul))
val vec_smul_mod_five: #w:lanes -> f:uint64xN w{uint64xN_fits f (4096 * max26)} -> Lemma
(vec_smul_mod f (u64 5) == vec_add_mod f (vec_shift_left f 2ul))
let vec_smul_mod_five #w f =
let r1 = vec_smul_mod f (u64 5) in
let r2 = vec_add_mod f (vec_shift_left f 2ul) in
Classical.forall_intro (vec_smul_mod_five_i #w f);
eq_intro (vec_v r1) (vec_v r2);
vecv_extensionality r1 r2
noextract
val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w
let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
// m_i <= 4096, x_i <= m_i * max26 * max26
// felem_wide_fits5 (x0, x1, x2, x3, x4) (m0, m1, m2, m3, m4)
let t0, c0 = carry26_wide_zero x0 in
// t0 <= max26 /\ c0 <= (m0 + 1) * max26
let t1, c1 = carry26_wide x1 c0 in
// t1 <= max26 /\ c1 <= (m1 + 1) * max26
let t2, c2 = carry26_wide x2 c1 in
// t2 <= max26 /\ c2 <= (m2 + 1) * max26
let t3, c3 = carry26_wide_zero x3 in
// t3 <= max26 /\ c3 <= (m3 + 1) * max26
let t3', c6 = carry26 t3 c2 in
// t3' <= max26 /\ c6 <= m2 + 2
let t4, c4 = carry26_wide x4 c3 in
// t4 <= max26 /\ c4 <= (m4 + 1) * max26
let t4' = vec_add_mod t4 c6 in
// t4' <= 2 * max26
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
// t0' <= max26 /\ c5 <= 5 * (m4 + 1) + 1
let t1' = vec_add_mod t1 c5 in
// t1' <= 2 * max26
(t0', t1', t2, t3', t4')
// felem_fits5 (t0', t1', t2, t3', t4') (1, 2, 1, 1, 2)
val carry26_wide_lemma_i:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] <= (m + 1) * max26 /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_wide_lemma_i #w #m l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 26)
val carry26_wide_fits_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 ((m + 1) * max26))
#push-options "--z3rlimit 100"
let carry26_wide_fits_lemma #w #m l cin =
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
#pop-options
val carry26_wide_eval_lemma:
#w:lanes
-> #m:scale64
-> l:uint64xN w{felem_wide_fits1 l m}
-> cin:uint64xN w{uint64xN_fits cin (4096 * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
//felem_fits1 l0 1 /\
uint64xN_fits l1 ((m + 1) * max26) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_wide_eval_lemma #w #m l cin =
carry26_wide_fits_lemma #w #m l cin;
match w with
| 1 ->
carry26_wide_lemma_i #w #m l cin 0
| 2 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1
| 4 ->
carry26_wide_lemma_i #w #m l cin 0;
carry26_wide_lemma_i #w #m l cin 1;
carry26_wide_lemma_i #w #m l cin 2;
carry26_wide_lemma_i #w #m l cin 3
val carry26_lemma_i:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)}
-> i:nat{i < w} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
(uint64xN_v l0).[i] <= max26 /\ (uint64xN_v l1).[i] < m + ml /\
(uint64xN_v l).[i] + (uint64xN_v cin).[i] == (uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i])
let carry26_lemma_i #w m ml l cin i =
let l = (vec_v l).[i] in
let cin = (vec_v cin).[i] in
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (v l + v cin) (pow2 64);
let l' = l +! cin in
let l0 = l' &. mask26 in
let l1 = l' >>. 26ul in
mod_mask_lemma l' 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 26 32;
FStar.Math.Lemmas.pow2_minus 32 26
val carry26_fits_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml))
let carry26_fits_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry26_eval_lemma:
#w:lanes
-> m:scale64
-> ml:scale32
-> l:uint64xN w{felem_fits1 l ml}
-> cin:uint64xN w{uint64xN_fits cin (m * max26)} ->
Lemma
(let (l0, l1) = carry26 #w l cin in
felem_fits1 l0 1 /\ uint64xN_fits l1 (m + ml) /\
(forall (i:nat). i < w ==> (uint64xN_v l).[i] + (uint64xN_v cin).[i] ==
(uint64xN_v l1).[i] * pow2 26 + (uint64xN_v l0).[i]))
let carry26_eval_lemma #w m ml l cin =
match w with
| 1 ->
carry26_lemma_i #w m ml l cin 0
| 2 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1
| 4 ->
carry26_lemma_i #w m ml l cin 0;
carry26_lemma_i #w m ml l cin 1;
carry26_lemma_i #w m ml l cin 2;
carry26_lemma_i #w m ml l cin 3
val carry_wide_felem5_fits_lemma0:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
felem_fits5 tmp (1, 1, 1, 1, 2) /\ felem_fits1 c4 31)
let carry_wide_felem5_fits_lemma0 #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
carry26_wide_zero_eq x0;
carry26_wide_fits_lemma #w #126 x0 (zero w);
let t1, c1 = carry26_wide x1 c0 in
carry26_wide_fits_lemma #w #102 x1 c0;
let t2, c2 = carry26_wide x2 c1 in
carry26_wide_fits_lemma #w #78 x2 c1;
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
carry26_wide_fits_lemma #w #30 x4 c3
val carry_wide_felem5_fits_lemma:
#w:lanes
-> inp:felem_wide5 w ->
Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures felem_fits5 (carry_wide_felem5 inp) (1, 2, 1, 1, 2))
#push-options "--z3rlimit 200"
let carry_wide_felem5_fits_lemma #w inp =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
vec_smul_mod_five c4;
let t0', c5 = carry26 t0 (vec_smul_mod c4 (u64 5)) in
carry26_fits_lemma 155 1 t0 (vec_smul_mod c4 (u64 5))
#pop-options
val carry_wide_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat -> vc6:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
v xi0 == vc0 * pow2 26 + v t0 /\
v xi1 + vc0 == vc1 * pow2 26 + v t1 /\
v xi2 + vc1 == vc2 * pow2 26 + v t2 /\
v xi3 + vc2 == vc3 * pow2 26 + vc6 * pow2 26 + v t3 /\
v xi4 + vc3 == vc4 * pow2 26 + v t4 - vc6))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_wide_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 vc6 =
let (t0, t1, t2, t3, t4) = tmp in
let (xi0, xi1, xi2, xi3, xi4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v xi0 + v xi1 * pow26 + v xi2 * pow52 + v xi3 * pow78 + v xi4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + vc6 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc6 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_wide_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma (let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
let t3', c6 = carry26 t3 c2 in
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_wide_felem5_eval_lemma_i1 #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let t0, c0 = carry26_wide_zero x0 in
let t1, c1 = carry26_wide x1 c0 in
let t2, c2 = carry26_wide x2 c1 in
let t3, c3 = carry26_wide_zero x3 in
carry26_wide_zero_eq x3;
carry26_wide_fits_lemma #w #54 x3 (zero w);
let t3', c6 = carry26 t3 c2 in
carry26_eval_lemma 79 1 t3 c2;
carry26_fits_lemma 79 1 t3 c2;
let t4, c4 = carry26_wide x4 c3 in
let t4' = vec_add_mod t4 c6 in
let tmp = (t0, t1, t2, t3, t4) in
let tmp' = (t0, t1, t2, t3', t4') in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (t0, t1, t2, t3', t4') = as_tup64_i tmp' i in
let (xi0, xi1, xi2, xi3, xi4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
let vc6 = (uint64xN_v c6).[i] in
carry26_wide_zero_eq x0;
carry26_wide_eval_lemma #w #126 x0 (zero w);
assert (v xi0 == vc0 * pow2 26 + v t0);
carry26_wide_eval_lemma #w #102 x1 c0;
assert (v xi1 + vc0 == vc1 * pow2 26 + v t1);
carry26_wide_eval_lemma #w #78 x2 c1;
assert (v xi2 + vc1 == vc2 * pow2 26 + v t2);
carry26_wide_zero_eq x3;
carry26_wide_eval_lemma #w #54 x3 (zero w);
assert (v xi3 == vc3 * pow2 26 + v t3);
assert (v t3 + vc2 == vc6 * pow2 26 + v t3');
carry26_wide_eval_lemma #w #30 x4 c3;
assert (v xi4 + vc3 == vc4 * pow2 26 + v t4);
carry26_wide_fits_lemma #w #30 x4 c3;
Math.Lemmas.small_mod (v t4 + vc6) (pow2 64);
assert (v t4' == v t4 + vc6);
carry_wide_felem5_eval_lemma_i0 (xi0, xi1, xi2, xi3, xi4) (t0, t1, t2, t3', t4') vc0 vc1 vc2 vc3 vc4 vc6;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3' * pow78 + v t4' * pow104) % prime)
val carry_wide_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_wide_fits5 inp (126, 102, 78, 54, 30)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_wide_felem5 #w inp)).[i] == (feval5 inp).[i])
#push-options "--z3rlimit 100"
let carry_wide_felem5_eval_lemma_i #w inp i =
let (x0, x1, x2, x3, x4) = inp in
let tmp0, c0 = carry26_wide_zero x0 in
let tmp1, c1 = carry26_wide x1 c0 in
let tmp2, c2 = carry26_wide x2 c1 in
let tmp3, c3 = carry26_wide_zero x3 in
let tmp3', c6 = carry26 tmp3 c2 in
let tmp4, c4 = carry26_wide x4 c3 in
let tmp4' = vec_add_mod tmp4 c6 in
carry_wide_felem5_fits_lemma0 #w inp;
Math.Lemmas.small_mod ((uint64xN_v c4).[i] * 5) (pow2 64);
let tmp0', c5 = carry26 tmp0 (vec_smul_mod c4 (u64 5)) in
carry26_eval_lemma 155 1 tmp0 (vec_smul_mod c4 (u64 5));
assert ((uint64xN_v tmp0).[i] + (uint64xN_v c4).[i] * 5 == (uint64xN_v c5).[i] * pow2 26 + (uint64xN_v tmp0').[i]);
let tmp1' = vec_add_mod tmp1 c5 in
Math.Lemmas.small_mod ((uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]) (pow2 64);
assert ((uint64xN_v tmp1').[i] == (uint64xN_v tmp1).[i] + (uint64xN_v c5).[i]);
let out = (tmp0', tmp1', tmp2, tmp3', tmp4') in
let tmp = (tmp0, tmp1, tmp2, tmp3', tmp4') in
let (o0, o1, o2, o3, o4) = as_tup64_i out i in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
let vc5 = (uint64xN_v c5).[i] in
calc (==) {
(feval5 out).[i];
(==) { }
(v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104) % prime;
(==) { }
(v t0 + vc4 * 5 + (v t1 + vc5) * pow26 - vc5 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime;
};
Math.Lemmas.distributivity_add_left (v t1) vc5 pow26;
assert ((feval5 out).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
carry_wide_felem5_eval_lemma_i1 #w inp i;
assert ((feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime);
assert ((feval5 out).[i] == (feval5 inp).[i]);
vec_smul_mod_five c4
#pop-options
val carry_wide_felem5_eval_lemma:
#w:lanes
-> inp:felem_wide5 w
-> Lemma
(requires felem_wide_fits5 inp (126, 102, 78, 54, 30))
(ensures feval5 (carry_wide_felem5 #w inp) == feval5 inp)
let carry_wide_felem5_eval_lemma #w inp =
let o = carry_wide_felem5 #w inp in
FStar.Classical.forall_intro (carry_wide_felem5_eval_lemma_i #w inp);
eq_intro (feval5 o) (feval5 inp)
val lemma_subtract_p5_0:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_0 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = max26);
assert_norm (0x3fffffb = max26 - 4);
assert (as_nat5 f == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104);
assert (as_nat5 f <= pow26 - 5 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 + (pow2 26 - 1) * pow78 + (pow2 26 - 1) * pow104);
assert_norm (pow2 26 * pow104 = pow2 130);
assert (as_nat5 f < pow2 130 - 5);
assert (as_nat5 f == as_nat5 f');
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5_1:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
(v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5_1 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
//assert_norm (max26 = pow2 26 - 1);
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fffffb = pow2 26 - 5);
assert (as_nat5 f' < prime);
calc (==) {
as_nat5 f' % prime;
(==) { }
(v f0' + v f1' * pow26 + v f2' * pow52 + v f3' * pow78 + v f4' * pow104) % prime;
(==) { }
(v f0 - (pow2 26 - 5) + (v f1 - (pow2 26 - 1)) * pow26 + (v f2 - (pow2 26 - 1)) * pow52 +
(v f3 - (pow2 26 - 1)) * pow78 + (v f4 - (pow2 26 - 1)) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130) }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104 - prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_sub (v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) prime 1 }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % prime;
(==) { }
as_nat5 f % prime;
};
assert (as_nat5 f' % prime == as_nat5 f % prime);
FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime
val lemma_subtract_p5:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> f':tup64_5 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
((v f4 = 0x3ffffff && v f3 = 0x3ffffff && v f2 = 0x3ffffff && v f1 = 0x3ffffff && v f0 >= 0x3fffffb) /\
(v f0' = v f0 - 0x3fffffb && v f1' = v f1 - 0x3ffffff && v f2' = v f2 - 0x3ffffff && v f3' = v f3 - 0x3ffffff && v f4' = v f4 - 0x3ffffff)) \/
((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) /\
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))))
(ensures as_nat5 f' == as_nat5 f % prime)
let lemma_subtract_p5 f f' =
let (f0, f1, f2, f3, f4) = f in
let (f0', f1', f2', f3', f4') = f' in
assert_norm (max26 = pow2 26 - 1);
if ((v f4 <> 0x3ffffff || v f3 <> 0x3ffffff || v f2 <> 0x3ffffff || v f1 <> 0x3ffffff || v f0 < 0x3fffffb) &&
(v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))
then lemma_subtract_p5_0 f f'
else lemma_subtract_p5_1 f f'
noextract
val subtract_p5_s:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Pure tup64_5
(requires True)
(ensures fun out ->
tup64_fits5 out (1, 1, 1, 1, 1) /\
as_nat5 out == as_nat5 (as_tup64_i f i) % prime)
#push-options "--z3rlimit 100"
let subtract_p5_s #w f i =
let (f0, f1, f2, f3, f4) = as_tup64_i f i in
let mask0 = eq_mask f4 (u64 0x3ffffff) in
let mask1 = mask0 &. eq_mask f3 (u64 0x3ffffff) in
let mask2 = mask1 &. eq_mask f2 (u64 0x3ffffff) in
let mask3 = mask2 &. eq_mask f1 (u64 0x3ffffff) in
let mask4 = mask3 &. gte_mask f0 (u64 0x3fffffb) in
let p0 = mask4 &. u64 0x3fffffb in
logand_lemma mask4 (u64 0x3fffffb);
let p1 = mask4 &. u64 0x3ffffff in
logand_lemma mask4 (u64 0x3ffffff);
let p2 = mask4 &. u64 0x3ffffff in
let p3 = mask4 &. u64 0x3ffffff in
let p4 = mask4 &. u64 0x3ffffff in
let f0' = f0 -. p0 in
let f1' = f1 -. p1 in
let f2' = f2 -. p2 in
let f3' = f3 -. p3 in
let f4' = f4 -. p4 in
lemma_subtract_p5 (f0, f1, f2, f3, f4) (f0', f1', f2', f3', f4');
(f0', f1', f2', f3', f4')
#pop-options
#push-options "--max_ifuel 1"
val subtract_p5_felem5_lemma_i:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)}
-> i:nat{i < w} ->
Lemma
(tup64_fits5 (as_tup64_i (subtract_p5 #w f) i) (1, 1, 1, 1, 1) /\
as_nat5 (as_tup64_i (subtract_p5 #w f) i) == as_nat5 (as_tup64_i f i) % prime)
let subtract_p5_felem5_lemma_i #w f i =
assert (subtract_p5_s #w f i == as_tup64_i (subtract_p5 #w f) i)
#pop-options
val subtract_p5_felem5_lemma:
#w:lanes
-> f:felem5 w{felem_fits5 f (1, 1, 1, 1, 1)} ->
Lemma
(felem_fits5 (subtract_p5 f) (1, 1, 1, 1, 1) /\
(fas_nat5 (subtract_p5 f)).[0] == (feval5 f).[0])
let subtract_p5_felem5_lemma #w f =
match w with
| 1 ->
subtract_p5_felem5_lemma_i #w f 0
| 2 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1
| 4 ->
subtract_p5_felem5_lemma_i #w f 0;
subtract_p5_felem5_lemma_i #w f 1;
subtract_p5_felem5_lemma_i #w f 2;
subtract_p5_felem5_lemma_i #w f 3
noextract
let acc_inv_t (#w:lanes) (acc:felem5 w) : Type0 =
let (o0, o1, o2, o3, o4) = acc in
forall (i:nat). i < w ==>
(if uint_v (vec_v o0).[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc i) (2, 1, 1, 1, 1) /\
uint_v (vec_v o0).[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc i) (1, 1, 1, 1, 1))
val acc_inv_lemma_i:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
let acc1 = (i0', i1, i2, i3, i4) in
(if (uint64xN_v i0').[i] >= pow2 26 then
tup64_fits5 (as_tup64_i acc1 i) (2, 1, 1, 1, 1) /\
(uint64xN_v i0').[i] % pow2 26 < 47
else tup64_fits5 (as_tup64_i acc1 i) (1, 1, 1, 1, 1)))
let acc_inv_lemma_i #w acc cin i =
let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
assert ((vec_v i0').[i] == (vec_v i0).[i] +. (vec_v cin).[i]);
assert ((uint64xN_v i0).[i] + (uint64xN_v cin).[i] <= max26 + 46);
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.euclidean_division_definition ((uint64xN_v i0).[i] + (uint64xN_v cin).[i]) (pow2 26)
val acc_inv_lemma:
#w:lanes
-> acc:felem5 w{felem_fits5 acc (1, 1, 1, 1, 1)}
-> cin:uint64xN w{uint64xN_fits cin 45} ->
Lemma
(let (i0, i1, i2, i3, i4) = acc in
let i0' = vec_add_mod i0 cin in
acc_inv_t (i0', i1, i2, i3, i4))
let acc_inv_lemma #w acc cin =
match w with
| 1 ->
acc_inv_lemma_i #w acc cin 0
| 2 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1
| 4 ->
acc_inv_lemma_i #w acc cin 0;
acc_inv_lemma_i #w acc cin 1;
acc_inv_lemma_i #w acc cin 2;
acc_inv_lemma_i #w acc cin 3
val carry_full_felem5_fits_lemma0: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1) /\ uint64xN_fits c4 9)
let carry_full_felem5_fits_lemma0 #w (f0, f1, f2, f3, f4) =
let tmp0,c0 = carry26 f0 (zero w) in
carry26_fits_lemma 1 8 f0 (zero w);
let tmp1,c1 = carry26 f1 c0 in
carry26_fits_lemma 1 8 f1 c0;
let tmp2,c2 = carry26 f2 c1 in
carry26_fits_lemma 1 8 f2 c1;
let tmp3,c3 = carry26 f3 c2 in
carry26_fits_lemma 1 8 f3 c2;
let tmp4,c4 = carry26 f4 c3 in
carry26_fits_lemma 1 8 f4 c3;
assert (felem_fits5 (tmp0, tmp1, tmp2, tmp3, tmp4) (1, 1, 1, 1, 1));
assert (uint64xN_fits c4 9)
val carry_full_felem5_fits_lemma: #w:lanes -> f:felem5 w{felem_fits5 f (8, 8, 8, 8, 8)} ->
Lemma (acc_inv_t (carry_full_felem5 f))
let carry_full_felem5_fits_lemma #w f =
let (f0, f1, f2, f3, f4) = f in
let tmp0,c0 = carry26 f0 (zero w) in
let tmp1,c1 = carry26 f1 c0 in
let tmp2,c2 = carry26 f2 c1 in
let tmp3,c3 = carry26 f3 c2 in
let tmp4,c4 = carry26 f4 c3 in
carry_full_felem5_fits_lemma0 #w f;
assert (felem_fits1 tmp0 1 /\ uint64xN_fits c4 9);
let tmp0' = vec_add_mod tmp0 (vec_smul_mod c4 (u64 5)) in
acc_inv_lemma (tmp0, tmp1, tmp2, tmp3, tmp4) (vec_smul_mod c4 (u64 5))
val carry_full_felem5_eval_lemma_i0:
inp:tup64_5
-> tmp:tup64_5
-> vc0:nat -> vc1:nat -> vc2:nat -> vc3:nat -> vc4:nat ->
Lemma
(requires
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
v ti0 == vc0 * pow2 26 + v t0 /\
v ti1 + vc0 == vc1 * pow2 26 + v t1 /\
v ti2 + vc1 == vc2 * pow2 26 + v t2 /\
v ti3 + vc2 == vc3 * pow2 26 + v t3 /\
v ti4 + vc3 == vc4 * pow2 26 + v t4))
(ensures
(let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
as_nat5 inp % prime ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime))
let carry_full_felem5_eval_lemma_i0 inp tmp vc0 vc1 vc2 vc3 vc4 =
let (t0, t1, t2, t3, t4) = tmp in
let (ti0, ti1, ti2, ti3, ti4) = inp in
let tmp_n = v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 in
calc (==) {
as_nat5 inp % prime;
(==) { }
(v ti0 + v ti1 * pow26 + v ti2 * pow52 + v ti3 * pow78 + v ti4 * pow104) % prime;
(==) { }
(vc0 * pow2 26 + v t0 +
(vc1 * pow2 26 + v t1 - vc0) * pow26 +
(vc2 * pow2 26 + v t2 - vc1) * pow52 +
(vc3 * pow2 26 + v t3 - vc2) * pow78 +
(vc4 * pow2 26 + v t4 - vc3) * pow104) % prime;
(==) {
assert_norm (pow2 26 * pow26 = pow52);
assert_norm (pow2 26 * pow52 = pow78);
assert_norm (pow2 26 * pow78 = pow104);
assert_norm (pow2 26 * pow104 = pow2 130)}
(v t0 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104 + vc4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * pow2 130) prime }
(tmp_n + (vc4 * pow2 130 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (vc4) (pow2 130) prime }
(tmp_n + (vc4 * (pow2 130 % prime) % prime)) % prime;
(==) { lemma_prime () }
(tmp_n + (vc4 * 5 % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp_n (vc4 * 5) prime }
(tmp_n + vc4 * 5) % prime;
};
assert (as_nat5 inp % prime == (tmp_n + vc4 * 5) % prime)
val carry_full_felem5_eval_lemma_i1:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma
(let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let vc4 = (uint64xN_v c4).[i] in
(feval5 inp).[i] == (v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
let carry_full_felem5_eval_lemma_i1 #w inp i =
let (i0, i1, i2, i3, i4) = inp in
let tmp0,c0 = carry26 i0 (zero w) in
let tmp1,c1 = carry26 i1 c0 in
let tmp2,c2 = carry26 i2 c1 in
let tmp3,c3 = carry26 i3 c2 in
let tmp4,c4 = carry26 i4 c3 in
let tmp = (tmp0, tmp1, tmp2, tmp3, tmp4) in
let (t0, t1, t2, t3, t4) = as_tup64_i tmp i in
let (ti0, ti1, ti2, ti3, ti4) = as_tup64_i inp i in
let vc0 = (uint64xN_v c0).[i] in
let vc1 = (uint64xN_v c1).[i] in
let vc2 = (uint64xN_v c2).[i] in
let vc3 = (uint64xN_v c3).[i] in
let vc4 = (uint64xN_v c4).[i] in
carry26_eval_lemma 1 8 i0 (zero w);
assert (v ti0 == vc0 * pow2 26 + v t0);
carry26_eval_lemma 1 8 i1 c0;
assert (v ti1 + vc0 == vc1 * pow2 26 + v t1);
carry26_eval_lemma 1 8 i2 c1;
assert (v ti2 + vc1 == vc2 * pow2 26 + v t2);
carry26_eval_lemma 1 8 i3 c2;
assert (v ti3 + vc2 == vc3 * pow2 26 + v t3);
carry26_eval_lemma 1 8 i4 c3;
assert (v ti4 + vc3 == vc4 * pow2 26 + v t4);
carry_full_felem5_eval_lemma_i0 (ti0, ti1, ti2, ti3, ti4) (t0, t1, t2, t3, t4) vc0 vc1 vc2 vc3 vc4;
assert ((feval5 inp).[i] ==
(v t0 + vc4 * 5 + v t1 * pow26 + v t2 * pow52 + v t3 * pow78 + v t4 * pow104) % prime)
val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas1.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val carry_full_felem5_eval_lemma_i:
#w:lanes
-> inp:felem_wide5 w{felem_fits5 inp (8, 8, 8, 8, 8)}
-> i:nat{i < w} ->
Lemma ((feval5 (carry_full_felem5 #w inp)).[i] == (feval5 inp).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
inp:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 inp (8, 8, 8, 8, 8)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.carry_full_felem5 inp)).[ i
] ==
(Hacl.Spec.Poly1305.Field32xN.feval5 inp).[ i ]) | {
"end_col": 47,
"end_line": 855,
"start_col": 45,
"start_line": 831
} |
Prims.GTot | [
{
"abbrev": true,
"full_module": "Hacl.Spec.P256.Montgomery",
"short_module": "SM"
},
{
"abbrev": true,
"full_module": "Spec.P256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Hacl.Impl.P256.Bignum",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Buffer",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "ST"
},
{
"abbrev": false,
"full_module": "FStar.HyperStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.HyperStack.All",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Impl.P256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Impl.P256",
"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
}
] | false | let fmont_as_nat (h:mem) (a:felem) = SM.from_mont (as_nat h a) | let fmont_as_nat (h: mem) (a: felem) = | false | null | false | SM.from_mont (as_nat h a) | {
"checked_file": "Hacl.Impl.P256.Field.fsti.checked",
"dependencies": [
"Spec.P256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Lib.Buffer.fsti.checked",
"Hacl.Spec.P256.Montgomery.fsti.checked",
"Hacl.Impl.P256.Bignum.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.All.fst.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "Hacl.Impl.P256.Field.fsti"
} | [
"sometrivial"
] | [
"FStar.Monotonic.HyperStack.mem",
"Hacl.Impl.P256.Bignum.felem",
"Hacl.Spec.P256.Montgomery.from_mont",
"Hacl.Impl.P256.Bignum.as_nat",
"Spec.P256.PointOps.felem"
] | [] | module Hacl.Impl.P256.Field
open FStar.Mul
open FStar.HyperStack.All
open FStar.HyperStack
module ST = FStar.HyperStack.ST
open Lib.IntTypes
open Lib.Buffer
open Hacl.Impl.P256.Bignum
module S = Spec.P256
module SM = Hacl.Spec.P256.Montgomery
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0" | false | false | Hacl.Impl.P256.Field.fsti | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fmont_as_nat : h: FStar.Monotonic.HyperStack.mem -> a: Hacl.Impl.P256.Bignum.felem
-> Prims.GTot Spec.P256.PointOps.felem | [] | Hacl.Impl.P256.Field.fmont_as_nat | {
"file_name": "code/ecdsap256/Hacl.Impl.P256.Field.fsti",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | h: FStar.Monotonic.HyperStack.mem -> a: Hacl.Impl.P256.Bignum.felem
-> Prims.GTot Spec.P256.PointOps.felem | {
"end_col": 62,
"end_line": 18,
"start_col": 37,
"start_line": 18
} |
|
Prims.Tot | val blake2b_update_key:Impl.blake2_update_key_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block | val blake2b_update_key:Impl.blake2_update_key_st Spec.Blake2B Core.M32
let blake2b_update_key:Impl.blake2_update_key_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update_key",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_update_block"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32 | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update_key:Impl.blake2_update_key_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update_key | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_key_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 69,
"end_line": 16,
"start_col": 2,
"start_line": 16
} |
Prims.Tot | val blake2b_malloc:Impl.blake2_malloc_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_malloc : Impl.blake2_malloc_st Spec.Blake2B Core.M32 =
Impl.blake2_malloc Spec.Blake2B Core.M32 | val blake2b_malloc:Impl.blake2_malloc_st Spec.Blake2B Core.M32
let blake2b_malloc:Impl.blake2_malloc_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_malloc Spec.Blake2B Core.M32 | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_malloc",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block
private
let blake2b_update_blocks : Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 =
Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last
[@CInline]
private
let blake2b_update : Impl.blake2_update_st Spec.Blake2B Core.M32 =
Impl.blake2_update #Spec.Blake2B #Core.M32 blake2b_update_key blake2b_update_blocks
let blake2b_finish : Impl.blake2_finish_st Spec.Blake2B Core.M32 =
Impl.blake2_finish #Spec.Blake2B #Core.M32
(* The one-shot hash *)
[@@ Comment "Write the BLAKE2b digest of message `d` using key `k` into `output`.
@param nn Length of the to-be-generated digest with 1 <= `nn` <= 64.
@param output Pointer to `nn` bytes of memory where the digest is written to.
@param ll Length of the input message.
@param d Pointer to `ll` bytes of memory where the input message is read from.
@param kk Length of the key. Can be 0.
@param k Pointer to `kk` bytes of memory where the key is read from."]
let blake2b : Impl.blake2_st Spec.Blake2B Core.M32 =
Impl.blake2 #Spec.Blake2B #Core.M32 blake2b_init blake2b_update blake2b_finish | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_malloc:Impl.blake2_malloc_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_malloc | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_malloc_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 42,
"end_line": 50,
"start_col": 2,
"start_line": 50
} |
Prims.Tot | val blake2b_update_multi:Impl.blake2_update_multi_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block | val blake2b_update_multi:Impl.blake2_update_multi_st Spec.Blake2B Core.M32
let blake2b_update_multi:Impl.blake2_update_multi_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update_multi",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_update_block"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update_multi:Impl.blake2_update_multi_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update_multi | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_multi_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 71,
"end_line": 19,
"start_col": 2,
"start_line": 19
} |
Prims.Tot | val blake2b_update_block:Impl.blake2_update_block_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32 | val blake2b_update_block:Impl.blake2_update_block_st Spec.Blake2B Core.M32
let blake2b_update_block:Impl.blake2_update_block_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update_block #Spec.Blake2B #Core.M32 | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update_block",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update_block:Impl.blake2_update_block_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update_block | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_block_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 50,
"end_line": 10,
"start_col": 2,
"start_line": 10
} |
Prims.Tot | val blake2b_update:Impl.blake2_update_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update : Impl.blake2_update_st Spec.Blake2B Core.M32 =
Impl.blake2_update #Spec.Blake2B #Core.M32 blake2b_update_key blake2b_update_blocks | val blake2b_update:Impl.blake2_update_st Spec.Blake2B Core.M32
let blake2b_update:Impl.blake2_update_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update #Spec.Blake2B #Core.M32 blake2b_update_key blake2b_update_blocks | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_update_key",
"Hacl.Blake2b_32.blake2b_update_blocks"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block
private
let blake2b_update_blocks : Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 =
Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last
[@CInline]
private | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update:Impl.blake2_update_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 85,
"end_line": 31,
"start_col": 2,
"start_line": 31
} |
Prims.Tot | val blake2b_update_last:Impl.blake2_update_last_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block | val blake2b_update_last:Impl.blake2_update_last_st Spec.Blake2B Core.M32
let blake2b_update_last:Impl.blake2_update_last_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update_last",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_update_block"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update_last:Impl.blake2_update_last_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update_last | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_last_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 70,
"end_line": 22,
"start_col": 2,
"start_line": 22
} |
Prims.Tot | val blake2b_finish:Impl.blake2_finish_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_finish : Impl.blake2_finish_st Spec.Blake2B Core.M32 =
Impl.blake2_finish #Spec.Blake2B #Core.M32 | val blake2b_finish:Impl.blake2_finish_st Spec.Blake2B Core.M32
let blake2b_finish:Impl.blake2_finish_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_finish #Spec.Blake2B #Core.M32 | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_finish",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block
private
let blake2b_update_blocks : Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 =
Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last
[@CInline]
private
let blake2b_update : Impl.blake2_update_st Spec.Blake2B Core.M32 =
Impl.blake2_update #Spec.Blake2B #Core.M32 blake2b_update_key blake2b_update_blocks | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_finish:Impl.blake2_finish_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_finish | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_finish_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 44,
"end_line": 34,
"start_col": 2,
"start_line": 34
} |
Prims.Tot | val blake2b_update_blocks:Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_update_blocks : Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 =
Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last | val blake2b_update_blocks:Impl.blake2_update_blocks_st Spec.Blake2B Core.M32
let blake2b_update_blocks:Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_update_blocks",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_update_multi",
"Hacl.Blake2b_32.blake2b_update_last"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block
private | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_update_blocks:Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_update_blocks | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_update_blocks_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 92,
"end_line": 26,
"start_col": 2,
"start_line": 26
} |
Prims.Tot | val blake2b_init:Impl.blake2_init_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32 | val blake2b_init:Impl.blake2_init_st Spec.Blake2B Core.M32
let blake2b_init:Impl.blake2_init_st Spec.Blake2B Core.M32 = | false | null | false | Impl.blake2_init #Spec.Blake2B #Core.M32 | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2_init",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32 | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b_init:Impl.blake2_init_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b_init | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_init_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 42,
"end_line": 13,
"start_col": 2,
"start_line": 13
} |
Prims.Tot | val blake2b:Impl.blake2_st Spec.Blake2B Core.M32 | [
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Core",
"short_module": "Core"
},
{
"abbrev": true,
"full_module": "Hacl.Impl.Blake2.Generic",
"short_module": "Impl"
},
{
"abbrev": true,
"full_module": "Spec.Blake2",
"short_module": "Spec"
},
{
"abbrev": false,
"full_module": "Hacl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl",
"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
}
] | false | let blake2b : Impl.blake2_st Spec.Blake2B Core.M32 =
Impl.blake2 #Spec.Blake2B #Core.M32 blake2b_init blake2b_update blake2b_finish | val blake2b:Impl.blake2_st Spec.Blake2B Core.M32
let blake2b:Impl.blake2_st Spec.Blake2B Core.M32 = | true | null | false | Impl.blake2 #Spec.Blake2B #Core.M32 blake2b_init blake2b_update blake2b_finish | {
"checked_file": "Hacl.Blake2b_32.fst.checked",
"dependencies": [
"Spec.Blake2.fst.checked",
"prims.fst.checked",
"Hacl.Impl.Blake2.Generic.fst.checked",
"Hacl.Impl.Blake2.Core.fsti.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Blake2b_32.fst"
} | [
"total"
] | [
"Hacl.Impl.Blake2.Generic.blake2",
"Spec.Blake2.Blake2B",
"Hacl.Impl.Blake2.Core.M32",
"Hacl.Blake2b_32.blake2b_init",
"Hacl.Blake2b_32.blake2b_update",
"Hacl.Blake2b_32.blake2b_finish"
] | [] | module Hacl.Blake2b_32
module Spec = Spec.Blake2
module Impl = Hacl.Impl.Blake2.Generic
module Core = Hacl.Impl.Blake2.Core
(* Some specialized components of blake2 *)
private
let blake2b_update_block : Impl.blake2_update_block_st Spec.Blake2B Core.M32 =
Impl.blake2_update_block #Spec.Blake2B #Core.M32
let blake2b_init : Impl.blake2_init_st Spec.Blake2B Core.M32 =
Impl.blake2_init #Spec.Blake2B #Core.M32
let blake2b_update_key : Impl.blake2_update_key_st Spec.Blake2B Core.M32 =
Impl.blake2_update_key #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_multi : Impl.blake2_update_multi_st Spec.Blake2B Core.M32 =
Impl.blake2_update_multi #Spec.Blake2B #Core.M32 blake2b_update_block
let blake2b_update_last : Impl.blake2_update_last_st Spec.Blake2B Core.M32 =
Impl.blake2_update_last #Spec.Blake2B #Core.M32 blake2b_update_block
private
let blake2b_update_blocks : Impl.blake2_update_blocks_st Spec.Blake2B Core.M32 =
Impl.blake2_update_blocks #Spec.Blake2B #Core.M32 blake2b_update_multi blake2b_update_last
[@CInline]
private
let blake2b_update : Impl.blake2_update_st Spec.Blake2B Core.M32 =
Impl.blake2_update #Spec.Blake2B #Core.M32 blake2b_update_key blake2b_update_blocks
let blake2b_finish : Impl.blake2_finish_st Spec.Blake2B Core.M32 =
Impl.blake2_finish #Spec.Blake2B #Core.M32
(* The one-shot hash *)
[@@ Comment "Write the BLAKE2b digest of message `d` using key `k` into `output`.
@param nn Length of the to-be-generated digest with 1 <= `nn` <= 64.
@param output Pointer to `nn` bytes of memory where the digest is written to.
@param ll Length of the input message.
@param d Pointer to `ll` bytes of memory where the input message is read from.
@param kk Length of the key. Can be 0.
@param k Pointer to `kk` bytes of memory where the key is read from."] | false | false | Hacl.Blake2b_32.fst | {
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val blake2b:Impl.blake2_st Spec.Blake2B Core.M32 | [] | Hacl.Blake2b_32.blake2b | {
"file_name": "code/blake2/Hacl.Blake2b_32.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Hacl.Impl.Blake2.Generic.blake2_st Spec.Blake2.Blake2B Hacl.Impl.Blake2.Core.M32 | {
"end_col": 80,
"end_line": 47,
"start_col": 2,
"start_line": 47
} |
Prims.Tot | val raise_frame_preserving_upd (#a: _) (#p: pcm a) (#x #y: a) (f: frame_preserving_upd p x y)
: frame_preserving_upd (raise p) (raise_val x) (raise_val y) | [
{
"abbrev": false,
"full_module": "FStar.Classical.Sugar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.PCM",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"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
}
] | false | let raise_frame_preserving_upd #a (#p:pcm a) (#x #y:a) (f:frame_preserving_upd p x y)
: frame_preserving_upd (raise p) (raise_val x) (raise_val y)
= fun v ->
let u = f (downgrade_val v) in
let v_new = raise_val u in
assert (forall frame. composable p y frame ==> composable (raise p) (raise_val y) (raise_val frame));
assert (forall frame. composable (raise p) (raise_val x) frame ==> composable p x (downgrade_val frame));
v_new | val raise_frame_preserving_upd (#a: _) (#p: pcm a) (#x #y: a) (f: frame_preserving_upd p x y)
: frame_preserving_upd (raise p) (raise_val x) (raise_val y)
let raise_frame_preserving_upd #a (#p: pcm a) (#x: a) (#y: a) (f: frame_preserving_upd p x y)
: frame_preserving_upd (raise p) (raise_val x) (raise_val y) = | false | null | false | fun v ->
let u = f (downgrade_val v) in
let v_new = raise_val u in
assert (forall frame.
composable p y frame ==> composable (raise p) (raise_val y) (raise_val frame));
assert (forall frame.
composable (raise p) (raise_val x) frame ==> composable p x (downgrade_val frame));
v_new | {
"checked_file": "FStar.Universe.PCM.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Universe.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.PCM.fst.checked",
"FStar.Classical.Sugar.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Universe.PCM.fst"
} | [
"total"
] | [
"FStar.PCM.pcm",
"FStar.PCM.frame_preserving_upd",
"FStar.Universe.raise_t",
"Prims.l_and",
"FStar.PCM.__proj__Mkpcm__item__refine",
"FStar.Universe.PCM.raise",
"FStar.PCM.compatible",
"FStar.Universe.raise_val",
"Prims.unit",
"Prims._assert",
"Prims.l_Forall",
"Prims.l_imp",
"FStar.PCM.composable",
"FStar.Universe.downgrade_val",
"Prims.eq2",
"FStar.PCM.op"
] | [] | (*
Copyright 2021 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.
Author: N. Swamy
*)
module FStar.Universe.PCM
(* Lift a PCM to a higher universe, including its frame-preserving updates *)
open FStar.PCM
open FStar.Universe
open FStar.Classical.Sugar
let raise (#a:Type) (p:pcm a)
: pcm (raise_t u#a u#b a)
= {
p = {
composable = (fun x y -> p.p.composable (downgrade_val x) (downgrade_val y));
op = (fun x y -> raise_val (p.p.op (downgrade_val x) (downgrade_val y)));
one = raise_val p.p.one;
};
comm = (fun x y -> p.comm (downgrade_val x) (downgrade_val y));
assoc = (fun x y z -> p.assoc (downgrade_val x) (downgrade_val y) (downgrade_val z));
assoc_r = (fun x y z -> p.assoc_r (downgrade_val x) (downgrade_val y) (downgrade_val z));
is_unit = (fun x -> p.is_unit (downgrade_val x));
refine = (fun x -> p.refine (downgrade_val x));
}
let raise_frame_preserving_upd #a (#p:pcm a) (#x #y:a) (f:frame_preserving_upd p x y) | false | false | FStar.Universe.PCM.fst | {
"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"
} | null | val raise_frame_preserving_upd (#a: _) (#p: pcm a) (#x #y: a) (f: frame_preserving_upd p x y)
: frame_preserving_upd (raise p) (raise_val x) (raise_val y) | [] | FStar.Universe.PCM.raise_frame_preserving_upd | {
"file_name": "ulib/experimental/FStar.Universe.PCM.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | f: FStar.PCM.frame_preserving_upd p x y
-> FStar.PCM.frame_preserving_upd (FStar.Universe.PCM.raise p)
(FStar.Universe.raise_val x)
(FStar.Universe.raise_val y) | {
"end_col": 11,
"end_line": 46,
"start_col": 4,
"start_line": 41
} |
Prims.Tot | val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a) | [
{
"abbrev": false,
"full_module": "FStar.Classical.Sugar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.PCM",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Universe",
"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
}
] | false | let raise (#a:Type) (p:pcm a)
: pcm (raise_t u#a u#b a)
= {
p = {
composable = (fun x y -> p.p.composable (downgrade_val x) (downgrade_val y));
op = (fun x y -> raise_val (p.p.op (downgrade_val x) (downgrade_val y)));
one = raise_val p.p.one;
};
comm = (fun x y -> p.comm (downgrade_val x) (downgrade_val y));
assoc = (fun x y z -> p.assoc (downgrade_val x) (downgrade_val y) (downgrade_val z));
assoc_r = (fun x y z -> p.assoc_r (downgrade_val x) (downgrade_val y) (downgrade_val z));
is_unit = (fun x -> p.is_unit (downgrade_val x));
refine = (fun x -> p.refine (downgrade_val x));
} | val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a)
let raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a) = | false | null | false | {
p
=
{
composable = (fun x y -> p.p.composable (downgrade_val x) (downgrade_val y));
op = (fun x y -> raise_val (p.p.op (downgrade_val x) (downgrade_val y)));
one = raise_val p.p.one
};
comm = (fun x y -> p.comm (downgrade_val x) (downgrade_val y));
assoc = (fun x y z -> p.assoc (downgrade_val x) (downgrade_val y) (downgrade_val z));
assoc_r = (fun x y z -> p.assoc_r (downgrade_val x) (downgrade_val y) (downgrade_val z));
is_unit = (fun x -> p.is_unit (downgrade_val x));
refine = (fun x -> p.refine (downgrade_val x))
} | {
"checked_file": "FStar.Universe.PCM.fst.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Universe.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.PCM.fst.checked",
"FStar.Classical.Sugar.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Universe.PCM.fst"
} | [
"total"
] | [
"FStar.PCM.pcm",
"FStar.PCM.Mkpcm",
"FStar.Universe.raise_t",
"FStar.PCM.Mkpcm'",
"FStar.PCM.__proj__Mkpcm'__item__composable",
"FStar.PCM.__proj__Mkpcm__item__p",
"FStar.Universe.downgrade_val",
"Prims.prop",
"FStar.Universe.raise_val",
"FStar.PCM.__proj__Mkpcm'__item__op",
"FStar.PCM.__proj__Mkpcm'__item__one",
"FStar.PCM.__proj__Mkpcm__item__comm",
"Prims.unit",
"Prims.l_and",
"FStar.PCM.__proj__Mkpcm__item__assoc",
"FStar.PCM.__proj__Mkpcm__item__assoc_r",
"FStar.PCM.__proj__Mkpcm__item__is_unit",
"FStar.PCM.__proj__Mkpcm__item__refine"
] | [] | (*
Copyright 2021 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.
Author: N. Swamy
*)
module FStar.Universe.PCM
(* Lift a PCM to a higher universe, including its frame-preserving updates *)
open FStar.PCM
open FStar.Universe
open FStar.Classical.Sugar
let raise (#a:Type) (p:pcm a)
: pcm (raise_t u#a u#b a) | false | false | FStar.Universe.PCM.fst | {
"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"
} | null | val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a) | [] | FStar.Universe.PCM.raise | {
"file_name": "ulib/experimental/FStar.Universe.PCM.fst",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | p: FStar.PCM.pcm a -> FStar.PCM.pcm (FStar.Universe.raise_t a) | {
"end_col": 53,
"end_line": 36,
"start_col": 6,
"start_line": 27
} |
Prims.Tot | val shift_gf128_key_1 (h: poly) : poly | [
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"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
}
] | false | let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h | val shift_gf128_key_1 (h: poly) : poly
let shift_gf128_key_1 (h: poly) : poly = | false | null | false | shift_key_1 128 gf128_modulus_low_terms h | {
"checked_file": "Vale.AES.OptPublic.fst.checked",
"dependencies": [
"Vale.Math.Poly2_s.fsti.checked",
"Vale.Math.Poly2.Bits_s.fsti.checked",
"Vale.Math.Poly2.Bits.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.AES.GF128_s.fsti.checked",
"Vale.AES.GF128.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": true,
"source_file": "Vale.AES.OptPublic.fst"
} | [
"total"
] | [
"Vale.Math.Poly2_s.poly",
"Vale.AES.GF128.shift_key_1",
"Vale.AES.GF128_s.gf128_modulus_low_terms"
] | [] | module Vale.AES.OptPublic
open FStar.Mul
open FStar.Seq
open Vale.Def.Types_s
open Vale.Math.Poly2_s
open Vale.Math.Poly2.Bits_s
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.Def.Words_s | false | true | Vale.AES.OptPublic.fst | {
"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"
} | null | val shift_gf128_key_1 (h: poly) : poly | [] | Vale.AES.OptPublic.shift_gf128_key_1 | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | h: Vale.Math.Poly2_s.poly -> Vale.Math.Poly2_s.poly | {
"end_col": 43,
"end_line": 13,
"start_col": 2,
"start_line": 13
} |
Prims.Tot | val gf128_power (h: poly) (n: nat) : poly | [
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"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
}
] | false | let gf128_power (h:poly) (n:nat) : poly = shift_gf128_key_1 (g_power h n) | val gf128_power (h: poly) (n: nat) : poly
let gf128_power (h: poly) (n: nat) : poly = | false | null | false | shift_gf128_key_1 (g_power h n) | {
"checked_file": "Vale.AES.OptPublic.fst.checked",
"dependencies": [
"Vale.Math.Poly2_s.fsti.checked",
"Vale.Math.Poly2.Bits_s.fsti.checked",
"Vale.Math.Poly2.Bits.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.AES.GF128_s.fsti.checked",
"Vale.AES.GF128.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": true,
"source_file": "Vale.AES.OptPublic.fst"
} | [
"total"
] | [
"Vale.Math.Poly2_s.poly",
"Prims.nat",
"Vale.AES.OptPublic.shift_gf128_key_1",
"Vale.AES.OptPublic.g_power"
] | [] | module Vale.AES.OptPublic
open FStar.Mul
open FStar.Seq
open Vale.Def.Types_s
open Vale.Math.Poly2_s
open Vale.Math.Poly2.Bits_s
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.Def.Words_s
let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h
let rec g_power (a:poly) (n:nat) : poly =
if n = 0 then zero else // arbitrary value for n = 0
if n = 1 then a else
a *~ g_power a (n - 1) | false | true | Vale.AES.OptPublic.fst | {
"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"
} | null | val gf128_power (h: poly) (n: nat) : poly | [] | Vale.AES.OptPublic.gf128_power | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.Math.Poly2_s.poly | {
"end_col": 73,
"end_line": 20,
"start_col": 42,
"start_line": 20
} |
FStar.Pervasives.Lemma | val lemma_of_quad32_inj (q q': quad32)
: Lemma (requires of_quad32 q == of_quad32 q') (ensures q == q') | [
{
"abbrev": false,
"full_module": "FStar.UInt",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.List.Tot",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"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
}
] | false | let lemma_of_quad32_inj (q q':quad32) : Lemma
(requires of_quad32 q == of_quad32 q')
(ensures q == q')
= lemma_to_of_quad32 q; lemma_to_of_quad32 q' | val lemma_of_quad32_inj (q q': quad32)
: Lemma (requires of_quad32 q == of_quad32 q') (ensures q == q')
let lemma_of_quad32_inj (q q': quad32)
: Lemma (requires of_quad32 q == of_quad32 q') (ensures q == q') = | false | null | true | lemma_to_of_quad32 q;
lemma_to_of_quad32 q' | {
"checked_file": "Vale.AES.OptPublic.fst.checked",
"dependencies": [
"Vale.Math.Poly2_s.fsti.checked",
"Vale.Math.Poly2.Bits_s.fsti.checked",
"Vale.Math.Poly2.Bits.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.AES.GF128_s.fsti.checked",
"Vale.AES.GF128.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": true,
"source_file": "Vale.AES.OptPublic.fst"
} | [
"lemma"
] | [
"Vale.Def.Types_s.quad32",
"Vale.Math.Poly2.Bits.lemma_to_of_quad32",
"Prims.unit",
"Prims.eq2",
"Vale.Math.Poly2_s.poly",
"Vale.Math.Poly2.Bits_s.of_quad32",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module Vale.AES.OptPublic
open FStar.Mul
open FStar.Seq
open Vale.Def.Types_s
open Vale.Math.Poly2_s
open Vale.Math.Poly2.Bits_s
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.Def.Words_s
let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h
let rec g_power (a:poly) (n:nat) : poly =
if n = 0 then zero else // arbitrary value for n = 0
if n = 1 then a else
a *~ g_power a (n - 1)
let gf128_power (h:poly) (n:nat) : poly = shift_gf128_key_1 (g_power h n)
let hkeys_reqs_pub (hkeys:seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0
=
let h = of_quad32 (reverse_bytes_quad32 (reverse_bytes_quad32 h_BE)) in
length hkeys >= 8 /\
of_quad32 (index hkeys 0) == gf128_power h 1 /\
of_quad32 (index hkeys 1) == gf128_power h 2 /\
index hkeys 2 == h_BE /\
of_quad32 (index hkeys 3) == gf128_power h 3 /\
of_quad32 (index hkeys 4) == gf128_power h 4 /\
index hkeys 5 == Mkfour 0 0 0 0 /\ // Not needed but we want injectivity
of_quad32 (index hkeys 6) == gf128_power h 5 /\
of_quad32 (index hkeys 7) == gf128_power h 6
#set-options "--z3rlimit 20 --max_fuel 0 --max_ifuel 0"
open FStar.List.Tot
open Vale.Math.Poly2.Bits
let get_hkeys_reqs h_BE =
let h = of_quad32 (reverse_bytes_quad32 (reverse_bytes_quad32 h_BE)) in
let l = [to_quad32 (gf128_power h 1);
to_quad32 (gf128_power h 2);
h_BE;
to_quad32 (gf128_power h 3);
to_quad32 (gf128_power h 4);
Mkfour 0 0 0 0;
to_quad32 (gf128_power h 5);
to_quad32 (gf128_power h 6)] in
assert_norm (length l = 8);
let s = Seq.seq_of_list l in
Seq.lemma_seq_of_list_induction l;
Seq.lemma_seq_of_list_induction (tl l);
Seq.lemma_seq_of_list_induction (tl (tl l));
Seq.lemma_seq_of_list_induction (tl (tl (tl l)));
Seq.lemma_seq_of_list_induction (tl (tl (tl (tl l))));
Seq.lemma_seq_of_list_induction (tl (tl (tl (tl (tl l)))));
Seq.lemma_seq_of_list_induction (tl (tl (tl (tl (tl (tl l))))));
Seq.lemma_seq_of_list_induction (tl (tl (tl (tl (tl (tl (tl l)))))));
Seq.lemma_seq_of_list_induction (tl (tl (tl (tl (tl (tl (tl (tl l))))))));
lemma_of_to_quad32 (gf128_power h 1);
lemma_of_to_quad32 (gf128_power h 2);
lemma_of_to_quad32 (gf128_power h 3);
lemma_of_to_quad32 (gf128_power h 4);
lemma_of_to_quad32 (gf128_power h 5);
lemma_of_to_quad32 (gf128_power h 6);
assert (hkeys_reqs_pub s h_BE);
s
open FStar.UInt
let lemma_of_quad32_inj (q q':quad32) : Lemma
(requires of_quad32 q == of_quad32 q') | false | false | Vale.AES.OptPublic.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"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": 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": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_of_quad32_inj (q q': quad32)
: Lemma (requires of_quad32 q == of_quad32 q') (ensures q == q') | [] | Vale.AES.OptPublic.lemma_of_quad32_inj | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | q: Vale.Def.Types_s.quad32 -> q': Vale.Def.Types_s.quad32
-> FStar.Pervasives.Lemma
(requires Vale.Math.Poly2.Bits_s.of_quad32 q == Vale.Math.Poly2.Bits_s.of_quad32 q')
(ensures q == q') | {
"end_col": 47,
"end_line": 75,
"start_col": 4,
"start_line": 75
} |
Prims.Tot | val g_power (a: poly) (n: nat) : poly | [
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"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
}
] | false | let rec g_power (a:poly) (n:nat) : poly =
if n = 0 then zero else // arbitrary value for n = 0
if n = 1 then a else
a *~ g_power a (n - 1) | val g_power (a: poly) (n: nat) : poly
let rec g_power (a: poly) (n: nat) : poly = | false | null | false | if n = 0 then zero else if n = 1 then a else a *~ g_power a (n - 1) | {
"checked_file": "Vale.AES.OptPublic.fst.checked",
"dependencies": [
"Vale.Math.Poly2_s.fsti.checked",
"Vale.Math.Poly2.Bits_s.fsti.checked",
"Vale.Math.Poly2.Bits.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.AES.GF128_s.fsti.checked",
"Vale.AES.GF128.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": true,
"source_file": "Vale.AES.OptPublic.fst"
} | [
"total"
] | [
"Vale.Math.Poly2_s.poly",
"Prims.nat",
"Prims.op_Equality",
"Prims.int",
"Vale.Math.Poly2_s.zero",
"Prims.bool",
"Vale.AES.GF128.op_Star_Tilde",
"Vale.AES.OptPublic.g_power",
"Prims.op_Subtraction"
] | [] | module Vale.AES.OptPublic
open FStar.Mul
open FStar.Seq
open Vale.Def.Types_s
open Vale.Math.Poly2_s
open Vale.Math.Poly2.Bits_s
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.Def.Words_s
let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h | false | true | Vale.AES.OptPublic.fst | {
"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"
} | null | val g_power (a: poly) (n: nat) : poly | [
"recursion"
] | Vale.AES.OptPublic.g_power | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.Math.Poly2_s.poly | {
"end_col": 24,
"end_line": 18,
"start_col": 2,
"start_line": 16
} |
Prims.Tot | val hkeys_reqs_pub (hkeys:FStar.Seq.seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0 | [
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.GF128_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2.Bits_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Math.Poly2_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES",
"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
}
] | false | let hkeys_reqs_pub (hkeys:seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0
=
let h = of_quad32 (reverse_bytes_quad32 (reverse_bytes_quad32 h_BE)) in
length hkeys >= 8 /\
of_quad32 (index hkeys 0) == gf128_power h 1 /\
of_quad32 (index hkeys 1) == gf128_power h 2 /\
index hkeys 2 == h_BE /\
of_quad32 (index hkeys 3) == gf128_power h 3 /\
of_quad32 (index hkeys 4) == gf128_power h 4 /\
index hkeys 5 == Mkfour 0 0 0 0 /\ // Not needed but we want injectivity
of_quad32 (index hkeys 6) == gf128_power h 5 /\
of_quad32 (index hkeys 7) == gf128_power h 6 | val hkeys_reqs_pub (hkeys:FStar.Seq.seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0
let hkeys_reqs_pub (hkeys: seq quad32) (h_BE: quad32) : Vale.Def.Prop_s.prop0 = | false | null | false | let h = of_quad32 (reverse_bytes_quad32 (reverse_bytes_quad32 h_BE)) in
length hkeys >= 8 /\ of_quad32 (index hkeys 0) == gf128_power h 1 /\
of_quad32 (index hkeys 1) == gf128_power h 2 /\ index hkeys 2 == h_BE /\
of_quad32 (index hkeys 3) == gf128_power h 3 /\ of_quad32 (index hkeys 4) == gf128_power h 4 /\
index hkeys 5 == Mkfour 0 0 0 0 /\ of_quad32 (index hkeys 6) == gf128_power h 5 /\
of_quad32 (index hkeys 7) == gf128_power h 6 | {
"checked_file": "Vale.AES.OptPublic.fst.checked",
"dependencies": [
"Vale.Math.Poly2_s.fsti.checked",
"Vale.Math.Poly2.Bits_s.fsti.checked",
"Vale.Math.Poly2.Bits.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.AES.GF128_s.fsti.checked",
"Vale.AES.GF128.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": true,
"source_file": "Vale.AES.OptPublic.fst"
} | [
"total"
] | [
"FStar.Seq.Base.seq",
"Vale.Def.Types_s.quad32",
"Prims.l_and",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Seq.Base.length",
"Prims.eq2",
"Vale.Math.Poly2_s.poly",
"Vale.Math.Poly2.Bits_s.of_quad32",
"FStar.Seq.Base.index",
"Vale.AES.OptPublic.gf128_power",
"Vale.Def.Words_s.four",
"Vale.Def.Types_s.nat32",
"Vale.Def.Words_s.Mkfour",
"Vale.Def.Types_s.reverse_bytes_quad32",
"Vale.Def.Prop_s.prop0"
] | [] | module Vale.AES.OptPublic
open FStar.Mul
open FStar.Seq
open Vale.Def.Types_s
open Vale.Math.Poly2_s
open Vale.Math.Poly2.Bits_s
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.Def.Words_s
let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h
let rec g_power (a:poly) (n:nat) : poly =
if n = 0 then zero else // arbitrary value for n = 0
if n = 1 then a else
a *~ g_power a (n - 1)
let gf128_power (h:poly) (n:nat) : poly = shift_gf128_key_1 (g_power h n) | false | true | Vale.AES.OptPublic.fst | {
"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"
} | null | val hkeys_reqs_pub (hkeys:FStar.Seq.seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0 | [] | Vale.AES.OptPublic.hkeys_reqs_pub | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | hkeys: FStar.Seq.Base.seq Vale.Def.Types_s.quad32 -> h_BE: Vale.Def.Types_s.quad32
-> Vale.Def.Prop_s.prop0 | {
"end_col": 46,
"end_line": 33,
"start_col": 3,
"start_line": 23
} |
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