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stringlengths 4
95
| original_source_type
stringlengths 0
23k
| source_type
stringlengths 9
23k
| source_definition
stringlengths 9
57.9k
| source
dict | source_range
dict | file_context
stringlengths 0
721k
| dependencies
dict | opens_and_abbrevs
listlengths 2
94
| vconfig
dict | interleaved
bool 1
class | verbose_type
stringlengths 1
7.42k
| effect
stringclasses 118
values | effect_flags
sequencelengths 0
2
| mutual_with
sequencelengths 0
11
| ideal_premises
sequencelengths 0
236
| proof_features
sequencelengths 0
1
| is_simple_lemma
bool 2
classes | is_div
bool 2
classes | is_proof
bool 2
classes | is_simply_typed
bool 2
classes | is_type
bool 2
classes | partial_definition
stringlengths 5
3.99k
| completed_definiton
stringlengths 1
1.63M
| isa_cross_project_example
bool 1
class |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_4 | 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))) | 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
= serialize32_bounded_int32' min max 4ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 40,
"end_line": 320,
"start_col": 0,
"start_line": 318
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let serialize32_bounded_int32_4 min max =
| serialize32_bounded_int32' min max 4ul | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_4 | 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))) | 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
= parse32_bounded_int32_le' min max 4ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 39,
"end_line": 356,
"start_col": 0,
"start_line": 354
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let parse32_bounded_int32_le_4 min max =
| parse32_bounded_int32_le' min max 4ul | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_compact | val carry_wide_felem5_compact: #w:lanes -> inp:felem_wide5 w -> felem5 w | 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') | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 26,
"end_line": 83,
"start_col": 0,
"start_line": 60
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | inp: Hacl.Spec.Poly1305.Field32xN.felem_wide5 w -> Hacl.Spec.Poly1305.Field32xN.felem5 w | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let carry_wide_felem5_compact #w (x0, x1, x2, x3, x4) =
| 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') | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_3 | 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))) | 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
= serialize32_bounded_int32_le' min max 3ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 43,
"end_line": 392,
"start_col": 0,
"start_line": 390
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let serialize32_bounded_int32_le_3 min max =
| serialize32_bounded_int32_le' min max 3ul | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.lemma_prime | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 40,
"end_line": 19,
"start_col": 0,
"start_line": 16
} | 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" | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | _: Prims.unit -> FStar.Pervasives.Lemma (ensures Prims.pow2 130 % Hacl.Spec.Poly1305.Vec.prime = 5) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | false | let lemma_prime () =
| assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 34,
"end_line": 469,
"start_col": 0,
"start_line": 466
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.parse32_bounded_int32_3 | 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))) | 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
= parse32_bounded_int32' min max 3ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 36,
"end_line": 279,
"start_col": 0,
"start_line": 277
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let parse32_bounded_int32_3 min max =
| parse32_bounded_int32' min max 3ul | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_2 | 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))) | 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
= serialize32_bounded_int32_le' min max 2ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 43,
"end_line": 388,
"start_col": 0,
"start_line": 386
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let serialize32_bounded_int32_le_2 min max =
| serialize32_bounded_int32_le' min max 2ul | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.parse32_bounded_int32_le' | 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))) | 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)))
= [@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)))
() | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 6,
"end_line": 340,
"start_col": 0,
"start_line": 324
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | 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)))
() | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero | val carry26_wide_zero: #w:lanes -> l:uint64xN w -> uint64xN w & uint64xN w | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 75,
"end_line": 23,
"start_col": 0,
"start_line": 23
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | l: Hacl.Spec.Poly1305.Field32xN.uint64xN w
-> Hacl.Spec.Poly1305.Field32xN.uint64xN w * Hacl.Spec.Poly1305.Field32xN.uint64xN w | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let carry26_wide_zero #w l =
| (vec_and l (mask26 w), vec_shift_right l 26ul) | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_4 | 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))) | 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
= serialize32_bounded_int32_le' min max 4ul | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 43,
"end_line": 396,
"start_col": 0,
"start_line": 394
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let serialize32_bounded_int32_le_4 min max =
| serialize32_bounded_int32_le' min max 4ul | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_zero_eq | val carry26_wide_zero_eq: #w:lanes -> f:uint64xN w -> Lemma
(carry26_wide_zero f == carry26_wide f (zero w)) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 26,
"end_line": 34,
"start_col": 0,
"start_line": 27
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five_i | 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)) | 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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 32,
"end_line": 46,
"start_col": 0,
"start_line": 38
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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)) | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le' | 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))) | 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)))
= [@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)
() | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 6,
"end_line": 377,
"start_col": 0,
"start_line": 359
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | 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)
() | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.serialize32_bounded_int32_le_fixed_size | 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))) | 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
= serialize32_filter serialize32_u32_le (in_bounds (U32.v min32) (U32.v max32)) | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 79,
"end_line": 404,
"start_col": 0,
"start_line": 402
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | let serialize32_bounded_int32_le_fixed_size min32 max32 =
| serialize32_filter serialize32_u32_le (in_bounds (U32.v min32) (U32.v max32)) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_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)) | 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 =
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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 55,
"end_line": 291,
"start_col": 0,
"start_line": 279
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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)) | false |
LowParse.SLow.BoundedInt.fst | LowParse.SLow.BoundedInt.parse32_bounded_int32_le_fixed_size | 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))) | 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
= parse32_filter parse32_u32_le (in_bounds (U32.v min32) (U32.v max32)) (fun x -> not (x `U32.lt` min32 || max32 `U32.lt` x)) | {
"file_name": "src/lowparse/LowParse.SLow.BoundedInt.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 125,
"end_line": 400,
"start_col": 0,
"start_line": 398
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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)) | Prims.Tot | [
"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"
] | [] | false | false | false | false | 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)) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5 | 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) | 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' | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 31,
"end_line": 558,
"start_col": 0,
"start_line": 551
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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' | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.vec_smul_mod_five | 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)) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 27,
"end_line": 55,
"start_col": 0,
"start_line": 50
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_t | val acc_inv_t (#w: lanes) (acc: felem5 w) : Type0 | val acc_inv_t (#w: lanes) (acc: felem5 w) : Type0 | 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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 56,
"end_line": 639,
"start_col": 0,
"start_line": 633
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | acc: Hacl.Spec.Poly1305.Field32xN.felem5 w -> Type0 | Prims.Tot | [
"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"
] | [] | false | false | false | false | true | 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)) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_eval_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])) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 38,
"end_line": 160,
"start_col": 0,
"start_line": 148
} | 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])) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_lemma_i | 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]) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 66,
"end_line": 109,
"start_col": 0,
"start_line": 97
} | 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]) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_fits_lemma0 | 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) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 38,
"end_line": 268,
"start_col": 0,
"start_line": 253
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 34,
"end_line": 868,
"start_col": 0,
"start_line": 865
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_lemma_i | 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]) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 36,
"end_line": 186,
"start_col": 0,
"start_line": 174
} | 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]) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_0 | 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) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 51,
"end_line": 495,
"start_col": 0,
"start_line": 484
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_felem5_lemma_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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 66,
"end_line": 608,
"start_col": 0,
"start_line": 607
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_eval_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])) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 35,
"end_line": 236,
"start_col": 0,
"start_line": 225
} | 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])) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_lemma_i | 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))) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 104,
"end_line": 661,
"start_col": 0,
"start_line": 655
} | 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))) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_lemma0 | 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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 29,
"end_line": 705,
"start_col": 0,
"start_line": 693
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_fits_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)) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 35,
"end_line": 210,
"start_col": 0,
"start_line": 199
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_s | 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) | 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 =
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') | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 27,
"end_line": 595,
"start_col": 0,
"start_line": 573
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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 | Prims.Pure | [] | [] | [
"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"
] | [] | false | false | false | false | 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') | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_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) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 32,
"end_line": 879,
"start_col": 0,
"start_line": 877
} | 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) /\ | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | false | let carry_full_felem5_lemma #w f =
| carry_full_felem5_eval_lemma f;
carry_full_felem5_fits_lemma f | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_fits_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)) | 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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 72,
"end_line": 720,
"start_col": 0,
"start_line": 710
} | 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)} -> | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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)) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_lemma_i | 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])) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 36,
"end_line": 909,
"start_col": 0,
"start_line": 897
} | 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])) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_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) | 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 =
carry_reduce_felem5_fits_lemma #w f;
carry_full_felem5_eval_lemma f | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 32,
"end_line": 1033,
"start_col": 0,
"start_line": 1031
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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) | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | false | let carry_reduce_felem5_lemma #w f =
| carry_reduce_felem5_fits_lemma #w f;
carry_full_felem5_eval_lemma f | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i1 | 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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 89,
"end_line": 822,
"start_col": 0,
"start_line": 792
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.subtract_p5_felem5_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]) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 37,
"end_line": 629,
"start_col": 0,
"start_line": 618
} | 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]) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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 ]) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i1 | 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)) | 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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 57,
"end_line": 977,
"start_col": 0,
"start_line": 964
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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)) | false |
MerkleTree.New.High.Correct.Insertion.fst | MerkleTree.New.High.Correct.Insertion.create_empty_mt_inv_ok | val create_empty_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
unit ->
Lemma (empty_olds_inv #_ #f 0;
mt_inv #hsz (create_empty_mt #_ #f ()) (empty_hashes 32)) | val create_empty_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
unit ->
Lemma (empty_olds_inv #_ #f 0;
mt_inv #hsz (create_empty_mt #_ #f ()) (empty_hashes 32)) | let create_empty_mt_inv_ok #_ #f _ =
merge_hs_empty #_ #f 32;
mt_hashes_inv_empty #_ #f 0 | {
"file_name": "src/MerkleTree.New.High.Correct.Insertion.fst",
"git_rev": "7d7bdc20f2033171e279c176b26e84f9069d23c6",
"git_url": "https://github.com/hacl-star/merkle-tree.git",
"project_name": "merkle-tree"
} | {
"end_col": 29,
"end_line": 182,
"start_col": 0,
"start_line": 180
} | module MerkleTree.New.High.Correct.Insertion
open EverCrypt
open EverCrypt.Helpers
open FStar.Classical
open FStar.Ghost
open FStar.Seq
module List = FStar.List.Tot
module S = FStar.Seq
module U32 = FStar.UInt32
module U8 = FStar.UInt8
type uint32_t = U32.t
type uint8_t = U8.t
module EHS = EverCrypt.Hash
module MTS = MerkleTree.Spec
open MerkleTree.New.High
open MerkleTree.New.High.Correct.Base
/// Correctness of insertion
val mt_hashes_next_rel_insert_odd:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 = 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1)
(S.snoc hs v) (S.snoc nhs (f (S.last hs) v))))
let mt_hashes_next_rel_insert_odd #_ #_ j hs v nhs = ()
val mt_hashes_next_rel_insert_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 <> 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1) (S.snoc hs v) nhs))
let mt_hashes_next_rel_insert_even #_ #_ j hs v nhs = ()
val insert_head:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (S.equal (S.index (insert_ #_ #f lv i j hs acc) lv)
(S.snoc (S.index hs lv) acc))
let insert_head #_ #_ lv i j hs acc = ()
val insert_inv_preserved_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (j % 2 <> 1 /\ mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 120 --max_fuel 2"
let insert_inv_preserved_even #_ #f lv i j olds hs acc =
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
remainder_2_not_1_div j;
insert_base #_ #f lv i j hs acc;
if lv = 31 then ()
else begin
// Facts
assert (S.index (merge_hs #_ #f olds hs) (lv + 1) ==
S.index (merge_hs #_ #f olds ihs) (lv + 1));
// Head proof of `mt_hashes_inv`
mt_hashes_next_rel_insert_even #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds ihs) lv)
(S.index (merge_hs #_ #f olds ihs) (lv + 1)));
// Tail proof of `mt_hashes_inv`
mt_hashes_lth_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
assert (mt_hashes_inv #_ #f (lv + 1) ((j + 1) / 2) (merge_hs #_ #f olds ihs))
end
val insert_inv_preserved:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 240 --max_fuel 1"
let rec insert_inv_preserved #_ #f lv i j olds hs acc =
if j % 2 = 1
then begin
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
remainder_2_1_div j;
insert_rec #_ #f lv i j hs acc;
// Recursion
mt_hashes_lth_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
let nacc = f (S.last (S.index hs lv)) acc in
let rihs = insert_ #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc in
insert_inv_preserved #_ #f (lv + 1) (i / 2) (j / 2) olds ihs nacc;
// Head proof of `mt_hashes_inv`
mt_olds_hs_lth_inv_ok #_ #f lv i (j + 1) olds rihs;
mt_hashes_next_rel_insert_odd #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (S.equal (S.index rihs lv) (S.index ihs lv));
insert_head #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc;
assert (S.equal (S.index ihs (lv + 1)) (S.index hs (lv + 1)));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds rihs) lv)
(S.index (merge_hs #_ #f olds rihs) (lv + 1)));
// Tail proof of `mt_hashes_inv` by recursion
assert (mt_olds_hs_inv #_ #f (lv + 1) (i / 2) ((j + 1) / 2) olds rihs);
assert (mt_hashes_inv #_ #f lv (j + 1) (merge_hs #_ #f olds rihs));
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds rihs);
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
else begin
insert_inv_preserved_even #_ #f lv i j olds hs acc;
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
#reset-options
val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds))
(ensures (mt_inv #hsz (mt_insert mt v) olds))
let mt_insert_inv_preserved #_ mt v olds =
insert_inv_preserved #_ #(MT?.hash_fun mt) 0 (MT?.i mt) (MT?.j mt) olds (MT?.hs mt) v
/// Correctness of `create_mt`
val empty_olds_inv:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv <= 32} ->
Lemma (requires True)
(ensures (mt_olds_inv #hsz lv 0 (empty_hashes 32)))
(decreases (32 - lv))
let rec empty_olds_inv #_ #f lv =
if lv = 32 then ()
else empty_olds_inv #_ #f (lv + 1)
val create_empty_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
unit ->
Lemma (empty_olds_inv #_ #f 0; | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"MerkleTree.Spec.fst.checked",
"MerkleTree.New.High.Correct.Base.fst.checked",
"MerkleTree.New.High.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.Ghost.fsti.checked",
"FStar.Classical.fsti.checked",
"EverCrypt.Helpers.fsti.checked",
"EverCrypt.Hash.fsti.checked"
],
"interface_file": false,
"source_file": "MerkleTree.New.High.Correct.Insertion.fst"
} | [
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High",
"short_module": null
},
{
"abbrev": true,
"full_module": "MerkleTree.Spec",
"short_module": "MTS"
},
{
"abbrev": true,
"full_module": "EverCrypt.Hash",
"short_module": "EHS"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "List"
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Ghost",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Classical",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt.Helpers",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | _: Prims.unit
-> FStar.Pervasives.Lemma
(ensures
(MerkleTree.New.High.Correct.Insertion.empty_olds_inv 0;
MerkleTree.New.High.Correct.Base.mt_inv (MerkleTree.New.High.create_empty_mt ())
(MerkleTree.New.High.Correct.Base.empty_hashes 32))) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"MerkleTree.Spec.hash_fun_t",
"Prims.unit",
"MerkleTree.New.High.Correct.Base.mt_hashes_inv_empty",
"MerkleTree.New.High.Correct.Base.merge_hs_empty"
] | [] | true | false | true | false | false | let create_empty_mt_inv_ok #_ #f _ =
| merge_hs_empty #_ #f 32;
mt_hashes_inv_empty #_ #f 0 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_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]) | 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]) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 47,
"end_line": 855,
"start_col": 0,
"start_line": 831
} | 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]) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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 ]) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 ]) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.acc_inv_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)) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 32,
"end_line": 683,
"start_col": 0,
"start_line": 672
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
MerkleTree.New.High.Correct.Insertion.fst | MerkleTree.New.High.Correct.Insertion.empty_olds_inv | val empty_olds_inv:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv <= 32} ->
Lemma (requires True)
(ensures (mt_olds_inv #hsz lv 0 (empty_hashes 32)))
(decreases (32 - lv)) | val empty_olds_inv:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv <= 32} ->
Lemma (requires True)
(ensures (mt_olds_inv #hsz lv 0 (empty_hashes 32)))
(decreases (32 - lv)) | let rec empty_olds_inv #_ #f lv =
if lv = 32 then ()
else empty_olds_inv #_ #f (lv + 1) | {
"file_name": "src/MerkleTree.New.High.Correct.Insertion.fst",
"git_rev": "7d7bdc20f2033171e279c176b26e84f9069d23c6",
"git_url": "https://github.com/hacl-star/merkle-tree.git",
"project_name": "merkle-tree"
} | {
"end_col": 36,
"end_line": 173,
"start_col": 0,
"start_line": 171
} | module MerkleTree.New.High.Correct.Insertion
open EverCrypt
open EverCrypt.Helpers
open FStar.Classical
open FStar.Ghost
open FStar.Seq
module List = FStar.List.Tot
module S = FStar.Seq
module U32 = FStar.UInt32
module U8 = FStar.UInt8
type uint32_t = U32.t
type uint8_t = U8.t
module EHS = EverCrypt.Hash
module MTS = MerkleTree.Spec
open MerkleTree.New.High
open MerkleTree.New.High.Correct.Base
/// Correctness of insertion
val mt_hashes_next_rel_insert_odd:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 = 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1)
(S.snoc hs v) (S.snoc nhs (f (S.last hs) v))))
let mt_hashes_next_rel_insert_odd #_ #_ j hs v nhs = ()
val mt_hashes_next_rel_insert_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 <> 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1) (S.snoc hs v) nhs))
let mt_hashes_next_rel_insert_even #_ #_ j hs v nhs = ()
val insert_head:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (S.equal (S.index (insert_ #_ #f lv i j hs acc) lv)
(S.snoc (S.index hs lv) acc))
let insert_head #_ #_ lv i j hs acc = ()
val insert_inv_preserved_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (j % 2 <> 1 /\ mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 120 --max_fuel 2"
let insert_inv_preserved_even #_ #f lv i j olds hs acc =
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
remainder_2_not_1_div j;
insert_base #_ #f lv i j hs acc;
if lv = 31 then ()
else begin
// Facts
assert (S.index (merge_hs #_ #f olds hs) (lv + 1) ==
S.index (merge_hs #_ #f olds ihs) (lv + 1));
// Head proof of `mt_hashes_inv`
mt_hashes_next_rel_insert_even #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds ihs) lv)
(S.index (merge_hs #_ #f olds ihs) (lv + 1)));
// Tail proof of `mt_hashes_inv`
mt_hashes_lth_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
assert (mt_hashes_inv #_ #f (lv + 1) ((j + 1) / 2) (merge_hs #_ #f olds ihs))
end
val insert_inv_preserved:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 240 --max_fuel 1"
let rec insert_inv_preserved #_ #f lv i j olds hs acc =
if j % 2 = 1
then begin
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
remainder_2_1_div j;
insert_rec #_ #f lv i j hs acc;
// Recursion
mt_hashes_lth_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
let nacc = f (S.last (S.index hs lv)) acc in
let rihs = insert_ #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc in
insert_inv_preserved #_ #f (lv + 1) (i / 2) (j / 2) olds ihs nacc;
// Head proof of `mt_hashes_inv`
mt_olds_hs_lth_inv_ok #_ #f lv i (j + 1) olds rihs;
mt_hashes_next_rel_insert_odd #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (S.equal (S.index rihs lv) (S.index ihs lv));
insert_head #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc;
assert (S.equal (S.index ihs (lv + 1)) (S.index hs (lv + 1)));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds rihs) lv)
(S.index (merge_hs #_ #f olds rihs) (lv + 1)));
// Tail proof of `mt_hashes_inv` by recursion
assert (mt_olds_hs_inv #_ #f (lv + 1) (i / 2) ((j + 1) / 2) olds rihs);
assert (mt_hashes_inv #_ #f lv (j + 1) (merge_hs #_ #f olds rihs));
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds rihs);
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
else begin
insert_inv_preserved_even #_ #f lv i j olds hs acc;
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
#reset-options
val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds))
(ensures (mt_inv #hsz (mt_insert mt v) olds))
let mt_insert_inv_preserved #_ mt v olds =
insert_inv_preserved #_ #(MT?.hash_fun mt) 0 (MT?.i mt) (MT?.j mt) olds (MT?.hs mt) v
/// Correctness of `create_mt`
val empty_olds_inv:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv <= 32} ->
Lemma (requires True)
(ensures (mt_olds_inv #hsz lv 0 (empty_hashes 32))) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"MerkleTree.Spec.fst.checked",
"MerkleTree.New.High.Correct.Base.fst.checked",
"MerkleTree.New.High.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.Ghost.fsti.checked",
"FStar.Classical.fsti.checked",
"EverCrypt.Helpers.fsti.checked",
"EverCrypt.Hash.fsti.checked"
],
"interface_file": false,
"source_file": "MerkleTree.New.High.Correct.Insertion.fst"
} | [
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High",
"short_module": null
},
{
"abbrev": true,
"full_module": "MerkleTree.Spec",
"short_module": "MTS"
},
{
"abbrev": true,
"full_module": "EverCrypt.Hash",
"short_module": "EHS"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "List"
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Ghost",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Classical",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt.Helpers",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | lv: Prims.nat{lv <= 32}
-> FStar.Pervasives.Lemma
(ensures
MerkleTree.New.High.Correct.Base.mt_olds_inv lv
0
(MerkleTree.New.High.Correct.Base.empty_hashes 32)) (decreases 32 - lv) | FStar.Pervasives.Lemma | [
"lemma",
""
] | [] | [
"Prims.pos",
"MerkleTree.Spec.hash_fun_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"MerkleTree.New.High.Correct.Insertion.empty_olds_inv",
"Prims.op_Addition",
"Prims.unit"
] | [
"recursion"
] | false | false | true | false | false | let rec empty_olds_inv #_ #f lv =
| if lv = 32 then () else empty_olds_inv #_ #f (lv + 1) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_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)) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 43,
"end_line": 1021,
"start_col": 0,
"start_line": 1010
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
MerkleTree.New.High.Correct.Insertion.fst | MerkleTree.New.High.Correct.Insertion.create_mt_inv_ok | val create_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
init:hash ->
Lemma (empty_olds_inv #_ #f 0;
mt_inv #hsz (mt_create hsz f init) (empty_hashes 32)) | val create_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
init:hash ->
Lemma (empty_olds_inv #_ #f 0;
mt_inv #hsz (mt_create hsz f init) (empty_hashes 32)) | let create_mt_inv_ok #hsz #f init =
create_empty_mt_inv_ok #_ #f ();
empty_olds_inv #_ #f 0;
mt_insert_inv_preserved #_ (create_empty_mt #hsz #f ()) init (empty_hashes 32) | {
"file_name": "src/MerkleTree.New.High.Correct.Insertion.fst",
"git_rev": "7d7bdc20f2033171e279c176b26e84f9069d23c6",
"git_url": "https://github.com/hacl-star/merkle-tree.git",
"project_name": "merkle-tree"
} | {
"end_col": 80,
"end_line": 192,
"start_col": 0,
"start_line": 189
} | module MerkleTree.New.High.Correct.Insertion
open EverCrypt
open EverCrypt.Helpers
open FStar.Classical
open FStar.Ghost
open FStar.Seq
module List = FStar.List.Tot
module S = FStar.Seq
module U32 = FStar.UInt32
module U8 = FStar.UInt8
type uint32_t = U32.t
type uint8_t = U8.t
module EHS = EverCrypt.Hash
module MTS = MerkleTree.Spec
open MerkleTree.New.High
open MerkleTree.New.High.Correct.Base
/// Correctness of insertion
val mt_hashes_next_rel_insert_odd:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 = 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1)
(S.snoc hs v) (S.snoc nhs (f (S.last hs) v))))
let mt_hashes_next_rel_insert_odd #_ #_ j hs v nhs = ()
val mt_hashes_next_rel_insert_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 <> 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1) (S.snoc hs v) nhs))
let mt_hashes_next_rel_insert_even #_ #_ j hs v nhs = ()
val insert_head:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (S.equal (S.index (insert_ #_ #f lv i j hs acc) lv)
(S.snoc (S.index hs lv) acc))
let insert_head #_ #_ lv i j hs acc = ()
val insert_inv_preserved_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (j % 2 <> 1 /\ mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 120 --max_fuel 2"
let insert_inv_preserved_even #_ #f lv i j olds hs acc =
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
remainder_2_not_1_div j;
insert_base #_ #f lv i j hs acc;
if lv = 31 then ()
else begin
// Facts
assert (S.index (merge_hs #_ #f olds hs) (lv + 1) ==
S.index (merge_hs #_ #f olds ihs) (lv + 1));
// Head proof of `mt_hashes_inv`
mt_hashes_next_rel_insert_even #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds ihs) lv)
(S.index (merge_hs #_ #f olds ihs) (lv + 1)));
// Tail proof of `mt_hashes_inv`
mt_hashes_lth_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
assert (mt_hashes_inv #_ #f (lv + 1) ((j + 1) / 2) (merge_hs #_ #f olds ihs))
end
val insert_inv_preserved:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 240 --max_fuel 1"
let rec insert_inv_preserved #_ #f lv i j olds hs acc =
if j % 2 = 1
then begin
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
remainder_2_1_div j;
insert_rec #_ #f lv i j hs acc;
// Recursion
mt_hashes_lth_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
let nacc = f (S.last (S.index hs lv)) acc in
let rihs = insert_ #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc in
insert_inv_preserved #_ #f (lv + 1) (i / 2) (j / 2) olds ihs nacc;
// Head proof of `mt_hashes_inv`
mt_olds_hs_lth_inv_ok #_ #f lv i (j + 1) olds rihs;
mt_hashes_next_rel_insert_odd #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (S.equal (S.index rihs lv) (S.index ihs lv));
insert_head #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc;
assert (S.equal (S.index ihs (lv + 1)) (S.index hs (lv + 1)));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds rihs) lv)
(S.index (merge_hs #_ #f olds rihs) (lv + 1)));
// Tail proof of `mt_hashes_inv` by recursion
assert (mt_olds_hs_inv #_ #f (lv + 1) (i / 2) ((j + 1) / 2) olds rihs);
assert (mt_hashes_inv #_ #f lv (j + 1) (merge_hs #_ #f olds rihs));
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds rihs);
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
else begin
insert_inv_preserved_even #_ #f lv i j olds hs acc;
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
#reset-options
val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds))
(ensures (mt_inv #hsz (mt_insert mt v) olds))
let mt_insert_inv_preserved #_ mt v olds =
insert_inv_preserved #_ #(MT?.hash_fun mt) 0 (MT?.i mt) (MT?.j mt) olds (MT?.hs mt) v
/// Correctness of `create_mt`
val empty_olds_inv:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv <= 32} ->
Lemma (requires True)
(ensures (mt_olds_inv #hsz lv 0 (empty_hashes 32)))
(decreases (32 - lv))
let rec empty_olds_inv #_ #f lv =
if lv = 32 then ()
else empty_olds_inv #_ #f (lv + 1)
val create_empty_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
unit ->
Lemma (empty_olds_inv #_ #f 0;
mt_inv #hsz (create_empty_mt #_ #f ()) (empty_hashes 32))
let create_empty_mt_inv_ok #_ #f _ =
merge_hs_empty #_ #f 32;
mt_hashes_inv_empty #_ #f 0
val create_mt_inv_ok:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
init:hash ->
Lemma (empty_olds_inv #_ #f 0; | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"MerkleTree.Spec.fst.checked",
"MerkleTree.New.High.Correct.Base.fst.checked",
"MerkleTree.New.High.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.Ghost.fsti.checked",
"FStar.Classical.fsti.checked",
"EverCrypt.Helpers.fsti.checked",
"EverCrypt.Hash.fsti.checked"
],
"interface_file": false,
"source_file": "MerkleTree.New.High.Correct.Insertion.fst"
} | [
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High",
"short_module": null
},
{
"abbrev": true,
"full_module": "MerkleTree.Spec",
"short_module": "MTS"
},
{
"abbrev": true,
"full_module": "EverCrypt.Hash",
"short_module": "EHS"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "List"
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Ghost",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Classical",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt.Helpers",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | init: MerkleTree.New.High.hash
-> FStar.Pervasives.Lemma
(ensures
(MerkleTree.New.High.Correct.Insertion.empty_olds_inv 0;
MerkleTree.New.High.Correct.Base.mt_inv (MerkleTree.New.High.mt_create hsz f init)
(MerkleTree.New.High.Correct.Base.empty_hashes 32))) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"MerkleTree.Spec.hash_fun_t",
"MerkleTree.New.High.hash",
"MerkleTree.New.High.Correct.Insertion.mt_insert_inv_preserved",
"MerkleTree.New.High.create_empty_mt",
"MerkleTree.New.High.Correct.Base.empty_hashes",
"Prims.unit",
"MerkleTree.New.High.Correct.Insertion.empty_olds_inv",
"MerkleTree.New.High.Correct.Insertion.create_empty_mt_inv_ok"
] | [] | true | false | true | false | false | let create_mt_inv_ok #hsz #f init =
| create_empty_mt_inv_ok #_ #f ();
empty_olds_inv #_ #f 0;
mt_insert_inv_preserved #_ (create_empty_mt #hsz #f ()) init (empty_hashes 32) | false |
MerkleTree.New.High.Correct.Insertion.fst | MerkleTree.New.High.Correct.Insertion.mt_insert_inv_preserved | val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds))
(ensures (mt_inv #hsz (mt_insert mt v) olds)) | val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds))
(ensures (mt_inv #hsz (mt_insert mt v) olds)) | let mt_insert_inv_preserved #_ mt v olds =
insert_inv_preserved #_ #(MT?.hash_fun mt) 0 (MT?.i mt) (MT?.j mt) olds (MT?.hs mt) v | {
"file_name": "src/MerkleTree.New.High.Correct.Insertion.fst",
"git_rev": "7d7bdc20f2033171e279c176b26e84f9069d23c6",
"git_url": "https://github.com/hacl-star/merkle-tree.git",
"project_name": "merkle-tree"
} | {
"end_col": 87,
"end_line": 161,
"start_col": 0,
"start_line": 160
} | module MerkleTree.New.High.Correct.Insertion
open EverCrypt
open EverCrypt.Helpers
open FStar.Classical
open FStar.Ghost
open FStar.Seq
module List = FStar.List.Tot
module S = FStar.Seq
module U32 = FStar.UInt32
module U8 = FStar.UInt8
type uint32_t = U32.t
type uint8_t = U8.t
module EHS = EverCrypt.Hash
module MTS = MerkleTree.Spec
open MerkleTree.New.High
open MerkleTree.New.High.Correct.Base
/// Correctness of insertion
val mt_hashes_next_rel_insert_odd:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 = 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1)
(S.snoc hs v) (S.snoc nhs (f (S.last hs) v))))
let mt_hashes_next_rel_insert_odd #_ #_ j hs v nhs = ()
val mt_hashes_next_rel_insert_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
j:nat{j % 2 <> 1} ->
hs:hashes #hsz {S.length hs = j} -> v:hash ->
nhs:hashes #hsz {S.length nhs = j / 2} ->
Lemma (requires (mt_hashes_next_rel #_ #f j hs nhs))
(ensures (mt_hashes_next_rel #_ #f (j + 1) (S.snoc hs v) nhs))
let mt_hashes_next_rel_insert_even #_ #_ j hs v nhs = ()
val insert_head:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (S.equal (S.index (insert_ #_ #f lv i j hs acc) lv)
(S.snoc (S.index hs lv) acc))
let insert_head #_ #_ lv i j hs acc = ()
val insert_inv_preserved_even:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (j % 2 <> 1 /\ mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 120 --max_fuel 2"
let insert_inv_preserved_even #_ #f lv i j olds hs acc =
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
remainder_2_not_1_div j;
insert_base #_ #f lv i j hs acc;
if lv = 31 then ()
else begin
// Facts
assert (S.index (merge_hs #_ #f olds hs) (lv + 1) ==
S.index (merge_hs #_ #f olds ihs) (lv + 1));
// Head proof of `mt_hashes_inv`
mt_hashes_next_rel_insert_even #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds ihs) lv)
(S.index (merge_hs #_ #f olds ihs) (lv + 1)));
// Tail proof of `mt_hashes_inv`
mt_hashes_lth_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) ((j + 1) / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
assert (mt_hashes_inv #_ #f (lv + 1) ((j + 1) / 2) (merge_hs #_ #f olds ihs))
end
val insert_inv_preserved:
#hsz:pos -> #f:MTS.hash_fun_t #hsz ->
lv:nat{lv < 32} ->
i:nat ->
j:nat{i <= j /\ j < pow2 (32 - lv) - 1} ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz lv i olds} ->
hs:hashess #hsz {S.length hs = 32 /\ hs_wf_elts lv hs i j} ->
acc:hash ->
Lemma (requires (mt_olds_hs_inv #_ #f lv i j olds hs))
(ensures (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc)))
(decreases (32 - lv))
#reset-options "--z3rlimit 240 --max_fuel 1"
let rec insert_inv_preserved #_ #f lv i j olds hs acc =
if j % 2 = 1
then begin
let ihs = hashess_insert lv i j hs acc in
mt_olds_hs_lth_inv_ok #_ #f lv i j olds hs;
merge_hs_slice_equal #_ #f olds hs olds ihs (lv + 1) 32;
assert (mt_hashes_inv #_ #f lv j (merge_hs #_ #f olds hs));
remainder_2_1_div j;
insert_rec #_ #f lv i j hs acc;
// Recursion
mt_hashes_lth_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
mt_hashes_inv_equiv #_ #f (lv + 1) (j / 2)
(merge_hs #_ #f olds hs) (merge_hs #_ #f olds ihs);
let nacc = f (S.last (S.index hs lv)) acc in
let rihs = insert_ #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc in
insert_inv_preserved #_ #f (lv + 1) (i / 2) (j / 2) olds ihs nacc;
// Head proof of `mt_hashes_inv`
mt_olds_hs_lth_inv_ok #_ #f lv i (j + 1) olds rihs;
mt_hashes_next_rel_insert_odd #_ #f j
(S.index (merge_hs #_ #f olds hs) lv) acc
(S.index (merge_hs #_ #f olds hs) (lv + 1));
assert (S.equal (S.index rihs lv) (S.index ihs lv));
insert_head #_ #f (lv + 1) (i / 2) (j / 2) ihs nacc;
assert (S.equal (S.index ihs (lv + 1)) (S.index hs (lv + 1)));
assert (mt_hashes_next_rel #_ #f (j + 1)
(S.index (merge_hs #_ #f olds rihs) lv)
(S.index (merge_hs #_ #f olds rihs) (lv + 1)));
// Tail proof of `mt_hashes_inv` by recursion
assert (mt_olds_hs_inv #_ #f (lv + 1) (i / 2) ((j + 1) / 2) olds rihs);
assert (mt_hashes_inv #_ #f lv (j + 1) (merge_hs #_ #f olds rihs));
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds rihs);
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
else begin
insert_inv_preserved_even #_ #f lv i j olds hs acc;
assert (mt_olds_hs_inv #_ #f lv i (j + 1) olds (insert_ #_ #f lv i j hs acc))
end
#reset-options
val mt_insert_inv_preserved:
#hsz:pos ->
mt:merkle_tree #hsz {mt_wf_elts mt /\ mt_not_full mt} -> v:hash ->
olds:hashess #hsz {S.length olds = 32 /\ mt_olds_inv #hsz 0 (MT?.i mt) olds} ->
Lemma (requires (mt_inv #hsz mt olds)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"MerkleTree.Spec.fst.checked",
"MerkleTree.New.High.Correct.Base.fst.checked",
"MerkleTree.New.High.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.Ghost.fsti.checked",
"FStar.Classical.fsti.checked",
"EverCrypt.Helpers.fsti.checked",
"EverCrypt.Hash.fsti.checked"
],
"interface_file": false,
"source_file": "MerkleTree.New.High.Correct.Insertion.fst"
} | [
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High",
"short_module": null
},
{
"abbrev": true,
"full_module": "MerkleTree.Spec",
"short_module": "MTS"
},
{
"abbrev": true,
"full_module": "EverCrypt.Hash",
"short_module": "EHS"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "List"
},
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Ghost",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Classical",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt.Helpers",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverCrypt",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "MerkleTree.New.High.Correct",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
mt:
MerkleTree.New.High.merkle_tree
{MerkleTree.New.High.mt_wf_elts mt /\ MerkleTree.New.High.mt_not_full mt} ->
v: MerkleTree.New.High.hash ->
olds:
MerkleTree.New.High.hashess
{ FStar.Seq.Base.length olds = 32 /\
MerkleTree.New.High.Correct.Base.mt_olds_inv 0 (MT?.i mt) olds }
-> FStar.Pervasives.Lemma (requires MerkleTree.New.High.Correct.Base.mt_inv mt olds)
(ensures MerkleTree.New.High.Correct.Base.mt_inv (MerkleTree.New.High.mt_insert mt v) olds) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"MerkleTree.New.High.merkle_tree",
"Prims.l_and",
"MerkleTree.New.High.mt_wf_elts",
"Prims.b2t",
"MerkleTree.New.High.mt_not_full",
"MerkleTree.New.High.hash",
"MerkleTree.New.High.hashess",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"MerkleTree.New.High.hashes",
"MerkleTree.New.High.Correct.Base.mt_olds_inv",
"MerkleTree.New.High.__proj__MT__item__i",
"MerkleTree.New.High.Correct.Insertion.insert_inv_preserved",
"MerkleTree.New.High.__proj__MT__item__hash_fun",
"MerkleTree.New.High.__proj__MT__item__j",
"MerkleTree.New.High.__proj__MT__item__hs",
"Prims.unit"
] | [] | true | false | true | false | false | let mt_insert_inv_preserved #_ mt v olds =
| insert_inv_preserved #_ #(MT?.hash_fun mt) 0 (MT?.i mt) (MT?.j mt) olds (MT?.hs mt) v | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.lemma_subtract_p5_1 | 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) | 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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 51,
"end_line": 535,
"start_col": 0,
"start_line": 509
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 (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 | false |
Test.Vectors.Chacha20Poly1305.fst | Test.Vectors.Chacha20Poly1305.output9 | val output9:(b: B.buffer UInt8.t {B.length b = 1040 /\ B.recallable b}) | val output9:(b: B.buffer UInt8.t {B.length b = 1040 /\ B.recallable b}) | let output9: (b: B.buffer UInt8.t { B.length b = 1040 /\ B.recallable b }) =
[@inline_let] let l = [ 0xe5uy; 0x26uy; 0xa4uy; 0x3duy; 0xbduy; 0x33uy; 0xd0uy; 0x4buy; 0x6fuy; 0x05uy; 0xa7uy; 0x6euy; 0x12uy; 0x7auy; 0xd2uy; 0x74uy; 0xa6uy; 0xdduy; 0xbduy; 0x95uy; 0xebuy; 0xf9uy; 0xa4uy; 0xf1uy; 0x59uy; 0x93uy; 0x91uy; 0x70uy; 0xd9uy; 0xfeuy; 0x9auy; 0xcduy; 0x53uy; 0x1fuy; 0x3auy; 0xabuy; 0xa6uy; 0x7cuy; 0x9fuy; 0xa6uy; 0x9euy; 0xbduy; 0x99uy; 0xd9uy; 0xb5uy; 0x97uy; 0x44uy; 0xd5uy; 0x14uy; 0x48uy; 0x4duy; 0x9duy; 0xc0uy; 0xd0uy; 0x05uy; 0x96uy; 0xebuy; 0x4cuy; 0x78uy; 0x55uy; 0x09uy; 0x08uy; 0x01uy; 0x02uy; 0x30uy; 0x90uy; 0x7buy; 0x96uy; 0x7auy; 0x7buy; 0x5fuy; 0x30uy; 0x41uy; 0x24uy; 0xceuy; 0x68uy; 0x61uy; 0x49uy; 0x86uy; 0x57uy; 0x82uy; 0xdduy; 0x53uy; 0x1cuy; 0x51uy; 0x28uy; 0x2buy; 0x53uy; 0x6euy; 0x2duy; 0xc2uy; 0x20uy; 0x4cuy; 0xdduy; 0x8fuy; 0x65uy; 0x10uy; 0x20uy; 0x50uy; 0xdduy; 0x9duy; 0x50uy; 0xe5uy; 0x71uy; 0x40uy; 0x53uy; 0x69uy; 0xfcuy; 0x77uy; 0x48uy; 0x11uy; 0xb9uy; 0xdeuy; 0xa4uy; 0x8duy; 0x58uy; 0xe4uy; 0xa6uy; 0x1auy; 0x18uy; 0x47uy; 0x81uy; 0x7euy; 0xfcuy; 0xdduy; 0xf6uy; 0xefuy; 0xceuy; 0x2fuy; 0x43uy; 0x68uy; 0xd6uy; 0x06uy; 0xe2uy; 0x74uy; 0x6auy; 0xaduy; 0x90uy; 0xf5uy; 0x37uy; 0xf3uy; 0x3duy; 0x82uy; 0x69uy; 0x40uy; 0xe9uy; 0x6buy; 0xa7uy; 0x3duy; 0xa8uy; 0x1euy; 0xd2uy; 0x02uy; 0x7cuy; 0xb7uy; 0x9buy; 0xe4uy; 0xdauy; 0x8fuy; 0x95uy; 0x06uy; 0xc5uy; 0xdfuy; 0x73uy; 0xa3uy; 0x20uy; 0x9auy; 0x49uy; 0xdeuy; 0x9cuy; 0xbcuy; 0xeeuy; 0x14uy; 0x3fuy; 0x81uy; 0x5euy; 0xf8uy; 0x3buy; 0x59uy; 0x3cuy; 0xe1uy; 0x68uy; 0x12uy; 0x5auy; 0x3auy; 0x76uy; 0x3auy; 0x3fuy; 0xf7uy; 0x87uy; 0x33uy; 0x0auy; 0x01uy; 0xb8uy; 0xd4uy; 0xeduy; 0xb6uy; 0xbeuy; 0x94uy; 0x5euy; 0x70uy; 0x40uy; 0x56uy; 0x67uy; 0x1fuy; 0x50uy; 0x44uy; 0x19uy; 0xceuy; 0x82uy; 0x70uy; 0x10uy; 0x87uy; 0x13uy; 0x20uy; 0x0buy; 0x4cuy; 0x5auy; 0xb6uy; 0xf6uy; 0xa7uy; 0xaeuy; 0x81uy; 0x75uy; 0x01uy; 0x81uy; 0xe6uy; 0x4buy; 0x57uy; 0x7cuy; 0xdduy; 0x6duy; 0xf8uy; 0x1cuy; 0x29uy; 0x32uy; 0xf7uy; 0xdauy; 0x3cuy; 0x2duy; 0xf8uy; 0x9buy; 0x25uy; 0x6euy; 0x00uy; 0xb4uy; 0xf7uy; 0x2fuy; 0xf7uy; 0x04uy; 0xf7uy; 0xa1uy; 0x56uy; 0xacuy; 0x4fuy; 0x1auy; 0x64uy; 0xb8uy; 0x47uy; 0x55uy; 0x18uy; 0x7buy; 0x07uy; 0x4duy; 0xbduy; 0x47uy; 0x24uy; 0x80uy; 0x5duy; 0xa2uy; 0x70uy; 0xc5uy; 0xdduy; 0x8euy; 0x82uy; 0xd4uy; 0xebuy; 0xecuy; 0xb2uy; 0x0cuy; 0x39uy; 0xd2uy; 0x97uy; 0xc1uy; 0xcbuy; 0xebuy; 0xf4uy; 0x77uy; 0x59uy; 0xb4uy; 0x87uy; 0xefuy; 0xcbuy; 0x43uy; 0x2duy; 0x46uy; 0x54uy; 0xd1uy; 0xa7uy; 0xd7uy; 0x15uy; 0x99uy; 0x0auy; 0x43uy; 0xa1uy; 0xe0uy; 0x99uy; 0x33uy; 0x71uy; 0xc1uy; 0xeduy; 0xfeuy; 0x72uy; 0x46uy; 0x33uy; 0x8euy; 0x91uy; 0x08uy; 0x9fuy; 0xc8uy; 0x2euy; 0xcauy; 0xfauy; 0xdcuy; 0x59uy; 0xd5uy; 0xc3uy; 0x76uy; 0x84uy; 0x9fuy; 0xa3uy; 0x37uy; 0x68uy; 0xc3uy; 0xf0uy; 0x47uy; 0x2cuy; 0x68uy; 0xdbuy; 0x5euy; 0xc3uy; 0x49uy; 0x4cuy; 0xe8uy; 0x92uy; 0x85uy; 0xe2uy; 0x23uy; 0xd3uy; 0x3fuy; 0xaduy; 0x32uy; 0xe5uy; 0x2buy; 0x82uy; 0xd7uy; 0x8fuy; 0x99uy; 0x0auy; 0x59uy; 0x5cuy; 0x45uy; 0xd9uy; 0xb4uy; 0x51uy; 0x52uy; 0xc2uy; 0xaeuy; 0xbfuy; 0x80uy; 0xcfuy; 0xc9uy; 0xc9uy; 0x51uy; 0x24uy; 0x2auy; 0x3buy; 0x3auy; 0x4duy; 0xaeuy; 0xebuy; 0xbduy; 0x22uy; 0xc3uy; 0x0euy; 0x0fuy; 0x59uy; 0x25uy; 0x92uy; 0x17uy; 0xe9uy; 0x74uy; 0xc7uy; 0x8buy; 0x70uy; 0x70uy; 0x36uy; 0x55uy; 0x95uy; 0x75uy; 0x4buy; 0xaduy; 0x61uy; 0x2buy; 0x09uy; 0xbcuy; 0x82uy; 0xf2uy; 0x6euy; 0x94uy; 0x43uy; 0xaeuy; 0xc3uy; 0xd5uy; 0xcduy; 0x8euy; 0xfeuy; 0x5buy; 0x9auy; 0x88uy; 0x43uy; 0x01uy; 0x75uy; 0xb2uy; 0x23uy; 0x09uy; 0xf7uy; 0x89uy; 0x83uy; 0xe7uy; 0xfauy; 0xf9uy; 0xb4uy; 0x9buy; 0xf8uy; 0xefuy; 0xbduy; 0x1cuy; 0x92uy; 0xc1uy; 0xdauy; 0x7euy; 0xfeuy; 0x05uy; 0xbauy; 0x5auy; 0xcduy; 0x07uy; 0x6auy; 0x78uy; 0x9euy; 0x5duy; 0xfbuy; 0x11uy; 0x2fuy; 0x79uy; 0x38uy; 0xb6uy; 0xc2uy; 0x5buy; 0x6buy; 0x51uy; 0xb4uy; 0x71uy; 0xdduy; 0xf7uy; 0x2auy; 0xe4uy; 0xf4uy; 0x72uy; 0x76uy; 0xaduy; 0xc2uy; 0xdduy; 0x64uy; 0x5duy; 0x79uy; 0xb6uy; 0xf5uy; 0x7auy; 0x77uy; 0x20uy; 0x05uy; 0x3duy; 0x30uy; 0x06uy; 0xd4uy; 0x4cuy; 0x0auy; 0x2cuy; 0x98uy; 0x5auy; 0xb9uy; 0xd4uy; 0x98uy; 0xa9uy; 0x3fuy; 0xc6uy; 0x12uy; 0xeauy; 0x3buy; 0x4buy; 0xc5uy; 0x79uy; 0x64uy; 0x63uy; 0x6buy; 0x09uy; 0x54uy; 0x3buy; 0x14uy; 0x27uy; 0xbauy; 0x99uy; 0x80uy; 0xc8uy; 0x72uy; 0xa8uy; 0x12uy; 0x90uy; 0x29uy; 0xbauy; 0x40uy; 0x54uy; 0x97uy; 0x2buy; 0x7buy; 0xfeuy; 0xebuy; 0xcduy; 0x01uy; 0x05uy; 0x44uy; 0x72uy; 0xdbuy; 0x99uy; 0xe4uy; 0x61uy; 0xc9uy; 0x69uy; 0xd6uy; 0xb9uy; 0x28uy; 0xd1uy; 0x05uy; 0x3euy; 0xf9uy; 0x0buy; 0x49uy; 0x0auy; 0x49uy; 0xe9uy; 0x8duy; 0x0euy; 0xa7uy; 0x4auy; 0x0fuy; 0xafuy; 0x32uy; 0xd0uy; 0xe0uy; 0xb2uy; 0x3auy; 0x55uy; 0x58uy; 0xfeuy; 0x5cuy; 0x28uy; 0x70uy; 0x51uy; 0x23uy; 0xb0uy; 0x7buy; 0x6auy; 0x5fuy; 0x1euy; 0xb8uy; 0x17uy; 0xd7uy; 0x94uy; 0x15uy; 0x8fuy; 0xeeuy; 0x20uy; 0xc7uy; 0x42uy; 0x25uy; 0x3euy; 0x9auy; 0x14uy; 0xd7uy; 0x60uy; 0x72uy; 0x39uy; 0x47uy; 0x48uy; 0xa9uy; 0xfeuy; 0xdduy; 0x47uy; 0x0auy; 0xb1uy; 0xe6uy; 0x60uy; 0x28uy; 0x8cuy; 0x11uy; 0x68uy; 0xe1uy; 0xffuy; 0xd7uy; 0xceuy; 0xc8uy; 0xbeuy; 0xb3uy; 0xfeuy; 0x27uy; 0x30uy; 0x09uy; 0x70uy; 0xd7uy; 0xfauy; 0x02uy; 0x33uy; 0x3auy; 0x61uy; 0x2euy; 0xc7uy; 0xffuy; 0xa4uy; 0x2auy; 0xa8uy; 0x6euy; 0xb4uy; 0x79uy; 0x35uy; 0x6duy; 0x4cuy; 0x1euy; 0x38uy; 0xf8uy; 0xeeuy; 0xd4uy; 0x84uy; 0x4euy; 0x6euy; 0x28uy; 0xa7uy; 0xceuy; 0xc8uy; 0xc1uy; 0xcfuy; 0x80uy; 0x05uy; 0xf3uy; 0x04uy; 0xefuy; 0xc8uy; 0x18uy; 0x28uy; 0x2euy; 0x8duy; 0x5euy; 0x0cuy; 0xdfuy; 0xb8uy; 0x5fuy; 0x96uy; 0xe8uy; 0xc6uy; 0x9cuy; 0x2fuy; 0xe5uy; 0xa6uy; 0x44uy; 0xd7uy; 0xe7uy; 0x99uy; 0x44uy; 0x0cuy; 0xecuy; 0xd7uy; 0x05uy; 0x60uy; 0x97uy; 0xbbuy; 0x74uy; 0x77uy; 0x58uy; 0xd5uy; 0xbbuy; 0x48uy; 0xdeuy; 0x5auy; 0xb2uy; 0x54uy; 0x7fuy; 0x0euy; 0x46uy; 0x70uy; 0x6auy; 0x6fuy; 0x78uy; 0xa5uy; 0x08uy; 0x89uy; 0x05uy; 0x4euy; 0x7euy; 0xa0uy; 0x69uy; 0xb4uy; 0x40uy; 0x60uy; 0x55uy; 0x77uy; 0x75uy; 0x9buy; 0x19uy; 0xf2uy; 0xd5uy; 0x13uy; 0x80uy; 0x77uy; 0xf9uy; 0x4buy; 0x3fuy; 0x1euy; 0xeeuy; 0xe6uy; 0x76uy; 0x84uy; 0x7buy; 0x8cuy; 0xe5uy; 0x27uy; 0xa8uy; 0x0auy; 0x91uy; 0x01uy; 0x68uy; 0x71uy; 0x8auy; 0x3fuy; 0x06uy; 0xabuy; 0xf6uy; 0xa9uy; 0xa5uy; 0xe6uy; 0x72uy; 0x92uy; 0xe4uy; 0x67uy; 0xe2uy; 0xa2uy; 0x46uy; 0x35uy; 0x84uy; 0x55uy; 0x7duy; 0xcauy; 0xa8uy; 0x85uy; 0xd0uy; 0xf1uy; 0x3fuy; 0xbeuy; 0xd7uy; 0x34uy; 0x64uy; 0xfcuy; 0xaeuy; 0xe3uy; 0xe4uy; 0x04uy; 0x9fuy; 0x66uy; 0x02uy; 0xb9uy; 0x88uy; 0x10uy; 0xd9uy; 0xc4uy; 0x4cuy; 0x31uy; 0x43uy; 0x7auy; 0x93uy; 0xe2uy; 0x9buy; 0x56uy; 0x43uy; 0x84uy; 0xdcuy; 0xdcuy; 0xdeuy; 0x1duy; 0xa4uy; 0x02uy; 0x0euy; 0xc2uy; 0xefuy; 0xc3uy; 0xf8uy; 0x78uy; 0xd1uy; 0xb2uy; 0x6buy; 0x63uy; 0x18uy; 0xc9uy; 0xa9uy; 0xe5uy; 0x72uy; 0xd8uy; 0xf3uy; 0xb9uy; 0xd1uy; 0x8auy; 0xc7uy; 0x1auy; 0x02uy; 0x27uy; 0x20uy; 0x77uy; 0x10uy; 0xe5uy; 0xc8uy; 0xd4uy; 0x4auy; 0x47uy; 0xe5uy; 0xdfuy; 0x5fuy; 0x01uy; 0xaauy; 0xb0uy; 0xd4uy; 0x10uy; 0xbbuy; 0x69uy; 0xe3uy; 0x36uy; 0xc8uy; 0xe1uy; 0x3duy; 0x43uy; 0xfbuy; 0x86uy; 0xcduy; 0xccuy; 0xbfuy; 0xf4uy; 0x88uy; 0xe0uy; 0x20uy; 0xcauy; 0xb7uy; 0x1buy; 0xf1uy; 0x2fuy; 0x5cuy; 0xeeuy; 0xd4uy; 0xd3uy; 0xa3uy; 0xccuy; 0xa4uy; 0x1euy; 0x1cuy; 0x47uy; 0xfbuy; 0xbfuy; 0xfcuy; 0xa2uy; 0x41uy; 0x55uy; 0x9duy; 0xf6uy; 0x5auy; 0x5euy; 0x65uy; 0x32uy; 0x34uy; 0x7buy; 0x52uy; 0x8duy; 0xd5uy; 0xd0uy; 0x20uy; 0x60uy; 0x03uy; 0xabuy; 0x3fuy; 0x8cuy; 0xd4uy; 0x21uy; 0xeauy; 0x2auy; 0xd9uy; 0xc4uy; 0xd0uy; 0xd3uy; 0x65uy; 0xd8uy; 0x7auy; 0x13uy; 0x28uy; 0x62uy; 0x32uy; 0x4buy; 0x2cuy; 0x87uy; 0x93uy; 0xa8uy; 0xb4uy; 0x52uy; 0x45uy; 0x09uy; 0x44uy; 0xecuy; 0xecuy; 0xc3uy; 0x17uy; 0xdbuy; 0x9auy; 0x4duy; 0x5cuy; 0xa9uy; 0x11uy; 0xd4uy; 0x7duy; 0xafuy; 0x9euy; 0xf1uy; 0x2duy; 0xb2uy; 0x66uy; 0xc5uy; 0x1duy; 0xeduy; 0xb7uy; 0xcduy; 0x0buy; 0x25uy; 0x5euy; 0x30uy; 0x47uy; 0x3fuy; 0x40uy; 0xf4uy; 0xa1uy; 0xa0uy; 0x00uy; 0x94uy; 0x10uy; 0xc5uy; 0x6auy; 0x63uy; 0x1auy; 0xd5uy; 0x88uy; 0x92uy; 0x8euy; 0x82uy; 0x39uy; 0x87uy; 0x3cuy; 0x78uy; 0x65uy; 0x58uy; 0x42uy; 0x75uy; 0x5buy; 0xdduy; 0x77uy; 0x3euy; 0x09uy; 0x4euy; 0x76uy; 0x5buy; 0xe6uy; 0x0euy; 0x4duy; 0x38uy; 0xb2uy; 0xc0uy; 0xb8uy; 0x95uy; 0x01uy; 0x7auy; 0x10uy; 0xe0uy; 0xfbuy; 0x07uy; 0xf2uy; 0xabuy; 0x2duy; 0x8cuy; 0x32uy; 0xeduy; 0x2buy; 0xc0uy; 0x46uy; 0xc2uy; 0xf5uy; 0x38uy; 0x83uy; 0xf0uy; 0x17uy; 0xecuy; 0xc1uy; 0x20uy; 0x6auy; 0x9auy; 0x0buy; 0x00uy; 0xa0uy; 0x98uy; 0x22uy; 0x50uy; 0x23uy; 0xd5uy; 0x80uy; 0x6buy; 0xf6uy; 0x1fuy; 0xc3uy; 0xccuy; 0x97uy; 0xc9uy; 0x24uy; 0x9fuy; 0xf3uy; 0xafuy; 0x43uy; 0x14uy; 0xd5uy; 0xa0uy; ] in
assert_norm (List.Tot.length l = 1040);
B.gcmalloc_of_list HyperStack.root l | {
"file_name": "providers/test/vectors/Test.Vectors.Chacha20Poly1305.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 38,
"end_line": 402,
"start_col": 0,
"start_line": 399
} | module Test.Vectors.Chacha20Poly1305
module B = LowStar.Buffer
#set-options "--max_fuel 0 --max_ifuel 0"
let key0: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x1cuy; 0x92uy; 0x40uy; 0xa5uy; 0xebuy; 0x55uy; 0xd3uy; 0x8auy; 0xf3uy; 0x33uy; 0x88uy; 0x86uy; 0x04uy; 0xf6uy; 0xb5uy; 0xf0uy; 0x47uy; 0x39uy; 0x17uy; 0xc1uy; 0x40uy; 0x2buy; 0x80uy; 0x09uy; 0x9duy; 0xcauy; 0x5cuy; 0xbcuy; 0x20uy; 0x70uy; 0x75uy; 0xc0uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key0_len: (x:UInt32.t { UInt32.v x = B.length key0 }) =
32ul
let nonce0: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x01uy; 0x02uy; 0x03uy; 0x04uy; 0x05uy; 0x06uy; 0x07uy; 0x08uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce0_len: (x:UInt32.t { UInt32.v x = B.length nonce0 }) =
12ul
let aad0: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0xf3uy; 0x33uy; 0x88uy; 0x86uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x4euy; 0x91uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad0_len: (x:UInt32.t { UInt32.v x = B.length aad0 }) =
12ul
let input0: (b: B.buffer UInt8.t { B.length b = 265 /\ B.recallable b /\ B.disjoint b aad0 }) =
B.recall aad0;[@inline_let] let l = [ 0x49uy; 0x6euy; 0x74uy; 0x65uy; 0x72uy; 0x6euy; 0x65uy; 0x74uy; 0x2duy; 0x44uy; 0x72uy; 0x61uy; 0x66uy; 0x74uy; 0x73uy; 0x20uy; 0x61uy; 0x72uy; 0x65uy; 0x20uy; 0x64uy; 0x72uy; 0x61uy; 0x66uy; 0x74uy; 0x20uy; 0x64uy; 0x6fuy; 0x63uy; 0x75uy; 0x6duy; 0x65uy; 0x6euy; 0x74uy; 0x73uy; 0x20uy; 0x76uy; 0x61uy; 0x6cuy; 0x69uy; 0x64uy; 0x20uy; 0x66uy; 0x6fuy; 0x72uy; 0x20uy; 0x61uy; 0x20uy; 0x6duy; 0x61uy; 0x78uy; 0x69uy; 0x6duy; 0x75uy; 0x6duy; 0x20uy; 0x6fuy; 0x66uy; 0x20uy; 0x73uy; 0x69uy; 0x78uy; 0x20uy; 0x6duy; 0x6fuy; 0x6euy; 0x74uy; 0x68uy; 0x73uy; 0x20uy; 0x61uy; 0x6euy; 0x64uy; 0x20uy; 0x6duy; 0x61uy; 0x79uy; 0x20uy; 0x62uy; 0x65uy; 0x20uy; 0x75uy; 0x70uy; 0x64uy; 0x61uy; 0x74uy; 0x65uy; 0x64uy; 0x2cuy; 0x20uy; 0x72uy; 0x65uy; 0x70uy; 0x6cuy; 0x61uy; 0x63uy; 0x65uy; 0x64uy; 0x2cuy; 0x20uy; 0x6fuy; 0x72uy; 0x20uy; 0x6fuy; 0x62uy; 0x73uy; 0x6fuy; 0x6cuy; 0x65uy; 0x74uy; 0x65uy; 0x64uy; 0x20uy; 0x62uy; 0x79uy; 0x20uy; 0x6fuy; 0x74uy; 0x68uy; 0x65uy; 0x72uy; 0x20uy; 0x64uy; 0x6fuy; 0x63uy; 0x75uy; 0x6duy; 0x65uy; 0x6euy; 0x74uy; 0x73uy; 0x20uy; 0x61uy; 0x74uy; 0x20uy; 0x61uy; 0x6euy; 0x79uy; 0x20uy; 0x74uy; 0x69uy; 0x6duy; 0x65uy; 0x2euy; 0x20uy; 0x49uy; 0x74uy; 0x20uy; 0x69uy; 0x73uy; 0x20uy; 0x69uy; 0x6euy; 0x61uy; 0x70uy; 0x70uy; 0x72uy; 0x6fuy; 0x70uy; 0x72uy; 0x69uy; 0x61uy; 0x74uy; 0x65uy; 0x20uy; 0x74uy; 0x6fuy; 0x20uy; 0x75uy; 0x73uy; 0x65uy; 0x20uy; 0x49uy; 0x6euy; 0x74uy; 0x65uy; 0x72uy; 0x6euy; 0x65uy; 0x74uy; 0x2duy; 0x44uy; 0x72uy; 0x61uy; 0x66uy; 0x74uy; 0x73uy; 0x20uy; 0x61uy; 0x73uy; 0x20uy; 0x72uy; 0x65uy; 0x66uy; 0x65uy; 0x72uy; 0x65uy; 0x6euy; 0x63uy; 0x65uy; 0x20uy; 0x6duy; 0x61uy; 0x74uy; 0x65uy; 0x72uy; 0x69uy; 0x61uy; 0x6cuy; 0x20uy; 0x6fuy; 0x72uy; 0x20uy; 0x74uy; 0x6fuy; 0x20uy; 0x63uy; 0x69uy; 0x74uy; 0x65uy; 0x20uy; 0x74uy; 0x68uy; 0x65uy; 0x6duy; 0x20uy; 0x6fuy; 0x74uy; 0x68uy; 0x65uy; 0x72uy; 0x20uy; 0x74uy; 0x68uy; 0x61uy; 0x6euy; 0x20uy; 0x61uy; 0x73uy; 0x20uy; 0x2fuy; 0xe2uy; 0x80uy; 0x9cuy; 0x77uy; 0x6fuy; 0x72uy; 0x6buy; 0x20uy; 0x69uy; 0x6euy; 0x20uy; 0x70uy; 0x72uy; 0x6fuy; 0x67uy; 0x72uy; 0x65uy; 0x73uy; 0x73uy; 0x2euy; 0x2fuy; 0xe2uy; 0x80uy; 0x9duy; ] in
assert_norm (List.Tot.length l = 265);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input0_len: (x:UInt32.t { UInt32.v x = B.length input0 }) =
265ul
let output0: (b: B.buffer UInt8.t { B.length b = 281 /\ B.recallable b }) =
[@inline_let] let l = [ 0x64uy; 0xa0uy; 0x86uy; 0x15uy; 0x75uy; 0x86uy; 0x1auy; 0xf4uy; 0x60uy; 0xf0uy; 0x62uy; 0xc7uy; 0x9buy; 0xe6uy; 0x43uy; 0xbduy; 0x5euy; 0x80uy; 0x5cuy; 0xfduy; 0x34uy; 0x5cuy; 0xf3uy; 0x89uy; 0xf1uy; 0x08uy; 0x67uy; 0x0auy; 0xc7uy; 0x6cuy; 0x8cuy; 0xb2uy; 0x4cuy; 0x6cuy; 0xfcuy; 0x18uy; 0x75uy; 0x5duy; 0x43uy; 0xeeuy; 0xa0uy; 0x9euy; 0xe9uy; 0x4euy; 0x38uy; 0x2duy; 0x26uy; 0xb0uy; 0xbduy; 0xb7uy; 0xb7uy; 0x3cuy; 0x32uy; 0x1buy; 0x01uy; 0x00uy; 0xd4uy; 0xf0uy; 0x3buy; 0x7fuy; 0x35uy; 0x58uy; 0x94uy; 0xcfuy; 0x33uy; 0x2fuy; 0x83uy; 0x0euy; 0x71uy; 0x0buy; 0x97uy; 0xceuy; 0x98uy; 0xc8uy; 0xa8uy; 0x4auy; 0xbduy; 0x0buy; 0x94uy; 0x81uy; 0x14uy; 0xaduy; 0x17uy; 0x6euy; 0x00uy; 0x8duy; 0x33uy; 0xbduy; 0x60uy; 0xf9uy; 0x82uy; 0xb1uy; 0xffuy; 0x37uy; 0xc8uy; 0x55uy; 0x97uy; 0x97uy; 0xa0uy; 0x6euy; 0xf4uy; 0xf0uy; 0xefuy; 0x61uy; 0xc1uy; 0x86uy; 0x32uy; 0x4euy; 0x2buy; 0x35uy; 0x06uy; 0x38uy; 0x36uy; 0x06uy; 0x90uy; 0x7buy; 0x6auy; 0x7cuy; 0x02uy; 0xb0uy; 0xf9uy; 0xf6uy; 0x15uy; 0x7buy; 0x53uy; 0xc8uy; 0x67uy; 0xe4uy; 0xb9uy; 0x16uy; 0x6cuy; 0x76uy; 0x7buy; 0x80uy; 0x4duy; 0x46uy; 0xa5uy; 0x9buy; 0x52uy; 0x16uy; 0xcduy; 0xe7uy; 0xa4uy; 0xe9uy; 0x90uy; 0x40uy; 0xc5uy; 0xa4uy; 0x04uy; 0x33uy; 0x22uy; 0x5euy; 0xe2uy; 0x82uy; 0xa1uy; 0xb0uy; 0xa0uy; 0x6cuy; 0x52uy; 0x3euy; 0xafuy; 0x45uy; 0x34uy; 0xd7uy; 0xf8uy; 0x3fuy; 0xa1uy; 0x15uy; 0x5buy; 0x00uy; 0x47uy; 0x71uy; 0x8cuy; 0xbcuy; 0x54uy; 0x6auy; 0x0duy; 0x07uy; 0x2buy; 0x04uy; 0xb3uy; 0x56uy; 0x4euy; 0xeauy; 0x1buy; 0x42uy; 0x22uy; 0x73uy; 0xf5uy; 0x48uy; 0x27uy; 0x1auy; 0x0buy; 0xb2uy; 0x31uy; 0x60uy; 0x53uy; 0xfauy; 0x76uy; 0x99uy; 0x19uy; 0x55uy; 0xebuy; 0xd6uy; 0x31uy; 0x59uy; 0x43uy; 0x4euy; 0xceuy; 0xbbuy; 0x4euy; 0x46uy; 0x6duy; 0xaeuy; 0x5auy; 0x10uy; 0x73uy; 0xa6uy; 0x72uy; 0x76uy; 0x27uy; 0x09uy; 0x7auy; 0x10uy; 0x49uy; 0xe6uy; 0x17uy; 0xd9uy; 0x1duy; 0x36uy; 0x10uy; 0x94uy; 0xfauy; 0x68uy; 0xf0uy; 0xffuy; 0x77uy; 0x98uy; 0x71uy; 0x30uy; 0x30uy; 0x5buy; 0xeauy; 0xbauy; 0x2euy; 0xdauy; 0x04uy; 0xdfuy; 0x99uy; 0x7buy; 0x71uy; 0x4duy; 0x6cuy; 0x6fuy; 0x2cuy; 0x29uy; 0xa6uy; 0xaduy; 0x5cuy; 0xb4uy; 0x02uy; 0x2buy; 0x02uy; 0x70uy; 0x9buy; 0xeeuy; 0xaduy; 0x9duy; 0x67uy; 0x89uy; 0x0cuy; 0xbbuy; 0x22uy; 0x39uy; 0x23uy; 0x36uy; 0xfeuy; 0xa1uy; 0x85uy; 0x1fuy; 0x38uy; ] in
assert_norm (List.Tot.length l = 281);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output0_len: (x:UInt32.t { UInt32.v x = B.length output0 }) =
281ul
let key1: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x4cuy; 0xf5uy; 0x96uy; 0x83uy; 0x38uy; 0xe6uy; 0xaeuy; 0x7fuy; 0x2duy; 0x29uy; 0x25uy; 0x76uy; 0xd5uy; 0x75uy; 0x27uy; 0x86uy; 0x91uy; 0x9auy; 0x27uy; 0x7auy; 0xfbuy; 0x46uy; 0xc5uy; 0xefuy; 0x94uy; 0x81uy; 0x79uy; 0x57uy; 0x14uy; 0x59uy; 0x40uy; 0x68uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key1_len: (x:UInt32.t { UInt32.v x = B.length key1 }) =
32ul
let nonce1: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xcauy; 0xbfuy; 0x33uy; 0x71uy; 0x32uy; 0x45uy; 0x77uy; 0x8euy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce1_len: (x:UInt32.t { UInt32.v x = B.length nonce1 }) =
12ul
let aad1: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b }) =
[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad1_len: (x:UInt32.t { UInt32.v x = B.length aad1 }) =
0ul
let input1: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b /\ B.disjoint b aad1 }) =
B.recall aad1;[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input1_len: (x:UInt32.t { UInt32.v x = B.length input1 }) =
0ul
let output1: (b: B.buffer UInt8.t { B.length b = 16 /\ B.recallable b }) =
[@inline_let] let l = [ 0xeauy; 0xe0uy; 0x1euy; 0x9euy; 0x2cuy; 0x91uy; 0xaauy; 0xe1uy; 0xdbuy; 0x5duy; 0x99uy; 0x3fuy; 0x8auy; 0xf7uy; 0x69uy; 0x92uy; ] in
assert_norm (List.Tot.length l = 16);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output1_len: (x:UInt32.t { UInt32.v x = B.length output1 }) =
16ul
let key2: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x2duy; 0xb0uy; 0x5duy; 0x40uy; 0xc8uy; 0xeduy; 0x44uy; 0x88uy; 0x34uy; 0xd1uy; 0x13uy; 0xafuy; 0x57uy; 0xa1uy; 0xebuy; 0x3auy; 0x2auy; 0x80uy; 0x51uy; 0x36uy; 0xecuy; 0x5buy; 0xbcuy; 0x08uy; 0x93uy; 0x84uy; 0x21uy; 0xb5uy; 0x13uy; 0x88uy; 0x3cuy; 0x0duy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key2_len: (x:UInt32.t { UInt32.v x = B.length key2 }) =
32ul
let nonce2: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x3duy; 0x86uy; 0xb5uy; 0x6buy; 0xc8uy; 0xa3uy; 0x1fuy; 0x1duy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce2_len: (x:UInt32.t { UInt32.v x = B.length nonce2 }) =
12ul
let aad2: (b: B.buffer UInt8.t { B.length b = 8 /\ B.recallable b }) =
[@inline_let] let l = [ 0x33uy; 0x10uy; 0x41uy; 0x12uy; 0x1fuy; 0xf3uy; 0xd2uy; 0x6buy; ] in
assert_norm (List.Tot.length l = 8);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad2_len: (x:UInt32.t { UInt32.v x = B.length aad2 }) =
8ul
let input2: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b /\ B.disjoint b aad2 }) =
B.recall aad2;[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input2_len: (x:UInt32.t { UInt32.v x = B.length input2 }) =
0ul
let output2: (b: B.buffer UInt8.t { B.length b = 16 /\ B.recallable b }) =
[@inline_let] let l = [ 0xdduy; 0x6buy; 0x3buy; 0x82uy; 0xceuy; 0x5auy; 0xbduy; 0xd6uy; 0xa9uy; 0x35uy; 0x83uy; 0xd8uy; 0x8cuy; 0x3duy; 0x85uy; 0x77uy; ] in
assert_norm (List.Tot.length l = 16);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output2_len: (x:UInt32.t { UInt32.v x = B.length output2 }) =
16ul
let key3: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x4buy; 0x28uy; 0x4buy; 0xa3uy; 0x7buy; 0xbeuy; 0xe9uy; 0xf8uy; 0x31uy; 0x80uy; 0x82uy; 0xd7uy; 0xd8uy; 0xe8uy; 0xb5uy; 0xa1uy; 0xe2uy; 0x18uy; 0x18uy; 0x8auy; 0x9cuy; 0xfauy; 0xa3uy; 0x3duy; 0x25uy; 0x71uy; 0x3euy; 0x40uy; 0xbcuy; 0x54uy; 0x7auy; 0x3euy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key3_len: (x:UInt32.t { UInt32.v x = B.length key3 }) =
32ul
let nonce3: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xd2uy; 0x32uy; 0x1fuy; 0x29uy; 0x28uy; 0xc6uy; 0xc4uy; 0xc4uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce3_len: (x:UInt32.t { UInt32.v x = B.length nonce3 }) =
12ul
let aad3: (b: B.buffer UInt8.t { B.length b = 8 /\ B.recallable b }) =
[@inline_let] let l = [ 0x6auy; 0xe2uy; 0xaduy; 0x3fuy; 0x88uy; 0x39uy; 0x5auy; 0x40uy; ] in
assert_norm (List.Tot.length l = 8);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad3_len: (x:UInt32.t { UInt32.v x = B.length aad3 }) =
8ul
let input3: (b: B.buffer UInt8.t { B.length b = 1 /\ B.recallable b /\ B.disjoint b aad3 }) =
B.recall aad3;[@inline_let] let l = [ 0xa4uy; ] in
assert_norm (List.Tot.length l = 1);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input3_len: (x:UInt32.t { UInt32.v x = B.length input3 }) =
1ul
let output3: (b: B.buffer UInt8.t { B.length b = 17 /\ B.recallable b }) =
[@inline_let] let l = [ 0xb7uy; 0x1buy; 0xb0uy; 0x73uy; 0x59uy; 0xb0uy; 0x84uy; 0xb2uy; 0x6duy; 0x8euy; 0xabuy; 0x94uy; 0x31uy; 0xa1uy; 0xaeuy; 0xacuy; 0x89uy; ] in
assert_norm (List.Tot.length l = 17);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output3_len: (x:UInt32.t { UInt32.v x = B.length output3 }) =
17ul
let key4: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x66uy; 0xcauy; 0x9cuy; 0x23uy; 0x2auy; 0x4buy; 0x4buy; 0x31uy; 0x0euy; 0x92uy; 0x89uy; 0x8buy; 0xf4uy; 0x93uy; 0xc7uy; 0x87uy; 0x98uy; 0xa3uy; 0xd8uy; 0x39uy; 0xf8uy; 0xf4uy; 0xa7uy; 0x01uy; 0xc0uy; 0x2euy; 0x0auy; 0xa6uy; 0x7euy; 0x5auy; 0x78uy; 0x87uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key4_len: (x:UInt32.t { UInt32.v x = B.length key4 }) =
32ul
let nonce4: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x20uy; 0x1cuy; 0xaauy; 0x5fuy; 0x9cuy; 0xbfuy; 0x92uy; 0x30uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce4_len: (x:UInt32.t { UInt32.v x = B.length nonce4 }) =
12ul
let aad4: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b }) =
[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad4_len: (x:UInt32.t { UInt32.v x = B.length aad4 }) =
0ul
let input4: (b: B.buffer UInt8.t { B.length b = 1 /\ B.recallable b /\ B.disjoint b aad4 }) =
B.recall aad4;[@inline_let] let l = [ 0x2duy; ] in
assert_norm (List.Tot.length l = 1);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input4_len: (x:UInt32.t { UInt32.v x = B.length input4 }) =
1ul
let output4: (b: B.buffer UInt8.t { B.length b = 17 /\ B.recallable b }) =
[@inline_let] let l = [ 0xbfuy; 0xe1uy; 0x5buy; 0x0buy; 0xdbuy; 0x6buy; 0xf5uy; 0x5euy; 0x6cuy; 0x5duy; 0x84uy; 0x44uy; 0x39uy; 0x81uy; 0xc1uy; 0x9cuy; 0xacuy; ] in
assert_norm (List.Tot.length l = 17);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output4_len: (x:UInt32.t { UInt32.v x = B.length output4 }) =
17ul
let key5: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x68uy; 0x7buy; 0x8duy; 0x8euy; 0xe3uy; 0xc4uy; 0xdduy; 0xaeuy; 0xdfuy; 0x72uy; 0x7fuy; 0x53uy; 0x72uy; 0x25uy; 0x1euy; 0x78uy; 0x91uy; 0xcbuy; 0x69uy; 0x76uy; 0x1fuy; 0x49uy; 0x93uy; 0xf9uy; 0x6fuy; 0x21uy; 0xccuy; 0x39uy; 0x9cuy; 0xaduy; 0xb1uy; 0x01uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key5_len: (x:UInt32.t { UInt32.v x = B.length key5 }) =
32ul
let nonce5: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xdfuy; 0x51uy; 0x84uy; 0x82uy; 0x42uy; 0x0cuy; 0x75uy; 0x9cuy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce5_len: (x:UInt32.t { UInt32.v x = B.length nonce5 }) =
12ul
let aad5: (b: B.buffer UInt8.t { B.length b = 7 /\ B.recallable b }) =
[@inline_let] let l = [ 0x70uy; 0xd3uy; 0x33uy; 0xf3uy; 0x8buy; 0x18uy; 0x0buy; ] in
assert_norm (List.Tot.length l = 7);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad5_len: (x:UInt32.t { UInt32.v x = B.length aad5 }) =
7ul
let input5: (b: B.buffer UInt8.t { B.length b = 129 /\ B.recallable b /\ B.disjoint b aad5 }) =
B.recall aad5;[@inline_let] let l = [ 0x33uy; 0x2fuy; 0x94uy; 0xc1uy; 0xa4uy; 0xefuy; 0xccuy; 0x2auy; 0x5buy; 0xa6uy; 0xe5uy; 0x8fuy; 0x1duy; 0x40uy; 0xf0uy; 0x92uy; 0x3cuy; 0xd9uy; 0x24uy; 0x11uy; 0xa9uy; 0x71uy; 0xf9uy; 0x37uy; 0x14uy; 0x99uy; 0xfauy; 0xbeuy; 0xe6uy; 0x80uy; 0xdeuy; 0x50uy; 0xc9uy; 0x96uy; 0xd4uy; 0xb0uy; 0xecuy; 0x9euy; 0x17uy; 0xecuy; 0xd2uy; 0x5euy; 0x72uy; 0x99uy; 0xfcuy; 0x0auy; 0xe1uy; 0xcbuy; 0x48uy; 0xd2uy; 0x85uy; 0xdduy; 0x2fuy; 0x90uy; 0xe0uy; 0x66uy; 0x3buy; 0xe6uy; 0x20uy; 0x74uy; 0xbeuy; 0x23uy; 0x8fuy; 0xcbuy; 0xb4uy; 0xe4uy; 0xdauy; 0x48uy; 0x40uy; 0xa6uy; 0xd1uy; 0x1buy; 0xc7uy; 0x42uy; 0xceuy; 0x2fuy; 0x0cuy; 0xa6uy; 0x85uy; 0x6euy; 0x87uy; 0x37uy; 0x03uy; 0xb1uy; 0x7cuy; 0x25uy; 0x96uy; 0xa3uy; 0x05uy; 0xd8uy; 0xb0uy; 0xf4uy; 0xeduy; 0xeauy; 0xc2uy; 0xf0uy; 0x31uy; 0x98uy; 0x6cuy; 0xd1uy; 0x14uy; 0x25uy; 0xc0uy; 0xcbuy; 0x01uy; 0x74uy; 0xd0uy; 0x82uy; 0xf4uy; 0x36uy; 0xf5uy; 0x41uy; 0xd5uy; 0xdcuy; 0xcauy; 0xc5uy; 0xbbuy; 0x98uy; 0xfeuy; 0xfcuy; 0x69uy; 0x21uy; 0x70uy; 0xd8uy; 0xa4uy; 0x4buy; 0xc8uy; 0xdeuy; 0x8fuy; ] in
assert_norm (List.Tot.length l = 129);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input5_len: (x:UInt32.t { UInt32.v x = B.length input5 }) =
129ul
let output5: (b: B.buffer UInt8.t { B.length b = 145 /\ B.recallable b }) =
[@inline_let] let l = [ 0x8buy; 0x06uy; 0xd3uy; 0x31uy; 0xb0uy; 0x93uy; 0x45uy; 0xb1uy; 0x75uy; 0x6euy; 0x26uy; 0xf9uy; 0x67uy; 0xbcuy; 0x90uy; 0x15uy; 0x81uy; 0x2cuy; 0xb5uy; 0xf0uy; 0xc6uy; 0x2buy; 0xc7uy; 0x8cuy; 0x56uy; 0xd1uy; 0xbfuy; 0x69uy; 0x6cuy; 0x07uy; 0xa0uy; 0xdauy; 0x65uy; 0x27uy; 0xc9uy; 0x90uy; 0x3duy; 0xefuy; 0x4buy; 0x11uy; 0x0fuy; 0x19uy; 0x07uy; 0xfduy; 0x29uy; 0x92uy; 0xd9uy; 0xc8uy; 0xf7uy; 0x99uy; 0x2euy; 0x4auy; 0xd0uy; 0xb8uy; 0x2cuy; 0xdcuy; 0x93uy; 0xf5uy; 0x9euy; 0x33uy; 0x78uy; 0xd1uy; 0x37uy; 0xc3uy; 0x66uy; 0xd7uy; 0x5euy; 0xbcuy; 0x44uy; 0xbfuy; 0x53uy; 0xa5uy; 0xbcuy; 0xc4uy; 0xcbuy; 0x7buy; 0x3auy; 0x8euy; 0x7fuy; 0x02uy; 0xbduy; 0xbbuy; 0xe7uy; 0xcauy; 0xa6uy; 0x6cuy; 0x6buy; 0x93uy; 0x21uy; 0x93uy; 0x10uy; 0x61uy; 0xe7uy; 0x69uy; 0xd0uy; 0x78uy; 0xf3uy; 0x07uy; 0x5auy; 0x1auy; 0x8fuy; 0x73uy; 0xaauy; 0xb1uy; 0x4euy; 0xd3uy; 0xdauy; 0x4fuy; 0xf3uy; 0x32uy; 0xe1uy; 0x66uy; 0x3euy; 0x6cuy; 0xc6uy; 0x13uy; 0xbauy; 0x06uy; 0x5buy; 0xfcuy; 0x6auy; 0xe5uy; 0x6fuy; 0x60uy; 0xfbuy; 0x07uy; 0x40uy; 0xb0uy; 0x8cuy; 0x9duy; 0x84uy; 0x43uy; 0x6buy; 0xc1uy; 0xf7uy; 0x8duy; 0x8duy; 0x31uy; 0xf7uy; 0x7auy; 0x39uy; 0x4duy; 0x8fuy; 0x9auy; 0xebuy; ] in
assert_norm (List.Tot.length l = 145);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output5_len: (x:UInt32.t { UInt32.v x = B.length output5 }) =
145ul
let key6: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x8duy; 0xb8uy; 0x91uy; 0x48uy; 0xf0uy; 0xe7uy; 0x0auy; 0xbduy; 0xf9uy; 0x3fuy; 0xcduy; 0xd9uy; 0xa0uy; 0x1euy; 0x42uy; 0x4cuy; 0xe7uy; 0xdeuy; 0x25uy; 0x3duy; 0xa3uy; 0xd7uy; 0x05uy; 0x80uy; 0x8duy; 0xf2uy; 0x82uy; 0xacuy; 0x44uy; 0x16uy; 0x51uy; 0x01uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key6_len: (x:UInt32.t { UInt32.v x = B.length key6 }) =
32ul
let nonce6: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xdeuy; 0x7buy; 0xefuy; 0xc3uy; 0x65uy; 0x1buy; 0x68uy; 0xb0uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce6_len: (x:UInt32.t { UInt32.v x = B.length nonce6 }) =
12ul
let aad6: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b }) =
[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad6_len: (x:UInt32.t { UInt32.v x = B.length aad6 }) =
0ul
let input6: (b: B.buffer UInt8.t { B.length b = 256 /\ B.recallable b /\ B.disjoint b aad6 }) =
B.recall aad6;[@inline_let] let l = [ 0x9buy; 0x18uy; 0xdbuy; 0xdduy; 0x9auy; 0x0fuy; 0x3euy; 0xa5uy; 0x15uy; 0x17uy; 0xdeuy; 0xdfuy; 0x08uy; 0x9duy; 0x65uy; 0x0auy; 0x67uy; 0x30uy; 0x12uy; 0xe2uy; 0x34uy; 0x77uy; 0x4buy; 0xc1uy; 0xd9uy; 0xc6uy; 0x1fuy; 0xabuy; 0xc6uy; 0x18uy; 0x50uy; 0x17uy; 0xa7uy; 0x9duy; 0x3cuy; 0xa6uy; 0xc5uy; 0x35uy; 0x8cuy; 0x1cuy; 0xc0uy; 0xa1uy; 0x7cuy; 0x9fuy; 0x03uy; 0x89uy; 0xcauy; 0xe1uy; 0xe6uy; 0xe9uy; 0xd4uy; 0xd3uy; 0x88uy; 0xdbuy; 0xb4uy; 0x51uy; 0x9duy; 0xecuy; 0xb4uy; 0xfcuy; 0x52uy; 0xeeuy; 0x6duy; 0xf1uy; 0x75uy; 0x42uy; 0xc6uy; 0xfduy; 0xbduy; 0x7auy; 0x8euy; 0x86uy; 0xfcuy; 0x44uy; 0xb3uy; 0x4fuy; 0xf3uy; 0xeauy; 0x67uy; 0x5auy; 0x41uy; 0x13uy; 0xbauy; 0xb0uy; 0xdcuy; 0xe1uy; 0xd3uy; 0x2auy; 0x7cuy; 0x22uy; 0xb3uy; 0xcauy; 0xacuy; 0x6auy; 0x37uy; 0x98uy; 0x3euy; 0x1duy; 0x40uy; 0x97uy; 0xf7uy; 0x9buy; 0x1duy; 0x36uy; 0x6buy; 0xb3uy; 0x28uy; 0xbduy; 0x60uy; 0x82uy; 0x47uy; 0x34uy; 0xaauy; 0x2fuy; 0x7duy; 0xe9uy; 0xa8uy; 0x70uy; 0x81uy; 0x57uy; 0xd4uy; 0xb9uy; 0x77uy; 0x0auy; 0x9duy; 0x29uy; 0xa7uy; 0x84uy; 0x52uy; 0x4fuy; 0xc2uy; 0x4auy; 0x40uy; 0x3buy; 0x3cuy; 0xd4uy; 0xc9uy; 0x2auy; 0xdbuy; 0x4auy; 0x53uy; 0xc4uy; 0xbeuy; 0x80uy; 0xe9uy; 0x51uy; 0x7fuy; 0x8fuy; 0xc7uy; 0xa2uy; 0xceuy; 0x82uy; 0x5cuy; 0x91uy; 0x1euy; 0x74uy; 0xd9uy; 0xd0uy; 0xbduy; 0xd5uy; 0xf3uy; 0xfduy; 0xdauy; 0x4duy; 0x25uy; 0xb4uy; 0xbbuy; 0x2duy; 0xacuy; 0x2fuy; 0x3duy; 0x71uy; 0x85uy; 0x7buy; 0xcfuy; 0x3cuy; 0x7buy; 0x3euy; 0x0euy; 0x22uy; 0x78uy; 0x0cuy; 0x29uy; 0xbfuy; 0xe4uy; 0xf4uy; 0x57uy; 0xb3uy; 0xcbuy; 0x49uy; 0xa0uy; 0xfcuy; 0x1euy; 0x05uy; 0x4euy; 0x16uy; 0xbcuy; 0xd5uy; 0xa8uy; 0xa3uy; 0xeeuy; 0x05uy; 0x35uy; 0xc6uy; 0x7cuy; 0xabuy; 0x60uy; 0x14uy; 0x55uy; 0x1auy; 0x8euy; 0xc5uy; 0x88uy; 0x5duy; 0xd5uy; 0x81uy; 0xc2uy; 0x81uy; 0xa5uy; 0xc4uy; 0x60uy; 0xdbuy; 0xafuy; 0x77uy; 0x91uy; 0xe1uy; 0xceuy; 0xa2uy; 0x7euy; 0x7fuy; 0x42uy; 0xe3uy; 0xb0uy; 0x13uy; 0x1cuy; 0x1fuy; 0x25uy; 0x60uy; 0x21uy; 0xe2uy; 0x40uy; 0x5fuy; 0x99uy; 0xb7uy; 0x73uy; 0xecuy; 0x9buy; 0x2buy; 0xf0uy; 0x65uy; 0x11uy; 0xc8uy; 0xd0uy; 0x0auy; 0x9fuy; 0xd3uy; ] in
assert_norm (List.Tot.length l = 256);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input6_len: (x:UInt32.t { UInt32.v x = B.length input6 }) =
256ul
let output6: (b: B.buffer UInt8.t { B.length b = 272 /\ B.recallable b }) =
[@inline_let] let l = [ 0x85uy; 0x04uy; 0xc2uy; 0xeduy; 0x8duy; 0xfduy; 0x97uy; 0x5cuy; 0xd2uy; 0xb7uy; 0xe2uy; 0xc1uy; 0x6buy; 0xa3uy; 0xbauy; 0xf8uy; 0xc9uy; 0x50uy; 0xc3uy; 0xc6uy; 0xa5uy; 0xe3uy; 0xa4uy; 0x7cuy; 0xc3uy; 0x23uy; 0x49uy; 0x5euy; 0xa9uy; 0xb9uy; 0x32uy; 0xebuy; 0x8auy; 0x7cuy; 0xcauy; 0xe5uy; 0xecuy; 0xfbuy; 0x7cuy; 0xc0uy; 0xcbuy; 0x7duy; 0xdcuy; 0x2cuy; 0x9duy; 0x92uy; 0x55uy; 0x21uy; 0x0auy; 0xc8uy; 0x43uy; 0x63uy; 0x59uy; 0x0auy; 0x31uy; 0x70uy; 0x82uy; 0x67uy; 0x41uy; 0x03uy; 0xf8uy; 0xdfuy; 0xf2uy; 0xacuy; 0xa7uy; 0x02uy; 0xd4uy; 0xd5uy; 0x8auy; 0x2duy; 0xc8uy; 0x99uy; 0x19uy; 0x66uy; 0xd0uy; 0xf6uy; 0x88uy; 0x2cuy; 0x77uy; 0xd9uy; 0xd4uy; 0x0duy; 0x6cuy; 0xbduy; 0x98uy; 0xdeuy; 0xe7uy; 0x7fuy; 0xaduy; 0x7euy; 0x8auy; 0xfbuy; 0xe9uy; 0x4buy; 0xe5uy; 0xf7uy; 0xe5uy; 0x50uy; 0xa0uy; 0x90uy; 0x3fuy; 0xd6uy; 0x22uy; 0x53uy; 0xe3uy; 0xfeuy; 0x1buy; 0xccuy; 0x79uy; 0x3buy; 0xecuy; 0x12uy; 0x47uy; 0x52uy; 0xa7uy; 0xd6uy; 0x04uy; 0xe3uy; 0x52uy; 0xe6uy; 0x93uy; 0x90uy; 0x91uy; 0x32uy; 0x73uy; 0x79uy; 0xb8uy; 0xd0uy; 0x31uy; 0xdeuy; 0x1fuy; 0x9fuy; 0x2fuy; 0x05uy; 0x38uy; 0x54uy; 0x2fuy; 0x35uy; 0x04uy; 0x39uy; 0xe0uy; 0xa7uy; 0xbauy; 0xc6uy; 0x52uy; 0xf6uy; 0x37uy; 0x65uy; 0x4cuy; 0x07uy; 0xa9uy; 0x7euy; 0xb3uy; 0x21uy; 0x6fuy; 0x74uy; 0x8cuy; 0xc9uy; 0xdeuy; 0xdbuy; 0x65uy; 0x1buy; 0x9buy; 0xaauy; 0x60uy; 0xb1uy; 0x03uy; 0x30uy; 0x6buy; 0xb2uy; 0x03uy; 0xc4uy; 0x1cuy; 0x04uy; 0xf8uy; 0x0fuy; 0x64uy; 0xafuy; 0x46uy; 0xe4uy; 0x65uy; 0x99uy; 0x49uy; 0xe2uy; 0xeauy; 0xceuy; 0x78uy; 0x00uy; 0xd8uy; 0x8buy; 0xd5uy; 0x2euy; 0xcfuy; 0xfcuy; 0x40uy; 0x49uy; 0xe8uy; 0x58uy; 0xdcuy; 0x34uy; 0x9cuy; 0x8cuy; 0x61uy; 0xbfuy; 0x0auy; 0x8euy; 0xecuy; 0x39uy; 0xa9uy; 0x30uy; 0x05uy; 0x5auy; 0xd2uy; 0x56uy; 0x01uy; 0xc7uy; 0xdauy; 0x8fuy; 0x4euy; 0xbbuy; 0x43uy; 0xa3uy; 0x3auy; 0xf9uy; 0x15uy; 0x2auy; 0xd0uy; 0xa0uy; 0x7auy; 0x87uy; 0x34uy; 0x82uy; 0xfeuy; 0x8auy; 0xd1uy; 0x2duy; 0x5euy; 0xc7uy; 0xbfuy; 0x04uy; 0x53uy; 0x5fuy; 0x3buy; 0x36uy; 0xd4uy; 0x25uy; 0x5cuy; 0x34uy; 0x7auy; 0x8duy; 0xd5uy; 0x05uy; 0xceuy; 0x72uy; 0xcauy; 0xefuy; 0x7auy; 0x4buy; 0xbcuy; 0xb0uy; 0x10uy; 0x5cuy; 0x96uy; 0x42uy; 0x3auy; 0x00uy; 0x98uy; 0xcduy; 0x15uy; 0xe8uy; 0xb7uy; 0x53uy; ] in
assert_norm (List.Tot.length l = 272);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output6_len: (x:UInt32.t { UInt32.v x = B.length output6 }) =
272ul
let key7: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0xf2uy; 0xaauy; 0x4fuy; 0x99uy; 0xfduy; 0x3euy; 0xa8uy; 0x53uy; 0xc1uy; 0x44uy; 0xe9uy; 0x81uy; 0x18uy; 0xdcuy; 0xf5uy; 0xf0uy; 0x3euy; 0x44uy; 0x15uy; 0x59uy; 0xe0uy; 0xc5uy; 0x44uy; 0x86uy; 0xc3uy; 0x91uy; 0xa8uy; 0x75uy; 0xc0uy; 0x12uy; 0x46uy; 0xbauy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key7_len: (x:UInt32.t { UInt32.v x = B.length key7 }) =
32ul
let nonce7: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0x0euy; 0x0duy; 0x57uy; 0xbbuy; 0x7buy; 0x40uy; 0x54uy; 0x02uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce7_len: (x:UInt32.t { UInt32.v x = B.length nonce7 }) =
12ul
let aad7: (b: B.buffer UInt8.t { B.length b = 0 /\ B.recallable b }) =
[@inline_let] let l = [ ] in
assert_norm (List.Tot.length l = 0);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad7_len: (x:UInt32.t { UInt32.v x = B.length aad7 }) =
0ul
let input7: (b: B.buffer UInt8.t { B.length b = 512 /\ B.recallable b /\ B.disjoint b aad7 }) =
B.recall aad7;[@inline_let] let l = [ 0xc3uy; 0x09uy; 0x94uy; 0x62uy; 0xe6uy; 0x46uy; 0x2euy; 0x10uy; 0xbeuy; 0x00uy; 0xe4uy; 0xfcuy; 0xf3uy; 0x40uy; 0xa3uy; 0xe2uy; 0x0fuy; 0xc2uy; 0x8buy; 0x28uy; 0xdcuy; 0xbauy; 0xb4uy; 0x3cuy; 0xe4uy; 0x21uy; 0x58uy; 0x61uy; 0xcduy; 0x8buy; 0xcduy; 0xfbuy; 0xacuy; 0x94uy; 0xa1uy; 0x45uy; 0xf5uy; 0x1cuy; 0xe1uy; 0x12uy; 0xe0uy; 0x3buy; 0x67uy; 0x21uy; 0x54uy; 0x5euy; 0x8cuy; 0xaauy; 0xcfuy; 0xdbuy; 0xb4uy; 0x51uy; 0xd4uy; 0x13uy; 0xdauy; 0xe6uy; 0x83uy; 0x89uy; 0xb6uy; 0x92uy; 0xe9uy; 0x21uy; 0x76uy; 0xa4uy; 0x93uy; 0x7duy; 0x0euy; 0xfduy; 0x96uy; 0x36uy; 0x03uy; 0x91uy; 0x43uy; 0x5cuy; 0x92uy; 0x49uy; 0x62uy; 0x61uy; 0x7buy; 0xebuy; 0x43uy; 0x89uy; 0xb8uy; 0x12uy; 0x20uy; 0x43uy; 0xd4uy; 0x47uy; 0x06uy; 0x84uy; 0xeeuy; 0x47uy; 0xe9uy; 0x8auy; 0x73uy; 0x15uy; 0x0fuy; 0x72uy; 0xcfuy; 0xeduy; 0xceuy; 0x96uy; 0xb2uy; 0x7fuy; 0x21uy; 0x45uy; 0x76uy; 0xebuy; 0x26uy; 0x28uy; 0x83uy; 0x6auy; 0xaduy; 0xaauy; 0xa6uy; 0x81uy; 0xd8uy; 0x55uy; 0xb1uy; 0xa3uy; 0x85uy; 0xb3uy; 0x0cuy; 0xdfuy; 0xf1uy; 0x69uy; 0x2duy; 0x97uy; 0x05uy; 0x2auy; 0xbcuy; 0x7cuy; 0x7buy; 0x25uy; 0xf8uy; 0x80uy; 0x9duy; 0x39uy; 0x25uy; 0xf3uy; 0x62uy; 0xf0uy; 0x66uy; 0x5euy; 0xf4uy; 0xa0uy; 0xcfuy; 0xd8uy; 0xfduy; 0x4fuy; 0xb1uy; 0x1fuy; 0x60uy; 0x3auy; 0x08uy; 0x47uy; 0xafuy; 0xe1uy; 0xf6uy; 0x10uy; 0x77uy; 0x09uy; 0xa7uy; 0x27uy; 0x8fuy; 0x9auy; 0x97uy; 0x5auy; 0x26uy; 0xfauy; 0xfeuy; 0x41uy; 0x32uy; 0x83uy; 0x10uy; 0xe0uy; 0x1duy; 0xbfuy; 0x64uy; 0x0duy; 0xf4uy; 0x1cuy; 0x32uy; 0x35uy; 0xe5uy; 0x1buy; 0x36uy; 0xefuy; 0xd4uy; 0x4auy; 0x93uy; 0x4duy; 0x00uy; 0x7cuy; 0xecuy; 0x02uy; 0x07uy; 0x8buy; 0x5duy; 0x7duy; 0x1buy; 0x0euy; 0xd1uy; 0xa6uy; 0xa5uy; 0x5duy; 0x7duy; 0x57uy; 0x88uy; 0xa8uy; 0xccuy; 0x81uy; 0xb4uy; 0x86uy; 0x4euy; 0xb4uy; 0x40uy; 0xe9uy; 0x1duy; 0xc3uy; 0xb1uy; 0x24uy; 0x3euy; 0x7fuy; 0xccuy; 0x8auy; 0x24uy; 0x9buy; 0xdfuy; 0x6duy; 0xf0uy; 0x39uy; 0x69uy; 0x3euy; 0x4cuy; 0xc0uy; 0x96uy; 0xe4uy; 0x13uy; 0xdauy; 0x90uy; 0xdauy; 0xf4uy; 0x95uy; 0x66uy; 0x8buy; 0x17uy; 0x17uy; 0xfeuy; 0x39uy; 0x43uy; 0x25uy; 0xaauy; 0xdauy; 0xa0uy; 0x43uy; 0x3cuy; 0xb1uy; 0x41uy; 0x02uy; 0xa3uy; 0xf0uy; 0xa7uy; 0x19uy; 0x59uy; 0xbcuy; 0x1duy; 0x7duy; 0x6cuy; 0x6duy; 0x91uy; 0x09uy; 0x5cuy; 0xb7uy; 0x5buy; 0x01uy; 0xd1uy; 0x6fuy; 0x17uy; 0x21uy; 0x97uy; 0xbfuy; 0x89uy; 0x71uy; 0xa5uy; 0xb0uy; 0x6euy; 0x07uy; 0x45uy; 0xfduy; 0x9duy; 0xeauy; 0x07uy; 0xf6uy; 0x7auy; 0x9fuy; 0x10uy; 0x18uy; 0x22uy; 0x30uy; 0x73uy; 0xacuy; 0xd4uy; 0x6buy; 0x72uy; 0x44uy; 0xeduy; 0xd9uy; 0x19uy; 0x9buy; 0x2duy; 0x4auy; 0x41uy; 0xdduy; 0xd1uy; 0x85uy; 0x5euy; 0x37uy; 0x19uy; 0xeduy; 0xd2uy; 0x15uy; 0x8fuy; 0x5euy; 0x91uy; 0xdbuy; 0x33uy; 0xf2uy; 0xe4uy; 0xdbuy; 0xffuy; 0x98uy; 0xfbuy; 0xa3uy; 0xb5uy; 0xcauy; 0x21uy; 0x69uy; 0x08uy; 0xe7uy; 0x8auy; 0xdfuy; 0x90uy; 0xffuy; 0x3euy; 0xe9uy; 0x20uy; 0x86uy; 0x3cuy; 0xe9uy; 0xfcuy; 0x0buy; 0xfeuy; 0x5cuy; 0x61uy; 0xaauy; 0x13uy; 0x92uy; 0x7fuy; 0x7buy; 0xecuy; 0xe0uy; 0x6duy; 0xa8uy; 0x23uy; 0x22uy; 0xf6uy; 0x6buy; 0x77uy; 0xc4uy; 0xfeuy; 0x40uy; 0x07uy; 0x3buy; 0xb6uy; 0xf6uy; 0x8euy; 0x5fuy; 0xd4uy; 0xb9uy; 0xb7uy; 0x0fuy; 0x21uy; 0x04uy; 0xefuy; 0x83uy; 0x63uy; 0x91uy; 0x69uy; 0x40uy; 0xa3uy; 0x48uy; 0x5cuy; 0xd2uy; 0x60uy; 0xf9uy; 0x4fuy; 0x6cuy; 0x47uy; 0x8buy; 0x3buy; 0xb1uy; 0x9fuy; 0x8euy; 0xeeuy; 0x16uy; 0x8auy; 0x13uy; 0xfcuy; 0x46uy; 0x17uy; 0xc3uy; 0xc3uy; 0x32uy; 0x56uy; 0xf8uy; 0x3cuy; 0x85uy; 0x3auy; 0xb6uy; 0x3euy; 0xaauy; 0x89uy; 0x4fuy; 0xb3uy; 0xdfuy; 0x38uy; 0xfduy; 0xf1uy; 0xe4uy; 0x3auy; 0xc0uy; 0xe6uy; 0x58uy; 0xb5uy; 0x8fuy; 0xc5uy; 0x29uy; 0xa2uy; 0x92uy; 0x4auy; 0xb6uy; 0xa0uy; 0x34uy; 0x7fuy; 0xabuy; 0xb5uy; 0x8auy; 0x90uy; 0xa1uy; 0xdbuy; 0x4duy; 0xcauy; 0xb6uy; 0x2cuy; 0x41uy; 0x3cuy; 0xf7uy; 0x2buy; 0x21uy; 0xc3uy; 0xfduy; 0xf4uy; 0x17uy; 0x5cuy; 0xb5uy; 0x33uy; 0x17uy; 0x68uy; 0x2buy; 0x08uy; 0x30uy; 0xf3uy; 0xf7uy; 0x30uy; 0x3cuy; 0x96uy; 0xe6uy; 0x6auy; 0x20uy; 0x97uy; 0xe7uy; 0x4duy; 0x10uy; 0x5fuy; 0x47uy; 0x5fuy; 0x49uy; 0x96uy; 0x09uy; 0xf0uy; 0x27uy; 0x91uy; 0xc8uy; 0xf8uy; 0x5auy; 0x2euy; 0x79uy; 0xb5uy; 0xe2uy; 0xb8uy; 0xe8uy; 0xb9uy; 0x7buy; 0xd5uy; 0x10uy; 0xcbuy; 0xffuy; 0x5duy; 0x14uy; 0x73uy; 0xf3uy; ] in
assert_norm (List.Tot.length l = 512);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input7_len: (x:UInt32.t { UInt32.v x = B.length input7 }) =
512ul
let output7: (b: B.buffer UInt8.t { B.length b = 528 /\ B.recallable b }) =
[@inline_let] let l = [ 0x14uy; 0xf6uy; 0x41uy; 0x37uy; 0xa6uy; 0xd4uy; 0x27uy; 0xcduy; 0xdbuy; 0x06uy; 0x3euy; 0x9auy; 0x4euy; 0xabuy; 0xd5uy; 0xb1uy; 0x1euy; 0x6buy; 0xd2uy; 0xbcuy; 0x11uy; 0xf4uy; 0x28uy; 0x93uy; 0x63uy; 0x54uy; 0xefuy; 0xbbuy; 0x5euy; 0x1duy; 0x3auy; 0x1duy; 0x37uy; 0x3cuy; 0x0auy; 0x6cuy; 0x1euy; 0xc2uy; 0xd1uy; 0x2cuy; 0xb5uy; 0xa3uy; 0xb5uy; 0x7buy; 0xb8uy; 0x8fuy; 0x25uy; 0xa6uy; 0x1buy; 0x61uy; 0x1cuy; 0xecuy; 0x28uy; 0x58uy; 0x26uy; 0xa4uy; 0xa8uy; 0x33uy; 0x28uy; 0x25uy; 0x5cuy; 0x45uy; 0x05uy; 0xe5uy; 0x6cuy; 0x99uy; 0xe5uy; 0x45uy; 0xc4uy; 0xa2uy; 0x03uy; 0x84uy; 0x03uy; 0x73uy; 0x1euy; 0x8cuy; 0x49uy; 0xacuy; 0x20uy; 0xdduy; 0x8duy; 0xb3uy; 0xc4uy; 0xf5uy; 0xe7uy; 0x4fuy; 0xf1uy; 0xeduy; 0xa1uy; 0x98uy; 0xdeuy; 0xa4uy; 0x96uy; 0xdduy; 0x2fuy; 0xabuy; 0xabuy; 0x97uy; 0xcfuy; 0x3euy; 0xd2uy; 0x9euy; 0xb8uy; 0x13uy; 0x07uy; 0x28uy; 0x29uy; 0x19uy; 0xafuy; 0xfduy; 0xf2uy; 0x49uy; 0x43uy; 0xeauy; 0x49uy; 0x26uy; 0x91uy; 0xc1uy; 0x07uy; 0xd6uy; 0xbbuy; 0x81uy; 0x75uy; 0x35uy; 0x0duy; 0x24uy; 0x7fuy; 0xc8uy; 0xdauy; 0xd4uy; 0xb7uy; 0xebuy; 0xe8uy; 0x5cuy; 0x09uy; 0xa2uy; 0x2fuy; 0xdcuy; 0x28uy; 0x7duy; 0x3auy; 0x03uy; 0xfauy; 0x94uy; 0xb5uy; 0x1duy; 0x17uy; 0x99uy; 0x36uy; 0xc3uy; 0x1cuy; 0x18uy; 0x34uy; 0xe3uy; 0x9fuy; 0xf5uy; 0x55uy; 0x7cuy; 0xb0uy; 0x60uy; 0x9duy; 0xffuy; 0xacuy; 0xd4uy; 0x61uy; 0xf2uy; 0xaduy; 0xf8uy; 0xceuy; 0xc7uy; 0xbeuy; 0x5cuy; 0xd2uy; 0x95uy; 0xa8uy; 0x4buy; 0x77uy; 0x13uy; 0x19uy; 0x59uy; 0x26uy; 0xc9uy; 0xb7uy; 0x8fuy; 0x6auy; 0xcbuy; 0x2duy; 0x37uy; 0x91uy; 0xeauy; 0x92uy; 0x9cuy; 0x94uy; 0x5buy; 0xdauy; 0x0buy; 0xceuy; 0xfeuy; 0x30uy; 0x20uy; 0xf8uy; 0x51uy; 0xaduy; 0xf2uy; 0xbeuy; 0xe7uy; 0xc7uy; 0xffuy; 0xb3uy; 0x33uy; 0x91uy; 0x6auy; 0xc9uy; 0x1auy; 0x41uy; 0xc9uy; 0x0fuy; 0xf3uy; 0x10uy; 0x0euy; 0xfduy; 0x53uy; 0xffuy; 0x6cuy; 0x16uy; 0x52uy; 0xd9uy; 0xf3uy; 0xf7uy; 0x98uy; 0x2euy; 0xc9uy; 0x07uy; 0x31uy; 0x2cuy; 0x0cuy; 0x72uy; 0xd7uy; 0xc5uy; 0xc6uy; 0x08uy; 0x2auy; 0x7buy; 0xdauy; 0xbduy; 0x7euy; 0x02uy; 0xeauy; 0x1auy; 0xbbuy; 0xf2uy; 0x04uy; 0x27uy; 0x61uy; 0x28uy; 0x8euy; 0xf5uy; 0x04uy; 0x03uy; 0x1fuy; 0x4cuy; 0x07uy; 0x55uy; 0x82uy; 0xecuy; 0x1euy; 0xd7uy; 0x8buy; 0x2fuy; 0x65uy; 0x56uy; 0xd1uy; 0xd9uy; 0x1euy; 0x3cuy; 0xe9uy; 0x1fuy; 0x5euy; 0x98uy; 0x70uy; 0x38uy; 0x4auy; 0x8cuy; 0x49uy; 0xc5uy; 0x43uy; 0xa0uy; 0xa1uy; 0x8buy; 0x74uy; 0x9duy; 0x4cuy; 0x62uy; 0x0duy; 0x10uy; 0x0cuy; 0xf4uy; 0x6cuy; 0x8fuy; 0xe0uy; 0xaauy; 0x9auy; 0x8duy; 0xb7uy; 0xe0uy; 0xbeuy; 0x4cuy; 0x87uy; 0xf1uy; 0x98uy; 0x2fuy; 0xccuy; 0xeduy; 0xc0uy; 0x52uy; 0x29uy; 0xdcuy; 0x83uy; 0xf8uy; 0xfcuy; 0x2cuy; 0x0euy; 0xa8uy; 0x51uy; 0x4duy; 0x80uy; 0x0duy; 0xa3uy; 0xfeuy; 0xd8uy; 0x37uy; 0xe7uy; 0x41uy; 0x24uy; 0xfcuy; 0xfbuy; 0x75uy; 0xe3uy; 0x71uy; 0x7buy; 0x57uy; 0x45uy; 0xf5uy; 0x97uy; 0x73uy; 0x65uy; 0x63uy; 0x14uy; 0x74uy; 0xb8uy; 0x82uy; 0x9fuy; 0xf8uy; 0x60uy; 0x2fuy; 0x8auy; 0xf2uy; 0x4euy; 0xf1uy; 0x39uy; 0xdauy; 0x33uy; 0x91uy; 0xf8uy; 0x36uy; 0xe0uy; 0x8duy; 0x3fuy; 0x1fuy; 0x3buy; 0x56uy; 0xdcuy; 0xa0uy; 0x8fuy; 0x3cuy; 0x9duy; 0x71uy; 0x52uy; 0xa7uy; 0xb8uy; 0xc0uy; 0xa5uy; 0xc6uy; 0xa2uy; 0x73uy; 0xdauy; 0xf4uy; 0x4buy; 0x74uy; 0x5buy; 0x00uy; 0x3duy; 0x99uy; 0xd7uy; 0x96uy; 0xbauy; 0xe6uy; 0xe1uy; 0xa6uy; 0x96uy; 0x38uy; 0xaduy; 0xb3uy; 0xc0uy; 0xd2uy; 0xbauy; 0x91uy; 0x6buy; 0xf9uy; 0x19uy; 0xdduy; 0x3buy; 0xbeuy; 0xbeuy; 0x9cuy; 0x20uy; 0x50uy; 0xbauy; 0xa1uy; 0xd0uy; 0xceuy; 0x11uy; 0xbduy; 0x95uy; 0xd8uy; 0xd1uy; 0xdduy; 0x33uy; 0x85uy; 0x74uy; 0xdcuy; 0xdbuy; 0x66uy; 0x76uy; 0x44uy; 0xdcuy; 0x03uy; 0x74uy; 0x48uy; 0x35uy; 0x98uy; 0xb1uy; 0x18uy; 0x47uy; 0x94uy; 0x7duy; 0xffuy; 0x62uy; 0xe4uy; 0x58uy; 0x78uy; 0xabuy; 0xeduy; 0x95uy; 0x36uy; 0xd9uy; 0x84uy; 0x91uy; 0x82uy; 0x64uy; 0x41uy; 0xbbuy; 0x58uy; 0xe6uy; 0x1cuy; 0x20uy; 0x6duy; 0x15uy; 0x6buy; 0x13uy; 0x96uy; 0xe8uy; 0x35uy; 0x7fuy; 0xdcuy; 0x40uy; 0x2cuy; 0xe9uy; 0xbcuy; 0x8auy; 0x4fuy; 0x92uy; 0xecuy; 0x06uy; 0x2duy; 0x50uy; 0xdfuy; 0x93uy; 0x5duy; 0x65uy; 0x5auy; 0xa8uy; 0xfcuy; 0x20uy; 0x50uy; 0x14uy; 0xa9uy; 0x8auy; 0x7euy; 0x1duy; 0x08uy; 0x1fuy; 0xe2uy; 0x99uy; 0xd0uy; 0xbeuy; 0xfbuy; 0x3auy; 0x21uy; 0x9duy; 0xaduy; 0x86uy; 0x54uy; 0xfduy; 0x0duy; 0x98uy; 0x1cuy; 0x5auy; 0x6fuy; 0x1fuy; 0x9auy; 0x40uy; 0xcduy; 0xa2uy; 0xffuy; 0x6auy; 0xf1uy; 0x54uy; ] in
assert_norm (List.Tot.length l = 528);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output7_len: (x:UInt32.t { UInt32.v x = B.length output7 }) =
528ul
let key8: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0xeauy; 0xbcuy; 0x56uy; 0x99uy; 0xe3uy; 0x50uy; 0xffuy; 0xc5uy; 0xccuy; 0x1auy; 0xd7uy; 0xc1uy; 0x57uy; 0x72uy; 0xeauy; 0x86uy; 0x5buy; 0x89uy; 0x88uy; 0x61uy; 0x3duy; 0x2fuy; 0x9buy; 0xb2uy; 0xe7uy; 0x9cuy; 0xecuy; 0x74uy; 0x6euy; 0x3euy; 0xf4uy; 0x3buy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key8_len: (x:UInt32.t { UInt32.v x = B.length key8 }) =
32ul
let nonce8: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xefuy; 0x2duy; 0x63uy; 0xeeuy; 0x6buy; 0x80uy; 0x8buy; 0x78uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce8_len: (x:UInt32.t { UInt32.v x = B.length nonce8 }) =
12ul
let aad8: (b: B.buffer UInt8.t { B.length b = 9 /\ B.recallable b }) =
[@inline_let] let l = [ 0x5auy; 0x27uy; 0xffuy; 0xebuy; 0xdfuy; 0x84uy; 0xb2uy; 0x9euy; 0xefuy; ] in
assert_norm (List.Tot.length l = 9);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad8_len: (x:UInt32.t { UInt32.v x = B.length aad8 }) =
9ul
let input8: (b: B.buffer UInt8.t { B.length b = 513 /\ B.recallable b /\ B.disjoint b aad8 }) =
B.recall aad8;[@inline_let] let l = [ 0xe6uy; 0xc3uy; 0xdbuy; 0x63uy; 0x55uy; 0x15uy; 0xe3uy; 0x5buy; 0xb7uy; 0x4buy; 0x27uy; 0x8buy; 0x5auy; 0xdduy; 0xc2uy; 0xe8uy; 0x3auy; 0x6buy; 0xd7uy; 0x81uy; 0x96uy; 0x35uy; 0x97uy; 0xcauy; 0xd7uy; 0x68uy; 0xe8uy; 0xefuy; 0xceuy; 0xabuy; 0xdauy; 0x09uy; 0x6euy; 0xd6uy; 0x8euy; 0xcbuy; 0x55uy; 0xb5uy; 0xe1uy; 0xe5uy; 0x57uy; 0xfduy; 0xc4uy; 0xe3uy; 0xe0uy; 0x18uy; 0x4fuy; 0x85uy; 0xf5uy; 0x3fuy; 0x7euy; 0x4buy; 0x88uy; 0xc9uy; 0x52uy; 0x44uy; 0x0fuy; 0xeauy; 0xafuy; 0x1fuy; 0x71uy; 0x48uy; 0x9fuy; 0x97uy; 0x6duy; 0xb9uy; 0x6fuy; 0x00uy; 0xa6uy; 0xdeuy; 0x2buy; 0x77uy; 0x8buy; 0x15uy; 0xaduy; 0x10uy; 0xa0uy; 0x2buy; 0x7buy; 0x41uy; 0x90uy; 0x03uy; 0x2duy; 0x69uy; 0xaeuy; 0xccuy; 0x77uy; 0x7cuy; 0xa5uy; 0x9duy; 0x29uy; 0x22uy; 0xc2uy; 0xeauy; 0xb4uy; 0x00uy; 0x1auy; 0xd2uy; 0x7auy; 0x98uy; 0x8auy; 0xf9uy; 0xf7uy; 0x82uy; 0xb0uy; 0xabuy; 0xd8uy; 0xa6uy; 0x94uy; 0x8duy; 0x58uy; 0x2fuy; 0x01uy; 0x9euy; 0x00uy; 0x20uy; 0xfcuy; 0x49uy; 0xdcuy; 0x0euy; 0x03uy; 0xe8uy; 0x45uy; 0x10uy; 0xd6uy; 0xa8uy; 0xdauy; 0x55uy; 0x10uy; 0x9auy; 0xdfuy; 0x67uy; 0x22uy; 0x8buy; 0x43uy; 0xabuy; 0x00uy; 0xbbuy; 0x02uy; 0xc8uy; 0xdduy; 0x7buy; 0x97uy; 0x17uy; 0xd7uy; 0x1duy; 0x9euy; 0x02uy; 0x5euy; 0x48uy; 0xdeuy; 0x8euy; 0xcfuy; 0x99uy; 0x07uy; 0x95uy; 0x92uy; 0x3cuy; 0x5fuy; 0x9fuy; 0xc5uy; 0x8auy; 0xc0uy; 0x23uy; 0xaauy; 0xd5uy; 0x8cuy; 0x82uy; 0x6euy; 0x16uy; 0x92uy; 0xb1uy; 0x12uy; 0x17uy; 0x07uy; 0xc3uy; 0xfbuy; 0x36uy; 0xf5uy; 0x6cuy; 0x35uy; 0xd6uy; 0x06uy; 0x1fuy; 0x9fuy; 0xa7uy; 0x94uy; 0xa2uy; 0x38uy; 0x63uy; 0x9cuy; 0xb0uy; 0x71uy; 0xb3uy; 0xa5uy; 0xd2uy; 0xd8uy; 0xbauy; 0x9fuy; 0x08uy; 0x01uy; 0xb3uy; 0xffuy; 0x04uy; 0x97uy; 0x73uy; 0x45uy; 0x1buy; 0xd5uy; 0xa9uy; 0x9cuy; 0x80uy; 0xafuy; 0x04uy; 0x9auy; 0x85uy; 0xdbuy; 0x32uy; 0x5buy; 0x5duy; 0x1auy; 0xc1uy; 0x36uy; 0x28uy; 0x10uy; 0x79uy; 0xf1uy; 0x3cuy; 0xbfuy; 0x1auy; 0x41uy; 0x5cuy; 0x4euy; 0xdfuy; 0xb2uy; 0x7cuy; 0x79uy; 0x3buy; 0x7auy; 0x62uy; 0x3duy; 0x4buy; 0xc9uy; 0x9buy; 0x2auy; 0x2euy; 0x7cuy; 0xa2uy; 0xb1uy; 0x11uy; 0x98uy; 0xa7uy; 0x34uy; 0x1auy; 0x00uy; 0xf3uy; 0xd1uy; 0xbcuy; 0x18uy; 0x22uy; 0xbauy; 0x02uy; 0x56uy; 0x62uy; 0x31uy; 0x10uy; 0x11uy; 0x6duy; 0xe0uy; 0x54uy; 0x9duy; 0x40uy; 0x1fuy; 0x26uy; 0x80uy; 0x41uy; 0xcauy; 0x3fuy; 0x68uy; 0x0fuy; 0x32uy; 0x1duy; 0x0auy; 0x8euy; 0x79uy; 0xd8uy; 0xa4uy; 0x1buy; 0x29uy; 0x1cuy; 0x90uy; 0x8euy; 0xc5uy; 0xe3uy; 0xb4uy; 0x91uy; 0x37uy; 0x9auy; 0x97uy; 0x86uy; 0x99uy; 0xd5uy; 0x09uy; 0xc5uy; 0xbbuy; 0xa3uy; 0x3fuy; 0x21uy; 0x29uy; 0x82uy; 0x14uy; 0x5cuy; 0xabuy; 0x25uy; 0xfbuy; 0xf2uy; 0x4fuy; 0x58uy; 0x26uy; 0xd4uy; 0x83uy; 0xaauy; 0x66uy; 0x89uy; 0x67uy; 0x7euy; 0xc0uy; 0x49uy; 0xe1uy; 0x11uy; 0x10uy; 0x7fuy; 0x7auy; 0xdauy; 0x29uy; 0x04uy; 0xffuy; 0xf0uy; 0xcbuy; 0x09uy; 0x7cuy; 0x9duy; 0xfauy; 0x03uy; 0x6fuy; 0x81uy; 0x09uy; 0x31uy; 0x60uy; 0xfbuy; 0x08uy; 0xfauy; 0x74uy; 0xd3uy; 0x64uy; 0x44uy; 0x7cuy; 0x55uy; 0x85uy; 0xecuy; 0x9cuy; 0x6euy; 0x25uy; 0xb7uy; 0x6cuy; 0xc5uy; 0x37uy; 0xb6uy; 0x83uy; 0x87uy; 0x72uy; 0x95uy; 0x8buy; 0x9duy; 0xe1uy; 0x69uy; 0x5cuy; 0x31uy; 0x95uy; 0x42uy; 0xa6uy; 0x2cuy; 0xd1uy; 0x36uy; 0x47uy; 0x1fuy; 0xecuy; 0x54uy; 0xabuy; 0xa2uy; 0x1cuy; 0xd8uy; 0x00uy; 0xccuy; 0xbcuy; 0x0duy; 0x65uy; 0xe2uy; 0x67uy; 0xbfuy; 0xbcuy; 0xeauy; 0xeeuy; 0x9euy; 0xe4uy; 0x36uy; 0x95uy; 0xbeuy; 0x73uy; 0xd9uy; 0xa6uy; 0xd9uy; 0x0fuy; 0xa0uy; 0xccuy; 0x82uy; 0x76uy; 0x26uy; 0xaduy; 0x5buy; 0x58uy; 0x6cuy; 0x4euy; 0xabuy; 0x29uy; 0x64uy; 0xd3uy; 0xd9uy; 0xa9uy; 0x08uy; 0x8cuy; 0x1duy; 0xa1uy; 0x4fuy; 0x80uy; 0xd8uy; 0x3fuy; 0x94uy; 0xfbuy; 0xd3uy; 0x7buy; 0xfcuy; 0xd1uy; 0x2buy; 0xc3uy; 0x21uy; 0xebuy; 0xe5uy; 0x1cuy; 0x84uy; 0x23uy; 0x7fuy; 0x4buy; 0xfauy; 0xdbuy; 0x34uy; 0x18uy; 0xa2uy; 0xc2uy; 0xe5uy; 0x13uy; 0xfeuy; 0x6cuy; 0x49uy; 0x81uy; 0xd2uy; 0x73uy; 0xe7uy; 0xe2uy; 0xd7uy; 0xe4uy; 0x4fuy; 0x4buy; 0x08uy; 0x6euy; 0xb1uy; 0x12uy; 0x22uy; 0x10uy; 0x9duy; 0xacuy; 0x51uy; 0x1euy; 0x17uy; 0xd9uy; 0x8auy; 0x0buy; 0x42uy; 0x88uy; 0x16uy; 0x81uy; 0x37uy; 0x7cuy; 0x6auy; 0xf7uy; 0xefuy; 0x2duy; 0xe3uy; 0xd9uy; 0xf8uy; 0x5fuy; 0xe0uy; 0x53uy; 0x27uy; 0x74uy; 0xb9uy; 0xe2uy; 0xd6uy; 0x1cuy; 0x80uy; 0x2cuy; 0x52uy; 0x65uy; ] in
assert_norm (List.Tot.length l = 513);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input8_len: (x:UInt32.t { UInt32.v x = B.length input8 }) =
513ul
let output8: (b: B.buffer UInt8.t { B.length b = 529 /\ B.recallable b }) =
[@inline_let] let l = [ 0xfduy; 0x81uy; 0x8duy; 0xd0uy; 0x3duy; 0xb4uy; 0xd5uy; 0xdfuy; 0xd3uy; 0x42uy; 0x47uy; 0x5auy; 0x6duy; 0x19uy; 0x27uy; 0x66uy; 0x4buy; 0x2euy; 0x0cuy; 0x27uy; 0x9cuy; 0x96uy; 0x4cuy; 0x72uy; 0x02uy; 0xa3uy; 0x65uy; 0xc3uy; 0xb3uy; 0x6fuy; 0x2euy; 0xbduy; 0x63uy; 0x8auy; 0x4auy; 0x5duy; 0x29uy; 0xa2uy; 0xd0uy; 0x28uy; 0x48uy; 0xc5uy; 0x3duy; 0x98uy; 0xa3uy; 0xbcuy; 0xe0uy; 0xbeuy; 0x3buy; 0x3fuy; 0xe6uy; 0x8auy; 0xa4uy; 0x7fuy; 0x53uy; 0x06uy; 0xfauy; 0x7fuy; 0x27uy; 0x76uy; 0x72uy; 0x31uy; 0xa1uy; 0xf5uy; 0xd6uy; 0x0cuy; 0x52uy; 0x47uy; 0xbauy; 0xcduy; 0x4fuy; 0xd7uy; 0xebuy; 0x05uy; 0x48uy; 0x0duy; 0x7cuy; 0x35uy; 0x4auy; 0x09uy; 0xc9uy; 0x76uy; 0x71uy; 0x02uy; 0xa3uy; 0xfbuy; 0xb7uy; 0x1auy; 0x65uy; 0xb7uy; 0xeduy; 0x98uy; 0xc6uy; 0x30uy; 0x8auy; 0x00uy; 0xaeuy; 0xa1uy; 0x31uy; 0xe5uy; 0xb5uy; 0x9euy; 0x6duy; 0x62uy; 0xdauy; 0xdauy; 0x07uy; 0x0fuy; 0x38uy; 0x38uy; 0xd3uy; 0xcbuy; 0xc1uy; 0xb0uy; 0xaduy; 0xecuy; 0x72uy; 0xecuy; 0xb1uy; 0xa2uy; 0x7buy; 0x59uy; 0xf3uy; 0x3duy; 0x2buy; 0xefuy; 0xcduy; 0x28uy; 0x5buy; 0x83uy; 0xccuy; 0x18uy; 0x91uy; 0x88uy; 0xb0uy; 0x2euy; 0xf9uy; 0x29uy; 0x31uy; 0x18uy; 0xf9uy; 0x4euy; 0xe9uy; 0x0auy; 0x91uy; 0x92uy; 0x9fuy; 0xaeuy; 0x2duy; 0xaduy; 0xf4uy; 0xe6uy; 0x1auy; 0xe2uy; 0xa4uy; 0xeeuy; 0x47uy; 0x15uy; 0xbfuy; 0x83uy; 0x6euy; 0xd7uy; 0x72uy; 0x12uy; 0x3buy; 0x2duy; 0x24uy; 0xe9uy; 0xb2uy; 0x55uy; 0xcbuy; 0x3cuy; 0x10uy; 0xf0uy; 0x24uy; 0x8auy; 0x4auy; 0x02uy; 0xeauy; 0x90uy; 0x25uy; 0xf0uy; 0xb4uy; 0x79uy; 0x3auy; 0xefuy; 0x6euy; 0xf5uy; 0x52uy; 0xdfuy; 0xb0uy; 0x0auy; 0xcduy; 0x24uy; 0x1cuy; 0xd3uy; 0x2euy; 0x22uy; 0x74uy; 0xeauy; 0x21uy; 0x6fuy; 0xe9uy; 0xbduy; 0xc8uy; 0x3euy; 0x36uy; 0x5buy; 0x19uy; 0xf1uy; 0xcauy; 0x99uy; 0x0auy; 0xb4uy; 0xa7uy; 0x52uy; 0x1auy; 0x4euy; 0xf2uy; 0xaduy; 0x8duy; 0x56uy; 0x85uy; 0xbbuy; 0x64uy; 0x89uy; 0xbauy; 0x26uy; 0xf9uy; 0xc7uy; 0xe1uy; 0x89uy; 0x19uy; 0x22uy; 0x77uy; 0xc3uy; 0xa8uy; 0xfcuy; 0xffuy; 0xaduy; 0xfeuy; 0xb9uy; 0x48uy; 0xaeuy; 0x12uy; 0x30uy; 0x9fuy; 0x19uy; 0xfbuy; 0x1buy; 0xefuy; 0x14uy; 0x87uy; 0x8auy; 0x78uy; 0x71uy; 0xf3uy; 0xf4uy; 0xb7uy; 0x00uy; 0x9cuy; 0x1duy; 0xb5uy; 0x3duy; 0x49uy; 0x00uy; 0x0cuy; 0x06uy; 0xd4uy; 0x50uy; 0xf9uy; 0x54uy; 0x45uy; 0xb2uy; 0x5buy; 0x43uy; 0xdbuy; 0x6duy; 0xcfuy; 0x1auy; 0xe9uy; 0x7auy; 0x7auy; 0xcfuy; 0xfcuy; 0x8auy; 0x4euy; 0x4duy; 0x0buy; 0x07uy; 0x63uy; 0x28uy; 0xd8uy; 0xe7uy; 0x08uy; 0x95uy; 0xdfuy; 0xa6uy; 0x72uy; 0x93uy; 0x2euy; 0xbbuy; 0xa0uy; 0x42uy; 0x89uy; 0x16uy; 0xf1uy; 0xd9uy; 0x0cuy; 0xf9uy; 0xa1uy; 0x16uy; 0xfduy; 0xd9uy; 0x03uy; 0xb4uy; 0x3buy; 0x8auy; 0xf5uy; 0xf6uy; 0xe7uy; 0x6buy; 0x2euy; 0x8euy; 0x4cuy; 0x3duy; 0xe2uy; 0xafuy; 0x08uy; 0x45uy; 0x03uy; 0xffuy; 0x09uy; 0xb6uy; 0xebuy; 0x2duy; 0xc6uy; 0x1buy; 0x88uy; 0x94uy; 0xacuy; 0x3euy; 0xf1uy; 0x9fuy; 0x0euy; 0x0euy; 0x2buy; 0xd5uy; 0x00uy; 0x4duy; 0x3fuy; 0x3buy; 0x53uy; 0xaeuy; 0xafuy; 0x1cuy; 0x33uy; 0x5fuy; 0x55uy; 0x6euy; 0x8duy; 0xafuy; 0x05uy; 0x7auy; 0x10uy; 0x34uy; 0xc9uy; 0xf4uy; 0x66uy; 0xcbuy; 0x62uy; 0x12uy; 0xa6uy; 0xeeuy; 0xe8uy; 0x1cuy; 0x5duy; 0x12uy; 0x86uy; 0xdbuy; 0x6fuy; 0x1cuy; 0x33uy; 0xc4uy; 0x1cuy; 0xdauy; 0x82uy; 0x2duy; 0x3buy; 0x59uy; 0xfeuy; 0xb1uy; 0xa4uy; 0x59uy; 0x41uy; 0x86uy; 0xd0uy; 0xefuy; 0xaeuy; 0xfbuy; 0xdauy; 0x6duy; 0x11uy; 0xb8uy; 0xcauy; 0xe9uy; 0x6euy; 0xffuy; 0xf7uy; 0xa9uy; 0xd9uy; 0x70uy; 0x30uy; 0xfcuy; 0x53uy; 0xe2uy; 0xd7uy; 0xa2uy; 0x4euy; 0xc7uy; 0x91uy; 0xd9uy; 0x07uy; 0x06uy; 0xaauy; 0xdduy; 0xb0uy; 0x59uy; 0x28uy; 0x1duy; 0x00uy; 0x66uy; 0xc5uy; 0x54uy; 0xc2uy; 0xfcuy; 0x06uy; 0xdauy; 0x05uy; 0x90uy; 0x52uy; 0x1duy; 0x37uy; 0x66uy; 0xeeuy; 0xf0uy; 0xb2uy; 0x55uy; 0x8auy; 0x5duy; 0xd2uy; 0x38uy; 0x86uy; 0x94uy; 0x9buy; 0xfcuy; 0x10uy; 0x4cuy; 0xa1uy; 0xb9uy; 0x64uy; 0x3euy; 0x44uy; 0xb8uy; 0x5fuy; 0xb0uy; 0x0cuy; 0xecuy; 0xe0uy; 0xc9uy; 0xe5uy; 0x62uy; 0x75uy; 0x3fuy; 0x09uy; 0xd5uy; 0xf5uy; 0xd9uy; 0x26uy; 0xbauy; 0x9euy; 0xd2uy; 0xf4uy; 0xb9uy; 0x48uy; 0x0auy; 0xbcuy; 0xa2uy; 0xd6uy; 0x7cuy; 0x36uy; 0x11uy; 0x7duy; 0x26uy; 0x81uy; 0x89uy; 0xcfuy; 0xa4uy; 0xaduy; 0x73uy; 0x0euy; 0xeeuy; 0xccuy; 0x06uy; 0xa9uy; 0xdbuy; 0xb1uy; 0xfduy; 0xfbuy; 0x09uy; 0x7fuy; 0x90uy; 0x42uy; 0x37uy; 0x2fuy; 0xe1uy; 0x9cuy; 0x0fuy; 0x6fuy; 0xcfuy; 0x43uy; 0xb5uy; 0xd9uy; 0x90uy; 0xe1uy; 0x85uy; 0xf5uy; 0xa8uy; 0xaeuy; ] in
assert_norm (List.Tot.length l = 529);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let output8_len: (x:UInt32.t { UInt32.v x = B.length output8 }) =
529ul
let key9: (b: B.buffer UInt8.t { B.length b = 32 /\ B.recallable b }) =
[@inline_let] let l = [ 0x47uy; 0x11uy; 0xebuy; 0x86uy; 0x2buy; 0x2cuy; 0xabuy; 0x44uy; 0x34uy; 0xdauy; 0x7fuy; 0x57uy; 0x03uy; 0x39uy; 0x0cuy; 0xafuy; 0x2cuy; 0x14uy; 0xfduy; 0x65uy; 0x23uy; 0xe9uy; 0x8euy; 0x74uy; 0xd5uy; 0x08uy; 0x68uy; 0x08uy; 0xe7uy; 0xb4uy; 0x72uy; 0xd7uy; ] in
assert_norm (List.Tot.length l = 32);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let key9_len: (x:UInt32.t { UInt32.v x = B.length key9 }) =
32ul
let nonce9: (b: B.buffer UInt8.t { B.length b = 12 /\ B.recallable b }) =
[@inline_let] let l = [ 0x00uy; 0x00uy; 0x00uy; 0x00uy; 0xdbuy; 0x92uy; 0x0fuy; 0x7fuy; 0x17uy; 0x54uy; 0x0cuy; 0x30uy; ] in
assert_norm (List.Tot.length l = 12);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let nonce9_len: (x:UInt32.t { UInt32.v x = B.length nonce9 }) =
12ul
let aad9: (b: B.buffer UInt8.t { B.length b = 16 /\ B.recallable b }) =
[@inline_let] let l = [ 0xd2uy; 0xa1uy; 0x70uy; 0xdbuy; 0x7auy; 0xf8uy; 0xfauy; 0x27uy; 0xbauy; 0x73uy; 0x0fuy; 0xbfuy; 0x3duy; 0x1euy; 0x82uy; 0xb2uy; ] in
assert_norm (List.Tot.length l = 16);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let aad9_len: (x:UInt32.t { UInt32.v x = B.length aad9 }) =
16ul
let input9: (b: B.buffer UInt8.t { B.length b = 1024 /\ B.recallable b /\ B.disjoint b aad9 }) =
B.recall aad9;[@inline_let] let l = [ 0x42uy; 0x93uy; 0xe4uy; 0xebuy; 0x97uy; 0xb0uy; 0x57uy; 0xbfuy; 0x1auy; 0x8buy; 0x1fuy; 0xe4uy; 0x5fuy; 0x36uy; 0x20uy; 0x3cuy; 0xefuy; 0x0auy; 0xa9uy; 0x48uy; 0x5fuy; 0x5fuy; 0x37uy; 0x22uy; 0x3auy; 0xdeuy; 0xe3uy; 0xaeuy; 0xbeuy; 0xaduy; 0x07uy; 0xccuy; 0xb1uy; 0xf6uy; 0xf5uy; 0xf9uy; 0x56uy; 0xdduy; 0xe7uy; 0x16uy; 0x1euy; 0x7fuy; 0xdfuy; 0x7auy; 0x9euy; 0x75uy; 0xb7uy; 0xc7uy; 0xbeuy; 0xbeuy; 0x8auy; 0x36uy; 0x04uy; 0xc0uy; 0x10uy; 0xf4uy; 0x95uy; 0x20uy; 0x03uy; 0xecuy; 0xdcuy; 0x05uy; 0xa1uy; 0x7duy; 0xc4uy; 0xa9uy; 0x2cuy; 0x82uy; 0xd0uy; 0xbcuy; 0x8buy; 0xc5uy; 0xc7uy; 0x45uy; 0x50uy; 0xf6uy; 0xa2uy; 0x1auy; 0xb5uy; 0x46uy; 0x3buy; 0x73uy; 0x02uy; 0xa6uy; 0x83uy; 0x4buy; 0x73uy; 0x82uy; 0x58uy; 0x5euy; 0x3buy; 0x65uy; 0x2fuy; 0x0euy; 0xfduy; 0x2buy; 0x59uy; 0x16uy; 0xceuy; 0xa1uy; 0x60uy; 0x9cuy; 0xe8uy; 0x3auy; 0x99uy; 0xeduy; 0x8duy; 0x5auy; 0xcfuy; 0xf6uy; 0x83uy; 0xafuy; 0xbauy; 0xd7uy; 0x73uy; 0x73uy; 0x40uy; 0x97uy; 0x3duy; 0xcauy; 0xefuy; 0x07uy; 0x57uy; 0xe6uy; 0xd9uy; 0x70uy; 0x0euy; 0x95uy; 0xaeuy; 0xa6uy; 0x8duy; 0x04uy; 0xccuy; 0xeeuy; 0xf7uy; 0x09uy; 0x31uy; 0x77uy; 0x12uy; 0xa3uy; 0x23uy; 0x97uy; 0x62uy; 0xb3uy; 0x7buy; 0x32uy; 0xfbuy; 0x80uy; 0x14uy; 0x48uy; 0x81uy; 0xc3uy; 0xe5uy; 0xeauy; 0x91uy; 0x39uy; 0x52uy; 0x81uy; 0xa2uy; 0x4fuy; 0xe4uy; 0xb3uy; 0x09uy; 0xffuy; 0xdeuy; 0x5euy; 0xe9uy; 0x58uy; 0x84uy; 0x6euy; 0xf9uy; 0x3duy; 0xdfuy; 0x25uy; 0xeauy; 0xaduy; 0xaeuy; 0xe6uy; 0x9auy; 0xd1uy; 0x89uy; 0x55uy; 0xd3uy; 0xdeuy; 0x6cuy; 0x52uy; 0xdbuy; 0x70uy; 0xfeuy; 0x37uy; 0xceuy; 0x44uy; 0x0auy; 0xa8uy; 0x25uy; 0x5fuy; 0x92uy; 0xc1uy; 0x33uy; 0x4auy; 0x4fuy; 0x9buy; 0x62uy; 0x35uy; 0xffuy; 0xceuy; 0xc0uy; 0xa9uy; 0x60uy; 0xceuy; 0x52uy; 0x00uy; 0x97uy; 0x51uy; 0x35uy; 0x26uy; 0x2euy; 0xb9uy; 0x36uy; 0xa9uy; 0x87uy; 0x6euy; 0x1euy; 0xccuy; 0x91uy; 0x78uy; 0x53uy; 0x98uy; 0x86uy; 0x5buy; 0x9cuy; 0x74uy; 0x7duy; 0x88uy; 0x33uy; 0xe1uy; 0xdfuy; 0x37uy; 0x69uy; 0x2buy; 0xbbuy; 0xf1uy; 0x4duy; 0xf4uy; 0xd1uy; 0xf1uy; 0x39uy; 0x93uy; 0x17uy; 0x51uy; 0x19uy; 0xe3uy; 0x19uy; 0x1euy; 0x76uy; 0x37uy; 0x25uy; 0xfbuy; 0x09uy; 0x27uy; 0x6auy; 0xabuy; 0x67uy; 0x6fuy; 0x14uy; 0x12uy; 0x64uy; 0xe7uy; 0xc4uy; 0x07uy; 0xdfuy; 0x4duy; 0x17uy; 0xbbuy; 0x6duy; 0xe0uy; 0xe9uy; 0xb9uy; 0xabuy; 0xcauy; 0x10uy; 0x68uy; 0xafuy; 0x7euy; 0xb7uy; 0x33uy; 0x54uy; 0x73uy; 0x07uy; 0x6euy; 0xf7uy; 0x81uy; 0x97uy; 0x9cuy; 0x05uy; 0x6fuy; 0x84uy; 0x5fuy; 0xd2uy; 0x42uy; 0xfbuy; 0x38uy; 0xcfuy; 0xd1uy; 0x2fuy; 0x14uy; 0x30uy; 0x88uy; 0x98uy; 0x4duy; 0x5auy; 0xa9uy; 0x76uy; 0xd5uy; 0x4fuy; 0x3euy; 0x70uy; 0x6cuy; 0x85uy; 0x76uy; 0xd7uy; 0x01uy; 0xa0uy; 0x1auy; 0xc8uy; 0x4euy; 0xaauy; 0xacuy; 0x78uy; 0xfeuy; 0x46uy; 0xdeuy; 0x6auy; 0x05uy; 0x46uy; 0xa7uy; 0x43uy; 0x0cuy; 0xb9uy; 0xdeuy; 0xb9uy; 0x68uy; 0xfbuy; 0xceuy; 0x42uy; 0x99uy; 0x07uy; 0x4duy; 0x0buy; 0x3buy; 0x5auy; 0x30uy; 0x35uy; 0xa8uy; 0xf9uy; 0x3auy; 0x73uy; 0xefuy; 0x0fuy; 0xdbuy; 0x1euy; 0x16uy; 0x42uy; 0xc4uy; 0xbauy; 0xaeuy; 0x58uy; 0xaauy; 0xf8uy; 0xe5uy; 0x75uy; 0x2fuy; 0x1buy; 0x15uy; 0x5cuy; 0xfduy; 0x0auy; 0x97uy; 0xd0uy; 0xe4uy; 0x37uy; 0x83uy; 0x61uy; 0x5fuy; 0x43uy; 0xa6uy; 0xc7uy; 0x3fuy; 0x38uy; 0x59uy; 0xe6uy; 0xebuy; 0xa3uy; 0x90uy; 0xc3uy; 0xaauy; 0xaauy; 0x5auy; 0xd3uy; 0x34uy; 0xd4uy; 0x17uy; 0xc8uy; 0x65uy; 0x3euy; 0x57uy; 0xbcuy; 0x5euy; 0xdduy; 0x9euy; 0xb7uy; 0xf0uy; 0x2euy; 0x5buy; 0xb2uy; 0x1fuy; 0x8auy; 0x08uy; 0x0duy; 0x45uy; 0x91uy; 0x0buy; 0x29uy; 0x53uy; 0x4fuy; 0x4cuy; 0x5auy; 0x73uy; 0x56uy; 0xfeuy; 0xafuy; 0x41uy; 0x01uy; 0x39uy; 0x0auy; 0x24uy; 0x3cuy; 0x7euy; 0xbeuy; 0x4euy; 0x53uy; 0xf3uy; 0xebuy; 0x06uy; 0x66uy; 0x51uy; 0x28uy; 0x1duy; 0xbduy; 0x41uy; 0x0auy; 0x01uy; 0xabuy; 0x16uy; 0x47uy; 0x27uy; 0x47uy; 0x47uy; 0xf7uy; 0xcbuy; 0x46uy; 0x0auy; 0x70uy; 0x9euy; 0x01uy; 0x9cuy; 0x09uy; 0xe1uy; 0x2auy; 0x00uy; 0x1auy; 0xd8uy; 0xd4uy; 0x79uy; 0x9duy; 0x80uy; 0x15uy; 0x8euy; 0x53uy; 0x2auy; 0x65uy; 0x83uy; 0x78uy; 0x3euy; 0x03uy; 0x00uy; 0x07uy; 0x12uy; 0x1fuy; 0x33uy; 0x3euy; 0x7buy; 0x13uy; 0x37uy; 0xf1uy; 0xc3uy; 0xefuy; 0xb7uy; 0xc1uy; 0x20uy; 0x3cuy; 0x3euy; 0x67uy; 0x66uy; 0x5duy; 0x88uy; 0xa7uy; 0x7duy; 0x33uy; 0x50uy; 0x77uy; 0xb0uy; 0x28uy; 0x8euy; 0xe7uy; 0x2cuy; 0x2euy; 0x7auy; 0xf4uy; 0x3cuy; 0x8duy; 0x74uy; 0x83uy; 0xafuy; 0x8euy; 0x87uy; 0x0fuy; 0xe4uy; 0x50uy; 0xffuy; 0x84uy; 0x5cuy; 0x47uy; 0x0cuy; 0x6auy; 0x49uy; 0xbfuy; 0x42uy; 0x86uy; 0x77uy; 0x15uy; 0x48uy; 0xa5uy; 0x90uy; 0x5duy; 0x93uy; 0xd6uy; 0x2auy; 0x11uy; 0xd5uy; 0xd5uy; 0x11uy; 0xaauy; 0xceuy; 0xe7uy; 0x6fuy; 0xa5uy; 0xb0uy; 0x09uy; 0x2cuy; 0x8duy; 0xd3uy; 0x92uy; 0xf0uy; 0x5auy; 0x2auy; 0xdauy; 0x5buy; 0x1euy; 0xd5uy; 0x9auy; 0xc4uy; 0xc4uy; 0xf3uy; 0x49uy; 0x74uy; 0x41uy; 0xcauy; 0xe8uy; 0xc1uy; 0xf8uy; 0x44uy; 0xd6uy; 0x3cuy; 0xaeuy; 0x6cuy; 0x1duy; 0x9auy; 0x30uy; 0x04uy; 0x4duy; 0x27uy; 0x0euy; 0xb1uy; 0x5fuy; 0x59uy; 0xa2uy; 0x24uy; 0xe8uy; 0xe1uy; 0x98uy; 0xc5uy; 0x6auy; 0x4cuy; 0xfeuy; 0x41uy; 0xd2uy; 0x27uy; 0x42uy; 0x52uy; 0xe1uy; 0xe9uy; 0x7duy; 0x62uy; 0xe4uy; 0x88uy; 0x0fuy; 0xaduy; 0xb2uy; 0x70uy; 0xcbuy; 0x9duy; 0x4cuy; 0x27uy; 0x2euy; 0x76uy; 0x1euy; 0x1auy; 0x63uy; 0x65uy; 0xf5uy; 0x3buy; 0xf8uy; 0x57uy; 0x69uy; 0xebuy; 0x5buy; 0x38uy; 0x26uy; 0x39uy; 0x33uy; 0x25uy; 0x45uy; 0x3euy; 0x91uy; 0xb8uy; 0xd8uy; 0xc7uy; 0xd5uy; 0x42uy; 0xc0uy; 0x22uy; 0x31uy; 0x74uy; 0xf4uy; 0xbcuy; 0x0cuy; 0x23uy; 0xf1uy; 0xcauy; 0xc1uy; 0x8duy; 0xd7uy; 0xbeuy; 0xc9uy; 0x62uy; 0xe4uy; 0x08uy; 0x1auy; 0xcfuy; 0x36uy; 0xd5uy; 0xfeuy; 0x55uy; 0x21uy; 0x59uy; 0x91uy; 0x87uy; 0x87uy; 0xdfuy; 0x06uy; 0xdbuy; 0xdfuy; 0x96uy; 0x45uy; 0x58uy; 0xdauy; 0x05uy; 0xcduy; 0x50uy; 0x4duy; 0xd2uy; 0x7duy; 0x05uy; 0x18uy; 0x73uy; 0x6auy; 0x8duy; 0x11uy; 0x85uy; 0xa6uy; 0x88uy; 0xe8uy; 0xdauy; 0xe6uy; 0x30uy; 0x33uy; 0xa4uy; 0x89uy; 0x31uy; 0x75uy; 0xbeuy; 0x69uy; 0x43uy; 0x84uy; 0x43uy; 0x50uy; 0x87uy; 0xdduy; 0x71uy; 0x36uy; 0x83uy; 0xc3uy; 0x78uy; 0x74uy; 0x24uy; 0x0auy; 0xeduy; 0x7buy; 0xdbuy; 0xa4uy; 0x24uy; 0x0buy; 0xb9uy; 0x7euy; 0x5duy; 0xffuy; 0xdeuy; 0xb1uy; 0xefuy; 0x61uy; 0x5auy; 0x45uy; 0x33uy; 0xf6uy; 0x17uy; 0x07uy; 0x08uy; 0x98uy; 0x83uy; 0x92uy; 0x0fuy; 0x23uy; 0x6duy; 0xe6uy; 0xaauy; 0x17uy; 0x54uy; 0xaduy; 0x6auy; 0xc8uy; 0xdbuy; 0x26uy; 0xbeuy; 0xb8uy; 0xb6uy; 0x08uy; 0xfauy; 0x68uy; 0xf1uy; 0xd7uy; 0x79uy; 0x6fuy; 0x18uy; 0xb4uy; 0x9euy; 0x2duy; 0x3fuy; 0x1buy; 0x64uy; 0xafuy; 0x8duy; 0x06uy; 0x0euy; 0x49uy; 0x28uy; 0xe0uy; 0x5duy; 0x45uy; 0x68uy; 0x13uy; 0x87uy; 0xfauy; 0xdeuy; 0x40uy; 0x7buy; 0xd2uy; 0xc3uy; 0x94uy; 0xd5uy; 0xe1uy; 0xd9uy; 0xc2uy; 0xafuy; 0x55uy; 0x89uy; 0xebuy; 0xb4uy; 0x12uy; 0x59uy; 0xa8uy; 0xd4uy; 0xc5uy; 0x29uy; 0x66uy; 0x38uy; 0xe6uy; 0xacuy; 0x22uy; 0x22uy; 0xd9uy; 0x64uy; 0x9buy; 0x34uy; 0x0auy; 0x32uy; 0x9fuy; 0xc2uy; 0xbfuy; 0x17uy; 0x6cuy; 0x3fuy; 0x71uy; 0x7auy; 0x38uy; 0x6buy; 0x98uy; 0xfbuy; 0x49uy; 0x36uy; 0x89uy; 0xc9uy; 0xe2uy; 0xd6uy; 0xc7uy; 0x5duy; 0xd0uy; 0x69uy; 0x5fuy; 0x23uy; 0x35uy; 0xc9uy; 0x30uy; 0xe2uy; 0xfduy; 0x44uy; 0x58uy; 0x39uy; 0xd7uy; 0x97uy; 0xfbuy; 0x5cuy; 0x00uy; 0xd5uy; 0x4fuy; 0x7auy; 0x1auy; 0x95uy; 0x8buy; 0x62uy; 0x4buy; 0xceuy; 0xe5uy; 0x91uy; 0x21uy; 0x7buy; 0x30uy; 0x00uy; 0xd6uy; 0xdduy; 0x6duy; 0x02uy; 0x86uy; 0x49uy; 0x0fuy; 0x3cuy; 0x1auy; 0x27uy; 0x3cuy; 0xd3uy; 0x0euy; 0x71uy; 0xf2uy; 0xffuy; 0xf5uy; 0x2fuy; 0x87uy; 0xacuy; 0x67uy; 0x59uy; 0x81uy; 0xa3uy; 0xf7uy; 0xf8uy; 0xd6uy; 0x11uy; 0x0cuy; 0x84uy; 0xa9uy; 0x03uy; 0xeeuy; 0x2auy; 0xc4uy; 0xf3uy; 0x22uy; 0xabuy; 0x7cuy; 0xe2uy; 0x25uy; 0xf5uy; 0x67uy; 0xa3uy; 0xe4uy; 0x11uy; 0xe0uy; 0x59uy; 0xb3uy; 0xcauy; 0x87uy; 0xa0uy; 0xaeuy; 0xc9uy; 0xa6uy; 0x62uy; 0x1buy; 0x6euy; 0x4duy; 0x02uy; 0x6buy; 0x07uy; 0x9duy; 0xfduy; 0xd0uy; 0x92uy; 0x06uy; 0xe1uy; 0xb2uy; 0x9auy; 0x4auy; 0x1fuy; 0x1fuy; 0x13uy; 0x49uy; 0x99uy; 0x97uy; 0x08uy; 0xdeuy; 0x7fuy; 0x98uy; 0xafuy; 0x51uy; 0x98uy; 0xeeuy; 0x2cuy; 0xcbuy; 0xf0uy; 0x0buy; 0xc6uy; 0xb6uy; 0xb7uy; 0x2duy; 0x9auy; 0xb1uy; 0xacuy; 0xa6uy; 0xe3uy; 0x15uy; 0x77uy; 0x9duy; 0x6buy; 0x1auy; 0xe4uy; 0xfcuy; 0x8buy; 0xf2uy; 0x17uy; 0x59uy; 0x08uy; 0x04uy; 0x58uy; 0x81uy; 0x9duy; 0x1buy; 0x1buy; 0x69uy; 0x55uy; 0xc2uy; 0xb4uy; 0x3cuy; 0x1fuy; 0x50uy; 0xf1uy; 0x7fuy; 0x77uy; 0x90uy; 0x4cuy; 0x66uy; 0x40uy; 0x5auy; 0xc0uy; 0x33uy; 0x1fuy; 0xcbuy; 0x05uy; 0x6duy; 0x5cuy; 0x06uy; 0x87uy; 0x52uy; 0xa2uy; 0x8fuy; 0x26uy; 0xd5uy; 0x4fuy; ] in
assert_norm (List.Tot.length l = 1024);
B.gcmalloc_of_list HyperStack.root l
inline_for_extraction let input9_len: (x:UInt32.t { UInt32.v x = B.length input9 }) =
1024ul | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"LowStar.Buffer.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "Test.Vectors.Chacha20Poly1305.fst"
} | [
{
"abbrev": true,
"full_module": "LowStar.Buffer",
"short_module": "B"
},
{
"abbrev": false,
"full_module": "Test.Vectors",
"short_module": null
},
{
"abbrev": false,
"full_module": "Test.Vectors",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 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": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b:
LowStar.Buffer.buffer FStar.UInt8.t
{LowStar.Monotonic.Buffer.length b = 1040 /\ LowStar.Monotonic.Buffer.recallable b} | Prims.Tot | [
"total"
] | [] | [
"LowStar.Buffer.gcmalloc_of_list",
"FStar.UInt8.t",
"FStar.Monotonic.HyperHeap.root",
"LowStar.Monotonic.Buffer.mbuffer",
"LowStar.Buffer.trivial_preorder",
"Prims.l_and",
"Prims.eq2",
"Prims.nat",
"LowStar.Monotonic.Buffer.length",
"FStar.Pervasives.normalize_term",
"FStar.List.Tot.Base.length",
"Prims.b2t",
"Prims.op_Negation",
"LowStar.Monotonic.Buffer.g_is_null",
"FStar.Monotonic.HyperHeap.rid",
"LowStar.Monotonic.Buffer.frameOf",
"LowStar.Monotonic.Buffer.recallable",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"LowStar.Buffer.buffer",
"Prims.list",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | false | false | false | false | false | let output9:(b: B.buffer UInt8.t {B.length b = 1040 /\ B.recallable b}) =
| [@@ inline_let ]let l =
[
0xe5uy; 0x26uy; 0xa4uy; 0x3duy; 0xbduy; 0x33uy; 0xd0uy; 0x4buy; 0x6fuy; 0x05uy; 0xa7uy; 0x6euy;
0x12uy; 0x7auy; 0xd2uy; 0x74uy; 0xa6uy; 0xdduy; 0xbduy; 0x95uy; 0xebuy; 0xf9uy; 0xa4uy; 0xf1uy;
0x59uy; 0x93uy; 0x91uy; 0x70uy; 0xd9uy; 0xfeuy; 0x9auy; 0xcduy; 0x53uy; 0x1fuy; 0x3auy; 0xabuy;
0xa6uy; 0x7cuy; 0x9fuy; 0xa6uy; 0x9euy; 0xbduy; 0x99uy; 0xd9uy; 0xb5uy; 0x97uy; 0x44uy; 0xd5uy;
0x14uy; 0x48uy; 0x4duy; 0x9duy; 0xc0uy; 0xd0uy; 0x05uy; 0x96uy; 0xebuy; 0x4cuy; 0x78uy; 0x55uy;
0x09uy; 0x08uy; 0x01uy; 0x02uy; 0x30uy; 0x90uy; 0x7buy; 0x96uy; 0x7auy; 0x7buy; 0x5fuy; 0x30uy;
0x41uy; 0x24uy; 0xceuy; 0x68uy; 0x61uy; 0x49uy; 0x86uy; 0x57uy; 0x82uy; 0xdduy; 0x53uy; 0x1cuy;
0x51uy; 0x28uy; 0x2buy; 0x53uy; 0x6euy; 0x2duy; 0xc2uy; 0x20uy; 0x4cuy; 0xdduy; 0x8fuy; 0x65uy;
0x10uy; 0x20uy; 0x50uy; 0xdduy; 0x9duy; 0x50uy; 0xe5uy; 0x71uy; 0x40uy; 0x53uy; 0x69uy; 0xfcuy;
0x77uy; 0x48uy; 0x11uy; 0xb9uy; 0xdeuy; 0xa4uy; 0x8duy; 0x58uy; 0xe4uy; 0xa6uy; 0x1auy; 0x18uy;
0x47uy; 0x81uy; 0x7euy; 0xfcuy; 0xdduy; 0xf6uy; 0xefuy; 0xceuy; 0x2fuy; 0x43uy; 0x68uy; 0xd6uy;
0x06uy; 0xe2uy; 0x74uy; 0x6auy; 0xaduy; 0x90uy; 0xf5uy; 0x37uy; 0xf3uy; 0x3duy; 0x82uy; 0x69uy;
0x40uy; 0xe9uy; 0x6buy; 0xa7uy; 0x3duy; 0xa8uy; 0x1euy; 0xd2uy; 0x02uy; 0x7cuy; 0xb7uy; 0x9buy;
0xe4uy; 0xdauy; 0x8fuy; 0x95uy; 0x06uy; 0xc5uy; 0xdfuy; 0x73uy; 0xa3uy; 0x20uy; 0x9auy; 0x49uy;
0xdeuy; 0x9cuy; 0xbcuy; 0xeeuy; 0x14uy; 0x3fuy; 0x81uy; 0x5euy; 0xf8uy; 0x3buy; 0x59uy; 0x3cuy;
0xe1uy; 0x68uy; 0x12uy; 0x5auy; 0x3auy; 0x76uy; 0x3auy; 0x3fuy; 0xf7uy; 0x87uy; 0x33uy; 0x0auy;
0x01uy; 0xb8uy; 0xd4uy; 0xeduy; 0xb6uy; 0xbeuy; 0x94uy; 0x5euy; 0x70uy; 0x40uy; 0x56uy; 0x67uy;
0x1fuy; 0x50uy; 0x44uy; 0x19uy; 0xceuy; 0x82uy; 0x70uy; 0x10uy; 0x87uy; 0x13uy; 0x20uy; 0x0buy;
0x4cuy; 0x5auy; 0xb6uy; 0xf6uy; 0xa7uy; 0xaeuy; 0x81uy; 0x75uy; 0x01uy; 0x81uy; 0xe6uy; 0x4buy;
0x57uy; 0x7cuy; 0xdduy; 0x6duy; 0xf8uy; 0x1cuy; 0x29uy; 0x32uy; 0xf7uy; 0xdauy; 0x3cuy; 0x2duy;
0xf8uy; 0x9buy; 0x25uy; 0x6euy; 0x00uy; 0xb4uy; 0xf7uy; 0x2fuy; 0xf7uy; 0x04uy; 0xf7uy; 0xa1uy;
0x56uy; 0xacuy; 0x4fuy; 0x1auy; 0x64uy; 0xb8uy; 0x47uy; 0x55uy; 0x18uy; 0x7buy; 0x07uy; 0x4duy;
0xbduy; 0x47uy; 0x24uy; 0x80uy; 0x5duy; 0xa2uy; 0x70uy; 0xc5uy; 0xdduy; 0x8euy; 0x82uy; 0xd4uy;
0xebuy; 0xecuy; 0xb2uy; 0x0cuy; 0x39uy; 0xd2uy; 0x97uy; 0xc1uy; 0xcbuy; 0xebuy; 0xf4uy; 0x77uy;
0x59uy; 0xb4uy; 0x87uy; 0xefuy; 0xcbuy; 0x43uy; 0x2duy; 0x46uy; 0x54uy; 0xd1uy; 0xa7uy; 0xd7uy;
0x15uy; 0x99uy; 0x0auy; 0x43uy; 0xa1uy; 0xe0uy; 0x99uy; 0x33uy; 0x71uy; 0xc1uy; 0xeduy; 0xfeuy;
0x72uy; 0x46uy; 0x33uy; 0x8euy; 0x91uy; 0x08uy; 0x9fuy; 0xc8uy; 0x2euy; 0xcauy; 0xfauy; 0xdcuy;
0x59uy; 0xd5uy; 0xc3uy; 0x76uy; 0x84uy; 0x9fuy; 0xa3uy; 0x37uy; 0x68uy; 0xc3uy; 0xf0uy; 0x47uy;
0x2cuy; 0x68uy; 0xdbuy; 0x5euy; 0xc3uy; 0x49uy; 0x4cuy; 0xe8uy; 0x92uy; 0x85uy; 0xe2uy; 0x23uy;
0xd3uy; 0x3fuy; 0xaduy; 0x32uy; 0xe5uy; 0x2buy; 0x82uy; 0xd7uy; 0x8fuy; 0x99uy; 0x0auy; 0x59uy;
0x5cuy; 0x45uy; 0xd9uy; 0xb4uy; 0x51uy; 0x52uy; 0xc2uy; 0xaeuy; 0xbfuy; 0x80uy; 0xcfuy; 0xc9uy;
0xc9uy; 0x51uy; 0x24uy; 0x2auy; 0x3buy; 0x3auy; 0x4duy; 0xaeuy; 0xebuy; 0xbduy; 0x22uy; 0xc3uy;
0x0euy; 0x0fuy; 0x59uy; 0x25uy; 0x92uy; 0x17uy; 0xe9uy; 0x74uy; 0xc7uy; 0x8buy; 0x70uy; 0x70uy;
0x36uy; 0x55uy; 0x95uy; 0x75uy; 0x4buy; 0xaduy; 0x61uy; 0x2buy; 0x09uy; 0xbcuy; 0x82uy; 0xf2uy;
0x6euy; 0x94uy; 0x43uy; 0xaeuy; 0xc3uy; 0xd5uy; 0xcduy; 0x8euy; 0xfeuy; 0x5buy; 0x9auy; 0x88uy;
0x43uy; 0x01uy; 0x75uy; 0xb2uy; 0x23uy; 0x09uy; 0xf7uy; 0x89uy; 0x83uy; 0xe7uy; 0xfauy; 0xf9uy;
0xb4uy; 0x9buy; 0xf8uy; 0xefuy; 0xbduy; 0x1cuy; 0x92uy; 0xc1uy; 0xdauy; 0x7euy; 0xfeuy; 0x05uy;
0xbauy; 0x5auy; 0xcduy; 0x07uy; 0x6auy; 0x78uy; 0x9euy; 0x5duy; 0xfbuy; 0x11uy; 0x2fuy; 0x79uy;
0x38uy; 0xb6uy; 0xc2uy; 0x5buy; 0x6buy; 0x51uy; 0xb4uy; 0x71uy; 0xdduy; 0xf7uy; 0x2auy; 0xe4uy;
0xf4uy; 0x72uy; 0x76uy; 0xaduy; 0xc2uy; 0xdduy; 0x64uy; 0x5duy; 0x79uy; 0xb6uy; 0xf5uy; 0x7auy;
0x77uy; 0x20uy; 0x05uy; 0x3duy; 0x30uy; 0x06uy; 0xd4uy; 0x4cuy; 0x0auy; 0x2cuy; 0x98uy; 0x5auy;
0xb9uy; 0xd4uy; 0x98uy; 0xa9uy; 0x3fuy; 0xc6uy; 0x12uy; 0xeauy; 0x3buy; 0x4buy; 0xc5uy; 0x79uy;
0x64uy; 0x63uy; 0x6buy; 0x09uy; 0x54uy; 0x3buy; 0x14uy; 0x27uy; 0xbauy; 0x99uy; 0x80uy; 0xc8uy;
0x72uy; 0xa8uy; 0x12uy; 0x90uy; 0x29uy; 0xbauy; 0x40uy; 0x54uy; 0x97uy; 0x2buy; 0x7buy; 0xfeuy;
0xebuy; 0xcduy; 0x01uy; 0x05uy; 0x44uy; 0x72uy; 0xdbuy; 0x99uy; 0xe4uy; 0x61uy; 0xc9uy; 0x69uy;
0xd6uy; 0xb9uy; 0x28uy; 0xd1uy; 0x05uy; 0x3euy; 0xf9uy; 0x0buy; 0x49uy; 0x0auy; 0x49uy; 0xe9uy;
0x8duy; 0x0euy; 0xa7uy; 0x4auy; 0x0fuy; 0xafuy; 0x32uy; 0xd0uy; 0xe0uy; 0xb2uy; 0x3auy; 0x55uy;
0x58uy; 0xfeuy; 0x5cuy; 0x28uy; 0x70uy; 0x51uy; 0x23uy; 0xb0uy; 0x7buy; 0x6auy; 0x5fuy; 0x1euy;
0xb8uy; 0x17uy; 0xd7uy; 0x94uy; 0x15uy; 0x8fuy; 0xeeuy; 0x20uy; 0xc7uy; 0x42uy; 0x25uy; 0x3euy;
0x9auy; 0x14uy; 0xd7uy; 0x60uy; 0x72uy; 0x39uy; 0x47uy; 0x48uy; 0xa9uy; 0xfeuy; 0xdduy; 0x47uy;
0x0auy; 0xb1uy; 0xe6uy; 0x60uy; 0x28uy; 0x8cuy; 0x11uy; 0x68uy; 0xe1uy; 0xffuy; 0xd7uy; 0xceuy;
0xc8uy; 0xbeuy; 0xb3uy; 0xfeuy; 0x27uy; 0x30uy; 0x09uy; 0x70uy; 0xd7uy; 0xfauy; 0x02uy; 0x33uy;
0x3auy; 0x61uy; 0x2euy; 0xc7uy; 0xffuy; 0xa4uy; 0x2auy; 0xa8uy; 0x6euy; 0xb4uy; 0x79uy; 0x35uy;
0x6duy; 0x4cuy; 0x1euy; 0x38uy; 0xf8uy; 0xeeuy; 0xd4uy; 0x84uy; 0x4euy; 0x6euy; 0x28uy; 0xa7uy;
0xceuy; 0xc8uy; 0xc1uy; 0xcfuy; 0x80uy; 0x05uy; 0xf3uy; 0x04uy; 0xefuy; 0xc8uy; 0x18uy; 0x28uy;
0x2euy; 0x8duy; 0x5euy; 0x0cuy; 0xdfuy; 0xb8uy; 0x5fuy; 0x96uy; 0xe8uy; 0xc6uy; 0x9cuy; 0x2fuy;
0xe5uy; 0xa6uy; 0x44uy; 0xd7uy; 0xe7uy; 0x99uy; 0x44uy; 0x0cuy; 0xecuy; 0xd7uy; 0x05uy; 0x60uy;
0x97uy; 0xbbuy; 0x74uy; 0x77uy; 0x58uy; 0xd5uy; 0xbbuy; 0x48uy; 0xdeuy; 0x5auy; 0xb2uy; 0x54uy;
0x7fuy; 0x0euy; 0x46uy; 0x70uy; 0x6auy; 0x6fuy; 0x78uy; 0xa5uy; 0x08uy; 0x89uy; 0x05uy; 0x4euy;
0x7euy; 0xa0uy; 0x69uy; 0xb4uy; 0x40uy; 0x60uy; 0x55uy; 0x77uy; 0x75uy; 0x9buy; 0x19uy; 0xf2uy;
0xd5uy; 0x13uy; 0x80uy; 0x77uy; 0xf9uy; 0x4buy; 0x3fuy; 0x1euy; 0xeeuy; 0xe6uy; 0x76uy; 0x84uy;
0x7buy; 0x8cuy; 0xe5uy; 0x27uy; 0xa8uy; 0x0auy; 0x91uy; 0x01uy; 0x68uy; 0x71uy; 0x8auy; 0x3fuy;
0x06uy; 0xabuy; 0xf6uy; 0xa9uy; 0xa5uy; 0xe6uy; 0x72uy; 0x92uy; 0xe4uy; 0x67uy; 0xe2uy; 0xa2uy;
0x46uy; 0x35uy; 0x84uy; 0x55uy; 0x7duy; 0xcauy; 0xa8uy; 0x85uy; 0xd0uy; 0xf1uy; 0x3fuy; 0xbeuy;
0xd7uy; 0x34uy; 0x64uy; 0xfcuy; 0xaeuy; 0xe3uy; 0xe4uy; 0x04uy; 0x9fuy; 0x66uy; 0x02uy; 0xb9uy;
0x88uy; 0x10uy; 0xd9uy; 0xc4uy; 0x4cuy; 0x31uy; 0x43uy; 0x7auy; 0x93uy; 0xe2uy; 0x9buy; 0x56uy;
0x43uy; 0x84uy; 0xdcuy; 0xdcuy; 0xdeuy; 0x1duy; 0xa4uy; 0x02uy; 0x0euy; 0xc2uy; 0xefuy; 0xc3uy;
0xf8uy; 0x78uy; 0xd1uy; 0xb2uy; 0x6buy; 0x63uy; 0x18uy; 0xc9uy; 0xa9uy; 0xe5uy; 0x72uy; 0xd8uy;
0xf3uy; 0xb9uy; 0xd1uy; 0x8auy; 0xc7uy; 0x1auy; 0x02uy; 0x27uy; 0x20uy; 0x77uy; 0x10uy; 0xe5uy;
0xc8uy; 0xd4uy; 0x4auy; 0x47uy; 0xe5uy; 0xdfuy; 0x5fuy; 0x01uy; 0xaauy; 0xb0uy; 0xd4uy; 0x10uy;
0xbbuy; 0x69uy; 0xe3uy; 0x36uy; 0xc8uy; 0xe1uy; 0x3duy; 0x43uy; 0xfbuy; 0x86uy; 0xcduy; 0xccuy;
0xbfuy; 0xf4uy; 0x88uy; 0xe0uy; 0x20uy; 0xcauy; 0xb7uy; 0x1buy; 0xf1uy; 0x2fuy; 0x5cuy; 0xeeuy;
0xd4uy; 0xd3uy; 0xa3uy; 0xccuy; 0xa4uy; 0x1euy; 0x1cuy; 0x47uy; 0xfbuy; 0xbfuy; 0xfcuy; 0xa2uy;
0x41uy; 0x55uy; 0x9duy; 0xf6uy; 0x5auy; 0x5euy; 0x65uy; 0x32uy; 0x34uy; 0x7buy; 0x52uy; 0x8duy;
0xd5uy; 0xd0uy; 0x20uy; 0x60uy; 0x03uy; 0xabuy; 0x3fuy; 0x8cuy; 0xd4uy; 0x21uy; 0xeauy; 0x2auy;
0xd9uy; 0xc4uy; 0xd0uy; 0xd3uy; 0x65uy; 0xd8uy; 0x7auy; 0x13uy; 0x28uy; 0x62uy; 0x32uy; 0x4buy;
0x2cuy; 0x87uy; 0x93uy; 0xa8uy; 0xb4uy; 0x52uy; 0x45uy; 0x09uy; 0x44uy; 0xecuy; 0xecuy; 0xc3uy;
0x17uy; 0xdbuy; 0x9auy; 0x4duy; 0x5cuy; 0xa9uy; 0x11uy; 0xd4uy; 0x7duy; 0xafuy; 0x9euy; 0xf1uy;
0x2duy; 0xb2uy; 0x66uy; 0xc5uy; 0x1duy; 0xeduy; 0xb7uy; 0xcduy; 0x0buy; 0x25uy; 0x5euy; 0x30uy;
0x47uy; 0x3fuy; 0x40uy; 0xf4uy; 0xa1uy; 0xa0uy; 0x00uy; 0x94uy; 0x10uy; 0xc5uy; 0x6auy; 0x63uy;
0x1auy; 0xd5uy; 0x88uy; 0x92uy; 0x8euy; 0x82uy; 0x39uy; 0x87uy; 0x3cuy; 0x78uy; 0x65uy; 0x58uy;
0x42uy; 0x75uy; 0x5buy; 0xdduy; 0x77uy; 0x3euy; 0x09uy; 0x4euy; 0x76uy; 0x5buy; 0xe6uy; 0x0euy;
0x4duy; 0x38uy; 0xb2uy; 0xc0uy; 0xb8uy; 0x95uy; 0x01uy; 0x7auy; 0x10uy; 0xe0uy; 0xfbuy; 0x07uy;
0xf2uy; 0xabuy; 0x2duy; 0x8cuy; 0x32uy; 0xeduy; 0x2buy; 0xc0uy; 0x46uy; 0xc2uy; 0xf5uy; 0x38uy;
0x83uy; 0xf0uy; 0x17uy; 0xecuy; 0xc1uy; 0x20uy; 0x6auy; 0x9auy; 0x0buy; 0x00uy; 0xa0uy; 0x98uy;
0x22uy; 0x50uy; 0x23uy; 0xd5uy; 0x80uy; 0x6buy; 0xf6uy; 0x1fuy; 0xc3uy; 0xccuy; 0x97uy; 0xc9uy;
0x24uy; 0x9fuy; 0xf3uy; 0xafuy; 0x43uy; 0x14uy; 0xd5uy; 0xa0uy
]
in
assert_norm (List.Tot.length l = 1040);
B.gcmalloc_of_list HyperStack.root l | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i | 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)) | 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)) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 57,
"end_line": 1001,
"start_col": 0,
"start_line": 986
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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)) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i0 | 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)) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 59,
"end_line": 343,
"start_col": 0,
"start_line": 313
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i1 | 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) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 118,
"end_line": 408,
"start_col": 0,
"start_line": 363
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_full_felem5_eval_lemma_i0 | 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)) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 59,
"end_line": 772,
"start_col": 0,
"start_line": 742
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_reduce_felem5_fits_lemma_i0 | 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)) | 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) | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 130,
"end_line": 946,
"start_col": 0,
"start_line": 928
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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) | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry_wide_felem5_eval_lemma_i | 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]) | 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 =
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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 456,
"start_col": 0,
"start_line": 418
} | 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]) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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 ]) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
Hacl.Poly1305.Field32xN.Lemmas1.fst | Hacl.Poly1305.Field32xN.Lemmas1.carry26_wide_fits_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)) | 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 =
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 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas1.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 38,
"end_line": 133,
"start_col": 0,
"start_line": 122
} | 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)) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false |
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)) | FStar.Pervasives.Lemma | [
"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"
] | [] | false | false | true | false | 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 | false |
FStar.Universe.PCM.fst | FStar.Universe.PCM.raise_frame_preserving_upd | 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) | 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 #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 | {
"file_name": "ulib/experimental/FStar.Universe.PCM.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 11,
"end_line": 46,
"start_col": 0,
"start_line": 39
} | (*
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));
} | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | 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) | Prims.Tot | [
"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"
] | [] | false | false | false | false | false | 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) =
| 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 | false |
FStar.Universe.PCM.fst | FStar.Universe.PCM.raise | val raise (#a: Type) (p: pcm a) : pcm (raise_t u#a u#b a) | 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)
= {
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));
} | {
"file_name": "ulib/experimental/FStar.Universe.PCM.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 5,
"end_line": 37,
"start_col": 0,
"start_line": 24
} | (*
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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | p: FStar.PCM.pcm a -> FStar.PCM.pcm (FStar.Universe.raise_t a) | Prims.Tot | [
"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"
] | [] | false | false | false | true | 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))
} | false |
EverParse3d.InputStream.All.fst | EverParse3d.InputStream.All.t | val t : Type0 | val t : Type0 | let t = t | {
"file_name": "src/3d/prelude/extern/EverParse3d.InputStream.All.fst",
"git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | {
"end_col": 9,
"end_line": 7,
"start_col": 0,
"start_line": 7
} | module EverParse3d.InputStream.All
open EverParse3d.InputStream.Extern
module Aux = EverParse3d.InputStream.Extern.Base | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"EverParse3d.InputStream.Extern.Base.fsti.checked",
"EverParse3d.InputStream.Extern.fst.checked"
],
"interface_file": true,
"source_file": "EverParse3d.InputStream.All.fst"
} | [
{
"abbrev": true,
"full_module": "EverParse3d.InputStream.Extern.Base",
"short_module": "Aux"
},
{
"abbrev": false,
"full_module": "EverParse3d.InputStream.Extern",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverParse3d.InputStream.Base",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverParse3d.InputStream",
"short_module": null
},
{
"abbrev": false,
"full_module": "EverParse3d.InputStream",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 2,
"max_fuel": 0,
"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": [
"smt.qi.eager_threshold=100"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 8,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | Type0 | Prims.Tot | [
"total"
] | [] | [
"EverParse3d.InputStream.Extern.t"
] | [] | false | false | false | true | true | let t =
| t | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.shift_gf128_key_1 | val shift_gf128_key_1 (h: poly) : poly | val shift_gf128_key_1 (h: poly) : poly | let shift_gf128_key_1 (h:poly) : poly =
shift_key_1 128 gf128_modulus_low_terms h | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 43,
"end_line": 13,
"start_col": 0,
"start_line": 12
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | h: Vale.Math.Poly2_s.poly -> Vale.Math.Poly2_s.poly | Prims.Tot | [
"total"
] | [] | [
"Vale.Math.Poly2_s.poly",
"Vale.AES.GF128.shift_key_1",
"Vale.AES.GF128_s.gf128_modulus_low_terms"
] | [] | false | false | false | true | false | let shift_gf128_key_1 (h: poly) : poly =
| shift_key_1 128 gf128_modulus_low_terms h | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.gf128_power | val gf128_power (h: poly) (n: nat) : poly | val gf128_power (h: poly) (n: nat) : poly | let gf128_power (h:poly) (n:nat) : poly = shift_gf128_key_1 (g_power h n) | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 73,
"end_line": 20,
"start_col": 0,
"start_line": 20
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.Math.Poly2_s.poly | Prims.Tot | [
"total"
] | [] | [
"Vale.Math.Poly2_s.poly",
"Prims.nat",
"Vale.AES.OptPublic.shift_gf128_key_1",
"Vale.AES.OptPublic.g_power"
] | [] | false | false | false | true | false | let gf128_power (h: poly) (n: nat) : poly =
| shift_gf128_key_1 (g_power h n) | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.get_hkeys_reqs_injective | val get_hkeys_reqs_injective (h_BE:quad32) (s1 s2:Seq.seq quad32) : Lemma
(requires
Seq.length s1 = 8 /\ Seq.length s2 = 8 /\
hkeys_reqs_pub s1 h_BE /\ hkeys_reqs_pub s2 h_BE)
(ensures s1 == s2) | val get_hkeys_reqs_injective (h_BE:quad32) (s1 s2:Seq.seq quad32) : Lemma
(requires
Seq.length s1 = 8 /\ Seq.length s2 = 8 /\
hkeys_reqs_pub s1 h_BE /\ hkeys_reqs_pub s2 h_BE)
(ensures s1 == s2) | let get_hkeys_reqs_injective h_BE s1 s2 =
lemma_of_quad32_inj (Seq.index s1 0) (Seq.index s2 0);
lemma_of_quad32_inj (Seq.index s1 1) (Seq.index s2 1);
lemma_of_quad32_inj (Seq.index s1 3) (Seq.index s2 3);
lemma_of_quad32_inj (Seq.index s1 4) (Seq.index s2 4);
lemma_of_quad32_inj (Seq.index s1 6) (Seq.index s2 6);
lemma_of_quad32_inj (Seq.index s1 7) (Seq.index s2 7);
assert (Seq.equal s1 s2) | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 26,
"end_line": 84,
"start_col": 0,
"start_line": 77
} | 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')
(ensures q == q')
= lemma_to_of_quad32 q; lemma_to_of_quad32 q' | {
"checked_file": "/",
"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"
} | [
{
"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": "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
}
] | {
"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"
} | false |
h_BE: Vale.Def.Types_s.quad32 ->
s1: FStar.Seq.Base.seq Vale.Def.Types_s.quad32 ->
s2: FStar.Seq.Base.seq Vale.Def.Types_s.quad32
-> FStar.Pervasives.Lemma
(requires
FStar.Seq.Base.length s1 = 8 /\ FStar.Seq.Base.length s2 = 8 /\
Vale.AES.OptPublic.hkeys_reqs_pub s1 h_BE /\ Vale.AES.OptPublic.hkeys_reqs_pub s2 h_BE)
(ensures s1 == s2) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Vale.Def.Types_s.quad32",
"FStar.Seq.Base.seq",
"Prims._assert",
"FStar.Seq.Base.equal",
"Prims.unit",
"Vale.AES.OptPublic.lemma_of_quad32_inj",
"FStar.Seq.Base.index"
] | [] | true | false | true | false | false | let get_hkeys_reqs_injective h_BE s1 s2 =
| lemma_of_quad32_inj (Seq.index s1 0) (Seq.index s2 0);
lemma_of_quad32_inj (Seq.index s1 1) (Seq.index s2 1);
lemma_of_quad32_inj (Seq.index s1 3) (Seq.index s2 3);
lemma_of_quad32_inj (Seq.index s1 4) (Seq.index s2 4);
lemma_of_quad32_inj (Seq.index s1 6) (Seq.index s2 6);
lemma_of_quad32_inj (Seq.index s1 7) (Seq.index s2 7);
assert (Seq.equal s1 s2) | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.lemma_of_quad32_inj | val lemma_of_quad32_inj (q q': quad32)
: Lemma (requires of_quad32 q == of_quad32 q') (ensures q == 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')
= lemma_to_of_quad32 q; lemma_to_of_quad32 q' | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 47,
"end_line": 75,
"start_col": 0,
"start_line": 72
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"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"
} | false | 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') | FStar.Pervasives.Lemma | [
"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"
] | [] | true | false | true | false | 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' | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.g_power | val g_power (a: poly) (n: nat) : poly | val g_power (a: poly) (n: nat) : poly | 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) | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 24,
"end_line": 18,
"start_col": 0,
"start_line": 15
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.Math.Poly2_s.poly | Prims.Tot | [
"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"
] | [
"recursion"
] | false | false | false | true | false | let rec g_power (a: poly) (n: nat) : poly =
| if n = 0 then zero else if n = 1 then a else a *~ g_power a (n - 1) | false |
FStar.BufferNG.fst | FStar.BufferNG.typ | val typ : Type0 | let typ = (t: P.typ { supported t } ) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 37,
"end_line": 43,
"start_col": 0,
"start_line": 43
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l' | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | Type0 | Prims.Tot | [
"total"
] | [] | [
"FStar.Pointer.Base.typ",
"Prims.b2t",
"FStar.BufferNG.supported"
] | [] | false | false | false | true | true | let typ =
| (t: P.typ{supported t}) | false |
|
FStar.BufferNG.fst | FStar.BufferNG.unused_in | val unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 | val unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 | let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 24,
"end_line": 57,
"start_col": 0,
"start_line": 56
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> h: FStar.Monotonic.HyperStack.mem -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Monotonic.HyperStack.mem",
"FStar.Pointer.Base.buffer_unused_in"
] | [] | false | false | false | false | true | let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
| P.buffer_unused_in b h | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.hkeys_reqs_pub | val hkeys_reqs_pub (hkeys:FStar.Seq.seq quad32) (h_BE:quad32) : Vale.Def.Prop_s.prop0 | 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
=
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 | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 46,
"end_line": 33,
"start_col": 0,
"start_line": 22
} | 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) | {
"checked_file": "/",
"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"
} | [
{
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | hkeys: FStar.Seq.Base.seq Vale.Def.Types_s.quad32 -> h_BE: Vale.Def.Types_s.quad32
-> Vale.Def.Prop_s.prop0 | Prims.Tot | [
"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"
] | [] | false | false | false | true | 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 /\ of_quad32 (index hkeys 6) == gf128_power h 5 /\
of_quad32 (index hkeys 7) == gf128_power h 6 | false |
FStar.BufferNG.fst | FStar.BufferNG.buffer | val buffer (t: typ) : Tot Type0 | val buffer (t: typ) : Tot Type0 | let buffer
(t: typ)
: Tot Type0
= P.buffer t | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 12,
"end_line": 49,
"start_col": 0,
"start_line": 46
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } ) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | t: FStar.BufferNG.typ -> Type0 | Prims.Tot | [
"total"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Pointer.Base.buffer"
] | [] | false | false | false | true | true | let buffer (t: typ) : Tot Type0 =
| P.buffer t | false |
FStar.BufferNG.fst | FStar.BufferNG.live | val live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 | val live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 | let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 23,
"end_line": 53,
"start_col": 0,
"start_line": 52
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | h: FStar.Monotonic.HyperStack.mem -> b: FStar.BufferNG.buffer a -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperStack.mem",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_readable"
] | [] | false | false | false | false | true | let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
| P.buffer_readable h b | false |
FStar.BufferNG.fst | FStar.BufferNG.frameOf | val frameOf (#a: typ) (b: buffer a) : GTot HH.rid | val frameOf (#a: typ) (b: buffer a) : GTot HH.rid | let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 20,
"end_line": 69,
"start_col": 0,
"start_line": 68
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> Prims.GTot FStar.Monotonic.HyperHeap.rid | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.frameOf_buffer",
"FStar.Monotonic.HyperHeap.rid"
] | [] | false | false | false | false | false | let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
| P.frameOf_buffer b | false |
FStar.BufferNG.fst | FStar.BufferNG.as_addr | val as_addr (#a: typ) (b: buffer a) : GTot nat | val as_addr (#a: typ) (b: buffer a) : GTot nat | let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 20,
"end_line": 65,
"start_col": 0,
"start_line": 64
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> Prims.GTot Prims.nat | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_as_addr",
"Prims.nat"
] | [] | false | false | false | false | false | let as_addr (#a: typ) (b: buffer a) : GTot nat =
| P.buffer_as_addr b | false |
FStar.BufferNG.fst | FStar.BufferNG.includes | val includes (#a: typ) (x y: buffer a) : GTot Type0 | val includes (#a: typ) (x y: buffer a) : GTot Type0 | let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 23,
"end_line": 84,
"start_col": 0,
"start_line": 80
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b' | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: FStar.BufferNG.buffer a -> y: FStar.BufferNG.buffer a -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_includes"
] | [] | false | false | false | false | true | let includes (#a: typ) (x y: buffer a) : GTot Type0 =
| P.buffer_includes x y | false |
FStar.BufferNG.fst | FStar.BufferNG.disjoint | val disjoint (#a #a': typ) (x: buffer a) (y: buffer a') : GTot Type0 | val disjoint (#a #a': typ) (x: buffer a) (y: buffer a') : GTot Type0 | let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 50,
"end_line": 109,
"start_col": 0,
"start_line": 108
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: FStar.BufferNG.buffer a -> y: FStar.BufferNG.buffer a' -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.loc_disjoint",
"FStar.Pointer.Base.loc_buffer"
] | [] | false | false | false | false | true | let disjoint (#a #a': typ) (x: buffer a) (y: buffer a') : GTot Type0 =
| P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y) | false |
FStar.BufferNG.fst | FStar.BufferNG.p | val p (#a: typ) (init: list (P.type_of_typ a)) : GTot Type0 | val p (#a: typ) (init: list (P.type_of_typ a)) : GTot Type0 | let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 58,
"end_line": 162,
"start_col": 7,
"start_line": 160
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | init: Prims.list (FStar.Pointer.Base.type_of_typ a) -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"Prims.list",
"FStar.Pointer.Base.type_of_typ",
"Prims.l_and",
"FStar.Pervasives.normalize",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.List.Tot.Base.length",
"FStar.UInt.max_int"
] | [] | false | false | false | false | true | let p (#a: typ) (init: list (P.type_of_typ a)) : GTot Type0 =
| normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32) | false |
FStar.BufferNG.fst | FStar.BufferNG.includes_trans | val includes_trans (#a: _) (x y z: buffer a)
: Lemma (requires (x `includes` y /\ y `includes` z)) (ensures (x `includes` z)) | val includes_trans (#a: _) (x y z: buffer a)
: Lemma (requires (x `includes` y /\ y `includes` z)) (ensures (x `includes` z)) | let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 31,
"end_line": 105,
"start_col": 0,
"start_line": 101
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: FStar.BufferNG.buffer a -> y: FStar.BufferNG.buffer a -> z: FStar.BufferNG.buffer a
-> FStar.Pervasives.Lemma (requires FStar.BufferNG.includes x y /\ FStar.BufferNG.includes y z)
(ensures FStar.BufferNG.includes x z) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_includes_trans",
"Prims.unit",
"Prims.l_and",
"FStar.BufferNG.includes",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let includes_trans #a (x: buffer a) (y: buffer a) (z: buffer a)
: Lemma (requires (x `includes` y /\ y `includes` z)) (ensures (x `includes` z)) =
| P.buffer_includes_trans x y z | false |
FStar.BufferNG.fst | FStar.BufferNG.q | val q (#a: typ) (len: nat) (buf: buffer a) : GTot Type0 | val q (#a: typ) (len: nat) (buf: buffer a) : GTot Type0 | let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 31,
"end_line": 165,
"start_col": 7,
"start_line": 164
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | len: Prims.nat -> buf: FStar.BufferNG.buffer a -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"Prims.nat",
"FStar.BufferNG.buffer",
"FStar.Pervasives.normalize",
"Prims.eq2",
"FStar.BufferNG.length"
] | [] | false | false | false | false | true | let q (#a: typ) (len: nat) (buf: buffer a) : GTot Type0 =
| normalize (length buf == len) | false |
FStar.BufferNG.fst | FStar.BufferNG.equal | val equal (#a: typ) (h: HS.mem) (b: buffer a) (h': HS.mem) (b': buffer a) : GTot Type0 | val equal (#a: typ) (h: HS.mem) (b: buffer a) (h': HS.mem) (b': buffer a) : GTot Type0 | let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b' | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 28,
"end_line": 77,
"start_col": 0,
"start_line": 76
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
h: FStar.Monotonic.HyperStack.mem ->
b: FStar.BufferNG.buffer a ->
h': FStar.Monotonic.HyperStack.mem ->
b': FStar.BufferNG.buffer a
-> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperStack.mem",
"FStar.BufferNG.buffer",
"Prims.eq2",
"FStar.Seq.Base.seq",
"FStar.Pointer.Base.type_of_typ",
"Prims.l_or",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.BufferNG.length",
"FStar.BufferNG.as_seq"
] | [] | false | false | false | false | true | let equal (#a: typ) (h: HS.mem) (b: buffer a) (h': HS.mem) (b': buffer a) : GTot Type0 =
| as_seq h b == as_seq h' b' | false |
FStar.BufferNG.fst | FStar.BufferNG.struct_typ_supported | val struct_typ_supported (l: list (string * P.typ)) : Tot bool | val struct_typ_supported (l: list (string * P.typ)) : Tot bool | let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l' | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 58,
"end_line": 41,
"start_col": 0,
"start_line": 28
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | l: Prims.list (Prims.string * FStar.Pointer.Base.typ) -> Prims.bool | Prims.Tot | [
"total"
] | [
"supported",
"struct_typ_supported"
] | [
"Prims.list",
"FStar.Pervasives.Native.tuple2",
"Prims.string",
"FStar.Pointer.Base.typ",
"Prims.op_AmpAmp",
"FStar.BufferNG.supported",
"FStar.BufferNG.struct_typ_supported",
"Prims.bool"
] | [
"mutual recursion"
] | false | false | false | true | false | let rec struct_typ_supported (l: list (string * P.typ)) : Tot bool =
| match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l' | false |
FStar.BufferNG.fst | FStar.BufferNG.length | val length (#a: typ) (b: buffer a) : GTot nat | val length (#a: typ) (b: buffer a) : GTot nat | let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 30,
"end_line": 61,
"start_col": 0,
"start_line": 60
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> Prims.GTot Prims.nat | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.v",
"FStar.Pointer.Base.buffer_length",
"Prims.nat"
] | [] | false | false | false | false | false | let length (#a: typ) (b: buffer a) : GTot nat =
| UInt32.v (P.buffer_length b) | false |
Vale.AES.OptPublic.fst | Vale.AES.OptPublic.get_hkeys_reqs | val get_hkeys_reqs (h_BE:quad32) : (s:Seq.lseq quad32 8{hkeys_reqs_pub s h_BE}) | val get_hkeys_reqs (h_BE:quad32) : (s:Seq.lseq quad32 8{hkeys_reqs_pub s h_BE}) | 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 | {
"file_name": "vale/code/crypto/aes/Vale.AES.OptPublic.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 3,
"end_line": 68,
"start_col": 0,
"start_line": 40
} | 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 | {
"checked_file": "/",
"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"
} | [
{
"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": "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
}
] | {
"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"
} | false | h_BE: Vale.Def.Types_s.quad32
-> s:
FStar.Seq.Properties.lseq Vale.Def.Types_s.quad32 8 {Vale.AES.OptPublic.hkeys_reqs_pub s h_BE} | Prims.Tot | [
"total"
] | [] | [
"Vale.Def.Types_s.quad32",
"Prims.unit",
"Prims._assert",
"Vale.AES.OptPublic.hkeys_reqs_pub",
"Vale.Math.Poly2.Bits.lemma_of_to_quad32",
"Vale.AES.OptPublic.gf128_power",
"FStar.Seq.Properties.lemma_seq_of_list_induction",
"FStar.List.Tot.Base.tl",
"FStar.Seq.Base.seq",
"Prims.eq2",
"Prims.nat",
"FStar.List.Tot.Base.length",
"FStar.Seq.Base.length",
"FStar.Seq.Base.seq_of_list",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Prims.list",
"Prims.Cons",
"Vale.Math.Poly2.Bits_s.to_quad32",
"Vale.Def.Words_s.Mkfour",
"Vale.Def.Types_s.nat32",
"Prims.Nil",
"Vale.Math.Poly2_s.poly",
"Vale.Math.Poly2.Bits_s.of_quad32",
"Vale.Def.Types_s.reverse_bytes_quad32",
"FStar.Seq.Properties.lseq"
] | [] | false | false | false | false | false | 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 | false |
FStar.BufferNG.fst | FStar.BufferNG.includes_live | val includes_live (#a: typ) (h: HS.mem) (x y: buffer a)
: Lemma (requires (x `includes` y /\ live h x)) (ensures (live h y)) | val includes_live (#a: typ) (h: HS.mem) (x y: buffer a)
: Lemma (requires (x `includes` y /\ live h x)) (ensures (live h y)) | let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 28,
"end_line": 93,
"start_col": 0,
"start_line": 86
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | h: FStar.Monotonic.HyperStack.mem -> x: FStar.BufferNG.buffer a -> y: FStar.BufferNG.buffer a
-> FStar.Pervasives.Lemma (requires FStar.BufferNG.includes x y /\ FStar.BufferNG.live h x)
(ensures FStar.BufferNG.live h y) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperStack.mem",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_includes_elim",
"Prims.unit",
"Prims.l_and",
"FStar.BufferNG.includes",
"FStar.BufferNG.live",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let includes_live (#a: typ) (h: HS.mem) (x y: buffer a)
: Lemma (requires (x `includes` y /\ live h x)) (ensures (live h y)) =
| P.buffer_includes_elim x y | false |
FStar.BufferNG.fst | FStar.BufferNG.lemma_disjoint_sub | val lemma_disjoint_sub (#a #a': _) (x subx: buffer a) (y: buffer a')
: Lemma (requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)] | val lemma_disjoint_sub (#a #a': _) (x subx: buffer a) (y: buffer a')
: Lemma (requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)] | let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 98,
"end_line": 123,
"start_col": 0,
"start_line": 118
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: FStar.BufferNG.buffer a -> subx: FStar.BufferNG.buffer a -> y: FStar.BufferNG.buffer a'
-> FStar.Pervasives.Lemma (requires FStar.BufferNG.includes x subx /\ FStar.BufferNG.disjoint x y)
(ensures FStar.BufferNG.disjoint subx y)
[SMTPat (FStar.BufferNG.disjoint subx y); SMTPat (FStar.BufferNG.includes x subx)] | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.loc_disjoint_includes",
"FStar.Pointer.Base.loc_buffer",
"Prims.unit",
"FStar.Pointer.Base.buffer_includes_loc_includes",
"Prims.l_and",
"FStar.BufferNG.includes",
"FStar.BufferNG.disjoint",
"Prims.squash",
"Prims.Cons",
"FStar.Pervasives.pattern",
"FStar.Pervasives.smt_pat",
"Prims.Nil"
] | [] | true | false | true | false | false | let lemma_disjoint_sub #a #a' (x: buffer a) (subx: buffer a) (y: buffer a')
: Lemma (requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)] =
| P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y) | false |
FStar.BufferNG.fst | FStar.BufferNG.supported | val supported (t: P.typ) : Tot bool | val supported (t: P.typ) : Tot bool | let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l' | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 58,
"end_line": 41,
"start_col": 0,
"start_line": 28
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | t: FStar.Pointer.Base.typ -> Prims.bool | Prims.Tot | [
"total"
] | [
"supported",
"struct_typ_supported"
] | [
"FStar.Pointer.Base.typ",
"FStar.Pointer.Base.base_typ",
"FStar.Pointer.Base.struct_typ",
"FStar.BufferNG.struct_typ_supported",
"FStar.Pointer.Base.__proj__Mkstruct_typ__item__fields",
"Prims.bool"
] | [
"mutual recursion"
] | false | false | false | true | false | let rec supported (t: P.typ) : Tot bool =
| match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false | false |
FStar.BufferNG.fst | FStar.BufferNG.gsub | val gsub (#a: typ) (b: buffer a) (i len: UInt32.t)
: Ghost (buffer a) (requires (UInt32.v i + UInt32.v len <= length b)) (ensures (fun _ -> True)) | val gsub (#a: typ) (b: buffer a) (i len: UInt32.t)
: Ghost (buffer a) (requires (UInt32.v i + UInt32.v len <= length b)) (ensures (fun _ -> True)) | let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 23,
"end_line": 275,
"start_col": 0,
"start_line": 267
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> i: FStar.UInt32.t -> len: FStar.UInt32.t
-> Prims.Ghost (FStar.BufferNG.buffer a) | Prims.Ghost | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.gsub_buffer",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"FStar.UInt32.v",
"FStar.BufferNG.length",
"Prims.l_True"
] | [] | false | false | false | false | false | let gsub (#a: typ) (b: buffer a) (i len: UInt32.t)
: Ghost (buffer a) (requires (UInt32.v i + UInt32.v len <= length b)) (ensures (fun _ -> True)) =
| P.gsub_buffer b i len | false |
FStar.BufferNG.fst | FStar.BufferNG.as_seq | val as_seq (#a: typ) (h: HS.mem) (b: buffer a)
: GTot (s: Seq.seq (P.type_of_typ a) {Seq.length s == length b}) | val as_seq (#a: typ) (h: HS.mem) (b: buffer a)
: GTot (s: Seq.seq (P.type_of_typ a) {Seq.length s == length b}) | let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 21,
"end_line": 73,
"start_col": 0,
"start_line": 72
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | h: FStar.Monotonic.HyperStack.mem -> b: FStar.BufferNG.buffer a
-> Prims.GTot
(s:
FStar.Seq.Base.seq (FStar.Pointer.Base.type_of_typ a)
{FStar.Seq.Base.length s == FStar.BufferNG.length b}) | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperStack.mem",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_as_seq",
"FStar.Seq.Base.seq",
"FStar.Pointer.Base.type_of_typ",
"Prims.eq2",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.BufferNG.length"
] | [] | false | false | false | false | false | let as_seq (#a: typ) (h: HS.mem) (b: buffer a)
: GTot (s: Seq.seq (P.type_of_typ a) {Seq.length s == length b}) =
| P.buffer_as_seq h b | false |
FStar.BufferNG.fst | FStar.BufferNG.create | val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
)) | val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
)) | let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 158,
"start_col": 0,
"start_line": 155
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | init: FStar.Pointer.Base.type_of_typ a -> len: FStar.UInt32.t
-> FStar.HyperStack.ST.StackInline (FStar.BufferNG.buffer a) | FStar.HyperStack.ST.StackInline | [] | [] | [
"FStar.BufferNG.typ",
"FStar.Pointer.Base.type_of_typ",
"FStar.UInt32.t",
"FStar.Pointer.Base.buffer_of_array_pointer",
"FStar.Pointer.Base.buffer",
"FStar.Pointer.Base.pointer",
"FStar.Pointer.Base.TArray",
"FStar.Pointer.Base.screate",
"FStar.Pervasives.Native.Some",
"FStar.Seq.Base.create",
"FStar.UInt32.v",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.array_length_t"
] | [] | false | true | false | false | false | let create #a init len =
| let len:P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content | false |
FStar.BufferNG.fst | FStar.BufferNG.offset | val offset (#a: typ) (b: buffer a) (i: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 -> live h0 b /\ UInt32.v i <= length b))
(ensures (fun h0 b' h1 -> h1 == h0 /\ UInt32.v i <= length b /\ b' == goffset b i)) | val offset (#a: typ) (b: buffer a) (i: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 -> live h0 b /\ UInt32.v i <= length b))
(ensures (fun h0 b' h1 -> h1 == h0 /\ UInt32.v i <= length b /\ b' == goffset b i)) | let offset
(#a:typ)
(b:buffer a)
(i:UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 ->
live h0 b /\
UInt32.v i <= length b
))
(ensures (fun h0 b' h1 ->
h1 == h0 /\
UInt32.v i <= length b /\
b' == goffset b i
))
= P.offset_buffer b i | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 21,
"end_line": 370,
"start_col": 0,
"start_line": 356
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *)
let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> i: FStar.UInt32.t
-> FStar.HyperStack.ST.Stack (FStar.BufferNG.buffer a) | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.offset_buffer",
"FStar.Pointer.Base.buffer",
"FStar.Monotonic.HyperStack.mem",
"Prims.l_and",
"FStar.BufferNG.live",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"FStar.BufferNG.length",
"Prims.eq2",
"FStar.BufferNG.goffset"
] | [] | false | true | false | false | false | let offset (#a: typ) (b: buffer a) (i: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 -> live h0 b /\ UInt32.v i <= length b))
(ensures (fun h0 b' h1 -> h1 == h0 /\ UInt32.v i <= length b /\ b' == goffset b i)) =
| P.offset_buffer b i | false |
FStar.BufferNG.fst | FStar.BufferNG.includes_as_seq | val includes_as_seq (#a h1 h2: _) (x y: buffer a)
: Lemma (requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y)) | val includes_as_seq (#a h1 h2: _) (x y: buffer a)
: Lemma (requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y)) | let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 28,
"end_line": 99,
"start_col": 0,
"start_line": 95
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
h1: FStar.Monotonic.HyperStack.mem ->
h2: FStar.Monotonic.HyperStack.mem ->
x: FStar.BufferNG.buffer a ->
y: FStar.BufferNG.buffer a
-> FStar.Pervasives.Lemma
(requires
FStar.BufferNG.includes x y /\ FStar.BufferNG.as_seq h1 x == FStar.BufferNG.as_seq h2 x)
(ensures FStar.BufferNG.as_seq h1 y == FStar.BufferNG.as_seq h2 y) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperStack.mem",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.buffer_includes_elim",
"Prims.unit",
"Prims.l_and",
"FStar.BufferNG.includes",
"Prims.eq2",
"FStar.Seq.Base.seq",
"FStar.Pointer.Base.type_of_typ",
"Prims.l_or",
"Prims.nat",
"FStar.Seq.Base.length",
"FStar.BufferNG.length",
"FStar.BufferNG.as_seq",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma (requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y)) =
| P.buffer_includes_elim x y | false |
FStar.BufferNG.fst | FStar.BufferNG.sub | val sub (#a: typ) (b: buffer a) (i len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h -> live h b /\ UInt32.v i + UInt32.v len <= length b))
(ensures
(fun h0 b' h1 ->
live h0 b /\ UInt32.v i + UInt32.v len <= length b /\ h1 == h0 /\ b' == gsub b i len /\
b `includes` b')) | val sub (#a: typ) (b: buffer a) (i len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h -> live h b /\ UInt32.v i + UInt32.v len <= length b))
(ensures
(fun h0 b' h1 ->
live h0 b /\ UInt32.v i + UInt32.v len <= length b /\ h1 == h0 /\ b' == gsub b i len /\
b `includes` b')) | let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 22,
"end_line": 294,
"start_col": 0,
"start_line": 277
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> i: FStar.UInt32.t -> len: FStar.UInt32.t
-> FStar.HyperStack.ST.Stack (FStar.BufferNG.buffer a) | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.sub_buffer",
"FStar.Pointer.Base.buffer",
"FStar.Monotonic.HyperStack.mem",
"Prims.l_and",
"FStar.BufferNG.live",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"FStar.UInt32.v",
"FStar.BufferNG.length",
"Prims.eq2",
"FStar.BufferNG.gsub",
"FStar.BufferNG.includes"
] | [] | false | true | false | false | false | let sub (#a: typ) (b: buffer a) (i len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h -> live h b /\ UInt32.v i + UInt32.v len <= length b))
(ensures
(fun h0 b' h1 ->
live h0 b /\ UInt32.v i + UInt32.v len <= length b /\ h1 == h0 /\ b' == gsub b i len /\
b `includes` b')) =
| P.sub_buffer b i len | false |
FStar.BufferNG.fst | FStar.BufferNG.createL | val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
)) | val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
)) | let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 191,
"start_col": 0,
"start_line": 187
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 1,
"max_fuel": 1,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | init: Prims.list (FStar.Pointer.Base.type_of_typ a)
-> FStar.HyperStack.ST.StackInline (FStar.BufferNG.buffer a) | FStar.HyperStack.ST.StackInline | [] | [] | [
"FStar.BufferNG.typ",
"Prims.list",
"FStar.Pointer.Base.type_of_typ",
"FStar.Pointer.Base.buffer_of_array_pointer",
"FStar.Pointer.Base.buffer",
"FStar.Pointer.Base.pointer",
"FStar.Pointer.Base.TArray",
"FStar.Pointer.Base.screate",
"FStar.Pervasives.Native.Some",
"FStar.BufferNG.buffer",
"FStar.Seq.Base.seq",
"Prims.eq2",
"Prims.nat",
"FStar.List.Tot.Base.length",
"FStar.Seq.Base.length",
"FStar.Seq.Base.seq_of_list",
"FStar.Pointer.Base.array_length_t",
"FStar.UInt32.uint_to_t"
] | [] | false | true | false | false | false | let createL #a init =
| let len:P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content | false |
FStar.BufferNG.fst | FStar.BufferNG.live_slice_middle | val live_slice_middle
(#t: typ)
(b: buffer t)
(i: UInt32.t)
(len: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b 0ul i) /\
live h (gsub b i len) /\ (
let off = UInt32.add i len in
live h (gsub b off (UInt32.sub (P.buffer_length b) off))
)))
(ensures (live h b))
[SMTPat (live h (gsub b i len))] | val live_slice_middle
(#t: typ)
(b: buffer t)
(i: UInt32.t)
(len: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b 0ul i) /\
live h (gsub b i len) /\ (
let off = UInt32.add i len in
live h (gsub b off (UInt32.sub (P.buffer_length b) off))
)))
(ensures (live h b))
[SMTPat (live h (gsub b i len))] | let live_slice_middle #t b i len h =
P.buffer_readable_gsub_merge b i len h | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 40,
"end_line": 442,
"start_col": 0,
"start_line": 441
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *)
let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i)
let offset
(#a:typ)
(b:buffer a)
(i:UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 ->
live h0 b /\
UInt32.v i <= length b
))
(ensures (fun h0 b' h1 ->
h1 == h0 /\
UInt32.v i <= length b /\
b' == goffset b i
))
= P.offset_buffer b i
let lemma_offset_spec
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i <= length b /\
live h b
))
(ensures (
UInt32.v i <= length b /\
as_seq h (goffset b i) == Seq.slice (as_seq h b) (UInt32.v i) (length b)
))
= ()
val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
))
let eqb #a b1 b2 len =
P.buffer_contents_equal b1 b2 len
(* JP: if the [val] is not specified, there's an issue with these functions
* taking an extra unification parameter at extraction-time... *)
val op_Array_Access: #a:typ -> b:buffer a -> n:UInt32.t -> HST.Stack (P.type_of_typ a)
(requires (fun h -> UInt32.v n<length b /\ live h b))
(ensures (fun h0 z h1 -> h1 == h0 /\
UInt32.v n<length b /\
z == Seq.index (as_seq h0 b) (UInt32.v n)))
let op_Array_Access #a b n = index #a b n
val op_Array_Assignment: #a:typ -> b:buffer a -> n:UInt32.t -> z:P.type_of_typ a -> HST.Stack unit
(requires (fun h -> live h b /\ UInt32.v n < length b))
(ensures (fun h0 _ h1 -> live h0 b /\ live h1 b /\ UInt32.v n < length b
/\ P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1
/\ as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z ))
let op_Array_Assignment #a b n z = upd #a b n z
val live_slice_middle
(#t: typ)
(b: buffer t)
(i: UInt32.t)
(len: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b 0ul i) /\
live h (gsub b i len) /\ (
let off = UInt32.add i len in
live h (gsub b off (UInt32.sub (P.buffer_length b) off))
)))
(ensures (live h b))
[SMTPat (live h (gsub b i len))] | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
b: FStar.BufferNG.buffer t ->
i: FStar.UInt32.t ->
len: FStar.UInt32.t ->
h: FStar.Monotonic.HyperStack.mem
-> FStar.Pervasives.Lemma
(requires
FStar.UInt32.v i + FStar.UInt32.v len <= FStar.BufferNG.length b /\
FStar.BufferNG.live h (FStar.BufferNG.gsub b 0ul i) /\
FStar.BufferNG.live h (FStar.BufferNG.gsub b i len) /\
(let off = FStar.UInt32.add i len in
FStar.BufferNG.live h
(FStar.BufferNG.gsub b off (FStar.UInt32.sub (FStar.Pointer.Base.buffer_length b) off)))
)
(ensures FStar.BufferNG.live h b)
[SMTPat (FStar.BufferNG.live h (FStar.BufferNG.gsub b i len))] | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Monotonic.HyperStack.mem",
"FStar.Pointer.Derived1.buffer_readable_gsub_merge",
"Prims.unit"
] | [] | true | false | true | false | false | let live_slice_middle #t b i len h =
| P.buffer_readable_gsub_merge b i len h | false |
FStar.BufferNG.fst | FStar.BufferNG.goffset | val goffset (#a: typ) (b: buffer a) (i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures
(fun b' -> UInt32.v i <= length b /\ b' == gsub b i (UInt32.sub (P.buffer_length b) i))) | val goffset (#a: typ) (b: buffer a) (i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures
(fun b' -> UInt32.v i <= length b /\ b' == gsub b i (UInt32.sub (P.buffer_length b) i))) | let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 54,
"end_line": 354,
"start_col": 0,
"start_line": 344
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> i: FStar.UInt32.t -> Prims.Ghost (FStar.BufferNG.buffer a) | Prims.Ghost | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.gsub_buffer",
"FStar.UInt32.sub",
"FStar.Pointer.Base.buffer_length",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.UInt32.v",
"FStar.BufferNG.length",
"Prims.l_and",
"Prims.eq2",
"FStar.BufferNG.gsub"
] | [] | false | false | false | false | false | let goffset (#a: typ) (b: buffer a) (i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures
(fun b' -> UInt32.v i <= length b /\ b' == gsub b i (UInt32.sub (P.buffer_length b) i))) =
| P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i) | false |
FStar.BufferNG.fst | FStar.BufferNG.op_Array_Access | val op_Array_Access: #a:typ -> b:buffer a -> n:UInt32.t -> HST.Stack (P.type_of_typ a)
(requires (fun h -> UInt32.v n<length b /\ live h b))
(ensures (fun h0 z h1 -> h1 == h0 /\
UInt32.v n<length b /\
z == Seq.index (as_seq h0 b) (UInt32.v n))) | val op_Array_Access: #a:typ -> b:buffer a -> n:UInt32.t -> HST.Stack (P.type_of_typ a)
(requires (fun h -> UInt32.v n<length b /\ live h b))
(ensures (fun h0 z h1 -> h1 == h0 /\
UInt32.v n<length b /\
z == Seq.index (as_seq h0 b) (UInt32.v n))) | let op_Array_Access #a b n = index #a b n | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 41,
"end_line": 415,
"start_col": 0,
"start_line": 415
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *)
let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i)
let offset
(#a:typ)
(b:buffer a)
(i:UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 ->
live h0 b /\
UInt32.v i <= length b
))
(ensures (fun h0 b' h1 ->
h1 == h0 /\
UInt32.v i <= length b /\
b' == goffset b i
))
= P.offset_buffer b i
let lemma_offset_spec
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i <= length b /\
live h b
))
(ensures (
UInt32.v i <= length b /\
as_seq h (goffset b i) == Seq.slice (as_seq h b) (UInt32.v i) (length b)
))
= ()
val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
))
let eqb #a b1 b2 len =
P.buffer_contents_equal b1 b2 len
(* JP: if the [val] is not specified, there's an issue with these functions
* taking an extra unification parameter at extraction-time... *)
val op_Array_Access: #a:typ -> b:buffer a -> n:UInt32.t -> HST.Stack (P.type_of_typ a)
(requires (fun h -> UInt32.v n<length b /\ live h b))
(ensures (fun h0 z h1 -> h1 == h0 /\
UInt32.v n<length b /\ | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> n: FStar.UInt32.t
-> FStar.HyperStack.ST.Stack (FStar.Pointer.Base.type_of_typ a) | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.BufferNG.index",
"FStar.Pointer.Base.type_of_typ"
] | [] | false | true | false | false | false | let ( .() ) #a b n =
| index #a b n | false |
FStar.BufferNG.fst | FStar.BufferNG.eqb | val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
)) | val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
)) | let eqb #a b1 b2 len =
P.buffer_contents_equal b1 b2 len | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 406,
"start_col": 0,
"start_line": 405
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *)
let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i)
let offset
(#a:typ)
(b:buffer a)
(i:UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 ->
live h0 b /\
UInt32.v i <= length b
))
(ensures (fun h0 b' h1 ->
h1 == h0 /\
UInt32.v i <= length b /\
b' == goffset b i
))
= P.offset_buffer b i
let lemma_offset_spec
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i <= length b /\
live h b
))
(ensures (
UInt32.v i <= length b /\
as_seq h (goffset b i) == Seq.slice (as_seq h b) (UInt32.v i) (length b)
))
= ()
val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b1: FStar.BufferNG.buffer a -> b2: FStar.BufferNG.buffer a -> len: FStar.UInt32.t
-> FStar.HyperStack.ST.ST Prims.bool | FStar.HyperStack.ST.ST | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Derived1.buffer_contents_equal",
"Prims.bool"
] | [] | false | true | false | false | false | let eqb #a b1 b2 len =
| P.buffer_contents_equal b1 b2 len | false |
FStar.BufferNG.fst | FStar.BufferNG.upd | val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
)) | val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
)) | let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z)) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 73,
"end_line": 259,
"start_col": 0,
"start_line": 255
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> n: FStar.UInt32.t -> z: FStar.Pointer.Base.type_of_typ a
-> FStar.HyperStack.ST.Stack Prims.unit | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.type_of_typ",
"Prims._assert",
"FStar.Seq.Base.equal",
"FStar.BufferNG.as_seq",
"FStar.Seq.Base.upd",
"FStar.UInt32.v",
"Prims.unit",
"FStar.Monotonic.HyperStack.mem",
"FStar.HyperStack.ST.get",
"FStar.Pointer.Base.write_buffer"
] | [] | false | true | false | false | false | let upd #a b n z =
| let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z)) | false |
FStar.BufferNG.fst | FStar.BufferNG.op_Array_Assignment | val op_Array_Assignment: #a:typ -> b:buffer a -> n:UInt32.t -> z:P.type_of_typ a -> HST.Stack unit
(requires (fun h -> live h b /\ UInt32.v n < length b))
(ensures (fun h0 _ h1 -> live h0 b /\ live h1 b /\ UInt32.v n < length b
/\ P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1
/\ as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z )) | val op_Array_Assignment: #a:typ -> b:buffer a -> n:UInt32.t -> z:P.type_of_typ a -> HST.Stack unit
(requires (fun h -> live h b /\ UInt32.v n < length b))
(ensures (fun h0 _ h1 -> live h0 b /\ live h1 b /\ UInt32.v n < length b
/\ P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1
/\ as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z )) | let op_Array_Assignment #a b n z = upd #a b n z | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 47,
"end_line": 422,
"start_col": 0,
"start_line": 422
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= ()
let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len))
(* Same here *)
let goffset
(#a: typ)
(b: buffer a)
(i: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i <= length b))
(ensures (fun b' ->
UInt32.v i <= length b /\
b' == gsub b i (UInt32.sub (P.buffer_length b) i)
))
= P.gsub_buffer b i (UInt32.sub (P.buffer_length b) i)
let offset
(#a:typ)
(b:buffer a)
(i:UInt32.t)
: HST.Stack (buffer a)
(requires (fun h0 ->
live h0 b /\
UInt32.v i <= length b
))
(ensures (fun h0 b' h1 ->
h1 == h0 /\
UInt32.v i <= length b /\
b' == goffset b i
))
= P.offset_buffer b i
let lemma_offset_spec
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i <= length b /\
live h b
))
(ensures (
UInt32.v i <= length b /\
as_seq h (goffset b i) == Seq.slice (as_seq h b) (UInt32.v i) (length b)
))
= ()
val eqb: #a:typ -> b1:buffer a -> b2:buffer a
-> len:UInt32.t
-> HST.ST bool
(requires (fun h ->
hasEq (P.type_of_typ a) /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
live h b1 /\
live h b2
))
(ensures (fun h0 z h1 ->
h1 == h0 /\
UInt32.v len <= length b1 /\
UInt32.v len <= length b2 /\
(z <==> equal h0 (gsub b1 0ul len) h0 (gsub b2 0ul len))
))
let eqb #a b1 b2 len =
P.buffer_contents_equal b1 b2 len
(* JP: if the [val] is not specified, there's an issue with these functions
* taking an extra unification parameter at extraction-time... *)
val op_Array_Access: #a:typ -> b:buffer a -> n:UInt32.t -> HST.Stack (P.type_of_typ a)
(requires (fun h -> UInt32.v n<length b /\ live h b))
(ensures (fun h0 z h1 -> h1 == h0 /\
UInt32.v n<length b /\
z == Seq.index (as_seq h0 b) (UInt32.v n)))
let op_Array_Access #a b n = index #a b n
val op_Array_Assignment: #a:typ -> b:buffer a -> n:UInt32.t -> z:P.type_of_typ a -> HST.Stack unit
(requires (fun h -> live h b /\ UInt32.v n < length b))
(ensures (fun h0 _ h1 -> live h0 b /\ live h1 b /\ UInt32.v n < length b
/\ P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> n: FStar.UInt32.t -> z: FStar.Pointer.Base.type_of_typ a
-> FStar.HyperStack.ST.Stack Prims.unit | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.type_of_typ",
"FStar.BufferNG.upd",
"Prims.unit"
] | [] | false | true | false | false | false | let ( .()<- ) #a b n z =
| upd #a b n z | false |
FStar.BufferNG.fst | FStar.BufferNG.index | val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
)) | val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
)) | let index #a b n =
P.read_buffer b n | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 19,
"end_line": 236,
"start_col": 0,
"start_line": 235
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: FStar.BufferNG.buffer a -> n: FStar.UInt32.t
-> FStar.HyperStack.ST.Stack (FStar.Pointer.Base.type_of_typ a) | FStar.HyperStack.ST.Stack | [] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Pointer.Base.read_buffer",
"FStar.Pointer.Base.type_of_typ"
] | [] | false | true | false | false | false | let index #a b n =
| P.read_buffer b n | false |
Vale.AES.GCTR_BE_s.fst | Vale.AES.GCTR_BE_s.is_gctr_plain | val is_gctr_plain (p: seq nat8) : prop0 | val is_gctr_plain (p: seq nat8) : prop0 | let is_gctr_plain (p:seq nat8) : prop0 = length p < pow2_32 | {
"file_name": "vale/specs/crypto/Vale.AES.GCTR_BE_s.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 59,
"end_line": 17,
"start_col": 0,
"start_line": 17
} | module Vale.AES.GCTR_BE_s
// IMPORTANT: Following NIST's specification, this spec is written assuming a big-endian mapping from bytes to quad32s
open Vale.Def.Prop_s
open Vale.Def.Opaque_s
open Vale.Def.Words_s
open Vale.Def.Words.Seq_s
open Vale.Def.Types_s
open Vale.Arch.Types
open FStar.Mul
open Vale.AES.AES_BE_s
open FStar.Seq
// The max length of pow2_32 corresponds to the max length of buffers in Low* | {
"checked_file": "/",
"dependencies": [
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Words.Seq_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.AES.AES_BE_s.fst.checked",
"prims.fst.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": false,
"source_file": "Vale.AES.GCTR_BE_s.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.AES_BE_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Words.Seq_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | p: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Vale.Def.Prop_s.prop0 | Prims.Tot | [
"total"
] | [] | [
"FStar.Seq.Base.seq",
"Vale.Def.Types_s.nat8",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Seq.Base.length",
"Vale.Def.Words_s.pow2_32",
"Vale.Def.Prop_s.prop0"
] | [] | false | false | false | true | false | let is_gctr_plain (p: seq nat8) : prop0 =
| length p < pow2_32 | false |
FStar.BufferNG.fst | FStar.BufferNG.lemma_sub_spec | val lemma_sub_spec (#a: typ) (b: buffer a) (i len: UInt32.t) (h: HS.mem)
: Lemma (requires (UInt32.v i + UInt32.v len <= length b /\ live h b))
(ensures
(UInt32.v i + UInt32.v len <= length b /\ live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [[SMTPat (gsub b i len); SMTPat (live h b)]; [SMTPat (live h (gsub b i len))]]] | val lemma_sub_spec (#a: typ) (b: buffer a) (i len: UInt32.t) (h: HS.mem)
: Lemma (requires (UInt32.v i + UInt32.v len <= length b /\ live h b))
(ensures
(UInt32.v i + UInt32.v len <= length b /\ live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [[SMTPat (gsub b i len); SMTPat (live h b)]; [SMTPat (live h (gsub b i len))]]] | let lemma_sub_spec (#a:typ) (b:buffer a)
(i:UInt32.t)
(len:UInt32.t)
(h: HS.mem)
: Lemma
(requires (
UInt32.v i + UInt32.v len <= length b /\
live h b
))
(ensures (
UInt32.v i + UInt32.v len <= length b /\
live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [
[SMTPat (gsub b i len); SMTPat (live h b)];
[SMTPat (live h (gsub b i len))]
]]
= Seq.lemma_eq_intro (as_seq h (gsub b i len)) (Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)) | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 114,
"end_line": 340,
"start_col": 0,
"start_line": 322
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
val index
(#a: typ)
(b: buffer a)
(n: UInt32.t)
: HST.Stack (P.type_of_typ a)
(requires (fun h ->
UInt32.v n < length b /\
live h b
))
(ensures (fun h0 z h1 ->
UInt32.v n < length b /\
h1 == h0 /\
z == Seq.index (as_seq h0 b) (UInt32.v n)
))
let index #a b n =
P.read_buffer b n
val upd
(#a: typ)
(b: buffer a)
(n: UInt32.t)
(z: P.type_of_typ a)
: HST.Stack unit
(requires (fun h ->
live h b /\
UInt32.v n < length b
))
(ensures (fun h0 _ h1 ->
live h1 b /\
UInt32.v n < length b /\
P.modifies (P.loc_pointer (P.gpointer_of_buffer_cell b n)) h0 h1 /\
as_seq h1 b == Seq.upd (as_seq h0 b) (UInt32.v n) z
))
let upd #a b n z =
let h0 = HST.get () in
P.write_buffer b n z;
let h1 = HST.get () in
assert (Seq.equal (as_seq h1 b) (Seq.upd (as_seq h0 b) (UInt32.v n) z))
(* NOTE: Here I cannot fully respect the Buffer interface,
because pure sub no longer exists, since it has been split
into ghost gsub and stateful sub
*)
unfold
let gsub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: Ghost (buffer a)
(requires (UInt32.v i + UInt32.v len <= length b))
(ensures (fun _ -> True))
= P.gsub_buffer b i len
let sub
(#a: typ)
(b: buffer a)
(i: UInt32.t)
(len: UInt32.t)
: HST.Stack (buffer a)
(requires (fun h ->
live h b /\
UInt32.v i + UInt32.v len <= length b
))
(ensures (fun h0 b' h1 ->
live h0 b /\
UInt32.v i + UInt32.v len <= length b /\
h1 == h0 /\
b' == gsub b i len /\
b `includes` b'
))
= P.sub_buffer b i len
let sub_sub
(#a: typ)
(b: buffer a)
(i1: UInt32.t)
(len1: UInt32.t)
(i2: UInt32.t)
(len2: UInt32.t)
: Lemma
(requires (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1
))
(ensures (
UInt32.v i1 + UInt32.v len1 <= length b /\
UInt32.v i2 + UInt32.v len2 <= UInt32.v len1 /\
gsub (gsub b i1 len1) i2 len2 == gsub b (UInt32.add i1 i2) len2
))
= ()
let sub_zero_length
(#a: typ)
(b: buffer a)
: Lemma
(ensures (gsub b (UInt32.uint_to_t 0) (UInt32.uint_to_t (length b)) == b))
= () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
b: FStar.BufferNG.buffer a ->
i: FStar.UInt32.t ->
len: FStar.UInt32.t ->
h: FStar.Monotonic.HyperStack.mem
-> FStar.Pervasives.Lemma
(requires
FStar.UInt32.v i + FStar.UInt32.v len <= FStar.BufferNG.length b /\ FStar.BufferNG.live h b)
(ensures
FStar.UInt32.v i + FStar.UInt32.v len <= FStar.BufferNG.length b /\
FStar.BufferNG.live h (FStar.BufferNG.gsub b i len) /\
FStar.BufferNG.as_seq h (FStar.BufferNG.gsub b i len) ==
FStar.Seq.Base.slice (FStar.BufferNG.as_seq h b)
(FStar.UInt32.v i)
(FStar.UInt32.v i + FStar.UInt32.v len))
[
SMTPatOr [
[SMTPat (FStar.BufferNG.gsub b i len); SMTPat (FStar.BufferNG.live h b)];
[SMTPat (FStar.BufferNG.live h (FStar.BufferNG.gsub b i len))]
]
] | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"FStar.BufferNG.typ",
"FStar.BufferNG.buffer",
"FStar.UInt32.t",
"FStar.Monotonic.HyperStack.mem",
"FStar.Seq.Base.lemma_eq_intro",
"FStar.Pointer.Base.type_of_typ",
"FStar.BufferNG.as_seq",
"FStar.BufferNG.gsub",
"FStar.Seq.Base.slice",
"FStar.UInt32.v",
"Prims.op_Addition",
"Prims.unit",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.BufferNG.length",
"FStar.BufferNG.live",
"Prims.squash",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Prims.Cons",
"FStar.Pervasives.pattern",
"FStar.Pervasives.smt_pat_or",
"Prims.list",
"FStar.Pervasives.smt_pat",
"Prims.Nil"
] | [] | true | false | true | false | false | let lemma_sub_spec (#a: typ) (b: buffer a) (i len: UInt32.t) (h: HS.mem)
: Lemma (requires (UInt32.v i + UInt32.v len <= length b /\ live h b))
(ensures
(UInt32.v i + UInt32.v len <= length b /\ live h (gsub b i len) /\
as_seq h (gsub b i len) == Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)
))
[SMTPatOr [[SMTPat (gsub b i len); SMTPat (live h b)]; [SMTPat (live h (gsub b i len))]]] =
| Seq.lemma_eq_intro (as_seq h (gsub b i len))
(Seq.slice (as_seq h b) (UInt32.v i) (UInt32.v i + UInt32.v len)) | false |
FStar.BufferNG.fst | FStar.BufferNG.rcreate | val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
)) | val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
)) | let rcreate #a r init len =
let len : P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content | {
"file_name": "ulib/legacy/FStar.BufferNG.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 218,
"start_col": 0,
"start_line": 215
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.BufferNG
module HH = FStar.HyperStack
module HS = FStar.HyperStack
module HST = FStar.HyperStack.ST
module P = FStar.Pointer
(* This module will help for the transition of some buffer-based code
It tries to sidestep the following two issues:
- the type of elements must be embeddable into P.typ
- all elements must always be readable (no uninitialized data)
*)
let rec supported
(t : P.typ)
: Tot bool
= match t with
| P.TBase _ -> true
| P.TStruct l -> struct_typ_supported l.P.fields
| _ -> false
and struct_typ_supported
(l: list (string * P.typ))
: Tot bool
= match l with
| [] -> true
| (_, t) :: l' -> supported t && struct_typ_supported l'
let typ = (t: P.typ { supported t } )
unfold
let buffer
(t: typ)
: Tot Type0
= P.buffer t
unfold
let live (#a: typ) (h: HS.mem) (b: buffer a) : GTot Type0 =
P.buffer_readable h b
unfold
let unused_in (#a: typ) (b: buffer a) (h: HS.mem) : GTot Type0 =
P.buffer_unused_in b h
unfold
let length (#a: typ) (b: buffer a) : GTot nat =
UInt32.v (P.buffer_length b)
unfold
let as_addr (#a: typ) (b: buffer a) : GTot nat =
P.buffer_as_addr b
unfold
let frameOf (#a: typ) (b: buffer a) : GTot HH.rid =
P.frameOf_buffer b
unfold
let as_seq (#a: typ) (h: HS.mem) (b: buffer a) : GTot (s: Seq.seq (P.type_of_typ a) { Seq.length s == length b } ) =
P.buffer_as_seq h b
unfold
let equal (#a: typ) (h: HS.mem) (b: buffer a) (h' : HS.mem) (b' : buffer a) : GTot Type0 =
as_seq h b == as_seq h' b'
unfold
let includes
(#a: typ)
(x y: buffer a)
: GTot Type0
= P.buffer_includes x y
let includes_live
(#a: typ)
(h: HS.mem)
(x y : buffer a)
: Lemma
(requires (x `includes` y /\ live h x))
(ensures (live h y))
= P.buffer_includes_elim x y
let includes_as_seq #a h1 h2 (x: buffer a) (y: buffer a)
: Lemma
(requires (x `includes` y /\ as_seq h1 x == as_seq h2 x))
(ensures (as_seq h1 y == as_seq h2 y))
= P.buffer_includes_elim x y
let includes_trans #a (x y z: buffer a)
: Lemma
(requires (x `includes` y /\ y `includes` z))
(ensures (x `includes` z))
= P.buffer_includes_trans x y z
unfold
let disjoint (#a #a' : typ) (x: buffer a) (y: buffer a') : GTot Type0 =
P.loc_disjoint (P.loc_buffer x) (P.loc_buffer y)
(* Disjointness is symmetric *)
let lemma_disjoint_symm #a #a' (x:buffer a) (y:buffer a') : Lemma
(requires True)
(ensures (disjoint x y <==> disjoint y x))
[SMTPat (disjoint x y)]
= ()
let lemma_disjoint_sub #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint subx y); SMTPat (includes x subx)]
= P.buffer_includes_loc_includes x subx;
P.loc_disjoint_includes (P.loc_buffer x) (P.loc_buffer y) (P.loc_buffer subx) (P.loc_buffer y)
let lemma_disjoint_sub' #a #a' (x:buffer a) (subx:buffer a) (y:buffer a') : Lemma
(requires (includes x subx /\ disjoint x y))
(ensures (disjoint subx y))
[SMTPat (disjoint y subx); SMTPat (includes x subx)]
= ()
let lemma_live_disjoint #a #a' h (b:buffer a) (b':buffer a') : Lemma
(requires (live h b /\ b' `unused_in` h))
(ensures (disjoint b b'))
[SMTPat (disjoint b b'); SMTPat (live h b)]
= ()
(** Concrete getters and setters *)
val create
(#a:typ)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.StackInline (buffer a)
(requires (fun h ->
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
UInt32.v len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
))
let create #a init len =
let len : P.array_length_t = len in
let content = P.screate (P.TArray len a) (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content
unfold let p (#a:typ) (init:list (P.type_of_typ a)) : GTot Type0 =
normalize (0 < FStar.List.Tot.length init) /\
normalize (FStar.List.Tot.length init < UInt.max_int 32)
unfold let q (#a:typ) (len:nat) (buf:buffer a) : GTot Type0 =
normalize (length buf == len)
val createL
(#a: typ)
(init:list (P.type_of_typ a))
: HST.StackInline (buffer a)
(requires (fun h -> p #a init))
(ensures (fun (h0: HS.mem) b h1 ->
let len = FStar.List.Tot.length init in
len > 0 /\
b `unused_in` h0 /\
live h1 b /\
length b == len /\
frameOf b == (HS.get_tip h0) /\
P.modifies_0 h0 h1 /\
as_seq h1 b == Seq.seq_of_list init /\
q #a len b
))
#set-options "--initial_fuel 1 --max_fuel 1" //the normalize_term (length init) in the pre-condition will be unfolded
//whereas the L.length init below will not
let createL #a init =
let len : P.array_length_t = UInt32.uint_to_t (List.Tot.length init) in
let s = Seq.seq_of_list init in
let content = P.screate (P.TArray len a) (Some s) in
P.buffer_of_array_pointer content
#reset-options "--initial_fuel 0 --max_fuel 0"
val rcreate
(#a: typ)
(r:HH.rid)
(init: P.type_of_typ a)
(len:UInt32.t)
: HST.ST (buffer a)
(requires (fun h ->
HST.is_eternal_region r /\
HST.witnessed (HST.region_contains_pred r) /\
UInt32.v len > 0
))
(ensures (fun (h0: HS.mem) b h1 ->
b `unused_in` h0 /\
live h1 b /\
length b == UInt32.v len /\
(HS.get_tip h1) == (HS.get_tip h0) /\
P.modifies (P.loc_addresses r Set.empty) h0 h1 /\
as_seq h1 b == Seq.create (UInt32.v len) init
)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Set.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pointer.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked",
"FStar.HyperStack.ST.fsti.checked",
"FStar.HyperStack.fst.checked"
],
"interface_file": false,
"source_file": "FStar.BufferNG.fst"
} | [
{
"abbrev": true,
"full_module": "FStar.Pointer",
"short_module": "P"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack.ST",
"short_module": "HST"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HS"
},
{
"abbrev": true,
"full_module": "FStar.HyperStack",
"short_module": "HH"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | r: FStar.Monotonic.HyperHeap.rid -> init: FStar.Pointer.Base.type_of_typ a -> len: FStar.UInt32.t
-> FStar.HyperStack.ST.ST (FStar.BufferNG.buffer a) | FStar.HyperStack.ST.ST | [] | [] | [
"FStar.BufferNG.typ",
"FStar.Monotonic.HyperHeap.rid",
"FStar.Pointer.Base.type_of_typ",
"FStar.UInt32.t",
"FStar.Pointer.Base.buffer_of_array_pointer",
"FStar.Pointer.Base.buffer",
"FStar.Pointer.Base.pointer",
"FStar.Pointer.Base.TArray",
"FStar.Pointer.Base.ecreate",
"FStar.Pervasives.Native.Some",
"FStar.Seq.Base.create",
"FStar.UInt32.v",
"FStar.BufferNG.buffer",
"FStar.Pointer.Base.array_length_t"
] | [] | false | true | false | false | false | let rcreate #a r init len =
| let len:P.array_length_t = len in
let content = P.ecreate (P.TArray len a) r (Some (Seq.create (UInt32.v len) init)) in
P.buffer_of_array_pointer content | false |
Vale.AES.GCTR_BE_s.fst | Vale.AES.GCTR_BE_s.gctr_encrypt | val gctr_encrypt : icb: Vale.Def.Types_s.quad32 ->
plain: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 ->
alg: Vale.AES.AES_common_s.algorithm ->
key: FStar.Seq.Base.seq Vale.Def.Types_s.nat32
-> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8) | let gctr_encrypt = opaque_make gctr_encrypt_def | {
"file_name": "vale/specs/crypto/Vale.AES.GCTR_BE_s.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 67,
"end_line": 69,
"start_col": 19,
"start_line": 69
} | module Vale.AES.GCTR_BE_s
// IMPORTANT: Following NIST's specification, this spec is written assuming a big-endian mapping from bytes to quad32s
open Vale.Def.Prop_s
open Vale.Def.Opaque_s
open Vale.Def.Words_s
open Vale.Def.Words.Seq_s
open Vale.Def.Types_s
open Vale.Arch.Types
open FStar.Mul
open Vale.AES.AES_BE_s
open FStar.Seq
// The max length of pow2_32 corresponds to the max length of buffers in Low*
// length plain < pow2_32 <= spec max of 2**39 - 256;
let is_gctr_plain (p:seq nat8) : prop0 = length p < pow2_32
type gctr_plain:eqtype = p:seq nat8 { is_gctr_plain p }
type gctr_plain_internal:eqtype = seq quad32
let inc32 (cb:quad32) (i:int) : quad32 =
Mkfour ((cb.lo0 + i) % pow2_32) cb.lo1 cb.hi2 cb.hi3
let gctr_encrypt_block (icb:quad32) (plain:quad32) (alg:algorithm) (key:seq nat32) (i:int) : Pure quad32
(requires is_aes_key_word alg key)
(ensures fun _ -> True)
=
quad32_xor plain (aes_encrypt_word alg key (inc32 icb i))
let rec gctr_encrypt_recursive (icb:quad32) (plain:gctr_plain_internal)
(alg:algorithm) (key:aes_key_word alg) (i:int) : Tot (seq quad32) (decreases %[length plain]) =
if length plain = 0 then empty
else
cons (gctr_encrypt_block icb (head plain) alg key i) (gctr_encrypt_recursive icb (tail plain) alg key (i + 1))
let pad_to_128_bits (p:seq nat8) : Pure (seq nat8)
(requires True)
(ensures fun q -> length q % 16 == 0 /\ length q <= length p + 15)
=
let num_extra_bytes = length p % 16 in
if num_extra_bytes = 0 then p
else p @| (create (16 - num_extra_bytes) 0)
let gctr_encrypt_def (icb:quad32) (plain:seq nat8) (alg:algorithm) (key:seq nat32) : Pure (seq nat8)
(requires is_gctr_plain plain /\ is_aes_key_word alg key)
(ensures fun _ -> True)
=
let num_extra = (length plain) % 16 in
if num_extra = 0 then
let plain_quads = be_bytes_to_seq_quad32 plain in
let cipher_quads = gctr_encrypt_recursive icb plain_quads alg key 0 in
seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE cipher_quads)
else
let full_bytes_len = (length plain) - num_extra in
let full_blocks, final_block = split plain full_bytes_len in
let full_quads = be_bytes_to_seq_quad32 full_blocks in
let final_quad = be_bytes_to_quad32 (pad_to_128_bits final_block) in
let cipher_quads = gctr_encrypt_recursive icb full_quads alg key 0 in
let final_cipher_quad = gctr_encrypt_block icb final_quad alg key (full_bytes_len / 16) in
let cipher_bytes_full = seq_nat32_to_seq_nat8_BE (seq_four_to_seq_BE cipher_quads) in
let final_cipher_bytes = slice (be_quad32_to_bytes final_cipher_quad) 0 num_extra in | {
"checked_file": "/",
"dependencies": [
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Words.Seq_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.AES.AES_BE_s.fst.checked",
"prims.fst.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": false,
"source_file": "Vale.AES.GCTR_BE_s.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Seq",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.AES.AES_BE_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Words.Seq_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Words_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"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
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
icb: Vale.Def.Types_s.quad32 ->
plain: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 ->
alg: Vale.AES.AES_common_s.algorithm ->
key: FStar.Seq.Base.seq Vale.Def.Types_s.nat32
-> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8) | Prims.Pure | [] | [] | [
"Vale.Def.Opaque_s.opaque_make",
"Vale.Def.Types_s.quad32",
"FStar.Seq.Base.seq",
"Vale.Def.Types_s.nat8",
"Vale.AES.AES_common_s.algorithm",
"Vale.Def.Types_s.nat32",
"Prims.l_and",
"Vale.AES.GCTR_BE_s.is_gctr_plain",
"Vale.AES.AES_BE_s.is_aes_key_word",
"Prims.l_True",
"Vale.AES.GCTR_BE_s.gctr_encrypt_def"
] | [] | false | false | false | false | false | let gctr_encrypt =
| opaque_make gctr_encrypt_def | false |
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