effect
stringclasses 48
values | original_source_type
stringlengths 0
23k
| opens_and_abbrevs
listlengths 2
92
| isa_cross_project_example
bool 1
class | source_definition
stringlengths 9
57.9k
| partial_definition
stringlengths 7
23.3k
| is_div
bool 2
classes | is_type
null | is_proof
bool 2
classes | completed_definiton
stringlengths 1
250k
| dependencies
dict | effect_flags
sequencelengths 0
2
| ideal_premises
sequencelengths 0
236
| mutual_with
sequencelengths 0
11
| file_context
stringlengths 0
407k
| interleaved
bool 1
class | is_simply_typed
bool 2
classes | file_name
stringlengths 5
48
| vconfig
dict | is_simple_lemma
null | source_type
stringlengths 10
23k
| proof_features
sequencelengths 0
1
| name
stringlengths 8
95
| source
dict | verbose_type
stringlengths 1
7.42k
| source_range
dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
FStar.Pervasives.Lemma | val lset_bit5_lemma1:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 1} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lset_bit5_lemma1 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[1] <- f.[1] |. b in
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
assert (v f1 * pow2 26 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f1 * pow2 26) i 26;
assert (v f1 < pow2 (i - 26));
assert (i - 26 == i % 26);
assert (v f.[1] < pow2 (i % 26));
lset_bit5_lemma_aux f.[1] i;
assert (v out.[1] == v f.[1] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[1]) (pow2 (i % 26));
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) * pow26 + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.pow2_plus (i % 26) 26 }
pow2 (i % 26 + 26) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4)) | val lset_bit5_lemma1:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 1} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma1 f i = | false | null | true | let b = u64 1 <<. size (i % 26) in
let out = f.[ 1 ] <- f.[ 1 ] |. b in
let f0, f1, f2, f3, f4 = (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]) in
let o0, o1, o2, o3, o4 = (out.[ 0 ], out.[ 1 ], out.[ 2 ], out.[ 3 ], out.[ 4 ]) in
assert (v f1 * pow2 26 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f1 * pow2 26) i 26;
assert (v f1 < pow2 (i - 26));
assert (i - 26 == i % 26);
assert (v f.[ 1 ] < pow2 (i % 26));
lset_bit5_lemma_aux f.[ 1 ] i;
assert (v out.[ 1 ] == v f.[ 1 ] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[ 1 ]) (pow2 (i % 26));
calc ( == ) {
as_nat5 (o0, o1, o2, o3, o4);
( == ) { () }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
( == ) { () }
pow2 (i % 26) * pow26 + as_nat5 (f0, f1, f2, f3, f4);
( == ) { FStar.Math.Lemmas.pow2_plus (i % 26) 26 }
pow2 (i % 26 + 26) + as_nat5 (f0, f1, f2, f3, f4);
( == ) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst"
} | [
"lemma"
] | [
"Lib.Sequence.lseq",
"Lib.IntTypes.uint64",
"Lib.IntTypes.size_nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Division",
"Prims._assert",
"Prims.eq2",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.op_Addition",
"Prims.pow2",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.nat",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Math.Lemmas.pow2_plus",
"FStar.Math.Lemmas.euclidean_division_definition",
"Hacl.Poly1305.Field32xN.Lemmas2.lemma_sum_lt_pow2_26",
"Lib.Sequence.op_String_Access",
"Hacl.Poly1305.Field32xN.Lemmas2.lset_bit5_lemma_aux",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"FStar.Math.Lemmas.lemma_div_lt_nat",
"FStar.Pervasives.Native.tuple5",
"Lib.IntTypes.int_t",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.upd",
"Lib.IntTypes.logor",
"Lib.Sequence.index",
"Prims.l_Forall",
"Prims.l_imp",
"Prims.op_disEquality",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.op_String_Assignment",
"Lib.IntTypes.op_Bar_Dot",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.u64",
"Lib.IntTypes.size"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas2
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
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val load_tup64_lemma0_lo: lo:uint64 ->
Lemma
(v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 +
v lo / pow2 52 * pow52 == v lo)
let load_tup64_lemma0_lo lo =
calc (==) {
v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 + v lo / pow2 52 * pow52;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo % pow2 52) / pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo % pow2 52) (pow2 26) }
(v lo % pow2 52) + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo) (pow2 52) }
v lo;
}
val load_tup64_lemma0_hi: hi:uint64 ->
Lemma
((v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104 ==
v hi * pow2 64)
let load_tup64_lemma0_hi hi =
calc (==) {
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) {
assert_norm (pow78 = pow2 14 * pow2 64);
assert_norm (pow104 = pow2 40 * pow2 64)}
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow2 14 * pow2 64 + v hi / pow2 40 * pow2 40 * pow2 64;
(==) { }
(v hi % pow2 14 + ((v hi / pow2 14) % pow2 26) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 40 }
(v hi % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi) 14 40 }
((v hi % pow2 40) % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi % pow2 40) (pow2 14) }
(v hi % pow2 40 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi) (pow2 40) }
v hi * pow2 64;
}
val load_tup64_lemma0:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures as_nat5 f == v hi * pow2 64 + v lo)
#push-options"--z3rlimit 100"
let load_tup64_lemma0 f lo hi =
let (f0, f1, f2, f3, f4) = f in
calc (==) {
as_nat5 f;
(==) { }
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104;
(==) { }
v lo % pow2 26 + (v lo / pow2 26) % pow2 26 * pow26 +
v lo / pow2 52 * pow52 + (v hi % pow2 14) * pow2 12 * pow52 +
(v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_lo lo }
v lo + (v hi % pow2 14) * pow2 12 * pow52 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v lo + (v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_hi hi }
v lo + v hi * pow2 64;
};
assert (as_nat5 f == v hi * pow2 64 + v lo)
#pop-options
val load_tup64_fits_lemma:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures tup64_fits5 f (1, 1, 1, 1, 1))
let load_tup64_fits_lemma f lo hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (pow26 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v lo) 64 52;
lemma_mult_le (v hi % pow2 14) (pow2 14 - 1) (pow2 12) (pow2 12);
assert_norm (pow2 14 * pow2 12 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v hi) 64 40;
assert_norm (pow2 24 < pow2 26)
val load_tup64_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(v ((lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul)) ==
v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_lemma_f2 lo hi =
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
let tmp = (hi &. u64 0x3fff) in
calc (==) {
v (tmp <<. 12ul) % pow2 12;
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
(v tmp * pow2 12 % pow2 64) % pow2 12;
(==) { assert_norm (pow2 64 = pow2 12 * pow2 52) }
(v tmp * pow2 12 % (pow2 12 * pow2 52)) % pow2 12;
(==) {FStar.Math.Lemmas.modulo_modulo_lemma (v tmp * pow2 12) (pow2 12) (pow2 52)}
v tmp * pow2 12 % pow2 12;
(==) {FStar.Math.Lemmas.multiple_modulo_lemma (v tmp) (pow2 12)}
0;
};
assert (v (tmp <<. 12ul) % pow2 12 = 0);
FStar.Math.Lemmas.lemma_div_lt (v lo) 64 52;
assert (v (lo >>. 52ul) < pow2 12);
logor_disjoint (lo >>. 52ul) ((hi &. u64 0x3fff) <<. 12ul) 12;
calc (==) {
v f2;
(==) { }
v (lo >>. 52ul) + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_right_lemma lo 52ul }
v lo / pow2 52 + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64;
};
assert (v f2 == v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64);
assert_norm (0x3fff = pow2 14 - 1);
mod_mask_lemma hi 14ul;
assert (v (mod_mask #U64 #SEC 14ul) == v (u64 0x3fff));
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 % pow2 64);
assert (v hi % pow2 14 < pow2 14);
assert_norm (pow2 14 * pow2 12 < pow2 64);
FStar.Math.Lemmas.small_modulo_lemma_1 ((v hi % pow2 14) * pow2 12) (pow2 64);
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
noextract
val load_tup64_lemma: lo:uint64 -> hi:uint64 ->
Pure tup64_5
(requires True)
(ensures fun f ->
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == v hi * pow2 64 + v lo)
let load_tup64_lemma lo hi =
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fff = pow2 14 - 1);
let f0 = lo &. mask26 in
mod_mask_lemma lo 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v f0 == v lo % pow2 26);
let f1 = (lo >>. 26ul) &. mask26 in
assert (v f1 == (v lo / pow2 26) % pow2 26);
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12);
let f3 = (hi >>. 14ul) &. mask26 in
assert (v f3 == (v hi / pow2 14) % pow2 26);
let f4 = hi >>. 40ul in
assert (v f4 == v hi / pow2 40);
let f = (f0, f1, f2, f3, f4) in
load_tup64_lemma0 f lo hi;
load_tup64_fits_lemma f lo hi;
assert (as_nat5 f < pow2 128);
assert_norm (pow2 128 < prime);
FStar.Math.Lemmas.small_modulo_lemma_1 (as_nat5 f) prime;
assert (as_nat5 f % prime == v hi * pow2 64 + v lo);
f
val load_felem5_lemma_i:
#w:lanes
-> lo:uint64xN w
-> hi:uint64xN w
-> i:nat{i < w} ->
Lemma
(let f = as_tup64_i (load_felem5 #w lo hi) i in
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == (uint64xN_v hi).[i] * pow2 64 + (uint64xN_v lo).[i])
let load_felem5_lemma_i #w lo hi i =
assert (as_tup64_i (load_felem5 #w lo hi) i == load_tup64_lemma (vec_v lo).[i] (vec_v hi).[i])
noextract
val load_tup64_4_compact: lo:uint64 -> hi:uint64 -> tup64_5
let load_tup64_4_compact lo hi =
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let o0 = lo &. mask26 in
let o1 = (lo >>. 26ul) &. mask26 in
let o2 = (t3 >>. 4ul) &. mask26 in
let o3 = (t3 >>. 30ul) &. mask26 in
let o4 = hi >>. 40ul in
(o0, o1, o2, o3, o4)
val load_tup64_4_compact_lemma_f2_mod: lo:uint64 -> hi:uint64 -> Lemma
((v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_4_compact_lemma_f2_mod lo hi =
calc (<) {
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
(<) { Math.Lemmas.lemma_div_lt (v lo) 64 52 }
pow2 12 + (v hi % pow2 14) * pow2 12;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 12) (v hi % pow2 14) (pow2 14 - 1) }
pow2 12 + (pow2 14 - 1) * pow2 12;
(==) { Math.Lemmas.distributivity_sub_left (pow2 14) 1 (pow2 12); Math.Lemmas.pow2_plus 14 12 }
pow2 26;
};
assert (v lo / pow2 52 + (v hi % pow2 14) * pow2 12 < pow2 26);
Math.Lemmas.small_modulo_lemma_1 (v lo / pow2 52 + (v hi % pow2 14) * pow2 12) (pow2 26)
val load_tup64_4_compact_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 4ul) &. u64 0x3ffffff) == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#push-options "--z3rlimit 100"
let load_tup64_4_compact_lemma_f2 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f2 = (t3 >>. 4ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 4;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 4;
(==) { Math.Lemmas.pow2_plus 12 4 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 12 * pow2 4) / pow2 4;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 4) ((v hi % pow2 48) * pow2 12) }
(v lo / pow2 48) / pow2 4 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 4); Math.Lemmas.pow2_plus 48 4 }
v lo / pow2 52 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 60 12 }
v lo / pow2 52 + (v hi * pow2 12) % pow2 60;
};
assert (v (t3 >>. 4ul) == v lo / pow2 52 + (v hi * pow2 12) % pow2 60);
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f2 == v (t3 >>. 4ul) % pow2 26);
calc (==) {
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60) % pow2 26;
(==) { Math.Lemmas.lemma_mod_plus_distr_r (v lo / pow2 52) ((v hi * pow2 12) % pow2 60) (pow2 26) }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60 % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi * pow2 12) 26 60 }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 26 12 }
(v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26;
(==) { load_tup64_4_compact_lemma_f2_mod lo hi }
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
};
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#pop-options
val load_tup64_4_compact_lemma_f3: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 30ul) &. u64 0x3ffffff) == (v hi / pow2 14) % pow2 26)
#push-options "--z3rlimit 200"
let load_tup64_4_compact_lemma_f3 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f3 = (t3 >>. 30ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 30;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 30;
(==) { Math.Lemmas.pow2_plus 16 14;
Math.Lemmas.division_multiplication_lemma (v lo / pow2 48 + (v hi % pow2 48) * pow2 16) (pow2 16) (pow2 14) }
((v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 16) / pow2 14;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 16) (v hi % pow2 48) }
((v lo / pow2 48) / pow2 16 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 16); Math.Lemmas.pow2_plus 48 16 }
(v lo / pow2 64 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.small_div (v lo) (pow2 64) }
(v hi % pow2 48) / pow2 14;
(==) { Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 48 }
(v hi / pow2 14) % pow2 34;
};
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f3 == v (t3 >>. 30ul) % pow2 26);
assert (v f3 == ((v hi / pow2 14) % pow2 34) % pow2 26);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi / pow2 14) 26 34
#pop-options
val load_tup64_4_compact_lemma: lo:uint64 -> hi:uint64 ->
Lemma (load_tup64_4_compact lo hi == load_tup64_lemma lo hi)
let load_tup64_4_compact_lemma lo hi =
let (l0, l1, l2, l3, l4) = load_tup64_4_compact lo hi in
let (r0, r1, r2, r3, r4) = load_tup64_lemma lo hi in
assert (l0 == r0 /\ l1 == r1 /\ l4 == r4);
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let l2 = (t3 >>. 4ul) &. mask26 in
load_tup64_4_compact_lemma_f2 lo hi;
let r2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v l2 == v r2);
let r3 = (hi >>. 14ul) &. mask26 in
mod_mask_lemma (hi >>. 14ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v r3 == (v hi / pow2 14) % pow2 26);
let l3 = (t3 >>. 30ul) &. mask26 in
load_tup64_4_compact_lemma_f3 lo hi
val lemma_store_felem_lo:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> lo:uint64 ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64)
#push-options "--z3rlimit 200"
#restart-solver
let lemma_store_felem_lo f lo =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
assert (v (f1 <<. 26ul) == v f1 * pow2 26 % pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f1 * pow2 26) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f1) 26 26;
logor_disjoint f0 (f1 <<. 26ul) 26;
assert (v (f0 |. (f1 <<. 26ul)) == v f0 + v f1 * pow2 26);
assert_norm (pow2 26 * pow2 26 = pow2 52);
assert (v f0 + v f1 * pow2 26 < pow2 52);
assert (((v f2 * pow2 52) % pow2 64) % pow2 52 = 0);
logor_disjoint (f0 |. (f1 <<. 26ul)) (f2 <<. 52ul) 52
#pop-options
val lemma_store_felem_hi: f:tup64_5 -> hi:uint64 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64))
let lemma_store_felem_hi f hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
FStar.Math.Lemmas.lemma_div_lt (v f2) 26 12;
assert (v f2 / pow2 12 < pow2 14);
assert (v (f3 <<. 14ul) == v f3 * pow2 14 % pow2 64);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26);
assert_norm (pow2 26 * pow2 14 = pow2 40);
assert_norm (pow2 40 < pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f3 * pow2 14) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f3) 14 14;
assert ((v f3 * pow2 14) % pow2 14 = 0);
logor_disjoint (f2 >>. 12ul) (f3 <<. 14ul) 14;
assert (v ((f2 >>. 12ul) |. (f3 <<. 14ul)) == v f2 / pow2 12 + v f3 * pow2 14);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26 - 1);
assert (v f2 / pow2 12 + v f3 * pow2 14 < pow2 40);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v f4 * pow2 40) 40 64;
assert (((v f4 * pow2 40) % pow2 64) % pow2 40 = (v f4 * pow2 40) % pow2 40);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f4) 40 40;
assert ((v f4 * pow2 40) % pow2 40 = 0);
logor_disjoint ((f2 >>. 12ul) |. (f3 <<. 14ul)) (f4 <<. 40ul) 40
val lemma_tup64_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 < pow2 128))
let lemma_tup64_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 in
assert (tmp <= pow2 26 - 1 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 +
(pow2 26 - 1) * pow78 + (pow2 24 - 1) * pow104);
assert (tmp <= pow2 24 * pow104 - 1);
assert_norm (pow2 24 * pow104 = pow2 128)
val lemma_tup64_mod_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
(as_nat5 f) % pow2 128 == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104))
let lemma_tup64_mod_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 in
calc (==) {
(as_nat5 f) % pow2 128;
(==) { }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % pow2 128;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f4 * pow104) (pow2 128) }
(tmp + (v f4 * pow104 % pow2 128)) % pow2 128;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 128 104 }
(tmp + (v f4 % pow2 24) * pow104) % pow2 128;
(==) { lemma_tup64_pow2_128 f; FStar.Math.Lemmas.modulo_lemma (tmp + (v f4 % pow2 24) * pow104) (pow2 128) }
tmp + (v f4 % pow2 24) * pow104;
};
assert ((as_nat5 f) % pow2 128 == tmp + (v f4 % pow2 24) * pow104)
noextract
val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128))
let store_tup64_lemma f =
let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
lemma_store_felem_lo f lo;
lemma_store_felem_hi f hi;
assert (v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64);
assert (v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64);
calc (==) {
v lo + v hi * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
(v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64) * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 * pow2 40) % pow2 64 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 40 }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 52 }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { assert_norm (pow2 40 * pow2 64 = pow104) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 14 * pow2 64 = pow78) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12 + v f2 / pow2 12 * pow2 12) * pow52 +
v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 12) }
v f0 + v f1 * pow2 26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { lemma_tup64_mod_pow2_128 f }
(as_nat5 f) % pow2 128;
};
assert (v lo + v hi * pow2 64 == (as_nat5 f) % pow2 128);
lo, hi
#push-options "--max_ifuel 1"
val store_felem5_lemma:
#w:lanes
-> f:felem5 w ->
Lemma
(requires felem_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (lo, hi) = store_felem5 f in
v hi * pow2 64 + v lo == (fas_nat5 f).[0] % pow2 128))
let store_felem5_lemma #w f =
let (lo, hi) = store_felem5 f in
assert (store_tup64_lemma (as_tup64_i f 0) == (lo, hi))
#pop-options
val lemma_sum_lt_pow2_26: i:nat -> a:nat{a < pow2 (i % 26)} -> b:nat{b <= pow2 (i % 26)} ->
Lemma (a + b <= max26)
let lemma_sum_lt_pow2_26 i a b =
assert (a + b < pow2 (i % 26) + pow2 (i % 26));
FStar.Math.Lemmas.pow2_le_compat 25 (i % 26);
assert (a + b < pow2 25 + pow2 25);
FStar.Math.Lemmas.pow2_double_sum 25;
assert_norm (pow26 = pow2 26)
val lset_bit5_lemma_aux: fi:uint64 -> i:size_nat{i <= 128} ->
Lemma
(requires v fi < pow2 (i % 26))
(ensures (v (fi |. (u64 1 <<. size (i % 26))) == v fi + pow2 (i % 26)))
let lset_bit5_lemma_aux fi i =
let b = u64 1 <<. size (i % 26) in
FStar.Math.Lemmas.pow2_lt_compat 26 (i % 26);
FStar.Math.Lemmas.pow2_lt_compat 64 26;
FStar.Math.Lemmas.modulo_lemma (pow2 (i % 26)) (pow2 64);
assert (v b == pow2 (i % 26));
logor_disjoint fi b (i % 26);
let out_i = fi |. b in
assert (v out_i == v fi + v b);
assert (v out_i == v fi + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v fi) (v b);
assert_norm (pow26 = pow2 26);
assert (v out_i <= max26)
val lset_bit5_lemma0:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 0} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma0 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[0] <- f.[0] |. b in
assert (v f.[i / 26] < pow2 (i % 26));
lset_bit5_lemma_aux f.[0] i;
assert (v out.[0] == v f.[0] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[0]) (pow2 (i % 26));
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4))
val lset_bit5_lemma1:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 1} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | false | false | Hacl.Poly1305.Field32xN.Lemmas2.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lset_bit5_lemma1:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 1} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | [] | Hacl.Poly1305.Field32xN.Lemmas2.lset_bit5_lemma1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas2.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Lib.Sequence.lseq Lib.IntTypes.uint64 5 -> i: Lib.IntTypes.size_nat{i <= 128 /\ i / 26 = 1}
-> FStar.Pervasives.Lemma
(requires
(forall (i: Prims.nat).
i < 5 ==> Lib.IntTypes.v f.[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26) /\
Hacl.Spec.Poly1305.Field32xN.as_nat5 (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]) <
Prims.pow2 i)
(ensures
(let b = Lib.IntTypes.u64 1 <<. Lib.IntTypes.size (i % 26) in
let out = f.[ i / 26 ] <- f.[ i / 26 ] |. b in
(forall (i: Prims.nat).
i < 5 ==> Lib.IntTypes.v out.[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26) /\
Hacl.Spec.Poly1305.Field32xN.as_nat5 (out.[ 0 ],
out.[ 1 ],
out.[ 2 ],
out.[ 3 ],
out.[ 4 ]) ==
Prims.pow2 i +
Hacl.Spec.Poly1305.Field32xN.as_nat5 (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]))) | {
"end_col": 80,
"end_line": 626,
"start_col": 26,
"start_line": 601
} |
FStar.Pervasives.Lemma | val lset_bit5_lemma4:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 4} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lset_bit5_lemma4 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[4] <- f.[4] |. b in
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
assert (v f4 * pow104 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f4 * pow104) i 104;
assert (v f4 < pow2 (i - 104));
assert (i - 104 == i % 26);
assert (v f.[4] < pow2 (i % 26));
lset_bit5_lemma_aux f.[4] i;
assert (v out.[4] == v f.[4] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[4]) (pow2 (i % 26));
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) * pow104 + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.pow2_plus (i % 26) 104 }
pow2 (i % 26 + 104) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4)) | val lset_bit5_lemma4:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 4} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma4 f i = | false | null | true | let b = u64 1 <<. size (i % 26) in
let out = f.[ 4 ] <- f.[ 4 ] |. b in
let f0, f1, f2, f3, f4 = (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]) in
let o0, o1, o2, o3, o4 = (out.[ 0 ], out.[ 1 ], out.[ 2 ], out.[ 3 ], out.[ 4 ]) in
assert (v f4 * pow104 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f4 * pow104) i 104;
assert (v f4 < pow2 (i - 104));
assert (i - 104 == i % 26);
assert (v f.[ 4 ] < pow2 (i % 26));
lset_bit5_lemma_aux f.[ 4 ] i;
assert (v out.[ 4 ] == v f.[ 4 ] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[ 4 ]) (pow2 (i % 26));
calc ( == ) {
as_nat5 (o0, o1, o2, o3, o4);
( == ) { () }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
( == ) { () }
pow2 (i % 26) * pow104 + as_nat5 (f0, f1, f2, f3, f4);
( == ) { FStar.Math.Lemmas.pow2_plus (i % 26) 104 }
pow2 (i % 26 + 104) + as_nat5 (f0, f1, f2, f3, f4);
( == ) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst"
} | [
"lemma"
] | [
"Lib.Sequence.lseq",
"Lib.IntTypes.uint64",
"Lib.IntTypes.size_nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Division",
"Prims._assert",
"Prims.eq2",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.op_Addition",
"Prims.pow2",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.nat",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Math.Lemmas.pow2_plus",
"FStar.Math.Lemmas.euclidean_division_definition",
"Hacl.Poly1305.Field32xN.Lemmas2.lemma_sum_lt_pow2_26",
"Lib.Sequence.op_String_Access",
"Hacl.Poly1305.Field32xN.Lemmas2.lset_bit5_lemma_aux",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"FStar.Math.Lemmas.lemma_div_lt_nat",
"FStar.Pervasives.Native.tuple5",
"Lib.IntTypes.int_t",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.upd",
"Lib.IntTypes.logor",
"Lib.Sequence.index",
"Prims.l_Forall",
"Prims.l_imp",
"Prims.op_disEquality",
"Prims.l_or",
"FStar.Seq.Base.index",
"Lib.Sequence.op_String_Assignment",
"Lib.IntTypes.op_Bar_Dot",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.u64",
"Lib.IntTypes.size"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas2
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
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val load_tup64_lemma0_lo: lo:uint64 ->
Lemma
(v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 +
v lo / pow2 52 * pow52 == v lo)
let load_tup64_lemma0_lo lo =
calc (==) {
v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 + v lo / pow2 52 * pow52;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo % pow2 52) / pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo % pow2 52) (pow2 26) }
(v lo % pow2 52) + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo) (pow2 52) }
v lo;
}
val load_tup64_lemma0_hi: hi:uint64 ->
Lemma
((v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104 ==
v hi * pow2 64)
let load_tup64_lemma0_hi hi =
calc (==) {
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) {
assert_norm (pow78 = pow2 14 * pow2 64);
assert_norm (pow104 = pow2 40 * pow2 64)}
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow2 14 * pow2 64 + v hi / pow2 40 * pow2 40 * pow2 64;
(==) { }
(v hi % pow2 14 + ((v hi / pow2 14) % pow2 26) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 40 }
(v hi % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi) 14 40 }
((v hi % pow2 40) % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi % pow2 40) (pow2 14) }
(v hi % pow2 40 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi) (pow2 40) }
v hi * pow2 64;
}
val load_tup64_lemma0:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures as_nat5 f == v hi * pow2 64 + v lo)
#push-options"--z3rlimit 100"
let load_tup64_lemma0 f lo hi =
let (f0, f1, f2, f3, f4) = f in
calc (==) {
as_nat5 f;
(==) { }
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104;
(==) { }
v lo % pow2 26 + (v lo / pow2 26) % pow2 26 * pow26 +
v lo / pow2 52 * pow52 + (v hi % pow2 14) * pow2 12 * pow52 +
(v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_lo lo }
v lo + (v hi % pow2 14) * pow2 12 * pow52 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v lo + (v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_hi hi }
v lo + v hi * pow2 64;
};
assert (as_nat5 f == v hi * pow2 64 + v lo)
#pop-options
val load_tup64_fits_lemma:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures tup64_fits5 f (1, 1, 1, 1, 1))
let load_tup64_fits_lemma f lo hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (pow26 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v lo) 64 52;
lemma_mult_le (v hi % pow2 14) (pow2 14 - 1) (pow2 12) (pow2 12);
assert_norm (pow2 14 * pow2 12 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v hi) 64 40;
assert_norm (pow2 24 < pow2 26)
val load_tup64_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(v ((lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul)) ==
v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_lemma_f2 lo hi =
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
let tmp = (hi &. u64 0x3fff) in
calc (==) {
v (tmp <<. 12ul) % pow2 12;
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
(v tmp * pow2 12 % pow2 64) % pow2 12;
(==) { assert_norm (pow2 64 = pow2 12 * pow2 52) }
(v tmp * pow2 12 % (pow2 12 * pow2 52)) % pow2 12;
(==) {FStar.Math.Lemmas.modulo_modulo_lemma (v tmp * pow2 12) (pow2 12) (pow2 52)}
v tmp * pow2 12 % pow2 12;
(==) {FStar.Math.Lemmas.multiple_modulo_lemma (v tmp) (pow2 12)}
0;
};
assert (v (tmp <<. 12ul) % pow2 12 = 0);
FStar.Math.Lemmas.lemma_div_lt (v lo) 64 52;
assert (v (lo >>. 52ul) < pow2 12);
logor_disjoint (lo >>. 52ul) ((hi &. u64 0x3fff) <<. 12ul) 12;
calc (==) {
v f2;
(==) { }
v (lo >>. 52ul) + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_right_lemma lo 52ul }
v lo / pow2 52 + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64;
};
assert (v f2 == v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64);
assert_norm (0x3fff = pow2 14 - 1);
mod_mask_lemma hi 14ul;
assert (v (mod_mask #U64 #SEC 14ul) == v (u64 0x3fff));
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 % pow2 64);
assert (v hi % pow2 14 < pow2 14);
assert_norm (pow2 14 * pow2 12 < pow2 64);
FStar.Math.Lemmas.small_modulo_lemma_1 ((v hi % pow2 14) * pow2 12) (pow2 64);
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
noextract
val load_tup64_lemma: lo:uint64 -> hi:uint64 ->
Pure tup64_5
(requires True)
(ensures fun f ->
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == v hi * pow2 64 + v lo)
let load_tup64_lemma lo hi =
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fff = pow2 14 - 1);
let f0 = lo &. mask26 in
mod_mask_lemma lo 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v f0 == v lo % pow2 26);
let f1 = (lo >>. 26ul) &. mask26 in
assert (v f1 == (v lo / pow2 26) % pow2 26);
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12);
let f3 = (hi >>. 14ul) &. mask26 in
assert (v f3 == (v hi / pow2 14) % pow2 26);
let f4 = hi >>. 40ul in
assert (v f4 == v hi / pow2 40);
let f = (f0, f1, f2, f3, f4) in
load_tup64_lemma0 f lo hi;
load_tup64_fits_lemma f lo hi;
assert (as_nat5 f < pow2 128);
assert_norm (pow2 128 < prime);
FStar.Math.Lemmas.small_modulo_lemma_1 (as_nat5 f) prime;
assert (as_nat5 f % prime == v hi * pow2 64 + v lo);
f
val load_felem5_lemma_i:
#w:lanes
-> lo:uint64xN w
-> hi:uint64xN w
-> i:nat{i < w} ->
Lemma
(let f = as_tup64_i (load_felem5 #w lo hi) i in
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == (uint64xN_v hi).[i] * pow2 64 + (uint64xN_v lo).[i])
let load_felem5_lemma_i #w lo hi i =
assert (as_tup64_i (load_felem5 #w lo hi) i == load_tup64_lemma (vec_v lo).[i] (vec_v hi).[i])
noextract
val load_tup64_4_compact: lo:uint64 -> hi:uint64 -> tup64_5
let load_tup64_4_compact lo hi =
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let o0 = lo &. mask26 in
let o1 = (lo >>. 26ul) &. mask26 in
let o2 = (t3 >>. 4ul) &. mask26 in
let o3 = (t3 >>. 30ul) &. mask26 in
let o4 = hi >>. 40ul in
(o0, o1, o2, o3, o4)
val load_tup64_4_compact_lemma_f2_mod: lo:uint64 -> hi:uint64 -> Lemma
((v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_4_compact_lemma_f2_mod lo hi =
calc (<) {
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
(<) { Math.Lemmas.lemma_div_lt (v lo) 64 52 }
pow2 12 + (v hi % pow2 14) * pow2 12;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 12) (v hi % pow2 14) (pow2 14 - 1) }
pow2 12 + (pow2 14 - 1) * pow2 12;
(==) { Math.Lemmas.distributivity_sub_left (pow2 14) 1 (pow2 12); Math.Lemmas.pow2_plus 14 12 }
pow2 26;
};
assert (v lo / pow2 52 + (v hi % pow2 14) * pow2 12 < pow2 26);
Math.Lemmas.small_modulo_lemma_1 (v lo / pow2 52 + (v hi % pow2 14) * pow2 12) (pow2 26)
val load_tup64_4_compact_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 4ul) &. u64 0x3ffffff) == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#push-options "--z3rlimit 100"
let load_tup64_4_compact_lemma_f2 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f2 = (t3 >>. 4ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 4;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 4;
(==) { Math.Lemmas.pow2_plus 12 4 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 12 * pow2 4) / pow2 4;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 4) ((v hi % pow2 48) * pow2 12) }
(v lo / pow2 48) / pow2 4 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 4); Math.Lemmas.pow2_plus 48 4 }
v lo / pow2 52 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 60 12 }
v lo / pow2 52 + (v hi * pow2 12) % pow2 60;
};
assert (v (t3 >>. 4ul) == v lo / pow2 52 + (v hi * pow2 12) % pow2 60);
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f2 == v (t3 >>. 4ul) % pow2 26);
calc (==) {
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60) % pow2 26;
(==) { Math.Lemmas.lemma_mod_plus_distr_r (v lo / pow2 52) ((v hi * pow2 12) % pow2 60) (pow2 26) }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60 % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi * pow2 12) 26 60 }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 26 12 }
(v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26;
(==) { load_tup64_4_compact_lemma_f2_mod lo hi }
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
};
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#pop-options
val load_tup64_4_compact_lemma_f3: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 30ul) &. u64 0x3ffffff) == (v hi / pow2 14) % pow2 26)
#push-options "--z3rlimit 200"
let load_tup64_4_compact_lemma_f3 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f3 = (t3 >>. 30ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 30;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 30;
(==) { Math.Lemmas.pow2_plus 16 14;
Math.Lemmas.division_multiplication_lemma (v lo / pow2 48 + (v hi % pow2 48) * pow2 16) (pow2 16) (pow2 14) }
((v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 16) / pow2 14;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 16) (v hi % pow2 48) }
((v lo / pow2 48) / pow2 16 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 16); Math.Lemmas.pow2_plus 48 16 }
(v lo / pow2 64 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.small_div (v lo) (pow2 64) }
(v hi % pow2 48) / pow2 14;
(==) { Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 48 }
(v hi / pow2 14) % pow2 34;
};
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f3 == v (t3 >>. 30ul) % pow2 26);
assert (v f3 == ((v hi / pow2 14) % pow2 34) % pow2 26);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi / pow2 14) 26 34
#pop-options
val load_tup64_4_compact_lemma: lo:uint64 -> hi:uint64 ->
Lemma (load_tup64_4_compact lo hi == load_tup64_lemma lo hi)
let load_tup64_4_compact_lemma lo hi =
let (l0, l1, l2, l3, l4) = load_tup64_4_compact lo hi in
let (r0, r1, r2, r3, r4) = load_tup64_lemma lo hi in
assert (l0 == r0 /\ l1 == r1 /\ l4 == r4);
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let l2 = (t3 >>. 4ul) &. mask26 in
load_tup64_4_compact_lemma_f2 lo hi;
let r2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v l2 == v r2);
let r3 = (hi >>. 14ul) &. mask26 in
mod_mask_lemma (hi >>. 14ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v r3 == (v hi / pow2 14) % pow2 26);
let l3 = (t3 >>. 30ul) &. mask26 in
load_tup64_4_compact_lemma_f3 lo hi
val lemma_store_felem_lo:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> lo:uint64 ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64)
#push-options "--z3rlimit 200"
#restart-solver
let lemma_store_felem_lo f lo =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
assert (v (f1 <<. 26ul) == v f1 * pow2 26 % pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f1 * pow2 26) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f1) 26 26;
logor_disjoint f0 (f1 <<. 26ul) 26;
assert (v (f0 |. (f1 <<. 26ul)) == v f0 + v f1 * pow2 26);
assert_norm (pow2 26 * pow2 26 = pow2 52);
assert (v f0 + v f1 * pow2 26 < pow2 52);
assert (((v f2 * pow2 52) % pow2 64) % pow2 52 = 0);
logor_disjoint (f0 |. (f1 <<. 26ul)) (f2 <<. 52ul) 52
#pop-options
val lemma_store_felem_hi: f:tup64_5 -> hi:uint64 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64))
let lemma_store_felem_hi f hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
FStar.Math.Lemmas.lemma_div_lt (v f2) 26 12;
assert (v f2 / pow2 12 < pow2 14);
assert (v (f3 <<. 14ul) == v f3 * pow2 14 % pow2 64);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26);
assert_norm (pow2 26 * pow2 14 = pow2 40);
assert_norm (pow2 40 < pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f3 * pow2 14) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f3) 14 14;
assert ((v f3 * pow2 14) % pow2 14 = 0);
logor_disjoint (f2 >>. 12ul) (f3 <<. 14ul) 14;
assert (v ((f2 >>. 12ul) |. (f3 <<. 14ul)) == v f2 / pow2 12 + v f3 * pow2 14);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26 - 1);
assert (v f2 / pow2 12 + v f3 * pow2 14 < pow2 40);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v f4 * pow2 40) 40 64;
assert (((v f4 * pow2 40) % pow2 64) % pow2 40 = (v f4 * pow2 40) % pow2 40);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f4) 40 40;
assert ((v f4 * pow2 40) % pow2 40 = 0);
logor_disjoint ((f2 >>. 12ul) |. (f3 <<. 14ul)) (f4 <<. 40ul) 40
val lemma_tup64_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 < pow2 128))
let lemma_tup64_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 in
assert (tmp <= pow2 26 - 1 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 +
(pow2 26 - 1) * pow78 + (pow2 24 - 1) * pow104);
assert (tmp <= pow2 24 * pow104 - 1);
assert_norm (pow2 24 * pow104 = pow2 128)
val lemma_tup64_mod_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
(as_nat5 f) % pow2 128 == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104))
let lemma_tup64_mod_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 in
calc (==) {
(as_nat5 f) % pow2 128;
(==) { }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % pow2 128;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f4 * pow104) (pow2 128) }
(tmp + (v f4 * pow104 % pow2 128)) % pow2 128;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 128 104 }
(tmp + (v f4 % pow2 24) * pow104) % pow2 128;
(==) { lemma_tup64_pow2_128 f; FStar.Math.Lemmas.modulo_lemma (tmp + (v f4 % pow2 24) * pow104) (pow2 128) }
tmp + (v f4 % pow2 24) * pow104;
};
assert ((as_nat5 f) % pow2 128 == tmp + (v f4 % pow2 24) * pow104)
noextract
val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128))
let store_tup64_lemma f =
let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
lemma_store_felem_lo f lo;
lemma_store_felem_hi f hi;
assert (v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64);
assert (v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64);
calc (==) {
v lo + v hi * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
(v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64) * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 * pow2 40) % pow2 64 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 40 }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 52 }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { assert_norm (pow2 40 * pow2 64 = pow104) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 14 * pow2 64 = pow78) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12 + v f2 / pow2 12 * pow2 12) * pow52 +
v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 12) }
v f0 + v f1 * pow2 26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { lemma_tup64_mod_pow2_128 f }
(as_nat5 f) % pow2 128;
};
assert (v lo + v hi * pow2 64 == (as_nat5 f) % pow2 128);
lo, hi
#push-options "--max_ifuel 1"
val store_felem5_lemma:
#w:lanes
-> f:felem5 w ->
Lemma
(requires felem_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (lo, hi) = store_felem5 f in
v hi * pow2 64 + v lo == (fas_nat5 f).[0] % pow2 128))
let store_felem5_lemma #w f =
let (lo, hi) = store_felem5 f in
assert (store_tup64_lemma (as_tup64_i f 0) == (lo, hi))
#pop-options
val lemma_sum_lt_pow2_26: i:nat -> a:nat{a < pow2 (i % 26)} -> b:nat{b <= pow2 (i % 26)} ->
Lemma (a + b <= max26)
let lemma_sum_lt_pow2_26 i a b =
assert (a + b < pow2 (i % 26) + pow2 (i % 26));
FStar.Math.Lemmas.pow2_le_compat 25 (i % 26);
assert (a + b < pow2 25 + pow2 25);
FStar.Math.Lemmas.pow2_double_sum 25;
assert_norm (pow26 = pow2 26)
val lset_bit5_lemma_aux: fi:uint64 -> i:size_nat{i <= 128} ->
Lemma
(requires v fi < pow2 (i % 26))
(ensures (v (fi |. (u64 1 <<. size (i % 26))) == v fi + pow2 (i % 26)))
let lset_bit5_lemma_aux fi i =
let b = u64 1 <<. size (i % 26) in
FStar.Math.Lemmas.pow2_lt_compat 26 (i % 26);
FStar.Math.Lemmas.pow2_lt_compat 64 26;
FStar.Math.Lemmas.modulo_lemma (pow2 (i % 26)) (pow2 64);
assert (v b == pow2 (i % 26));
logor_disjoint fi b (i % 26);
let out_i = fi |. b in
assert (v out_i == v fi + v b);
assert (v out_i == v fi + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v fi) (v b);
assert_norm (pow26 = pow2 26);
assert (v out_i <= max26)
val lset_bit5_lemma0:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 0} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma0 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[0] <- f.[0] |. b in
assert (v f.[i / 26] < pow2 (i % 26));
lset_bit5_lemma_aux f.[0] i;
assert (v out.[0] == v f.[0] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[0]) (pow2 (i % 26));
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4))
val lset_bit5_lemma1:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 1} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma1 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[1] <- f.[1] |. b in
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
assert (v f1 * pow2 26 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f1 * pow2 26) i 26;
assert (v f1 < pow2 (i - 26));
assert (i - 26 == i % 26);
assert (v f.[1] < pow2 (i % 26));
lset_bit5_lemma_aux f.[1] i;
assert (v out.[1] == v f.[1] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[1]) (pow2 (i % 26));
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) * pow26 + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.pow2_plus (i % 26) 26 }
pow2 (i % 26 + 26) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4))
val lset_bit5_lemma2:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 2} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma2 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[2] <- f.[2] |. b in
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
assert (v f2 * pow52 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f2 * pow52) i 52;
assert (v f2 < pow2 (i - 52));
assert (i - 52 == i % 26);
assert (v f.[2] < pow2 (i % 26));
lset_bit5_lemma_aux f.[2] i;
assert (v out.[2] == v f.[2] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[2]) (pow2 (i % 26));
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) * pow52 + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.pow2_plus (i % 26) 52 }
pow2 (i % 26 + 52) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4))
val lset_bit5_lemma3:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 3} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4])))
let lset_bit5_lemma3 f i =
let b = u64 1 <<. size (i % 26) in
let out = f.[3] <- f.[3] |. b in
let (f0, f1, f2, f3, f4) = (f.[0], f.[1], f.[2], f.[3], f.[4]) in
let (o0, o1, o2, o3, o4) = (out.[0], out.[1], out.[2], out.[3], out.[4]) in
assert (v f3 * pow78 < pow2 i);
FStar.Math.Lemmas.lemma_div_lt_nat (v f3 * pow78) i 78;
assert (v f3 < pow2 (i - 78));
assert (i - 78 == i % 26);
assert (v f.[3] < pow2 (i % 26));
lset_bit5_lemma_aux f.[3] i;
assert (v out.[3] == v f.[3] + pow2 (i % 26));
lemma_sum_lt_pow2_26 i (v f.[3]) (pow2 (i % 26));
calc (==) {
as_nat5 (o0, o1, o2, o3, o4);
(==) { }
v o0 + v o1 * pow26 + v o2 * pow52 + v o3 * pow78 + v o4 * pow104;
(==) { }
pow2 (i % 26) * pow78 + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.pow2_plus (i % 26) 78 }
pow2 (i % 26 + 78) + as_nat5 (f0, f1, f2, f3, f4);
(==) { FStar.Math.Lemmas.euclidean_division_definition i 26 }
pow2 i + as_nat5 (f0, f1, f2, f3, f4);
};
assert (as_nat5 (o0, o1, o2, o3, o4) == pow2 i + as_nat5 (f0, f1, f2, f3, f4))
val lset_bit5_lemma4:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 4} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | false | false | Hacl.Poly1305.Field32xN.Lemmas2.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lset_bit5_lemma4:
f:lseq uint64 5
-> i:size_nat{i <= 128 /\ i / 26 = 4} ->
Lemma
(requires
(forall (i:nat). i < 5 ==> v f.[i] <= max26) /\
as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]) < pow2 i)
(ensures
(let b = u64 1 <<. size (i % 26) in
let out = f.[i / 26] <- f.[i / 26] |. b in
(forall (i:nat). i < 5 ==> v out.[i] <= max26) /\
as_nat5 (out.[0], out.[1], out.[2], out.[3], out.[4]) ==
pow2 i + as_nat5 (f.[0], f.[1], f.[2], f.[3], f.[4]))) | [] | Hacl.Poly1305.Field32xN.Lemmas2.lset_bit5_lemma4 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas2.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Lib.Sequence.lseq Lib.IntTypes.uint64 5 -> i: Lib.IntTypes.size_nat{i <= 128 /\ i / 26 = 4}
-> FStar.Pervasives.Lemma
(requires
(forall (i: Prims.nat).
i < 5 ==> Lib.IntTypes.v f.[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26) /\
Hacl.Spec.Poly1305.Field32xN.as_nat5 (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]) <
Prims.pow2 i)
(ensures
(let b = Lib.IntTypes.u64 1 <<. Lib.IntTypes.size (i % 26) in
let out = f.[ i / 26 ] <- f.[ i / 26 ] |. b in
(forall (i: Prims.nat).
i < 5 ==> Lib.IntTypes.v out.[ i ] <= Hacl.Spec.Poly1305.Field32xN.max26) /\
Hacl.Spec.Poly1305.Field32xN.as_nat5 (out.[ 0 ],
out.[ 1 ],
out.[ 2 ],
out.[ 3 ],
out.[ 4 ]) ==
Prims.pow2 i +
Hacl.Spec.Poly1305.Field32xN.as_nat5 (f.[ 0 ], f.[ 1 ], f.[ 2 ], f.[ 3 ], f.[ 4 ]))) | {
"end_col": 80,
"end_line": 752,
"start_col": 26,
"start_line": 727
} |
Prims.Pure | val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let store_tup64_lemma f =
let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
lemma_store_felem_lo f lo;
lemma_store_felem_hi f hi;
assert (v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64);
assert (v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64);
calc (==) {
v lo + v hi * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
(v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64) * pow2 64;
(==) { }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 * pow2 40) % pow2 64 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 40 }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 52 }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow2 40 * pow2 64;
(==) { assert_norm (pow2 40 * pow2 64 = pow104) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow2 14 * pow2 64 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 14 * pow2 64 = pow78) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 +
v f2 / pow2 12 * pow2 64 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12 + v f2 / pow2 12 * pow2 12) * pow52 +
v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 12) }
v f0 + v f1 * pow2 26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
(==) { lemma_tup64_mod_pow2_128 f }
(as_nat5 f) % pow2 128;
};
assert (v lo + v hi * pow2 64 == (as_nat5 f) % pow2 128);
lo, hi | val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128))
let store_tup64_lemma f = | false | null | false | let f0, f1, f2, f3, f4 = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
lemma_store_felem_lo f lo;
lemma_store_felem_hi f hi;
assert (v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64);
assert (v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64);
calc ( == ) {
v lo + v hi * pow2 64;
( == ) { () }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 +
(v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64) * pow2 64;
( == ) { () }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 + (v f2 / pow2 12) * pow2 64 +
(v f3 * pow2 14) * pow2 64 +
((v f4 * pow2 40) % pow2 64) * pow2 64;
( == ) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 40 }
v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64 + (v f2 / pow2 12) * pow2 64 +
(v f3 * pow2 14) * pow2 64 +
((v f4 % pow2 24) * pow2 40) * pow2 64;
( == ) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 52 }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 + (v f2 / pow2 12) * pow2 64 +
(v f3 * pow2 14) * pow2 64 +
((v f4 % pow2 24) * pow2 40) * pow2 64;
( == ) { assert_norm (pow2 40 * pow2 64 = pow104) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 + (v f2 / pow2 12) * pow2 64 +
(v f3 * pow2 14) * pow2 64 +
(v f4 % pow2 24) * pow104;
( == ) { assert_norm (pow2 14 * pow2 64 = pow78) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12) * pow2 52 + (v f2 / pow2 12) * pow2 64 + v f3 * pow78 +
(v f4 % pow2 24) * pow104;
( == ) { assert_norm (pow2 12 * pow52 = pow2 64) }
v f0 + v f1 * pow2 26 + (v f2 % pow2 12 + (v f2 / pow2 12) * pow2 12) * pow52 + v f3 * pow78 +
(v f4 % pow2 24) * pow104;
( == ) { FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 12) }
v f0 + v f1 * pow2 26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104;
( == ) { lemma_tup64_mod_pow2_128 f }
(as_nat5 f) % pow2 128;
};
assert (v lo + v hi * pow2 64 == (as_nat5 f) % pow2 128);
lo, hi | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas2.fst"
} | [] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Lib.IntTypes.uint64",
"FStar.Pervasives.Native.Mktuple2",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.op_Modulus",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.op_Division",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"FStar.Math.Lemmas.euclidean_division_definition",
"Hacl.Poly1305.Field32xN.Lemmas2.lemma_tup64_mod_pow2_128",
"Hacl.Poly1305.Field32xN.Lemmas2.lemma_store_felem_hi",
"Hacl.Poly1305.Field32xN.Lemmas2.lemma_store_felem_lo",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Bar_Dot",
"Lib.IntTypes.op_Greater_Greater_Dot",
"FStar.UInt32.__uint_to_t",
"Lib.IntTypes.op_Less_Less_Dot",
"FStar.Pervasives.Native.tuple2"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas2
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
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val load_tup64_lemma0_lo: lo:uint64 ->
Lemma
(v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 +
v lo / pow2 52 * pow52 == v lo)
let load_tup64_lemma0_lo lo =
calc (==) {
v lo % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow26 + v lo / pow2 52 * pow52;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo / pow2 26) % pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v lo) 26 52 }
(v lo % pow2 52) % pow2 26 + ((v lo % pow2 52) / pow2 26) * pow2 26 + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo % pow2 52) (pow2 26) }
(v lo % pow2 52) + v lo / pow2 52 * pow2 52;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v lo) (pow2 52) }
v lo;
}
val load_tup64_lemma0_hi: hi:uint64 ->
Lemma
((v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104 ==
v hi * pow2 64)
let load_tup64_lemma0_hi hi =
calc (==) {
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) {
assert_norm (pow78 = pow2 14 * pow2 64);
assert_norm (pow104 = pow2 40 * pow2 64)}
(v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow2 14 * pow2 64 + v hi / pow2 40 * pow2 40 * pow2 64;
(==) { }
(v hi % pow2 14 + ((v hi / pow2 14) % pow2 26) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 40 }
(v hi % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi) 14 40 }
((v hi % pow2 40) % pow2 14 + ((v hi % pow2 40) / pow2 14) * pow2 14 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi % pow2 40) (pow2 14) }
(v hi % pow2 40 + (v hi / pow2 40) * pow2 40) * pow2 64;
(==) { FStar.Math.Lemmas.euclidean_division_definition (v hi) (pow2 40) }
v hi * pow2 64;
}
val load_tup64_lemma0:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures as_nat5 f == v hi * pow2 64 + v lo)
#push-options"--z3rlimit 100"
let load_tup64_lemma0 f lo hi =
let (f0, f1, f2, f3, f4) = f in
calc (==) {
as_nat5 f;
(==) { }
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104;
(==) { }
v lo % pow2 26 + (v lo / pow2 26) % pow2 26 * pow26 +
v lo / pow2 52 * pow52 + (v hi % pow2 14) * pow2 12 * pow52 +
(v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_lo lo }
v lo + (v hi % pow2 14) * pow2 12 * pow52 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { assert_norm (pow2 12 * pow52 = pow2 64) }
v lo + (v hi % pow2 14) * pow2 64 + (v hi / pow2 14) % pow2 26 * pow78 + v hi / pow2 40 * pow104;
(==) { load_tup64_lemma0_hi hi }
v lo + v hi * pow2 64;
};
assert (as_nat5 f == v hi * pow2 64 + v lo)
#pop-options
val load_tup64_fits_lemma:
f:tup64_5
-> lo:uint64
-> hi:uint64 ->
Lemma
(requires
(let (f0, f1, f2, f3, f4) = f in
v f0 == v lo % pow2 26 /\
v f1 == (v lo / pow2 26) % pow2 26 /\
v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 /\
v f3 == (v hi / pow2 14) % pow2 26 /\
v f4 == v hi / pow2 40))
(ensures tup64_fits5 f (1, 1, 1, 1, 1))
let load_tup64_fits_lemma f lo hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (pow26 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v lo) 64 52;
lemma_mult_le (v hi % pow2 14) (pow2 14 - 1) (pow2 12) (pow2 12);
assert_norm (pow2 14 * pow2 12 = pow2 26);
FStar.Math.Lemmas.lemma_div_lt_nat (v hi) 64 40;
assert_norm (pow2 24 < pow2 26)
val load_tup64_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(v ((lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul)) ==
v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_lemma_f2 lo hi =
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
let tmp = (hi &. u64 0x3fff) in
calc (==) {
v (tmp <<. 12ul) % pow2 12;
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
(v tmp * pow2 12 % pow2 64) % pow2 12;
(==) { assert_norm (pow2 64 = pow2 12 * pow2 52) }
(v tmp * pow2 12 % (pow2 12 * pow2 52)) % pow2 12;
(==) {FStar.Math.Lemmas.modulo_modulo_lemma (v tmp * pow2 12) (pow2 12) (pow2 52)}
v tmp * pow2 12 % pow2 12;
(==) {FStar.Math.Lemmas.multiple_modulo_lemma (v tmp) (pow2 12)}
0;
};
assert (v (tmp <<. 12ul) % pow2 12 = 0);
FStar.Math.Lemmas.lemma_div_lt (v lo) 64 52;
assert (v (lo >>. 52ul) < pow2 12);
logor_disjoint (lo >>. 52ul) ((hi &. u64 0x3fff) <<. 12ul) 12;
calc (==) {
v f2;
(==) { }
v (lo >>. 52ul) + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_right_lemma lo 52ul }
v lo / pow2 52 + v ((hi &. u64 0x3fff) <<. 12ul);
(==) { shift_left_lemma (hi &. u64 0x3fff) 12ul }
v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64;
};
assert (v f2 == v lo / pow2 52 + v (hi &. u64 0x3fff) * pow2 12 % pow2 64);
assert_norm (0x3fff = pow2 14 - 1);
mod_mask_lemma hi 14ul;
assert (v (mod_mask #U64 #SEC 14ul) == v (u64 0x3fff));
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12 % pow2 64);
assert (v hi % pow2 14 < pow2 14);
assert_norm (pow2 14 * pow2 12 < pow2 64);
FStar.Math.Lemmas.small_modulo_lemma_1 ((v hi % pow2 14) * pow2 12) (pow2 64);
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
noextract
val load_tup64_lemma: lo:uint64 -> hi:uint64 ->
Pure tup64_5
(requires True)
(ensures fun f ->
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == v hi * pow2 64 + v lo)
let load_tup64_lemma lo hi =
let mask26 = u64 0x3ffffff in
assert_norm (0x3ffffff = pow2 26 - 1);
assert_norm (0x3fff = pow2 14 - 1);
let f0 = lo &. mask26 in
mod_mask_lemma lo 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v f0 == v lo % pow2 26);
let f1 = (lo >>. 26ul) &. mask26 in
assert (v f1 == (v lo / pow2 26) % pow2 26);
let f2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12);
let f3 = (hi >>. 14ul) &. mask26 in
assert (v f3 == (v hi / pow2 14) % pow2 26);
let f4 = hi >>. 40ul in
assert (v f4 == v hi / pow2 40);
let f = (f0, f1, f2, f3, f4) in
load_tup64_lemma0 f lo hi;
load_tup64_fits_lemma f lo hi;
assert (as_nat5 f < pow2 128);
assert_norm (pow2 128 < prime);
FStar.Math.Lemmas.small_modulo_lemma_1 (as_nat5 f) prime;
assert (as_nat5 f % prime == v hi * pow2 64 + v lo);
f
val load_felem5_lemma_i:
#w:lanes
-> lo:uint64xN w
-> hi:uint64xN w
-> i:nat{i < w} ->
Lemma
(let f = as_tup64_i (load_felem5 #w lo hi) i in
tup64_fits5 f (1, 1, 1, 1, 1) /\
as_nat5 f < pow2 128 /\
as_nat5 f % prime == (uint64xN_v hi).[i] * pow2 64 + (uint64xN_v lo).[i])
let load_felem5_lemma_i #w lo hi i =
assert (as_tup64_i (load_felem5 #w lo hi) i == load_tup64_lemma (vec_v lo).[i] (vec_v hi).[i])
noextract
val load_tup64_4_compact: lo:uint64 -> hi:uint64 -> tup64_5
let load_tup64_4_compact lo hi =
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let o0 = lo &. mask26 in
let o1 = (lo >>. 26ul) &. mask26 in
let o2 = (t3 >>. 4ul) &. mask26 in
let o3 = (t3 >>. 30ul) &. mask26 in
let o4 = hi >>. 40ul in
(o0, o1, o2, o3, o4)
val load_tup64_4_compact_lemma_f2_mod: lo:uint64 -> hi:uint64 -> Lemma
((v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
let load_tup64_4_compact_lemma_f2_mod lo hi =
calc (<) {
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
(<) { Math.Lemmas.lemma_div_lt (v lo) 64 52 }
pow2 12 + (v hi % pow2 14) * pow2 12;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 12) (v hi % pow2 14) (pow2 14 - 1) }
pow2 12 + (pow2 14 - 1) * pow2 12;
(==) { Math.Lemmas.distributivity_sub_left (pow2 14) 1 (pow2 12); Math.Lemmas.pow2_plus 14 12 }
pow2 26;
};
assert (v lo / pow2 52 + (v hi % pow2 14) * pow2 12 < pow2 26);
Math.Lemmas.small_modulo_lemma_1 (v lo / pow2 52 + (v hi % pow2 14) * pow2 12) (pow2 26)
val load_tup64_4_compact_lemma_f2: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 4ul) &. u64 0x3ffffff) == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#push-options "--z3rlimit 100"
let load_tup64_4_compact_lemma_f2 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f2 = (t3 >>. 4ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 4;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 4;
(==) { Math.Lemmas.pow2_plus 12 4 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 12 * pow2 4) / pow2 4;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 4) ((v hi % pow2 48) * pow2 12) }
(v lo / pow2 48) / pow2 4 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 4); Math.Lemmas.pow2_plus 48 4 }
v lo / pow2 52 + (v hi % pow2 48) * pow2 12;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 60 12 }
v lo / pow2 52 + (v hi * pow2 12) % pow2 60;
};
assert (v (t3 >>. 4ul) == v lo / pow2 52 + (v hi * pow2 12) % pow2 60);
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f2 == v (t3 >>. 4ul) % pow2 26);
calc (==) {
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60) % pow2 26;
(==) { Math.Lemmas.lemma_mod_plus_distr_r (v lo / pow2 52) ((v hi * pow2 12) % pow2 60) (pow2 26) }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 60 % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi * pow2 12) 26 60 }
(v lo / pow2 52 + (v hi * pow2 12) % pow2 26) % pow2 26;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 26 12 }
(v lo / pow2 52 + (v hi % pow2 14) * pow2 12) % pow2 26;
(==) { load_tup64_4_compact_lemma_f2_mod lo hi }
v lo / pow2 52 + (v hi % pow2 14) * pow2 12;
};
assert (v f2 == v lo / pow2 52 + (v hi % pow2 14) * pow2 12)
#pop-options
val load_tup64_4_compact_lemma_f3: lo:uint64 -> hi:uint64 -> Lemma
(let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
v ((t3 >>. 30ul) &. u64 0x3ffffff) == (v hi / pow2 14) % pow2 26)
#push-options "--z3rlimit 200"
let load_tup64_4_compact_lemma_f3 lo hi =
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let f3 = (t3 >>. 30ul) &. u64 0x3ffffff in
Math.Lemmas.lemma_div_lt (v lo) 64 48;
logor_disjoint (lo >>. 48ul) (hi <<. 16ul) 16;
assert (v t3 == v lo / pow2 48 + (v hi * pow2 16) % pow2 64);
calc (==) {
(v lo / pow2 48 + (v hi * pow2 16) % pow2 64) / pow2 30;
(==) { Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v hi) 64 16 }
(v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 30;
(==) { Math.Lemmas.pow2_plus 16 14;
Math.Lemmas.division_multiplication_lemma (v lo / pow2 48 + (v hi % pow2 48) * pow2 16) (pow2 16) (pow2 14) }
((v lo / pow2 48 + (v hi % pow2 48) * pow2 16) / pow2 16) / pow2 14;
(==) { Math.Lemmas.division_addition_lemma (v lo / pow2 48) (pow2 16) (v hi % pow2 48) }
((v lo / pow2 48) / pow2 16 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.division_multiplication_lemma (v lo) (pow2 48) (pow2 16); Math.Lemmas.pow2_plus 48 16 }
(v lo / pow2 64 + (v hi % pow2 48)) / pow2 14;
(==) { Math.Lemmas.small_div (v lo) (pow2 64) }
(v hi % pow2 48) / pow2 14;
(==) { Math.Lemmas.pow2_modulo_division_lemma_1 (v hi) 14 48 }
(v hi / pow2 14) % pow2 34;
};
assert_norm (0x3ffffff = pow2 26 - 1);
mod_mask_lemma (t3 >>. 4ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v (u64 0x3ffffff));
assert (v f3 == v (t3 >>. 30ul) % pow2 26);
assert (v f3 == ((v hi / pow2 14) % pow2 34) % pow2 26);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v hi / pow2 14) 26 34
#pop-options
val load_tup64_4_compact_lemma: lo:uint64 -> hi:uint64 ->
Lemma (load_tup64_4_compact lo hi == load_tup64_lemma lo hi)
let load_tup64_4_compact_lemma lo hi =
let (l0, l1, l2, l3, l4) = load_tup64_4_compact lo hi in
let (r0, r1, r2, r3, r4) = load_tup64_lemma lo hi in
assert (l0 == r0 /\ l1 == r1 /\ l4 == r4);
let mask26 = u64 0x3ffffff in
let t3 = (lo >>. 48ul) |. (hi <<. 16ul) in
let l2 = (t3 >>. 4ul) &. mask26 in
load_tup64_4_compact_lemma_f2 lo hi;
let r2 = (lo >>. 52ul) |. ((hi &. u64 0x3fff) <<. 12ul) in
load_tup64_lemma_f2 lo hi;
assert (v l2 == v r2);
let r3 = (hi >>. 14ul) &. mask26 in
mod_mask_lemma (hi >>. 14ul) 26ul;
assert (v (mod_mask #U64 #SEC 26ul) == v mask26);
assert (v r3 == (v hi / pow2 14) % pow2 26);
let l3 = (t3 >>. 30ul) &. mask26 in
load_tup64_4_compact_lemma_f3 lo hi
val lemma_store_felem_lo:
f:tup64_5{tup64_fits5 f (1, 1, 1, 1, 1)}
-> lo:uint64 ->
Lemma
(let (f0, f1, f2, f3, f4) = f in
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
v lo == v f0 + v f1 * pow2 26 + (v f2 * pow2 52) % pow2 64)
#push-options "--z3rlimit 200"
#restart-solver
let lemma_store_felem_lo f lo =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let lo = f0 |. (f1 <<. 26ul) |. (f2 <<. 52ul) in
assert (v (f1 <<. 26ul) == v f1 * pow2 26 % pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f1 * pow2 26) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f1) 26 26;
logor_disjoint f0 (f1 <<. 26ul) 26;
assert (v (f0 |. (f1 <<. 26ul)) == v f0 + v f1 * pow2 26);
assert_norm (pow2 26 * pow2 26 = pow2 52);
assert (v f0 + v f1 * pow2 26 < pow2 52);
assert (((v f2 * pow2 52) % pow2 64) % pow2 52 = 0);
logor_disjoint (f0 |. (f1 <<. 26ul)) (f2 <<. 52ul) 52
#pop-options
val lemma_store_felem_hi: f:tup64_5 -> hi:uint64 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
v hi == v f2 / pow2 12 + v f3 * pow2 14 + (v f4 * pow2 40) % pow2 64))
let lemma_store_felem_hi f hi =
let (f0, f1, f2, f3, f4) = f in
assert_norm (max26 = pow2 26 - 1);
let hi = (f2 >>. 12ul) |. (f3 <<. 14ul) |. (f4 <<. 40ul) in
FStar.Math.Lemmas.lemma_div_lt (v f2) 26 12;
assert (v f2 / pow2 12 < pow2 14);
assert (v (f3 <<. 14ul) == v f3 * pow2 14 % pow2 64);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26);
assert_norm (pow2 26 * pow2 14 = pow2 40);
assert_norm (pow2 40 < pow2 64);
FStar.Math.Lemmas.modulo_lemma (v f3 * pow2 14) (pow2 64);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f3) 14 14;
assert ((v f3 * pow2 14) % pow2 14 = 0);
logor_disjoint (f2 >>. 12ul) (f3 <<. 14ul) 14;
assert (v ((f2 >>. 12ul) |. (f3 <<. 14ul)) == v f2 / pow2 12 + v f3 * pow2 14);
FStar.Math.Lemmas.lemma_mult_le_right (pow2 14) (v f3) (pow2 26 - 1);
assert (v f2 / pow2 12 + v f3 * pow2 14 < pow2 40);
FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v f4 * pow2 40) 40 64;
assert (((v f4 * pow2 40) % pow2 64) % pow2 40 = (v f4 * pow2 40) % pow2 40);
FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 (v f4) 40 40;
assert ((v f4 * pow2 40) % pow2 40 = 0);
logor_disjoint ((f2 >>. 12ul) |. (f3 <<. 14ul)) (f4 <<. 40ul) 40
val lemma_tup64_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 < pow2 128))
let lemma_tup64_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104 in
assert (tmp <= pow2 26 - 1 + (pow2 26 - 1) * pow26 + (pow2 26 - 1) * pow52 +
(pow2 26 - 1) * pow78 + (pow2 24 - 1) * pow104);
assert (tmp <= pow2 24 * pow104 - 1);
assert_norm (pow2 24 * pow104 = pow2 128)
val lemma_tup64_mod_pow2_128: f:tup64_5 ->
Lemma
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures
(let (f0, f1, f2, f3, f4) = f in
(as_nat5 f) % pow2 128 == v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + (v f4 % pow2 24) * pow104))
let lemma_tup64_mod_pow2_128 f =
let (f0, f1, f2, f3, f4) = f in
let tmp = v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 in
calc (==) {
(as_nat5 f) % pow2 128;
(==) { }
(v f0 + v f1 * pow26 + v f2 * pow52 + v f3 * pow78 + v f4 * pow104) % pow2 128;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f4 * pow104) (pow2 128) }
(tmp + (v f4 * pow104 % pow2 128)) % pow2 128;
(==) { FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 128 104 }
(tmp + (v f4 % pow2 24) * pow104) % pow2 128;
(==) { lemma_tup64_pow2_128 f; FStar.Math.Lemmas.modulo_lemma (tmp + (v f4 % pow2 24) * pow104) (pow2 128) }
tmp + (v f4 % pow2 24) * pow104;
};
assert ((as_nat5 f) % pow2 128 == tmp + (v f4 % pow2 24) * pow104)
noextract
val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128)) | false | false | Hacl.Poly1305.Field32xN.Lemmas2.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val store_tup64_lemma: f:tup64_5 ->
Pure (uint64 & uint64)
(requires tup64_fits5 f (1, 1, 1, 1, 1))
(ensures (fun (lo, hi) -> v hi * pow2 64 + v lo == as_nat5 f % pow2 128)) | [] | Hacl.Poly1305.Field32xN.Lemmas2.store_tup64_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas2.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | f: Hacl.Spec.Poly1305.Field32xN.tup64_5 -> Prims.Pure (Lib.IntTypes.uint64 * Lib.IntTypes.uint64) | {
"end_col": 8,
"end_line": 503,
"start_col": 25,
"start_line": 464
} |
FStar.Pervasives.Lemma | val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b) | val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b = | false | null | true | ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint64",
"Hacl.Spec.K256.MathLemmas.lemma_bound_mul64_wide",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.unit"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
ma: Prims.nat ->
mb: Prims.nat ->
mma: Prims.nat ->
mmb: Prims.nat ->
a: Lib.IntTypes.uint64 ->
b: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma (requires Lib.IntTypes.v a <= ma * mma /\ Lib.IntTypes.v b <= mb * mmb)
(ensures
(let r = Lib.IntTypes.mul64_wide a b in
Lib.IntTypes.v r = Lib.IntTypes.v a * Lib.IntTypes.v b /\
Lib.IntTypes.v r <= (ma * mb) * (mma * mmb))) | {
"end_col": 53,
"end_line": 22,
"start_col": 2,
"start_line": 22
} |
FStar.Pervasives.Lemma | val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32 | val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 = | false | null | true | lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32 | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.pow2_plus",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Prims.pow2",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div64_max48"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_c0 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | c0: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v c0 <=
4096 * (Hacl.Spec.K256.Field52.Definitions.max48 * Hacl.Spec.K256.Field52.Definitions.max48)
) (ensures Lib.IntTypes.v c0 / Prims.pow2 64 <= Prims.pow2 44) | {
"end_col": 29,
"end_line": 443,
"start_col": 2,
"start_line": 441
} |
FStar.Pervasives.Lemma | val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52) | val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a = | false | null | true | Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) ((md * max52) * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.multiple_division_lemma",
"FStar.Mul.op_Star",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.lemma_div_le",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Math.Lemmas.lemma_mult_lt_left"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.pos -> a: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a <=
(md * Hacl.Spec.K256.Field52.Definitions.max52) * Hacl.Spec.K256.Field52.Definitions.max52)
(ensures Lib.IntTypes.v a / Prims.pow2 52 <= md * Hacl.Spec.K256.Field52.Definitions.max52) | {
"end_col": 60,
"end_line": 399,
"start_col": 2,
"start_line": 397
} |
FStar.Pervasives.Lemma | val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64) | val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a = | false | null | true | assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.multiple_division_lemma",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus",
"FStar.Math.Lemmas.lemma_div_le",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims._assert",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.lemma_mult_le_left",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.MathLemmas.lemma_ab_lt_cd",
"FStar.Pervasives.assert_norm"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div64_max52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.pos -> a: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))
(ensures Lib.IntTypes.v a / Prims.pow2 64 <= md * Prims.pow2 40) | {
"end_col": 62,
"end_line": 433,
"start_col": 2,
"start_line": 424
} |
FStar.Pervasives.Lemma | val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
} | val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a = | false | null | true | assert_norm (16 * (max52 * max48) < max52 * max52);
calc ( < ) {
(a * 16) * (max52 * max48);
( == ) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
( < ) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Mul.op_Star",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_lt_left",
"FStar.Pervasives.assert_norm"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Prims.pos
-> FStar.Pervasives.Lemma
(ensures
(a * 16) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max48) <
a * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52)) | {
"end_col": 3,
"end_line": 58,
"start_col": 2,
"start_line": 51
} |
FStar.Pervasives.Lemma | val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128) | val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_four_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
b0: Lib.IntTypes.uint64 ->
b1: Lib.IntTypes.uint64 ->
b2: Lib.IntTypes.uint64 ->
b3: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b3 64)
(ensures
(let d =
Lib.IntTypes.mul64_wide a0 b3 +. Lib.IntTypes.mul64_wide a1 b2 +.
Lib.IntTypes.mul64_wide a2 b1 +.
Lib.IntTypes.mul64_wide a3 b0
in
Lib.IntTypes.v d =
Lib.IntTypes.v a0 * Lib.IntTypes.v b3 + Lib.IntTypes.v a1 * Lib.IntTypes.v b2 +
Lib.IntTypes.v a2 * Lib.IntTypes.v b1 +
Lib.IntTypes.v a3 * Lib.IntTypes.v b0 /\
Lib.IntTypes.v d <=
16384 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 90,
"end_line": 46,
"start_col": 2,
"start_line": 37
} |
FStar.Pervasives.Lemma | val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4') | val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' = | false | null | true | let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4') | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.op_Addition",
"Prims.unit",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Math.Lemmas.pow2_lt_compat",
"Prims.op_LessThan",
"FStar.Math.Lemmas.pow2_double_sum",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Plus_Dot"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_mod_add_last | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | c12: Lib.IntTypes.uint64 -> t4': Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires Lib.IntTypes.v c12 < Prims.pow2 48 /\ Lib.IntTypes.v t4' < Prims.pow2 48)
(ensures
(let r4 = c12 +. t4' in
Lib.IntTypes.v r4 = Lib.IntTypes.v c12 + Lib.IntTypes.v t4' /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 r4 2)) | {
"end_col": 31,
"end_line": 573,
"start_col": 32,
"start_line": 566
} |
FStar.Pervasives.Lemma | val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64) | val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a = | false | null | true | assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.multiple_division_lemma",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus",
"FStar.Math.Lemmas.lemma_div_le",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims._assert",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Math.Lemmas.lemma_mult_le_left",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Hacl.Spec.K256.MathLemmas.lemma_ab_lt_cd",
"FStar.Pervasives.assert_norm"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div64_max48 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.pos -> a: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a <=
md * (Hacl.Spec.K256.Field52.Definitions.max48 * Hacl.Spec.K256.Field52.Definitions.max48))
(ensures Lib.IntTypes.v a / Prims.pow2 64 <= md * Prims.pow2 32) | {
"end_col": 62,
"end_line": 416,
"start_col": 2,
"start_line": 407
} |
FStar.Pervasives.Lemma | val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64 | val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d = | false | null | true | let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64 | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Lib.IntTypes.U64",
"Prims.op_Modulus",
"Prims.pow2",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.lemma_mask52",
"Lib.IntTypes.to_u64",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Amp_Dot",
"Hacl.Spec.K256.Field52.Definitions.mask52"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_to_u64_mask52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | d: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(ensures
(let r = Lib.IntTypes.to_u64 d &. Hacl.Spec.K256.Field52.Definitions.mask52 in
Lib.IntTypes.v r = Lib.IntTypes.v d % Prims.pow2 52 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 r 1)) | {
"end_col": 52,
"end_line": 475,
"start_col": 32,
"start_line": 471
} |
FStar.Pervasives.Lemma | val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40 | val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 = | false | null | true | lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40 | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.pow2_plus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mult_le_right",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div64_max52"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_d10 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | d10: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d10 <=
513 * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))
(ensures Lib.IntTypes.v d10 / Prims.pow2 64 < Prims.pow2 50) | {
"end_col": 29,
"end_line": 454,
"start_col": 2,
"start_line": 451
} |
FStar.Pervasives.Lemma | val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d | val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d = | false | null | true | lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"Lib.IntTypes.uint128",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_div52",
"Prims.unit",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_to_u64_mask52"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mask52_rsh52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.pos -> d: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
md <= 16385)
(ensures
(let r = Lib.IntTypes.to_u64 d &. Hacl.Spec.K256.Field52.Definitions.mask52 in
let k = d >>. 52ul in
Lib.IntTypes.v r = Lib.IntTypes.v d % Prims.pow2 52 /\
Lib.IntTypes.v k = Lib.IntTypes.v d / Prims.pow2 52 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 r 1 /\
Lib.IntTypes.v k <= md * Hacl.Spec.K256.Field52.Definitions.max52)) | {
"end_col": 23,
"end_line": 486,
"start_col": 2,
"start_line": 485
} |
FStar.Pervasives.Lemma | val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c | val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c = | false | null | true | let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_add_mul64_wide",
"Prims.unit",
"FStar.Math.Lemmas.pow2_lt_compat",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_r_lsh12",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.u64",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_add_mul64_wide_r_lsh12 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> d: Lib.IntTypes.uint128 -> c: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
md <= 12801 /\ Lib.IntTypes.v c <= Prims.pow2 44)
(ensures
(let r = d +. Lib.IntTypes.mul64_wide (Lib.IntTypes.u64 0x1000003D10 <<. 12ul) c in
Lib.IntTypes.v r = Lib.IntTypes.v d + (0x1000003D10 * Prims.pow2 12) * Lib.IntTypes.v c /\
Lib.IntTypes.v r <=
(md + 1) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 38,
"end_line": 347,
"start_col": 47,
"start_line": 343
} |
FStar.Pervasives.Lemma | val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64) | val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a = | false | null | true | let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Division",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.lemma_div_lt",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.IntTypes.U64",
"Prims.op_Modulus",
"Lib.IntTypes.int_t",
"Lib.IntTypes.to_u64",
"Lib.IntTypes.op_Greater_Greater_Dot",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_rsh64_to | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(ensures Lib.IntTypes.v (Lib.IntTypes.to_u64 (a >>. 64ul)) = Lib.IntTypes.v a / Prims.pow2 64) | {
"end_col": 49,
"end_line": 464,
"start_col": 28,
"start_line": 460
} |
FStar.Pervasives.Lemma | val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
} | val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 = | false | null | true | let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert ((v a0 * 2) * v a3 + (v a1 * 2) * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod ((v a0 * 2) * v a3 + (v a1 * 2) * v a2) (pow2 128);
calc ( == ) {
(v a0 * 2) * v a3 + (v a1 * 2) * v a2;
( == ) { (Math.Lemmas.swap_mul (v a0) 2;
Math.Lemmas.paren_mul_right 2 (v a0) (v a3)) }
v a0 * v a3 + v a0 * v a3 + (v a1 * 2) * v a2;
( == ) { (Math.Lemmas.swap_mul (v a1) 2;
Math.Lemmas.paren_mul_right 2 (v a1) (v a2)) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint64",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Prims.l_and",
"Prims.op_Equality",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_four_sqr64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64)
(ensures
(let d =
Lib.IntTypes.mul64_wide (a0 *. Lib.IntTypes.u64 2) a3 +.
Lib.IntTypes.mul64_wide (a1 *. Lib.IntTypes.u64 2) a2
in
Lib.IntTypes.v d =
Lib.IntTypes.v a0 * Lib.IntTypes.v a3 + Lib.IntTypes.v a1 * Lib.IntTypes.v a2 +
Lib.IntTypes.v a2 * Lib.IntTypes.v a1 +
Lib.IntTypes.v a3 * Lib.IntTypes.v a0 /\
Lib.IntTypes.v d <=
16384 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 3,
"end_line": 629,
"start_col": 39,
"start_line": 610
} |
FStar.Pervasives.Lemma | val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64) | val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d = | false | null | true | let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint128",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Division",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_lt_compat",
"FStar.Math.Lemmas.lemma_div_lt",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.IntTypes.U64",
"Prims.op_Modulus",
"Lib.IntTypes.int_t",
"Lib.IntTypes.to_u64",
"Lib.IntTypes.op_Greater_Greater_Dot",
"FStar.UInt32.__uint_to_t",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_u128_to_u64_mask52",
"Lib.IntTypes.op_Amp_Dot",
"Hacl.Spec.K256.Field52.Definitions.mask52"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mask52_rsh52_sp | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | d: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma (requires Lib.IntTypes.v d < Prims.pow2 100)
(ensures
(let r = Lib.IntTypes.to_u64 d &. Hacl.Spec.K256.Field52.Definitions.mask52 in
let k = Lib.IntTypes.to_u64 (d >>. 52ul) in
Lib.IntTypes.v r = Lib.IntTypes.v d % Prims.pow2 52 /\
Lib.IntTypes.v k = Lib.IntTypes.v d / Prims.pow2 52 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 r 1 /\ Lib.IntTypes.v k < Prims.pow2 48)) | {
"end_col": 49,
"end_line": 527,
"start_col": 35,
"start_line": 519
} |
FStar.Pervasives.Lemma | val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12) | val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () = | false | null | true | let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc ( < ) {
0x1000003D10 * pow2 12;
( < ) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
( == ) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Prims.pow2",
"FStar.Math.Lemmas.small_mod",
"FStar.Math.Lemmas.pow2_lt_compat",
"FStar.Calc.calc_finish",
"Prims.op_LessThan",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"Prims.squash",
"FStar.Math.Lemmas.pow2_plus",
"Prims.op_Modulus",
"FStar.Pervasives.assert_norm",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.u64",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_r_lsh12 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit
-> FStar.Pervasives.Lemma
(ensures
(let rs = Lib.IntTypes.u64 0x1000003D10 <<. 12ul in
Lib.IntTypes.v rs = 0x1000003D10 * Prims.pow2 12 /\ Lib.IntTypes.v rs < Prims.pow2 49)) | {
"end_col": 40,
"end_line": 286,
"start_col": 22,
"start_line": 271
} |
FStar.Pervasives.Lemma | val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4 | val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () = | false | null | true | let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4 | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.unit",
"FStar.Math.Lemmas.lemma_div_lt",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.u64",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_r_rsh4 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit
-> FStar.Pervasives.Lemma
(ensures
(let rs = Lib.IntTypes.u64 0x1000003D10 >>. 4ul in
Lib.IntTypes.v rs = 0x1000003D10 / Prims.pow2 4 /\ Lib.IntTypes.v rs < Prims.pow2 33)) | {
"end_col": 44,
"end_line": 296,
"start_col": 21,
"start_line": 293
} |
FStar.Pervasives.Lemma | val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c) | val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c = | false | null | true | assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_add_mul64_wide",
"Lib.IntTypes.u64",
"Lib.IntTypes.to_u64",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_add_mul64_wide_r | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> d: Lib.IntTypes.uint128 -> c: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
md <= 16384)
(ensures
(let r =
d +. Lib.IntTypes.mul64_wide (Lib.IntTypes.u64 0x1000003D10) (Lib.IntTypes.to_u64 c)
in
Lib.IntTypes.v r = Lib.IntTypes.v d + 0x1000003D10 * (Lib.IntTypes.v c % Prims.pow2 64) /\
Lib.IntTypes.v r <=
(md + 1) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 63,
"end_line": 335,
"start_col": 2,
"start_line": 334
} |
FStar.Pervasives.Lemma | val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48 | val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 = | false | null | true | LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48 | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.lemma_div_lt",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.unit",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.lemma_mask48"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mask48_rsh48 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | t4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma (requires Hacl.Spec.K256.Field52.Definitions.felem_fits1 t4 1)
(ensures
(let tx = t4 >>. 48ul in
let r = t4 &. Hacl.Spec.K256.Field52.Definitions.mask48 in
Lib.IntTypes.v tx = Lib.IntTypes.v t4 / Prims.pow2 48 /\
Lib.IntTypes.v r = Lib.IntTypes.v t4 % Prims.pow2 48 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 r 1 /\
Lib.IntTypes.v tx < Prims.pow2 4)) | {
"end_col": 39,
"end_line": 510,
"start_col": 2,
"start_line": 509
} |
FStar.Pervasives.Lemma | val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c | val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c = | false | null | true | let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_add_mul64_wide",
"Prims.unit",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_r_rsh4",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.u64",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_add_mul64_wide_r_rsh4 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> d: Lib.IntTypes.uint128 -> c: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
md <= 4096 /\ Lib.IntTypes.v c < Prims.pow2 56)
(ensures
(let r = d +. Lib.IntTypes.mul64_wide c (Lib.IntTypes.u64 0x1000003D10 >>. 4ul) in
Lib.IntTypes.v r = Lib.IntTypes.v d + Lib.IntTypes.v c * (0x1000003D10 / Prims.pow2 4) /\
Lib.IntTypes.v r <=
(md + 1) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 38,
"end_line": 358,
"start_col": 46,
"start_line": 355
} |
FStar.Pervasives.Lemma | val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128) | val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc ( <= ) {
md * max52 + 8192 * (max52 * max52);
( <= ) { (assert_norm (4097 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 8192 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.op_LessThanOrEqual",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_le_right",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_two_mul64_wide52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
b0: Lib.IntTypes.uint64 ->
b1: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 4097 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b1 64)
(ensures
(let d1 = d +. Lib.IntTypes.mul64_wide a0 b1 +. Lib.IntTypes.mul64_wide a1 b0 in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v b1 +
Lib.IntTypes.v a1 * Lib.IntTypes.v b0 /\
Lib.IntTypes.v d1 <=
8193 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 68,
"end_line": 233,
"start_col": 2,
"start_line": 219
} |
FStar.Pervasives.Lemma | val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128) | val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <= md * max52 + 12288 * (max52 * max52));
calc ( <= ) {
md * max52 + 12288 * (max52 * max52);
( <= ) { (assert_norm (8194 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 12288 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.op_LessThanOrEqual",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_le_right",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_three_mul64_wide52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
b0: Lib.IntTypes.uint64 ->
b1: Lib.IntTypes.uint64 ->
b2: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 8194 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b2 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a0 b2 +. Lib.IntTypes.mul64_wide a1 b1 +.
Lib.IntTypes.mul64_wide a2 b0
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v b2 +
Lib.IntTypes.v a1 * Lib.IntTypes.v b1 +
Lib.IntTypes.v a2 * Lib.IntTypes.v b0 /\
Lib.IntTypes.v d1 <=
12289 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 82,
"end_line": 170,
"start_col": 2,
"start_line": 153
} |
FStar.Pervasives.Lemma | val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64) | val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a = | false | null | true | let r = a *. u64 2 in
calc ( <= ) {
v a * 2;
( <= ) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
(m * max) * 2;
( == ) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
( == ) { Math.Lemmas.paren_mul_right 2 m max }
(2 * m) * max;
};
assert (v a * 2 <= (2 * m) * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"FStar.Mul.op_Star",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.MathLemmas.lemma_ab_le_cd",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_le_right",
"Prims.squash",
"FStar.Math.Lemmas.swap_mul",
"FStar.Math.Lemmas.paren_mul_right",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | m: Prims.nat -> max: Prims.nat -> a: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a <= m * max /\ 2 * m <= 4096 /\
max <= Hacl.Spec.K256.Field52.Definitions.max52)
(ensures
(let r = a *. Lib.IntTypes.u64 2 in
Lib.IntTypes.v r = Lib.IntTypes.v a * 2 /\ Lib.IntTypes.v r <= (2 * m) * max)) | {
"end_col": 43,
"end_line": 598,
"start_col": 27,
"start_line": 583
} |
FStar.Pervasives.Lemma | val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10) | val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 = | false | null | true | let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.pos",
"Lib.IntTypes.uint128",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_add_mul64_wide",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mask52_rsh52",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.to_u64",
"Lib.IntTypes.U128",
"Hacl.Spec.K256.Field52.Definitions.mask52"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_add_mul64_wide_r_mask52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.pos -> d8: Lib.IntTypes.uint128 -> c5: Lib.IntTypes.uint128
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d8 <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
Lib.IntTypes.v c5 <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
md <= 8193)
(ensures
(let r =
c5 +.
Lib.IntTypes.mul64_wide (Lib.IntTypes.to_u64 d8 &.
Hacl.Spec.K256.Field52.Definitions.mask52)
(Lib.IntTypes.u64 0x1000003D10)
in
let d9 = d8 >>. 52ul in
Lib.IntTypes.v d9 = Lib.IntTypes.v d8 / Prims.pow2 52 /\
Lib.IntTypes.v d9 <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\
Lib.IntTypes.v r = Lib.IntTypes.v c5 + (Lib.IntTypes.v d8 % Prims.pow2 52) * 0x1000003D10 /\
Lib.IntTypes.v r <=
(md + 1) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 56,
"end_line": 499,
"start_col": 50,
"start_line": 495
} |
FStar.Pervasives.Lemma | val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128) | val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc ( < ) {
md * max52 + 8192 * (max52 * max48);
( < ) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
( <= ) { (assert_norm (8193 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 512 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"FStar.Math.Lemmas.swap_mul",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_two_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64 ->
b3: Lib.IntTypes.uint64 ->
b4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 8193 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 b4 64)
(ensures
(let d1 = d +. Lib.IntTypes.mul64_wide a3 b4 +. Lib.IntTypes.mul64_wide a4 b3 in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a3 * Lib.IntTypes.v b4 +
Lib.IntTypes.v a4 * Lib.IntTypes.v b3 /\
Lib.IntTypes.v d1 <=
513 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 68,
"end_line": 264,
"start_col": 2,
"start_line": 247
} |
FStar.Pervasives.Lemma | val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128) | val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b = | false | null | true | let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc ( < ) {
md * (max52 * max52) + pow2 pa * pow2 pb;
( == ) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
( <= ) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
( < ) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
( == ) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.pow2_plus",
"Prims.squash",
"FStar.Math.Lemmas.pow2_le_compat",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntTypes.mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
pa: Prims.nat ->
pb: Prims.nat ->
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a: Lib.IntTypes.uint64 ->
b: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a < Prims.pow2 pa /\ Lib.IntTypes.v b < Prims.pow2 pb /\ md + 1 <= 16385 /\
Lib.IntTypes.v d <=
md * (Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52) /\
pa + pb <= 103)
(ensures
(let r = d +. Lib.IntTypes.mul64_wide a b in
Lib.IntTypes.v r = Lib.IntTypes.v d + Lib.IntTypes.v a * Lib.IntTypes.v b /\
Lib.IntTypes.v r <=
(md + 1) *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 52,
"end_line": 325,
"start_col": 41,
"start_line": 306
} |
FStar.Pervasives.Lemma | val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56) | val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 = | false | null | true | let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc ( <= ) {
v u0 * pow2 4;
( <= ) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
( == ) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
( == ) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"Prims.eq2",
"Prims.int",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Lib.IntTypes.logor_disjoint",
"Lib.IntTypes.op_Less_Less_Dot",
"FStar.UInt32.__uint_to_t",
"FStar.Math.Lemmas.cancel_mul_mod",
"FStar.Math.Lemmas.lemma_div_lt",
"Prims.op_Equality",
"FStar.Math.Lemmas.small_mod",
"FStar.Math.Lemmas.pow2_lt_compat",
"Prims.op_LessThanOrEqual",
"Prims.op_Subtraction",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_le_right",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_sub_left",
"FStar.Math.Lemmas.pow2_plus",
"Prims.op_Modulus",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Bar_Dot"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_tx_logor_u0_lsh4 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | tx: Lib.IntTypes.uint64 -> u0: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v tx < Prims.pow2 4 /\ Hacl.Spec.K256.Field52.Definitions.felem_fits1 u0 1)
(ensures
(let u0' = tx |. u0 <<. 4ul in
Lib.IntTypes.v u0' == Lib.IntTypes.v tx + Lib.IntTypes.v u0 * Prims.pow2 4 /\
Lib.IntTypes.v u0' < Prims.pow2 56)) | {
"end_col": 26,
"end_line": 558,
"start_col": 34,
"start_line": 535
} |
FStar.Pervasives.Lemma | val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128) | val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
( < ) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
( <= ) { (assert_norm (12802 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 8704 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_four_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64 ->
b1: Lib.IntTypes.uint64 ->
b2: Lib.IntTypes.uint64 ->
b3: Lib.IntTypes.uint64 ->
b4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 12802 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 b4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a1 b4 +. Lib.IntTypes.mul64_wide a2 b3 +.
Lib.IntTypes.mul64_wide a3 b2 +.
Lib.IntTypes.mul64_wide a4 b1
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a1 * Lib.IntTypes.v b4 +
Lib.IntTypes.v a2 * Lib.IntTypes.v b3 +
Lib.IntTypes.v a3 * Lib.IntTypes.v b2 +
Lib.IntTypes.v a4 * Lib.IntTypes.v b1 /\
Lib.IntTypes.v d1 <=
8705 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 96,
"end_line": 138,
"start_col": 2,
"start_line": 117
} |
FStar.Pervasives.Lemma | val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128) | val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
( < ) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
( <= ) { (assert_norm (8705 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 4608 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"FStar.Math.Lemmas.swap_mul",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_three_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64 ->
b2: Lib.IntTypes.uint64 ->
b3: Lib.IntTypes.uint64 ->
b4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 8705 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 b4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a2 b4 +. Lib.IntTypes.mul64_wide a3 b3 +.
Lib.IntTypes.mul64_wide a4 b2
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a2 * Lib.IntTypes.v b4 +
Lib.IntTypes.v a3 * Lib.IntTypes.v b3 +
Lib.IntTypes.v a4 * Lib.IntTypes.v b2 /\
Lib.IntTypes.v d1 <=
4609 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 82,
"end_line": 205,
"start_col": 2,
"start_line": 185
} |
FStar.Pervasives.Lemma | val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128) | val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 = | false | null | true | lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
( < ) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
( <= ) { (assert_norm (16385 < max52);
Math.Lemmas.lemma_mult_le_right max52 md max52) }
max52 * max52 + 12800 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0)
(pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"FStar.Math.Lemmas.swap_mul",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_five_mul64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64 ->
b0: Lib.IntTypes.uint64 ->
b1: Lib.IntTypes.uint64 ->
b2: Lib.IntTypes.uint64 ->
b3: Lib.IntTypes.uint64 ->
b4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 16385 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 b3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 b4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a0 b4 +. Lib.IntTypes.mul64_wide a1 b3 +.
Lib.IntTypes.mul64_wide a2 b2 +.
Lib.IntTypes.mul64_wide a3 b1 +.
Lib.IntTypes.mul64_wide a4 b0
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v b4 +
Lib.IntTypes.v a1 * Lib.IntTypes.v b3 +
Lib.IntTypes.v a2 * Lib.IntTypes.v b2 +
Lib.IntTypes.v a3 * Lib.IntTypes.v b1 +
Lib.IntTypes.v a4 * Lib.IntTypes.v b0 /\
Lib.IntTypes.v d1 <=
12801 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 110,
"end_line": 100,
"start_col": 2,
"start_line": 76
} |
FStar.Pervasives.Lemma | val lemma_add_three_sqr64_wide52 (md:nat) (d:uint128) (a0 a1 a2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a2 +. mul64_wide a1 a1 in
v d1 == v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 /\
v d1 <= 12289 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_three_sqr64_wide52 md d a0 a1 a2 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 a1;
assert (v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 <=
md * max52 + 12288 * (max52 * max52));
calc (<) {
md * max52 + 12288 * (max52 * max52);
(<) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12288 }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a2 + v a1 * v a1) (pow2 128);
calc (==) {
v d + v a0 * 2 * v a2 + v a1 * v a1;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a2) }
v d + v a0 * v a2 + v a2 * v a0 + v a1 * v a1;
} | val lemma_add_three_sqr64_wide52 (md:nat) (d:uint128) (a0 a1 a2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a2 +. mul64_wide a1 a1 in
v d1 == v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_sqr64_wide52 md d a0 a1 a2 = | false | null | true | lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 a1;
assert (v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 <= md * max52 + 12288 * (max52 * max52));
calc ( < ) {
md * max52 + 12288 * (max52 * max52);
( < ) { (assert_norm (8194 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 12288 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12288 }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + (v a0 * 2) * v a2) (pow2 128);
Math.Lemmas.small_mod (v d + (v a0 * 2) * v a2 + v a1 * v a1) (pow2 128);
calc ( == ) {
v d + (v a0 * 2) * v a2 + v a1 * v a1;
( == ) { (Math.Lemmas.swap_mul (v a0) 2;
Math.Lemmas.paren_mul_right 2 (v a0) (v a2)) }
v d + v a0 * v a2 + v a2 * v a0 + v a1 * v a1;
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
}
val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + v a2 * 2 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
(<) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc (==) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
(==) { Math.Lemmas.swap_mul (v a2) 2; Math.Lemmas.paren_mul_right 2 (v a2) (v a3) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) (2 * v a4); Math.Lemmas.paren_mul_right 2 (v a4) (v a1) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
}
val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_sqr64_wide52 md d a0 a1 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a1;
assert (v d + v a0 * 2 * v a1 <= md * max52 + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max52);
(<) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8192 }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a1) (pow2 128)
val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_sqr64_wide md d a2 a3 a4 =
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a2 (a4 *. u64 2);
lemma_bound_mul64_wide 64 64 max52 max52 a3 a3;
assert (v d + v a2 * (v a4 * 2) + v a3 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 4096 * (max52 * max52);
(<) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 4608 }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2) + v a3 * v a3) (pow2 128);
calc (==) {
v d + v a2 * (v a4 * 2) + v a3 * v a3;
(==) { Math.Lemmas.paren_mul_right (v a2) (v a4) 2 }
v d + v a2 * v a4 + v a4 * v a2 + v a3 * v a3;
}
val lemma_add_three_sqr64_wide52 (md:nat) (d:uint128) (a0 a1 a2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a2 +. mul64_wide a1 a1 in
v d1 == v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 /\
v d1 <= 12289 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_three_sqr64_wide52 (md:nat) (d:uint128) (a0 a1 a2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a2 +. mul64_wide a1 a1 in
v d1 == v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 /\
v d1 <= 12289 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_three_sqr64_wide52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 8194 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide (a0 *. Lib.IntTypes.u64 2) a2 +.
Lib.IntTypes.mul64_wide a1 a1
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v a2 +
Lib.IntTypes.v a1 * Lib.IntTypes.v a1 +
Lib.IntTypes.v a2 * Lib.IntTypes.v a0 /\
Lib.IntTypes.v d1 <=
12289 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 3,
"end_line": 823,
"start_col": 2,
"start_line": 802
} |
FStar.Pervasives.Lemma | val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_two_sqr64_wide52 md d a0 a1 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a1;
assert (v d + v a0 * 2 * v a1 <= md * max52 + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max52);
(<) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8192 }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a1) (pow2 128) | val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_sqr64_wide52 md d a0 a1 = | false | null | true | lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a1;
assert (v d + (v a0 * 2) * v a1 <= md * max52 + 8192 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max52);
( < ) { (assert_norm (4097 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 8192 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8192 }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + (v a0 * 2) * v a1) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
}
val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + v a2 * 2 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
(<) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc (==) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
(==) { Math.Lemmas.swap_mul (v a2) 2; Math.Lemmas.paren_mul_right 2 (v a2) (v a3) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) (2 * v a4); Math.Lemmas.paren_mul_right 2 (v a4) (v a1) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
}
val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_two_sqr64_wide52 | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> d: Lib.IntTypes.uint128 -> a0: Lib.IntTypes.uint64 -> a1: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 4097 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64)
(ensures
(let d1 = d +. Lib.IntTypes.mul64_wide (a0 *. Lib.IntTypes.u64 2) a1 in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v a1 +
Lib.IntTypes.v a1 * Lib.IntTypes.v a0 /\
Lib.IntTypes.v d1 <=
8193 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 58,
"end_line": 749,
"start_col": 2,
"start_line": 737
} |
FStar.Pervasives.Lemma | val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_three_sqr64_wide md d a2 a3 a4 =
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a2 (a4 *. u64 2);
lemma_bound_mul64_wide 64 64 max52 max52 a3 a3;
assert (v d + v a2 * (v a4 * 2) + v a3 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 4096 * (max52 * max52);
(<) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 4608 }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2) + v a3 * v a3) (pow2 128);
calc (==) {
v d + v a2 * (v a4 * 2) + v a3 * v a3;
(==) { Math.Lemmas.paren_mul_right (v a2) (v a4) 2 }
v d + v a2 * v a4 + v a4 * v a2 + v a3 * v a3;
} | val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_sqr64_wide md d a2 a3 a4 = | false | null | true | assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a2 (a4 *. u64 2);
lemma_bound_mul64_wide 64 64 max52 max52 a3 a3;
assert (v d + v a2 * (v a4 * 2) + v a3 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
( <= ) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 4096 * (max52 * max52);
( < ) { (assert_norm (8705 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 4608 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 4608 }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2) + v a3 * v a3) (pow2 128);
calc ( == ) {
v d + v a2 * (v a4 * 2) + v a3 * v a3;
( == ) { Math.Lemmas.paren_mul_right (v a2) (v a4) 2 }
v d + v a2 * v a4 + v a4 * v a2 + v a3 * v a3;
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"Prims.squash",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
}
val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + v a2 * 2 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
(<) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc (==) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
(==) { Math.Lemmas.swap_mul (v a2) 2; Math.Lemmas.paren_mul_right 2 (v a2) (v a3) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) (2 * v a4); Math.Lemmas.paren_mul_right 2 (v a4) (v a1) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
}
val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_sqr64_wide52 md d a0 a1 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a1;
assert (v d + v a0 * 2 * v a1 <= md * max52 + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max52);
(<) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8192 }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a1) (pow2 128)
val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_three_sqr64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 8705 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a2 (a4 *. Lib.IntTypes.u64 2) +.
Lib.IntTypes.mul64_wide a3 a3
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a2 * Lib.IntTypes.v a4 +
Lib.IntTypes.v a3 * Lib.IntTypes.v a3 +
Lib.IntTypes.v a4 * Lib.IntTypes.v a2 /\
Lib.IntTypes.v d1 <=
4609 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 3,
"end_line": 788,
"start_col": 2,
"start_line": 763
} |
FStar.Pervasives.Lemma | val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
} | val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 = | false | null | true | let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + (v a1 * 2) * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
( <= ) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
( < ) { (assert_norm (16385 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 12800 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + (v a1 * 2) * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + (v a1 * 2) * v a3 + v a2 * v a2) (pow2 128);
calc ( == ) {
v d + v a0 * (v a4 * 2) + (v a1 * 2) * v a3 + v a2 * v a2;
( == ) { (Math.Lemmas.swap_mul (v a1) 2;
Math.Lemmas.paren_mul_right 2 (v a1) (v a3)) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
( == ) { (Math.Lemmas.paren_mul_right (v a0) (v a4) 2;
Math.Lemmas.swap_mul 2 (v a0 * v a4)) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Prims.l_and",
"Prims.op_Equality",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_five_sqr64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a0: Lib.IntTypes.uint64 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 16385 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a0 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a0 (a4 *. Lib.IntTypes.u64 2) +.
Lib.IntTypes.mul64_wide (a1 *. Lib.IntTypes.u64 2) a3 +.
Lib.IntTypes.mul64_wide a2 a2
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a0 * Lib.IntTypes.v a4 +
Lib.IntTypes.v a1 * Lib.IntTypes.v a3 +
Lib.IntTypes.v a2 * Lib.IntTypes.v a2 +
Lib.IntTypes.v a3 * Lib.IntTypes.v a1 +
Lib.IntTypes.v a4 * Lib.IntTypes.v a0 /\
Lib.IntTypes.v d1 <=
12801 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 3,
"end_line": 678,
"start_col": 51,
"start_line": 643
} |
FStar.Pervasives.Lemma | val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100)) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128) | val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 = | false | null | true | let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc ( < ) {
md * max52 + pow2 49 * pow2 50 + max52;
( == ) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
( == ) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
( <= ) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
( < ) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_lt_compat",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.op_LessThanOrEqual",
"Prims.eq2",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.pow2_plus",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_add_left",
"FStar.Math.Lemmas.lemma_mult_le_right",
"FStar.Pervasives.assert_norm",
"Prims._assert",
"Prims.l_and",
"Prims.op_Equality",
"Lib.IntTypes.mul64_wide",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntTypes.to_u128",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_r_lsh12",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.u64",
"FStar.UInt32.__uint_to_t"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100)) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100)) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_add_mul64_wide_r_lsh12_add | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> c: Lib.IntTypes.uint128 -> d: Lib.IntTypes.uint64 -> t3: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v c <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 12290 /\
Lib.IntTypes.v d < Prims.pow2 50 /\ Hacl.Spec.K256.Field52.Definitions.felem_fits1 t3 1)
(ensures
(let r =
c +. Lib.IntTypes.mul64_wide (Lib.IntTypes.u64 0x1000003D10 <<. 12ul) d +.
Lib.IntTypes.to_u128 t3
in
Lib.IntTypes.v r =
Lib.IntTypes.v c + (0x1000003D10 * Prims.pow2 12) * Lib.IntTypes.v d + Lib.IntTypes.v t3 /\
Lib.IntTypes.v r < Prims.pow2 100)) | {
"end_col": 60,
"end_line": 389,
"start_col": 54,
"start_line": 366
} |
FStar.Pervasives.Lemma | val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + v a2 * 2 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
(<) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc (==) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
(==) { Math.Lemmas.swap_mul (v a2) 2; Math.Lemmas.paren_mul_right 2 (v a2) (v a3) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) (2 * v a4); Math.Lemmas.paren_mul_right 2 (v a4) (v a1) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
} | val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 = | false | null | true | let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + (v a2 * 2) * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc ( < ) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
( <= ) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
( < ) { (assert_norm (12802 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 8704 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc ( == ) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
( == ) { (Math.Lemmas.swap_mul (v a2) 2;
Math.Lemmas.paren_mul_right 2 (v a2) (v a3)) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
( == ) { (Math.Lemmas.swap_mul (v a1) (2 * v a4);
Math.Lemmas.paren_mul_right 2 (v a4) (v a1)) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
} | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.small_mod",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.op_LessThanOrEqual",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Lib.IntTypes.int_t",
"Lib.IntTypes.op_Plus_Dot",
"Lib.IntTypes.mul64_wide",
"Prims.l_and",
"Prims.op_Equality",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
}
val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_four_sqr64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
md: Prims.nat ->
d: Lib.IntTypes.uint128 ->
a1: Lib.IntTypes.uint64 ->
a2: Lib.IntTypes.uint64 ->
a3: Lib.IntTypes.uint64 ->
a4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 12802 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a1 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a2 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64)
(ensures
(let d1 =
d +. Lib.IntTypes.mul64_wide a1 (a4 *. Lib.IntTypes.u64 2) +.
Lib.IntTypes.mul64_wide (a2 *. Lib.IntTypes.u64 2) a3
in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a1 * Lib.IntTypes.v a4 +
Lib.IntTypes.v a2 * Lib.IntTypes.v a3 +
Lib.IntTypes.v a3 * Lib.IntTypes.v a2 +
Lib.IntTypes.v a4 * Lib.IntTypes.v a1 /\
Lib.IntTypes.v d1 <=
8705 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 5,
"end_line": 724,
"start_col": 48,
"start_line": 691
} |
FStar.Pervasives.Lemma | val lemma_add_two_sqr64_wide (md:nat) (d:uint128) (a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 64193 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a3 (a4 *. u64 2) in
v d1 == v d + v a3 * v a4 + v a4 * v a3 /\
v d1 <= 513 * (max52 * max52))) | [
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas",
"short_module": "LD"
},
{
"abbrev": true,
"full_module": "Hacl.Spec.K256.MathLemmas",
"short_module": "ML"
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52.Definitions",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.K256",
"short_module": "S"
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.K256.Field52",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_add_two_sqr64_wide md d a3 a4 =
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a3 (a4 *. u64 2);
assert (v d + v a3 * (v a4 * 2) <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<) { assert_norm (64193 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 512 }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * (v a4 * 2)) (pow2 128) | val lemma_add_two_sqr64_wide (md:nat) (d:uint128) (a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 64193 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a3 (a4 *. u64 2) in
v d1 == v d + v a3 * v a4 + v a4 * v a3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_sqr64_wide md d a3 a4 = | false | null | true | assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a3 (a4 *. u64 2);
assert (v d + v a3 * (v a4 * 2) <= md * max52 + 8192 * (max52 * max48));
calc ( < ) {
md * max52 + 8192 * (max52 * max48);
( <= ) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
( < ) { (assert_norm (64193 < max52);
Math.Lemmas.lemma_mult_lt_right max52 md max52) }
max52 * max52 + 512 * (max52 * max52);
( == ) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 512 }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * (v a4 * 2)) (pow2 128) | {
"checked_file": "Hacl.Spec.K256.Field52.Lemmas5.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.K256.MathLemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked",
"Hacl.Spec.K256.Field52.Definitions.fst.checked",
"Hacl.Spec.K256.Field52.fst.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Spec.K256.Field52.Lemmas5.fst"
} | [
"lemma"
] | [
"Prims.nat",
"Lib.IntTypes.uint128",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U128",
"Lib.IntTypes.SEC",
"FStar.Mul.op_Star",
"Lib.IntTypes.U64",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.K256.Field52.Definitions.max52",
"FStar.Calc.calc_finish",
"Prims.int",
"Hacl.Spec.K256.Field52.Definitions.max48",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.eq2",
"Prims.op_LessThanOrEqual",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_16_max52_max48",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lemmas.distributivity_add_left",
"Prims._assert",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_bound_mul64_wide",
"Lib.IntTypes.op_Star_Dot",
"Lib.IntTypes.u64",
"Hacl.Spec.K256.Field52.Lemmas5.lemma_mul_by2"
] | [] | module Hacl.Spec.K256.Field52.Lemmas5
open FStar.Mul
open Lib.IntTypes
module S = Spec.K256
include Hacl.Spec.K256.Field52.Definitions
include Hacl.Spec.K256.Field52
module ML = Hacl.Spec.K256.MathLemmas
module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
val lemma_bound_mul64_wide (ma mb:nat) (mma mmb:nat) (a b:uint64) : Lemma
(requires v a <= ma * mma /\ v b <= mb * mmb)
(ensures (let r = mul64_wide a b in
v r = v a * v b /\ v r <= ma * mb * (mma * mmb)))
let lemma_bound_mul64_wide ma mb mma mmb a b =
ML.lemma_bound_mul64_wide ma mb mma mmb (v a) (v b)
val lemma_four_mul64_wide (a0 a1 a2 a3 b0 b1 b2 b3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64)
(ensures
(let d = mul64_wide a0 b3 +. mul64_wide a1 b2 +. mul64_wide a2 b1 +. mul64_wide a3 b0 in
v d = v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_mul64_wide a0 a1 a2 a3 b0 b1 b2 b3 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b0;
assert (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1) (pow2 128);
Math.Lemmas.small_mod (v a0 * v b3 + v a1 * v b2 + v a2 * v b1 + v a3 * v b0) (pow2 128)
val lemma_16_max52_max48: a:pos -> Lemma ((a * 16) * (max52 * max48) < a * (max52 * max52))
let lemma_16_max52_max48 a =
assert_norm (16 * (max52 * max48) < max52 * max52);
calc (<) {
(a * 16) * (max52 * max48);
(==) { Math.Lemmas.paren_mul_right a 16 (max52 * max48) }
a * (16 * (max52 * max48));
(<) { Math.Lemmas.lemma_mult_lt_left a (16 * (max52 * max48)) (max52 * max52) }
a * (max52 * max52);
}
val lemma_add_five_mul64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a0 b4 +. mul64_wide a1 b3 +.
mul64_wide a2 b2 +. mul64_wide a3 b1 +. mul64_wide a4 b0 in
v d1 == v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_mul64_wide md d a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a0 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b1;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b0;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 12800 * (max52 * max52);
(<=) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12800 (max52 * max52) }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b4 + v a1 * v b3 + v a2 * v b2 + v a3 * v b1 + v a4 * v b0) (pow2 128)
val lemma_add_four_mul64_wide (md:nat) (d:uint128) (a1 a2 a3 a4 b1 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a1 b4 +. mul64_wide a2 b3 +.
mul64_wide a3 b2 +. mul64_wide a4 b1 in
v d1 == v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_mul64_wide md d a1 a2 a3 a4 b1 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a1 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b3;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b2;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b1;
assert (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 8704 * (max52 * max52);
(<=) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8704 (max52 * max52) }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * v b4 + v a2 * v b3 + v a3 * v b2 + v a4 * v b1) (pow2 128)
val lemma_add_three_mul64_wide52 (md:nat) (d:uint128) (a0 a1 a2 b0 b1 b2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64)
(ensures
(let d1 = d +. mul64_wide a0 b2 +. mul64_wide a1 b1 +. mul64_wide a2 b0 in
v d1 == v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_mul64_wide52 md d a0 a1 a2 b0 b1 b2 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a2 b0;
assert (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0 <=
md * max52 + 12288 * (max52 * max52));
calc (<=) {
md * max52 + 12288 * (max52 * max52);
(<=) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 12288 (max52 * max52) }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b2 + v a1 * v b1 + v a2 * v b0) (pow2 128)
val lemma_add_three_mul64_wide (md:nat) (d:uint128) (a2 a3 a4 b2 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 b2 64 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a2 b4 +. mul64_wide a3 b3 +. mul64_wide a4 b2 in
v d1 == v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_mul64_wide md d a2 a3 a4 b2 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a2 b4;
lemma_bound_mul64_wide 64 64 max52 max52 a3 b3;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b2;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<) { lemma_16_max52_max48 512 }
md * max52 + 4608 * (max52 * max52);
(<=) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 4608 (max52 * max52) }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * v b4 + v a3 * v b3 + v a4 * v b2) (pow2 128)
val lemma_add_two_mul64_wide52 (md:nat) (d:uint128) (a0 a1 b0 b1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 b0 64 /\
felem_fits1 a1 64 /\ felem_fits1 b1 64)
(ensures
(let d1 = d +. mul64_wide a0 b1 +. mul64_wide a1 b0 in
v d1 == v d + v a0 * v b1 + v a1 * v b0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_mul64_wide52 md d a0 a1 b0 b1 =
lemma_bound_mul64_wide 64 64 max52 max52 a0 b1;
lemma_bound_mul64_wide 64 64 max52 max52 a1 b0;
assert (v d + v a0 * v b1 + v a1 * v b0 <= md * max52 + 8192 * (max52 * max52));
calc (<=) {
md * max52 + 8192 * (max52 * max52);
(<=) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 8192 (max52 * max52) }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * v b1 + v a1 * v b0) (pow2 128)
val lemma_add_two_mul64_wide (md:nat) (d:uint128) (a3 a4 b3 b4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8193 /\
felem_fits1 a3 64 /\ felem_fits1 b3 64 /\
felem_fits_last1 a4 64 /\ felem_fits_last1 b4 64)
(ensures
(let d1 = d +. mul64_wide a3 b4 +. mul64_wide a4 b3 in
v d1 == v d + v a3 * v b4 + v a4 * v b3 /\
v d1 <= 513 * (max52 * max52)))
let lemma_add_two_mul64_wide md d a3 a4 b3 b4 =
lemma_bound_mul64_wide 64 64 max52 max48 a3 b4;
lemma_bound_mul64_wide 64 64 max48 max52 a4 b3;
Math.Lemmas.swap_mul max52 max48;
assert (v d + v a3 * v b4 + v a4 * v b3 <= md * max52 + 8192 * (max52 * max48));
calc (<) {
md * max52 + 8192 * (max52 * max48);
(<) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52);
(<=) { assert_norm (8193 < max52); Math.Lemmas.lemma_mult_le_right max52 md max52 }
max52 * max52 + 512 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left 1 512 (max52 * max52) }
513 * (max52 * max52);
};
assert_norm (513 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4) (pow2 128);
Math.Lemmas.small_mod (v d + v a3 * v b4 + v a4 * v b3) (pow2 128)
val lemma_r_lsh12: unit ->
Lemma (let rs = u64 0x1000003D10 <<. 12ul in
v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49)
let lemma_r_lsh12 () =
let rs = u64 0x1000003D10 <<. 12ul in
assert_norm (0x1000003D10 < pow2 37);
assert (v rs = 0x1000003D10 * pow2 12 % pow2 64);
calc (<) {
0x1000003D10 * pow2 12;
(<) { Math.Lemmas.lemma_mult_lt_right (pow2 12) 0x1000003D10 (pow2 37) }
pow2 37 * pow2 12;
(==) { Math.Lemmas.pow2_plus 12 37 }
pow2 49;
};
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (0x1000003D10 * pow2 12) (pow2 64);
assert (v rs = 0x1000003D10 * pow2 12)
val lemma_r_rsh4: unit ->
Lemma (let rs = u64 0x1000003D10 >>. 4ul in
v rs = 0x1000003D10 / pow2 4 /\ v rs < pow2 33)
let lemma_r_rsh4 () =
let rs = u64 0x1000003D10 >>. 4ul in
assert_norm (0x1000003D10 < pow2 37);
Math.Lemmas.lemma_div_lt 0x1000003D10 37 4
val lemma_add_mul64_wide (pa pb md:nat) (d:uint128) (a b:uint64) : Lemma
(requires
v a < pow2 pa /\ v b < pow2 pb /\ md + 1 <= 16385 /\ // md + 1 <= pow2 24
v d <= md * (max52 * max52) /\ pa + pb <= 103)
(ensures (let r = d +. mul64_wide a b in
v r = v d + v a * v b /\ v r <= (md + 1) * (max52 * max52)))
let lemma_add_mul64_wide pa pb md d a b =
let r = d +. mul64_wide a b in
lemma_bound_mul64_wide 1 1 (pow2 pa) (pow2 pb) a b;
assert (v d + v a * v b <= md * (max52 * max52) + pow2 pa * pow2 pb);
calc (<) {
md * (max52 * max52) + pow2 pa * pow2 pb;
(==) { Math.Lemmas.pow2_plus pa pb }
md * (max52 * max52) + pow2 (pa + pb);
(<=) { Math.Lemmas.pow2_le_compat 103 (pa + pb) }
md * (max52 * max52) + pow2 103;
(<) { assert_norm (pow2 103 < max52 * max52) }
md * (max52 * max52) + max52 * max52;
(==) { Math.Lemmas.distributivity_add_left md 1 (max52 * max52) }
(md + 1) * (max52 * max52);
};
Math.Lemmas.lemma_mult_le_right (max52 * max52) (md + 1) 16385;
assert_norm (16385 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a * v b) (pow2 128)
val lemma_bound_add_mul64_wide_r (md:nat) (d c:uint128) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16384)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10) (to_u64 c) in
v r = v d + 0x1000003D10 * (v c % pow2 64) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r md d c =
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 37 64 md d (u64 0x1000003D10) (to_u64 c)
val lemma_bound_add_mul64_wide_r_lsh12 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 12801 /\ v c <= pow2 44)
(ensures (let r = d +. mul64_wide (u64 0x1000003D10 <<. 12ul) c in
v r = v d + 0x1000003D10 * pow2 12 * v c /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_lsh12 md d c =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
Math.Lemmas.pow2_lt_compat 45 44;
lemma_add_mul64_wide 49 45 md d rs c
val lemma_bound_add_mul64_wide_r_rsh4 (md:nat) (d:uint128) (c:uint64) : Lemma
(requires v d <= md * (max52 * max52) /\ md <= 4096 /\ v c < pow2 56)
(ensures (let r = d +. mul64_wide c (u64 0x1000003D10 >>. 4ul) in
v r = v d + v c * (0x1000003D10 / pow2 4) /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_rsh4 md d c =
let rs = u64 0x1000003D10 >>. 4ul in
lemma_r_rsh4 ();
lemma_add_mul64_wide 33 56 md d rs c
val lemma_bound_add_mul64_wide_r_lsh12_add (md:nat) (c:uint128) (d t3:uint64) : Lemma
(requires v c <= md * max52 /\ md <= 12290 /\ v d < pow2 50 /\ felem_fits1 t3 1)
(ensures (let r = c +. mul64_wide (u64 0x1000003D10 <<. 12ul) d +. to_u128 t3 in
v r = v c + 0x1000003D10 * pow2 12 * v d + v t3 /\ v r < pow2 100))
let lemma_bound_add_mul64_wide_r_lsh12_add md c d t3 =
let rs = u64 0x1000003D10 <<. 12ul in
lemma_r_lsh12 ();
assert (v rs = 0x1000003D10 * pow2 12 /\ v rs < pow2 49);
let r = c +. mul64_wide rs d +. to_u128 t3 in
lemma_bound_mul64_wide 1 1 (pow2 49) (pow2 50) rs d;
assert (v (mul64_wide rs d) = v rs * v d /\ v rs * v d < pow2 49 * pow2 50);
calc (<) {
md * max52 + pow2 49 * pow2 50 + max52;
(==) { Math.Lemmas.pow2_plus 49 50 }
md * max52 + pow2 99 + max52;
(==) { Math.Lemmas.distributivity_add_left md 1 max52 }
(md + 1) * max52 + pow2 99;
(<=) { Math.Lemmas.lemma_mult_le_right max52 (md + 1) 12291 }
12291 * max52 + pow2 99;
(<) { assert_norm (12291 * max52 + pow2 99 < pow2 100) }
pow2 100;
};
Math.Lemmas.pow2_lt_compat 128 100;
Math.Lemmas.small_mod (v c + v rs * v d) (pow2 128);
Math.Lemmas.small_mod (v c + v rs * v d + v t3) (pow2 128)
val lemma_u128_div52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * max52 * max52)
(ensures v a / pow2 52 <= md * max52)
let lemma_u128_div52 md a =
Math.Lemmas.lemma_mult_lt_left (md * max52) max52 (pow2 52);
Math.Lemmas.lemma_div_le (v a) (md * max52 * pow2 52) (pow2 52);
Math.Lemmas.multiple_division_lemma (md * max52) (pow2 52)
val lemma_u128_div64_max48: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max48 * max48))
(ensures v a / pow2 64 <= md * pow2 32)
let lemma_u128_div64_max48 md a =
assert_norm (max48 < pow2 48);
ML.lemma_ab_lt_cd max48 max48 (pow2 48) (pow2 48);
Math.Lemmas.pow2_plus 48 48;
assert (max48 * max48 < pow2 96);
Math.Lemmas.lemma_mult_le_left md (max48 * max48) (pow2 96);
assert (v a < md * pow2 96);
Math.Lemmas.lemma_div_le (v a) (md * pow2 96) (pow2 64);
Math.Lemmas.pow2_plus 64 32;
Math.Lemmas.multiple_division_lemma (md * pow2 32) (pow2 64)
val lemma_u128_div64_max52: md:pos -> a:uint128 -> Lemma
(requires v a <= md * (max52 * max52))
(ensures v a / pow2 64 <= md * pow2 40)
let lemma_u128_div64_max52 md a =
assert_norm (max52 < pow2 52);
ML.lemma_ab_lt_cd max52 max52 (pow2 52) (pow2 52);
Math.Lemmas.pow2_plus 52 52;
assert (max52 * max52 < pow2 104);
Math.Lemmas.lemma_mult_le_left md (max52 * max52) (pow2 104);
assert (v a < md * pow2 104);
Math.Lemmas.lemma_div_le (v a) (md * pow2 104) (pow2 64);
Math.Lemmas.pow2_plus 64 40;
Math.Lemmas.multiple_division_lemma (md * pow2 40) (pow2 64)
val lemma_bound_c0: c0:uint128 -> Lemma
(requires v c0 <= 4096 * (max48 * max48))
(ensures v c0 / pow2 64 <= pow2 44)
let lemma_bound_c0 c0 =
lemma_u128_div64_max48 4096 c0;
assert_norm (pow2 12 = 4096);
Math.Lemmas.pow2_plus 12 32
val lemma_bound_d10: d10:uint128 -> Lemma
(requires v d10 <= 513 * (max52 * max52))
(ensures v d10 / pow2 64 < pow2 50)
let lemma_bound_d10 d10 =
lemma_u128_div64_max52 513 d10;
assert_norm (513 < pow2 10);
Math.Lemmas.lemma_mult_le_right (pow2 38) 513 (pow2 10);
Math.Lemmas.pow2_plus 10 40
val lemma_bound_rsh64_to: a:uint128 ->
Lemma (v (to_u64 (a >>. 64ul)) = v a / pow2 64)
let lemma_bound_rsh64_to a =
let r = to_u64 (a >>. 64ul) in
assert (v r == (v a / pow2 64) % pow2 64);
Math.Lemmas.lemma_div_lt (v a) 128 64;
Math.Lemmas.small_mod (v a / pow2 64) (pow2 64)
val lemma_u128_to_u64_mask52: d:uint128 ->
Lemma (let r = to_u64 d &. mask52 in
v r = v d % pow2 52 /\ felem_fits1 r 1)
let lemma_u128_to_u64_mask52 d =
let r = to_u64 d &. mask52 in
LD.lemma_mask52 (to_u64 d);
assert (v r = v d % pow2 64 % pow2 52);
Math.Lemmas.pow2_modulo_modulo_lemma_1 (v d) 52 64
val lemma_bound_mask52_rsh52: md:pos -> d:uint128 -> Lemma
(requires v d <= md * (max52 * max52) /\ md <= 16385)
(ensures (let r = to_u64 d &. mask52 in let k = d >>. 52ul in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k <= md * max52))
let lemma_bound_mask52_rsh52 md d =
lemma_u128_to_u64_mask52 d;
lemma_u128_div52 md d
val lemma_bound_add_mul64_wide_r_mask52 (md:pos) (d8 c5:uint128) : Lemma
(requires v d8 <= md * (max52 * max52) /\ v c5 <= md * (max52 * max52) /\ md <= 8193)
(ensures (let r = c5 +. mul64_wide (to_u64 d8 &. mask52) (u64 0x1000003D10) in
let d9 = d8 >>. 52ul in v d9 = v d8 / pow2 52 /\ v d9 <= md * max52 /\
v r = v c5 + v d8 % pow2 52 * 0x1000003D10 /\ v r <= (md + 1) * (max52 * max52)))
let lemma_bound_add_mul64_wide_r_mask52 md d8 c5 =
let tm = to_u64 d8 &. mask52 in
lemma_bound_mask52_rsh52 md d8;
assert_norm (0x1000003D10 < pow2 37);
lemma_add_mul64_wide 64 37 md c5 tm (u64 0x1000003D10)
val lemma_bound_mask48_rsh48: t4:uint64 -> Lemma
(requires felem_fits1 t4 1)
(ensures (let tx = t4 >>. 48ul in let r = t4 &. mask48 in
v tx = v t4 / pow2 48 /\ v r = v t4 % pow2 48 /\
felem_fits_last1 r 1 /\ v tx < pow2 4))
let lemma_bound_mask48_rsh48 t4 =
LD.lemma_mask48 t4;
Math.Lemmas.lemma_div_lt (v t4) 52 48
val lemma_bound_mask52_rsh52_sp: d:uint128 -> Lemma
(requires v d < pow2 100)
(ensures (let r = to_u64 d &. mask52 in let k = to_u64 (d >>. 52ul) in
v r = v d % pow2 52 /\ v k = v d / pow2 52 /\
felem_fits1 r 1 /\ v k < pow2 48))
let lemma_bound_mask52_rsh52_sp d =
let r = to_u64 d &. mask52 in
lemma_u128_to_u64_mask52 d;
let k = to_u64 (d >>. 52ul) in
assert (v k == v d / pow2 52 % pow2 64);
Math.Lemmas.lemma_div_lt (v d) 100 52;
Math.Lemmas.pow2_lt_compat 64 48;
Math.Lemmas.small_mod (v d / pow2 52) (pow2 64)
val lemma_tx_logor_u0_lsh4 (tx u0:uint64) : Lemma
(requires v tx < pow2 4 /\ felem_fits1 u0 1)
(ensures (let u0' = tx |. (u0 <<. 4ul) in
v u0' == v tx + v u0 * pow2 4 /\ v u0' < pow2 56))
let lemma_tx_logor_u0_lsh4 tx u0 =
let u0' = tx |. (u0 <<. 4ul) in
assert (v (u0 <<. 4ul) = v u0 * pow2 4 % pow2 64);
calc (<=) {
v u0 * pow2 4;
(<=) { Math.Lemmas.lemma_mult_le_right (pow2 4) (v u0) (pow2 52 - 1) }
(pow2 52 - 1) * pow2 4;
(==) { Math.Lemmas.distributivity_sub_left (pow2 52) 1 (pow2 4) }
pow2 52 * pow2 4 - pow2 4;
(==) { Math.Lemmas.pow2_plus 52 4 }
pow2 56 - pow2 4;
};
assert (v u0 * pow2 4 <= pow2 56 - pow2 4);
Math.Lemmas.pow2_lt_compat 64 56;
Math.Lemmas.small_mod (v u0 * pow2 4) (pow2 64);
assert (v (u0 <<. 4ul) = v u0 * pow2 4);
Math.Lemmas.lemma_div_lt (v u0) 52 4;
Math.Lemmas.cancel_mul_mod (v u0) (pow2 4);
logor_disjoint tx (u0 <<. 4ul) 4;
assert (v u0' == v tx + v u0 * pow2 4);
assert (v u0' < pow2 56)
val lemma_mod_add_last (c12 t4':uint64) : Lemma
(requires v c12 < pow2 48 /\ v t4' < pow2 48)
(ensures (let r4 = c12 +. t4' in
v r4 = v c12 + v t4' /\ felem_fits_last1 r4 2))
let lemma_mod_add_last c12 t4' =
let r4 = c12 +. t4' in
assert (v c12 + v t4' < pow2 48 + pow2 48);
Math.Lemmas.pow2_double_sum 48;
assert (v c12 + v t4' < pow2 49);
Math.Lemmas.pow2_lt_compat 64 49;
Math.Lemmas.small_mod (v c12 + v t4') (pow2 64);
assert (v r4 = v c12 + v t4')
/// squaring
val lemma_mul_by2: m:nat -> max:nat -> a:uint64 -> Lemma
(requires v a <= m * max /\ 2 * m <= 4096 /\ max <= max52)
(ensures (let r = a *. u64 2 in
v r = v a * 2 /\ v r <= (2 * m) * max))
let lemma_mul_by2 m max a =
let r = a *. u64 2 in
calc (<=) {
v a * 2;
(<=) { Math.Lemmas.lemma_mult_le_right 2 (v a) (m * max) }
m * max * 2;
(==) { Math.Lemmas.swap_mul (m * max) 2 }
2 * (m * max);
(==) { Math.Lemmas.paren_mul_right 2 m max }
2 * m * max;
};
assert (v a * 2 <= 2 * m * max);
ML.lemma_ab_le_cd (2 * m) max 4096 max52;
assert_norm (4096 * max52 < pow2 64);
Math.Lemmas.small_mod (v a * 2) (pow2 64)
val lemma_four_sqr64_wide (a0 a1 a2 a3:uint64) : Lemma
(requires
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64)
(ensures
(let d = mul64_wide (a0 *. u64 2) a3 +. mul64_wide (a1 *. u64 2) a2 in
v d = v a0 * v a3 + v a1 * v a2 + v a2 * v a1 + v a3 * v a0 /\
v d <= 16384 * (max52 * max52)))
let lemma_four_sqr64_wide a0 a1 a2 a3 =
let r0 = a0 *. u64 2 in
let r1 = a1 *. u64 2 in
lemma_mul_by2 64 max52 a0;
lemma_mul_by2 64 max52 a1;
assert (v r0 = v a0 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 128 64 max52 max52 r0 a3;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a2;
assert (v a0 * 2 * v a3 + v a1 * 2 * v a2 <= 16384 * (max52 * max52));
assert_norm (16384 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v a0 * 2 * v a3 + v a1 * 2 * v a2) (pow2 128);
calc (==) {
v a0 * 2 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a3) }
v a0 * v a3 + v a0 * v a3 + v a1 * 2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a2) }
v a0 * v a3 + v a0 * v a3 + v a1 * v a2 + v a2 * v a1;
}
val lemma_add_five_sqr64_wide (md:nat) (d:uint128) (a0 a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 16385 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a0 (a4 *. u64 2) +. mul64_wide (a1 *. u64 2) a3 +. mul64_wide a2 a2 in
v d1 == v d + v a0 * v a4 + v a1 * v a3 + v a2 * v a2 + v a3 * v a1 + v a4 * v a0 /\
v d1 <= 12801 * (max52 * max52)))
let lemma_add_five_sqr64_wide md d a0 a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r1 = a1 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a1;
assert (v r4 = v a4 * 2 /\ v r1 = v a1 * 2);
lemma_bound_mul64_wide 64 128 max52 max48 a0 r4;
lemma_bound_mul64_wide 128 64 max52 max52 r1 a3;
lemma_bound_mul64_wide 64 64 max52 max52 a2 a2;
assert (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2 <=
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 12288 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 12288 * (max52 * max52);
(<) { assert_norm (16385 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12800 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12800 }
12801 * (max52 * max52);
};
assert_norm (12801 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2) (pow2 128);
calc (==) {
v d + v a0 * (v a4 * 2) + v a1 * 2 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) 2; Math.Lemmas.paren_mul_right 2 (v a1) (v a3) }
v d + v a0 * (v a4 * 2) + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
(==) { Math.Lemmas.paren_mul_right (v a0) (v a4) 2; Math.Lemmas.swap_mul 2 (v a0 * v a4) }
v d + v a0 * v a4 + v a0 * v a4 + v a1 * v a3 + v a1 * v a3 + v a2 * v a2;
}
val lemma_add_four_sqr64_wide (md:nat) (d:uint128) (a1 a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 12802 /\
felem_fits1 a1 64 /\ felem_fits1 a2 64 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a1 (a4 *. u64 2) +. mul64_wide (a2 *. u64 2) a3 in
v d1 == v d + v a1 * v a4 + v a2 * v a3 + v a3 * v a2 + v a4 * v a1 /\
v d1 <= 8705 * (max52 * max52)))
let lemma_add_four_sqr64_wide md d a1 a2 a3 a4 =
let r4 = a4 *. u64 2 in
let r2 = a2 *. u64 2 in
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_mul_by2 64 max52 a2;
assert (v r2 = v a2 * 2 /\ v r4 = v a4 * 2);
let d1 = d +. mul64_wide a1 r4 +. mul64_wide r2 a3 in
lemma_bound_mul64_wide 64 128 max52 max48 a1 (a4 *. u64 2);
lemma_bound_mul64_wide 128 64 max52 max52 (a2 *. u64 2) a3;
assert (v d + v a1 * (v a4 * 2) + v a2 * 2 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 8192 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 8192 * (max52 * max52);
(<) { assert_norm (12802 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8704 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8704 }
8705 * (max52 * max52);
};
assert_norm (8705 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4)) (pow2 128);
Math.Lemmas.small_mod (v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3) (pow2 128);
calc (==) {
v d + v a1 * (2 * v a4) + (v a2 * 2) * v a3;
(==) { Math.Lemmas.swap_mul (v a2) 2; Math.Lemmas.paren_mul_right 2 (v a2) (v a3) }
v d + v a1 * (2 * v a4) + v a2 * v a3 + v a3 * v a2;
(==) { Math.Lemmas.swap_mul (v a1) (2 * v a4); Math.Lemmas.paren_mul_right 2 (v a4) (v a1) }
v d + v a1 * v a4 + v a4 * v a1 + v a2 * v a3 + v a3 * v a2;
}
val lemma_add_two_sqr64_wide52 (md:nat) (d:uint128) (a0 a1:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 4097 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a1 in
v d1 == v d + v a0 * v a1 + v a1 * v a0 /\
v d1 <= 8193 * (max52 * max52)))
let lemma_add_two_sqr64_wide52 md d a0 a1 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a1;
assert (v d + v a0 * 2 * v a1 <= md * max52 + 8192 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max52);
(<) { assert_norm (4097 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 8192 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 8192 }
8193 * (max52 * max52);
};
assert_norm (8193 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a1) (pow2 128)
val lemma_add_three_sqr64_wide (md:nat) (d:uint128) (a2 a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8705 /\
felem_fits1 a2 64 /\ felem_fits1 a3 64 /\
felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a2 (a4 *. u64 2) +. mul64_wide a3 a3 in
v d1 == v d + v a2 * v a4 + v a3 * v a3 + v a4 * v a2 /\
v d1 <= 4609 * (max52 * max52)))
let lemma_add_three_sqr64_wide md d a2 a3 a4 =
assert_norm (max48 < max52);
lemma_mul_by2 64 max48 a4;
lemma_bound_mul64_wide 64 128 max52 max48 a2 (a4 *. u64 2);
lemma_bound_mul64_wide 64 64 max52 max52 a3 a3;
assert (v d + v a2 * (v a4 * 2) + v a3 * v a3 <=
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52));
calc (<) {
md * max52 + 8192 * (max52 * max48) + 4096 * (max52 * max52);
(<=) { lemma_16_max52_max48 512 }
md * max52 + 512 * (max52 * max52) + 4096 * (max52 * max52);
(<) { assert_norm (8705 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 4608 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 4608 }
4609 * (max52 * max52);
};
assert_norm (4609 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2)) (pow2 128);
Math.Lemmas.small_mod (v d + v a2 * (v a4 * 2) + v a3 * v a3) (pow2 128);
calc (==) {
v d + v a2 * (v a4 * 2) + v a3 * v a3;
(==) { Math.Lemmas.paren_mul_right (v a2) (v a4) 2 }
v d + v a2 * v a4 + v a4 * v a2 + v a3 * v a3;
}
val lemma_add_three_sqr64_wide52 (md:nat) (d:uint128) (a0 a1 a2:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 8194 /\
felem_fits1 a0 64 /\ felem_fits1 a1 64 /\
felem_fits1 a2 64)
(ensures
(let d1 = d +. mul64_wide (a0 *. u64 2) a2 +. mul64_wide a1 a1 in
v d1 == v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 /\
v d1 <= 12289 * (max52 * max52)))
let lemma_add_three_sqr64_wide52 md d a0 a1 a2 =
lemma_mul_by2 64 max52 a0;
lemma_bound_mul64_wide 128 64 max52 max52 (a0 *. u64 2) a2;
lemma_bound_mul64_wide 64 64 max52 max52 a1 a1;
assert (v d + v a0 * v a2 + v a1 * v a1 + v a2 * v a0 <=
md * max52 + 12288 * (max52 * max52));
calc (<) {
md * max52 + 12288 * (max52 * max52);
(<) { assert_norm (8194 < max52); Math.Lemmas.lemma_mult_lt_right max52 md max52 }
max52 * max52 + 12288 * (max52 * max52);
(==) { Math.Lemmas.distributivity_add_left (max52 * max52) 1 12288 }
12289 * (max52 * max52);
};
assert_norm (12289 * (max52 * max52) < pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a2) (pow2 128);
Math.Lemmas.small_mod (v d + v a0 * 2 * v a2 + v a1 * v a1) (pow2 128);
calc (==) {
v d + v a0 * 2 * v a2 + v a1 * v a1;
(==) { Math.Lemmas.swap_mul (v a0) 2; Math.Lemmas.paren_mul_right 2 (v a0) (v a2) }
v d + v a0 * v a2 + v a2 * v a0 + v a1 * v a1;
}
val lemma_add_two_sqr64_wide (md:nat) (d:uint128) (a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 64193 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a3 (a4 *. u64 2) in
v d1 == v d + v a3 * v a4 + v a4 * v a3 /\
v d1 <= 513 * (max52 * max52))) | false | false | Hacl.Spec.K256.Field52.Lemmas5.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_add_two_sqr64_wide (md:nat) (d:uint128) (a3 a4:uint64) : Lemma
(requires
v d <= md * max52 /\ md <= 64193 /\
felem_fits1 a3 64 /\ felem_fits_last1 a4 64)
(ensures
(let d1 = d +. mul64_wide a3 (a4 *. u64 2) in
v d1 == v d + v a3 * v a4 + v a4 * v a3 /\
v d1 <= 513 * (max52 * max52))) | [] | Hacl.Spec.K256.Field52.Lemmas5.lemma_add_two_sqr64_wide | {
"file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas5.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | md: Prims.nat -> d: Lib.IntTypes.uint128 -> a3: Lib.IntTypes.uint64 -> a4: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v d <= md * Hacl.Spec.K256.Field52.Definitions.max52 /\ md <= 64193 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits1 a3 64 /\
Hacl.Spec.K256.Field52.Definitions.felem_fits_last1 a4 64)
(ensures
(let d1 = d +. Lib.IntTypes.mul64_wide a3 (a4 *. Lib.IntTypes.u64 2) in
Lib.IntTypes.v d1 ==
Lib.IntTypes.v d + Lib.IntTypes.v a3 * Lib.IntTypes.v a4 +
Lib.IntTypes.v a4 * Lib.IntTypes.v a3 /\
Lib.IntTypes.v d1 <=
513 *
(Hacl.Spec.K256.Field52.Definitions.max52 * Hacl.Spec.K256.Field52.Definitions.max52))) | {
"end_col": 60,
"end_line": 851,
"start_col": 2,
"start_line": 836
} |
Prims.Tot | val parse_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l | val parse_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (parser parse_u32_kind (bitfields uint32 0 32 l))
let parse_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) = | false | null | false | parse_bitfield parse_u32 uint32 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.parse_bitfield",
"FStar.UInt32.t",
"LowParse.Spec.Int.parse_u32_kind",
"LowParse.Spec.Int.parse_u32",
"LowParse.BitFields.uint32",
"LowParse.Spec.Base.parser",
"LowParse.Spec.BitFields.bitfields"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) | [] | LowParse.Spec.BitFields.parse_bitfield32 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 32 l}
-> LowParse.Spec.Base.parser LowParse.Spec.Int.parse_u32_kind
(LowParse.Spec.BitFields.bitfields LowParse.BitFields.uint32 0 32 l) | {
"end_col": 35,
"end_line": 161,
"start_col": 2,
"start_line": 161
} |
Prims.Tot | val serialize_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (serializer (parse_bitfield8 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l | val serialize_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (serializer (parse_bitfield8 l))
let serialize_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (serializer (parse_bitfield8 l)) = | false | null | false | serialize_bitfield serialize_u8 uint8 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.serialize_bitfield",
"FStar.UInt8.t",
"LowParse.Spec.Int.parse_u8_kind",
"LowParse.Spec.Int.parse_u8",
"LowParse.Spec.Int.serialize_u8",
"LowParse.BitFields.uint8",
"LowParse.Spec.Base.serializer",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.parse_bitfield8"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (serializer (parse_bitfield8 l)) | [] | LowParse.Spec.BitFields.serialize_bitfield8 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 8 l}
-> LowParse.Spec.Base.serializer (LowParse.Spec.BitFields.parse_bitfield8 l) | {
"end_col": 41,
"end_line": 176,
"start_col": 2,
"start_line": 176
} |
Prims.Tot | val serialize_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (serializer (parse_bitfield32 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l | val serialize_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (serializer (parse_bitfield32 l))
let serialize_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (serializer (parse_bitfield32 l)) = | false | null | false | serialize_bitfield serialize_u32 uint32 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.serialize_bitfield",
"FStar.UInt32.t",
"LowParse.Spec.Int.parse_u32_kind",
"LowParse.Spec.Int.parse_u32",
"LowParse.Spec.Int.serialize_u32",
"LowParse.BitFields.uint32",
"LowParse.Spec.Base.serializer",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.parse_bitfield32"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_bitfield32 (l: list nat {valid_bitfield_widths 0 32 l})
: Tot (serializer (parse_bitfield32 l)) | [] | LowParse.Spec.BitFields.serialize_bitfield32 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 32 l}
-> LowParse.Spec.Base.serializer (LowParse.Spec.BitFields.parse_bitfield32 l) | {
"end_col": 43,
"end_line": 164,
"start_col": 2,
"start_line": 164
} |
Prims.Tot | val parse_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l | val parse_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (parser parse_u64_kind (bitfields uint64 0 64 l))
let parse_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) = | false | null | false | parse_bitfield parse_u64 uint64 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.parse_bitfield",
"FStar.UInt64.t",
"LowParse.Spec.Int.parse_u64_kind",
"LowParse.Spec.Int.parse_u64",
"LowParse.BitFields.uint64",
"LowParse.Spec.Base.parser",
"LowParse.Spec.BitFields.bitfields"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
() | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) | [] | LowParse.Spec.BitFields.parse_bitfield64 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 64 l}
-> LowParse.Spec.Base.parser LowParse.Spec.Int.parse_u64_kind
(LowParse.Spec.BitFields.bitfields LowParse.BitFields.uint64 0 64 l) | {
"end_col": 35,
"end_line": 155,
"start_col": 2,
"start_line": 155
} |
Prims.Tot | val serialize_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (serializer (parse_bitfield16 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l | val serialize_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (serializer (parse_bitfield16 l))
let serialize_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (serializer (parse_bitfield16 l)) = | false | null | false | serialize_bitfield serialize_u16 uint16 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.serialize_bitfield",
"FStar.UInt16.t",
"LowParse.Spec.Int.parse_u16_kind",
"LowParse.Spec.Int.parse_u16",
"LowParse.Spec.Int.serialize_u16",
"LowParse.BitFields.uint16",
"LowParse.Spec.Base.serializer",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.parse_bitfield16"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (serializer (parse_bitfield16 l)) | [] | LowParse.Spec.BitFields.serialize_bitfield16 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 16 l}
-> LowParse.Spec.Base.serializer (LowParse.Spec.BitFields.parse_bitfield16 l) | {
"end_col": 43,
"end_line": 170,
"start_col": 2,
"start_line": 170
} |
Prims.Tot | val parse_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l | val parse_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (parser parse_u16_kind (bitfields uint16 0 16 l))
let parse_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) = | false | null | false | parse_bitfield parse_u16 uint16 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.parse_bitfield",
"FStar.UInt16.t",
"LowParse.Spec.Int.parse_u16_kind",
"LowParse.Spec.Int.parse_u16",
"LowParse.BitFields.uint16",
"LowParse.Spec.Base.parser",
"LowParse.Spec.BitFields.bitfields"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse_bitfield16 (l: list nat {valid_bitfield_widths 0 16 l})
: Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) | [] | LowParse.Spec.BitFields.parse_bitfield16 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 16 l}
-> LowParse.Spec.Base.parser LowParse.Spec.Int.parse_u16_kind
(LowParse.Spec.BitFields.bitfields LowParse.BitFields.uint16 0 16 l) | {
"end_col": 35,
"end_line": 167,
"start_col": 2,
"start_line": 167
} |
Prims.Tot | val serialize_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (serializer (parse_bitfield64 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l | val serialize_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (serializer (parse_bitfield64 l))
let serialize_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (serializer (parse_bitfield64 l)) = | false | null | false | serialize_bitfield serialize_u64 uint64 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.serialize_bitfield",
"FStar.UInt64.t",
"LowParse.Spec.Int.parse_u64_kind",
"LowParse.Spec.Int.parse_u64",
"LowParse.Spec.Int.serialize_u64",
"LowParse.BitFields.uint64",
"LowParse.Spec.Base.serializer",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.parse_bitfield64"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_bitfield64 (l: list nat {valid_bitfield_widths 0 64 l})
: Tot (serializer (parse_bitfield64 l)) | [] | LowParse.Spec.BitFields.serialize_bitfield64 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 64 l}
-> LowParse.Spec.Base.serializer (LowParse.Spec.BitFields.parse_bitfield64 l) | {
"end_col": 43,
"end_line": 158,
"start_col": 2,
"start_line": 158
} |
Prims.Tot | val parse_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l | val parse_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (parser parse_u8_kind (bitfields uint8 0 8 l))
let parse_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) = | false | null | false | parse_bitfield parse_u8 uint8 l | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.parse_bitfield",
"FStar.UInt8.t",
"LowParse.Spec.Int.parse_u8_kind",
"LowParse.Spec.Int.parse_u8",
"LowParse.BitFields.uint8",
"LowParse.Spec.Base.parser",
"LowParse.Spec.BitFields.bitfields"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse_bitfield8 (l: list nat {valid_bitfield_widths 0 8 l})
: Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) | [] | LowParse.Spec.BitFields.parse_bitfield8 | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 8 l}
-> LowParse.Spec.Base.parser LowParse.Spec.Int.parse_u8_kind
(LowParse.Spec.BitFields.bitfields LowParse.BitFields.uint8 0 8 l) | {
"end_col": 33,
"end_line": 173,
"start_col": 2,
"start_line": 173
} |
Prims.Tot | val synth_bitfield_recip
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x | val synth_bitfield_recip
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t
let synth_bitfield_recip
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t = | false | null | false | synth_bitfield_recip' cl lo hi l x | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield_recip'"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_recip
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t | [] | LowParse.Spec.BitFields.synth_bitfield_recip | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: LowParse.Spec.BitFields.bitfields cl lo hi l
-> t | {
"end_col": 231,
"end_line": 103,
"start_col": 197,
"start_line": 103
} |
Prims.Tot | val synth_bitfield
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x | val synth_bitfield
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l)
let synth_bitfield
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) = | false | null | false | synth_bitfield' cl lo hi l x | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.synth_bitfield'",
"LowParse.Spec.BitFields.bitfields"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) | [] | LowParse.Spec.BitFields.synth_bitfield | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: t
-> LowParse.Spec.BitFields.bitfields cl lo hi l | {
"end_col": 221,
"end_line": 45,
"start_col": 193,
"start_line": 45
} |
Prims.Tot | val mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
= norm [delta_only [`%mk_bitfields_destr'; `%bitfields_destr_nil; `%bitfields_destr_cons_nil; `%bitfields_destr_cons]; iota; zeta; primops] (mk_bitfields_destr' cl lo hi l) | val mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l)
let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) = | false | null | false | norm [
delta_only [
`%mk_bitfields_destr';
`%bitfields_destr_nil;
`%bitfields_destr_cons_nil;
`%bitfields_destr_cons
];
iota;
zeta;
primops
]
(mk_bitfields_destr' cl lo hi l) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"FStar.Pervasives.norm",
"Prims.Cons",
"FStar.Pervasives.norm_step",
"FStar.Pervasives.delta_only",
"Prims.string",
"Prims.Nil",
"FStar.Pervasives.iota",
"FStar.Pervasives.zeta",
"FStar.Pervasives.primops",
"LowParse.Spec.BitFields.bitfields_destr_t",
"LowParse.Spec.BitFields.mk_bitfields_destr'"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f ()
noextract
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
(decreases l)
= match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q)
inline_for_extraction
noextract
let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l }) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) | [] | LowParse.Spec.BitFields.mk_bitfields_destr | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l}
-> LowParse.Spec.BitFields.bitfields_destr_t cl lo hi l | {
"end_col": 172,
"end_line": 262,
"start_col": 2,
"start_line": 262
} |
Prims.Tot | val valid_bitfield_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) | [
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q | val valid_bitfield_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l)
let rec valid_bitfield_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) = | false | null | false | match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"Prims.op_Equality",
"Prims.op_AmpAmp",
"Prims.op_Addition",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"Prims.bool"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val valid_bitfield_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.valid_bitfield_widths | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | lo: Prims.nat -> hi: Prims.nat{lo <= hi} -> l: Prims.list Prims.nat -> Prims.Tot Prims.bool | {
"end_col": 68,
"end_line": 19,
"start_col": 2,
"start_line": 17
} |
Prims.Pure | val bounds_of_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat)
: Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l) | [
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q | val bounds_of_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat)
: Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
let rec bounds_of_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat)
: Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l) = | false | null | false | match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"Prims.Nil",
"Prims.Cons",
"Prims.op_Addition",
"LowParse.Spec.BitFields.bounds_of_widths",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.valid_bitfield_bounds"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res)) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bounds_of_widths (lo: nat) (hi: nat{lo <= hi}) (l: list nat)
: Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.bounds_of_widths | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | lo: Prims.nat -> hi: Prims.nat{lo <= hi} -> l: Prims.list Prims.nat
-> Prims.Pure (Prims.list Prims.nat) | {
"end_col": 59,
"end_line": 28,
"start_col": 2,
"start_line": 25
} |
Prims.Tot | val valid_bitfield_bounds (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) | [
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q | val valid_bitfield_bounds (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l)
let rec valid_bitfield_bounds (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) = | false | null | false | match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"Prims.op_AmpAmp",
"LowParse.Spec.BitFields.valid_bitfield_bounds",
"Prims.bool"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion. | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val valid_bitfield_bounds (lo: nat) (hi: nat{lo <= hi}) (l: list nat) : Tot bool (decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.valid_bitfield_bounds | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | lo: Prims.nat -> hi: Prims.nat{lo <= hi} -> l: Prims.list Prims.nat -> Prims.Tot Prims.bool | {
"end_col": 68,
"end_line": 14,
"start_col": 2,
"start_line": 12
} |
Prims.Tot | val valid_bitfield_widths_prefix
(lo: nat)
(hi: nat{lo <= hi})
(prefix: list nat)
(suffix: list nat {valid_bitfield_widths lo hi (prefix `L.append` suffix)})
: Tot (mi: nat{lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix}) (decreases prefix) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec valid_bitfield_widths_prefix
(lo: nat)
(hi: nat { lo <= hi })
(prefix: list nat)
(suffix: list nat { valid_bitfield_widths lo hi (prefix `L.append` suffix) })
: Tot (mi: nat { lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix })
(decreases prefix)
= match prefix with
| [] -> lo
| sz :: q -> valid_bitfield_widths_prefix (lo + sz) hi q suffix | val valid_bitfield_widths_prefix
(lo: nat)
(hi: nat{lo <= hi})
(prefix: list nat)
(suffix: list nat {valid_bitfield_widths lo hi (prefix `L.append` suffix)})
: Tot (mi: nat{lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix}) (decreases prefix)
let rec valid_bitfield_widths_prefix
(lo: nat)
(hi: nat{lo <= hi})
(prefix: list nat)
(suffix: list nat {valid_bitfield_widths lo hi (prefix `L.append` suffix)})
: Tot (mi: nat{lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix}) (decreases prefix) = | false | null | false | match prefix with
| [] -> lo
| sz :: q -> valid_bitfield_widths_prefix (lo + sz) hi q suffix | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"FStar.List.Tot.Base.append",
"LowParse.Spec.BitFields.valid_bitfield_widths_prefix",
"Prims.op_Addition",
"Prims.l_and"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f ()
noextract
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
(decreases l)
= match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q)
inline_for_extraction
noextract
let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
= norm [delta_only [`%mk_bitfields_destr'; `%bitfields_destr_nil; `%bitfields_destr_cons_nil; `%bitfields_destr_cons]; iota; zeta; primops] (mk_bitfields_destr' cl lo hi l)
module L = FStar.List.Tot
let rec valid_bitfield_widths_inj
(lo: nat)
(hi1: nat { lo <= hi1 })
(hi2: nat { lo <= hi2 })
(l: list nat)
: Lemma
(requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l)
= match l with
| [] -> ()
| sz :: q -> valid_bitfield_widths_inj (lo + sz) hi1 hi2 q
let rec valid_bitfield_widths_prefix
(lo: nat)
(hi: nat { lo <= hi })
(prefix: list nat)
(suffix: list nat { valid_bitfield_widths lo hi (prefix `L.append` suffix) })
: Tot (mi: nat { lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix }) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val valid_bitfield_widths_prefix
(lo: nat)
(hi: nat{lo <= hi})
(prefix: list nat)
(suffix: list nat {valid_bitfield_widths lo hi (prefix `L.append` suffix)})
: Tot (mi: nat{lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix}) (decreases prefix) | [
"recursion"
] | LowParse.Spec.BitFields.valid_bitfield_widths_prefix | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
lo: Prims.nat ->
hi: Prims.nat{lo <= hi} ->
prefix: Prims.list Prims.nat ->
suffix:
Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi (prefix @ suffix)}
-> Prims.Tot
(mi:
Prims.nat{lo <= mi /\ mi <= hi /\ LowParse.Spec.BitFields.valid_bitfield_widths lo mi prefix}) | {
"end_col": 65,
"end_line": 288,
"start_col": 2,
"start_line": 286
} |
FStar.Pervasives.Lemma | val valid_bitfield_widths_inj (lo: nat) (hi1: nat{lo <= hi1}) (hi2: nat{lo <= hi2}) (l: list nat)
: Lemma (requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec valid_bitfield_widths_inj
(lo: nat)
(hi1: nat { lo <= hi1 })
(hi2: nat { lo <= hi2 })
(l: list nat)
: Lemma
(requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l)
= match l with
| [] -> ()
| sz :: q -> valid_bitfield_widths_inj (lo + sz) hi1 hi2 q | val valid_bitfield_widths_inj (lo: nat) (hi1: nat{lo <= hi1}) (hi2: nat{lo <= hi2}) (l: list nat)
: Lemma (requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l)
let rec valid_bitfield_widths_inj
(lo: nat)
(hi1: nat{lo <= hi1})
(hi2: nat{lo <= hi2})
(l: list nat)
: Lemma (requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l) = | false | null | true | match l with
| [] -> ()
| sz :: q -> valid_bitfield_widths_inj (lo + sz) hi1 hi2 q | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma",
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths_inj",
"Prims.op_Addition",
"Prims.unit",
"Prims.l_and",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"Prims.squash",
"Prims.eq2",
"Prims.l_or",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f ()
noextract
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
(decreases l)
= match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q)
inline_for_extraction
noextract
let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
= norm [delta_only [`%mk_bitfields_destr'; `%bitfields_destr_nil; `%bitfields_destr_cons_nil; `%bitfields_destr_cons]; iota; zeta; primops] (mk_bitfields_destr' cl lo hi l)
module L = FStar.List.Tot
let rec valid_bitfield_widths_inj
(lo: nat)
(hi1: nat { lo <= hi1 })
(hi2: nat { lo <= hi2 })
(l: list nat)
: Lemma
(requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2)) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val valid_bitfield_widths_inj (lo: nat) (hi1: nat{lo <= hi1}) (hi2: nat{lo <= hi2}) (l: list nat)
: Lemma (requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.valid_bitfield_widths_inj | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | lo: Prims.nat -> hi1: Prims.nat{lo <= hi1} -> hi2: Prims.nat{lo <= hi2} -> l: Prims.list Prims.nat
-> FStar.Pervasives.Lemma
(requires
LowParse.Spec.BitFields.valid_bitfield_widths lo hi1 l /\
LowParse.Spec.BitFields.valid_bitfield_widths lo hi2 l) (ensures hi1 == hi2) (decreases l) | {
"end_col": 60,
"end_line": 277,
"start_col": 2,
"start_line": 275
} |
Prims.Tot | val synth_bitfield'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) (decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x) | val synth_bitfield'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) (decreases l)
let rec synth_bitfield'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) (decreases l) = | false | null | false | match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q ->
(((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.BitFields.__proj__Mkuint_t__item__get_bitfield",
"FStar.Pervasives.Native.Mktuple2",
"LowParse.BitFields.bitfield",
"LowParse.Spec.BitFields.bitfields",
"Prims.op_Addition",
"LowParse.Spec.BitFields.synth_bitfield'"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: t)
: Tot (bitfields cl lo hi l) (decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.synth_bitfield' | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: t
-> Prims.Tot (LowParse.Spec.BitFields.bitfields cl lo hi l) | {
"end_col": 111,
"end_line": 43,
"start_col": 2,
"start_line": 40
} |
Prims.Tot | val synth_bitfield_recip'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t (decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd | val synth_bitfield_recip'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t (decreases l)
let rec synth_bitfield_recip'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t (decreases l) = | false | null | false | match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let hd, tl = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.bitfields",
"LowParse.BitFields.__proj__Mkuint_t__item__uint_to_t",
"LowParse.BitFields.__proj__Mkuint_t__item__set_bitfield",
"LowParse.BitFields.bitfield",
"Prims.op_Addition",
"LowParse.Spec.BitFields.synth_bitfield_recip'",
"FStar.Pervasives.Native.tuple2"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_recip'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Tot t (decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.synth_bitfield_recip' | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: LowParse.Spec.BitFields.bitfields cl lo hi l
-> Prims.Tot t | {
"end_col": 80,
"end_line": 101,
"start_col": 2,
"start_line": 96
} |
Prims.Tot | val mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) (decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
(decreases l)
= match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q) | val mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) (decreases l)
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) (decreases l) = | false | null | false | match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.bitfields_destr_nil",
"LowParse.Spec.BitFields.bitfields_destr_cons_nil",
"LowParse.Spec.BitFields.bitfields_destr_cons",
"LowParse.Spec.BitFields.mk_bitfields_destr'",
"Prims.op_Addition",
"LowParse.Spec.BitFields.bitfields_destr_t"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f ()
noextract
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
: Tot (bitfields_destr_t cl lo hi l) (decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.mk_bitfields_destr' | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l}
-> Prims.Tot (LowParse.Spec.BitFields.bitfields_destr_t cl lo hi l) | {
"end_col": 89,
"end_line": 250,
"start_col": 2,
"start_line": 247
} |
Prims.Tot | val parse_bitfield
(#t: Type)
(#k: parser_kind)
(p: parser k t)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (parser k (bitfields cl 0 tot l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l | val parse_bitfield
(#t: Type)
(#k: parser_kind)
(p: parser k t)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (parser k (bitfields cl 0 tot l))
let parse_bitfield
(#t: Type)
(#k: parser_kind)
(p: parser k t)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (parser k (bitfields cl 0 tot l)) = | false | null | false | p `parse_synth` (synth_bitfield cl 0 tot l) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"LowParse.Spec.Base.parser_kind",
"LowParse.Spec.Base.parser",
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.Combinators.parse_synth",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val parse_bitfield
(#t: Type)
(#k: parser_kind)
(p: parser k t)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (parser k (bitfields cl 0 tot l)) | [] | LowParse.Spec.BitFields.parse_bitfield | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
p: LowParse.Spec.Base.parser k t ->
cl: LowParse.BitFields.uint_t tot t ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 tot l}
-> LowParse.Spec.Base.parser k (LowParse.Spec.BitFields.bitfields cl 0 tot l) | {
"end_col": 43,
"end_line": 93,
"start_col": 2,
"start_line": 93
} |
FStar.Pervasives.Lemma | val synth_bitfield_recip_inverse
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma
((lo == 0 /\ hi == tot) ==>
synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[
SMTPat
(synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l)
)
] | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
) | val synth_bitfield_recip_inverse
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma
((lo == 0 /\ hi == tot) ==>
synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[
SMTPat
(synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l)
)
]
let synth_bitfield_recip_inverse
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma
((lo == 0 /\ hi == tot) ==>
synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[
SMTPat
(synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l)
)
] = | false | null | true | synth_inverse_intro' (synth_bitfield cl 0 tot l)
(synth_bitfield_recip cl 0 tot l)
(fun x -> synth_bitfield_recip_inverse' cl 0 tot l x) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.Combinators.synth_inverse_intro'",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield",
"LowParse.Spec.BitFields.synth_bitfield_recip",
"LowParse.Spec.BitFields.synth_bitfield_recip_inverse'",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"Prims.l_imp",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThan",
"Prims.op_GreaterThanOrEqual",
"LowParse.Spec.Combinators.synth_inverse",
"Prims.Cons",
"FStar.Pervasives.pattern",
"FStar.Pervasives.smt_pat",
"Prims.Nil"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))] | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_recip_inverse
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma
((lo == 0 /\ hi == tot) ==>
synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[
SMTPat
(synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l)
)
] | [] | LowParse.Spec.BitFields.synth_bitfield_recip_inverse | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 tot l}
-> FStar.Pervasives.Lemma
(ensures
lo == 0 /\ hi == tot ==>
LowParse.Spec.Combinators.synth_inverse (LowParse.Spec.BitFields.synth_bitfield cl lo hi l)
(LowParse.Spec.BitFields.synth_bitfield_recip cl lo hi l))
[
SMTPat (LowParse.Spec.Combinators.synth_inverse (LowParse.Spec.BitFields.synth_bitfield cl
lo
hi
l)
(LowParse.Spec.BitFields.synth_bitfield_recip cl lo hi l))
] | {
"end_col": 3,
"end_line": 141,
"start_col": 2,
"start_line": 139
} |
FStar.Pervasives.Lemma | val synth_bitfield_injective
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))] | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y))) | val synth_bitfield_injective
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
let synth_bitfield_injective
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))] = | false | null | true | synth_injective_intro' (synth_bitfield cl 0 tot l)
(fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y))) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.Combinators.synth_injective_intro'",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield",
"Prims._assert",
"Prims.eq2",
"LowParse.BitFields.__proj__Mkuint_t__item__uint_to_t",
"LowParse.BitFields.__proj__Mkuint_t__item__v",
"Prims.unit",
"LowParse.BitFields.get_bitfield_full",
"LowParse.Spec.BitFields.synth_bitfield_injective'",
"Prims.l_True",
"Prims.squash",
"Prims.l_imp",
"Prims.int",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"Prims.op_GreaterThan",
"LowParse.Spec.Combinators.synth_injective",
"Prims.Cons",
"FStar.Pervasives.pattern",
"FStar.Pervasives.smt_pat",
"Prims.Nil"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))] | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_injective
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths 0 tot l})
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))] | [] | LowParse.Spec.BitFields.synth_bitfield_injective | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 tot l}
-> FStar.Pervasives.Lemma
(ensures
lo == 0 /\ hi == tot ==>
LowParse.Spec.Combinators.synth_injective (LowParse.Spec.BitFields.synth_bitfield cl lo hi l
))
[
SMTPat (LowParse.Spec.Combinators.synth_injective (LowParse.Spec.BitFields.synth_bitfield cl
lo
hi
l))
] | {
"end_col": 60,
"end_line": 68,
"start_col": 2,
"start_line": 64
} |
Prims.Tot | val serialize_bitfield
(#t: Type)
(#k: parser_kind)
(#p: parser k t)
(s: serializer p)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (serializer (parse_bitfield p cl l)) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
() | val serialize_bitfield
(#t: Type)
(#k: parser_kind)
(#p: parser k t)
(s: serializer p)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (serializer (parse_bitfield p cl l))
let serialize_bitfield
(#t: Type)
(#k: parser_kind)
(#p: parser k t)
(s: serializer p)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (serializer (parse_bitfield p cl l)) = | false | null | false | serialize_synth p (synth_bitfield cl 0 tot l) s (synth_bitfield_recip cl 0 tot l) () | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"LowParse.Spec.Base.parser_kind",
"LowParse.Spec.Base.parser",
"LowParse.Spec.Base.serializer",
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.list",
"Prims.nat",
"Prims.b2t",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.Combinators.serialize_synth",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield",
"LowParse.Spec.BitFields.synth_bitfield_recip",
"LowParse.Spec.BitFields.parse_bitfield"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_bitfield
(#t: Type)
(#k: parser_kind)
(#p: parser k t)
(s: serializer p)
(#tot: pos)
(cl: uint_t tot t)
(l: list nat {valid_bitfield_widths 0 tot l})
: Tot (serializer (parse_bitfield p cl l)) | [] | LowParse.Spec.BitFields.serialize_bitfield | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
s: LowParse.Spec.Base.serializer p ->
cl: LowParse.BitFields.uint_t tot t ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths 0 tot l}
-> LowParse.Spec.Base.serializer (LowParse.Spec.BitFields.parse_bitfield p cl l) | {
"end_col": 6,
"end_line": 152,
"start_col": 2,
"start_line": 147
} |
Prims.Tot | val bitfields_destr_nil (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat{lo <= tot})
: Tot (bitfields_destr_t cl lo lo []) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f () | val bitfields_destr_nil (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat{lo <= tot})
: Tot (bitfields_destr_t cl lo lo [])
let bitfields_destr_nil (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat{lo <= tot})
: Tot (bitfields_destr_t cl lo lo []) = | false | null | false | fun f_t f x -> f () | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"LowParse.Spec.BitFields.bitfields",
"Prims.Nil",
"LowParse.Spec.BitFields.synth_bitfield",
"LowParse.Spec.BitFields.bitfields_destr_t"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } ) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bitfields_destr_nil (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat{lo <= tot})
: Tot (bitfields_destr_t cl lo lo []) | [] | LowParse.Spec.BitFields.bitfields_destr_nil | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | cl: LowParse.BitFields.uint_t tot t -> lo: Prims.nat{lo <= tot}
-> LowParse.Spec.BitFields.bitfields_destr_t cl lo lo [] | {
"end_col": 8,
"end_line": 235,
"start_col": 2,
"start_line": 234
} |
Prims.Tot | val bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat{lo + sz <= tot})
: Tot (bitfields_destr_t cl lo (lo + sz) [sz]) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz)) | val bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat{lo + sz <= tot})
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat{lo + sz <= tot})
: Tot (bitfields_destr_t cl lo (lo + sz) [sz]) = | false | null | false | fun f_t f x -> f (cl.get_bitfield x lo (lo + sz)) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"total"
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"LowParse.Spec.BitFields.bitfields",
"Prims.Cons",
"Prims.Nil",
"LowParse.BitFields.__proj__Mkuint_t__item__get_bitfield",
"LowParse.Spec.BitFields.synth_bitfield",
"LowParse.Spec.BitFields.bitfields_destr_t"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot }) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat{lo + sz <= tot})
: Tot (bitfields_destr_t cl lo (lo + sz) [sz]) | [] | LowParse.Spec.BitFields.bitfields_destr_cons_nil | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} | cl: LowParse.BitFields.uint_t tot t -> lo: Prims.nat -> sz: Prims.nat{lo + sz <= tot}
-> LowParse.Spec.BitFields.bitfields_destr_t cl lo (lo + sz) [sz] | {
"end_col": 38,
"end_line": 224,
"start_col": 2,
"start_line": 223
} |
FStar.Pervasives.Lemma | val synth_bitfield_recip_inverse'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Lemma (ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x) | val synth_bitfield_recip_inverse'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Lemma (ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
let rec synth_bitfield_recip_inverse'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Lemma (ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l) = | false | null | true | match l with
| [] -> assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) ==
cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let hd, tl = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x)
<:
(bitfield cl sz & bitfields cl (lo + sz) hi q)))) ==
cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl
(lo + sz)
hi
q
tl)
lo
(lo + sz)
hd)
lo
(lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.bitfields",
"Prims._assert",
"Prims.eq2",
"LowParse.Spec.BitFields.synth_bitfield",
"LowParse.Spec.BitFields.synth_bitfield_recip",
"LowParse.BitFields.bitfield",
"Prims.unit",
"LowParse.BitFields.__proj__Mkuint_t__item__uint_to_t",
"LowParse.BitFields.__proj__Mkuint_t__item__v",
"LowParse.BitFields.__proj__Mkuint_t__item__get_bitfield",
"LowParse.BitFields.__proj__Mkuint_t__item__set_bitfield",
"LowParse.BitFields.get_bitfield_set_bitfield_same",
"Prims.op_Addition",
"FStar.Pervasives.Native.fst",
"FStar.Pervasives.Native.tuple2",
"LowParse.Spec.BitFields.synth_bitfield_recip_inverse'",
"LowParse.Spec.BitFields.synth_bitfield_ext",
"LowParse.BitFields.get_bitfield_set_bitfield_other",
"Prims.l_True",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 64,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_recip_inverse'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x: bitfields cl lo hi l)
: Lemma (ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.synth_bitfield_recip_inverse' | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: LowParse.Spec.BitFields.bitfields cl lo hi l
-> FStar.Pervasives.Lemma
(ensures
LowParse.Spec.BitFields.synth_bitfield cl
lo
hi
l
(LowParse.Spec.BitFields.synth_bitfield_recip cl lo hi l x) ==
x) (decreases l) | {
"end_col": 79,
"end_line": 131,
"start_col": 2,
"start_line": 113
} |
FStar.Pervasives.Lemma | val valid_bitfield_widths_append
(lo: nat)
(mi: nat{lo <= mi})
(hi: nat{mi <= hi})
(prefix: list nat {valid_bitfield_widths lo mi prefix})
(suffix: list nat {valid_bitfield_widths mi hi suffix})
: Lemma (ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix))) (decreases prefix) | [
{
"abbrev": true,
"full_module": "FStar.List.Tot",
"short_module": "L"
},
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec valid_bitfield_widths_append
(lo: nat)
(mi: nat { lo <= mi })
(hi: nat { mi <= hi })
(prefix: list nat { valid_bitfield_widths lo mi prefix })
(suffix: list nat { valid_bitfield_widths mi hi suffix })
: Lemma
(ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix)))
(decreases prefix)
= match prefix with
| [] -> ()
| sz :: q -> valid_bitfield_widths_append (lo + sz) mi hi q suffix | val valid_bitfield_widths_append
(lo: nat)
(mi: nat{lo <= mi})
(hi: nat{mi <= hi})
(prefix: list nat {valid_bitfield_widths lo mi prefix})
(suffix: list nat {valid_bitfield_widths mi hi suffix})
: Lemma (ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix))) (decreases prefix)
let rec valid_bitfield_widths_append
(lo: nat)
(mi: nat{lo <= mi})
(hi: nat{mi <= hi})
(prefix: list nat {valid_bitfield_widths lo mi prefix})
(suffix: list nat {valid_bitfield_widths mi hi suffix})
: Lemma (ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix))) (decreases prefix) = | false | null | true | match prefix with
| [] -> ()
| sz :: q -> valid_bitfield_widths_append (lo + sz) mi hi q suffix | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma",
""
] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.Spec.BitFields.valid_bitfield_widths_append",
"Prims.op_Addition",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"FStar.List.Tot.Base.append",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
#pop-options
let parse_bitfield (#t: Type) (#k: parser_kind) (p: parser k t) (#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l }) : Tot (parser k (bitfields cl 0 tot l)) =
p `parse_synth` synth_bitfield cl 0 tot l
let rec synth_bitfield_recip' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t (decreases l) =
match l with
| [] -> cl.uint_to_t 0
| [_] -> cl.set_bitfield (cl.uint_to_t 0) lo hi x
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
cl.set_bitfield (synth_bitfield_recip' cl (lo + sz) hi q tl) lo (lo + sz) hd
let synth_bitfield_recip (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l) : Tot t = synth_bitfield_recip' cl lo hi l x
#push-options "--z3rlimit 64"
let rec synth_bitfield_recip_inverse'
(#tot: pos) (#t: Type) (cl: uint_t tot t)
(lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: bitfields cl lo hi l)
: Lemma
(ensures (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x))
(decreases l)
= match l with
| [] ->
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| [sz] ->
let x = x <: bitfield cl sz in
BF.get_bitfield_set_bitfield_same 0 lo hi (cl.v x);
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) ==
cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi);
assert (cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (cl.uint_to_t 0) lo hi x) lo hi)) == cl.uint_to_t (cl.v x));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
| sz :: q ->
let (hd, tl) = x <: (bitfield cl sz & bitfields cl (lo + sz) hi q) in
let y = synth_bitfield_recip cl (lo + sz) hi q tl in
BF.get_bitfield_set_bitfield_same (cl.v y) lo (lo + sz) (cl.v hd);
BF.get_bitfield_set_bitfield_other (cl.v y) lo (lo + sz) (cl.v hd) (lo + sz) hi;
synth_bitfield_ext cl (lo + sz) hi q y (cl.set_bitfield y lo (lo + sz) hd);
synth_bitfield_recip_inverse' cl (lo + sz) hi q tl;
assert (cl.uint_to_t (cl.v (fst (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) <: (bitfield cl sz & bitfields cl (lo + sz) hi q)))) == cl.uint_to_t (cl.v (cl.get_bitfield (cl.set_bitfield (synth_bitfield_recip cl (lo + sz) hi q tl) lo (lo + sz) hd) lo (lo + sz))));
assert (synth_bitfield cl lo hi l (synth_bitfield_recip cl lo hi l x) == x)
#pop-options
let synth_bitfield_recip_inverse (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_inverse (synth_bitfield cl lo hi l) (synth_bitfield_recip cl lo hi l))
[SMTPat (synth_inverse (synth_bitfield #tot #t cl lo hi l) (synth_bitfield_recip #tot #t cl lo hi l))]
=
synth_inverse_intro' (synth_bitfield cl 0 tot l) (synth_bitfield_recip cl 0 tot l) (fun x ->
synth_bitfield_recip_inverse' cl 0 tot l x
)
let serialize_bitfield
(#t: Type) (#k: parser_kind) (#p: parser k t) (s: serializer p)
(#tot: pos) (cl: uint_t tot t) (l: list nat { valid_bitfield_widths 0 tot l })
: Tot (serializer (parse_bitfield p cl l))
= serialize_synth
p
(synth_bitfield cl 0 tot l)
s
(synth_bitfield_recip cl 0 tot l)
()
let parse_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (parser parse_u64_kind (bitfields uint64 0 64 l)) =
parse_bitfield parse_u64 uint64 l
let serialize_bitfield64 (l: list nat { valid_bitfield_widths 0 64 l }) : Tot (serializer (parse_bitfield64 l)) =
serialize_bitfield serialize_u64 uint64 l
let parse_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (parser parse_u32_kind (bitfields uint32 0 32 l)) =
parse_bitfield parse_u32 uint32 l
let serialize_bitfield32 (l: list nat { valid_bitfield_widths 0 32 l }) : Tot (serializer (parse_bitfield32 l)) =
serialize_bitfield serialize_u32 uint32 l
let parse_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (parser parse_u16_kind (bitfields uint16 0 16 l)) =
parse_bitfield parse_u16 uint16 l
let serialize_bitfield16 (l: list nat { valid_bitfield_widths 0 16 l }) : Tot (serializer (parse_bitfield16 l)) =
serialize_bitfield serialize_u16 uint16 l
let parse_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (parser parse_u8_kind (bitfields uint8 0 8 l)) =
parse_bitfield parse_u8 uint8 l
let serialize_bitfield8 (l: list nat { valid_bitfield_widths 0 8 l }) : Tot (serializer (parse_bitfield8 l)) =
serialize_bitfield serialize_u8 uint8 l
(* Universal destructor *)
inline_for_extraction
noextract
let bitfields_destr_t
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot Type
=
(f_t: (bitfields cl lo hi l -> Tot Type)) ->
(f: ((x: bitfields cl lo hi l) -> Tot (f_t x))) ->
(x: t) ->
Tot (f_t (synth_bitfield cl lo hi l x))
inline_for_extraction
noextract
let bitfields_destr_cons
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat)
(hi: nat { lo + sz <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths (lo + sz) hi l /\ Cons? l })
(phi: bitfields_destr_t cl (lo + sz) hi l)
: Tot (bitfields_destr_t cl lo hi (sz :: l))
= fun f_t f x ->
phi
(fun x' -> f_t (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
(fun x' -> f (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), x'))
x
inline_for_extraction
noextract
let bitfields_destr_cons_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(sz: nat { lo + sz <= tot })
: Tot (bitfields_destr_t cl lo (lo + sz) [sz])
= fun f_t f x ->
f (cl.get_bitfield x lo (lo + sz))
inline_for_extraction
noextract
let bitfields_destr_nil
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat { lo <= tot } )
: Tot (bitfields_destr_t cl lo lo [])
= fun f_t f x ->
f ()
noextract
let rec mk_bitfields_destr'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
(decreases l)
= match l with
| [] -> bitfields_destr_nil cl lo
| [sz] -> bitfields_destr_cons_nil cl lo sz
| sz :: q -> bitfields_destr_cons cl lo sz hi q (mk_bitfields_destr' cl (lo + sz) hi q)
inline_for_extraction
noextract
let mk_bitfields_destr
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat { lo <= hi /\ hi <= tot })
(l: list nat { valid_bitfield_widths lo hi l })
: Tot (bitfields_destr_t cl lo hi l)
= norm [delta_only [`%mk_bitfields_destr'; `%bitfields_destr_nil; `%bitfields_destr_cons_nil; `%bitfields_destr_cons]; iota; zeta; primops] (mk_bitfields_destr' cl lo hi l)
module L = FStar.List.Tot
let rec valid_bitfield_widths_inj
(lo: nat)
(hi1: nat { lo <= hi1 })
(hi2: nat { lo <= hi2 })
(l: list nat)
: Lemma
(requires (valid_bitfield_widths lo hi1 l /\ valid_bitfield_widths lo hi2 l))
(ensures (hi1 == hi2))
(decreases l)
= match l with
| [] -> ()
| sz :: q -> valid_bitfield_widths_inj (lo + sz) hi1 hi2 q
let rec valid_bitfield_widths_prefix
(lo: nat)
(hi: nat { lo <= hi })
(prefix: list nat)
(suffix: list nat { valid_bitfield_widths lo hi (prefix `L.append` suffix) })
: Tot (mi: nat { lo <= mi /\ mi <= hi /\ valid_bitfield_widths lo mi prefix })
(decreases prefix)
= match prefix with
| [] -> lo
| sz :: q -> valid_bitfield_widths_prefix (lo + sz) hi q suffix
let rec valid_bitfield_widths_append
(lo: nat)
(mi: nat { lo <= mi })
(hi: nat { mi <= hi })
(prefix: list nat { valid_bitfield_widths lo mi prefix })
(suffix: list nat { valid_bitfield_widths mi hi suffix })
: Lemma
(ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix))) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val valid_bitfield_widths_append
(lo: nat)
(mi: nat{lo <= mi})
(hi: nat{mi <= hi})
(prefix: list nat {valid_bitfield_widths lo mi prefix})
(suffix: list nat {valid_bitfield_widths mi hi suffix})
: Lemma (ensures (valid_bitfield_widths lo hi (prefix `L.append` suffix))) (decreases prefix) | [
"recursion"
] | LowParse.Spec.BitFields.valid_bitfield_widths_append | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
lo: Prims.nat ->
mi: Prims.nat{lo <= mi} ->
hi: Prims.nat{mi <= hi} ->
prefix: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo mi prefix} ->
suffix: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths mi hi suffix}
-> FStar.Pervasives.Lemma
(ensures LowParse.Spec.BitFields.valid_bitfield_widths lo hi (prefix @ suffix))
(decreases prefix) | {
"end_col": 68,
"end_line": 301,
"start_col": 2,
"start_line": 299
} |
FStar.Pervasives.Lemma | val synth_bitfield_injective'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y) | val synth_bitfield_injective'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
let rec synth_bitfield_injective'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l) = | false | null | true | match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"LowParse.BitFields.get_bitfield_empty",
"LowParse.BitFields.__proj__Mkuint_t__item__v",
"Prims.unit",
"LowParse.BitFields.get_bitfield_partition_2_gen",
"Prims.op_Addition",
"LowParse.Spec.BitFields.synth_bitfield_injective'",
"Prims.eq2",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield",
"Prims.squash",
"LowParse.BitFields.ubitfield",
"Prims.op_Subtraction",
"LowParse.BitFields.get_bitfield",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi)) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_injective'
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.synth_bitfield_injective' | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: t ->
y: t
-> FStar.Pervasives.Lemma
(requires
LowParse.Spec.BitFields.synth_bitfield cl lo hi l x ==
LowParse.Spec.BitFields.synth_bitfield cl lo hi l y)
(ensures
LowParse.BitFields.get_bitfield (Mkuint_t?.v cl x) lo hi ==
LowParse.BitFields.get_bitfield (Mkuint_t?.v cl y) lo hi)
(decreases l) | {
"end_col": 69,
"end_line": 58,
"start_col": 2,
"start_line": 51
} |
FStar.Pervasives.Lemma | val synth_bitfield_ext
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l) | [
{
"abbrev": true,
"full_module": "FStar.UInt",
"short_module": "U"
},
{
"abbrev": true,
"full_module": "LowParse.BitFields",
"short_module": "BF"
},
{
"abbrev": false,
"full_module": "LowParse.BitFields",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Int",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec.Combinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "LowParse.Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
= match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) == cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) == cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y) | val synth_bitfield_ext
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l)
let rec synth_bitfield_ext
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l) = | false | null | true | match l with
| [] -> assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| [_] ->
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo hi)) ==
cl.uint_to_t (cl.v (cl.get_bitfield y lo hi)));
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)
| sz :: q ->
BF.get_bitfield_get_bitfield (cl.v x) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v x) lo hi sz (hi - lo);
BF.get_bitfield_get_bitfield (cl.v y) lo hi 0 sz;
BF.get_bitfield_get_bitfield (cl.v y) lo hi sz (hi - lo);
assert (cl.uint_to_t (cl.v (cl.get_bitfield x lo (lo + sz))) ==
cl.uint_to_t (cl.v (cl.get_bitfield y lo (lo + sz))));
synth_bitfield_ext cl (lo + sz) hi q x y;
assert (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y) | {
"checked_file": "LowParse.Spec.BitFields.fst.checked",
"dependencies": [
"prims.fst.checked",
"LowParse.Spec.Int.fsti.checked",
"LowParse.Spec.Combinators.fsti.checked",
"LowParse.BitFields.fsti.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.List.Tot.fst.checked"
],
"interface_file": false,
"source_file": "LowParse.Spec.BitFields.fst"
} | [
"lemma",
""
] | [
"Prims.pos",
"LowParse.BitFields.uint_t",
"Prims.nat",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.list",
"LowParse.Spec.BitFields.valid_bitfield_widths",
"Prims._assert",
"Prims.eq2",
"LowParse.Spec.BitFields.bitfields",
"LowParse.Spec.BitFields.synth_bitfield",
"Prims.unit",
"LowParse.BitFields.__proj__Mkuint_t__item__uint_to_t",
"LowParse.BitFields.__proj__Mkuint_t__item__v",
"LowParse.BitFields.__proj__Mkuint_t__item__get_bitfield",
"LowParse.Spec.BitFields.synth_bitfield_ext",
"Prims.op_Addition",
"LowParse.BitFields.get_bitfield_get_bitfield",
"Prims.op_Subtraction",
"LowParse.BitFields.ubitfield",
"LowParse.BitFields.get_bitfield",
"Prims.squash",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module LowParse.Spec.BitFields
include LowParse.Spec.Combinators
include LowParse.Spec.Int
include LowParse.BitFields
module BF = LowParse.BitFields
// IMPORTANT: these bitfield operators are defined in a least
// significant bit (LSB) first fashion.
let rec valid_bitfield_bounds (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> true
| mi :: q -> lo <= mi && mi <= hi && valid_bitfield_bounds mi hi q
let rec valid_bitfield_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Tot bool (decreases l) =
match l with
| [] -> lo = hi
| sz :: q -> lo + sz <= hi && valid_bitfield_widths (lo + sz) hi q
let rec bounds_of_widths (lo: nat) (hi: nat { lo <= hi }) (l: list nat) : Pure (list nat)
(requires (valid_bitfield_widths lo hi l))
(ensures (fun res -> valid_bitfield_bounds lo hi res))
(decreases l)
= match l with
| [] -> []
| [_] -> []
| sz :: q -> (lo + sz) :: bounds_of_widths (lo + sz) hi q
module U = FStar.UInt
noextract
let rec bitfields (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) : Tot Type (decreases l) =
match l with
| [] -> unit
| [sz] -> bitfield cl sz
| sz :: q -> bitfield cl sz & bitfields cl (lo + sz) hi q
let rec synth_bitfield' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) (decreases l) =
match l with
| [] -> ()
| [_] -> cl.get_bitfield x lo hi
| sz :: q -> (((cl.get_bitfield x lo (lo + sz) <: t) <: bitfield cl sz), synth_bitfield' cl (lo + sz) hi q x)
let synth_bitfield (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x: t) : Tot (bitfields cl lo hi l) = synth_bitfield' cl lo hi l x
let rec synth_bitfield_injective' (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(ensures (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(decreases l)
= match l with
| [] ->
BF.get_bitfield_empty (cl.v x) lo;
BF.get_bitfield_empty (cl.v y) lo
| [_] -> ()
| sz :: q ->
synth_bitfield_injective' cl (lo + sz) hi q x y;
BF.get_bitfield_partition_2_gen lo (lo + sz) hi (cl.v x) (cl.v y)
let synth_bitfield_injective (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths 0 tot l })
: Lemma ((lo == 0 /\ hi == tot) ==> synth_injective (synth_bitfield cl lo hi l))
[SMTPat (synth_injective (synth_bitfield #tot #t cl lo hi l))]
=
synth_injective_intro' (synth_bitfield cl 0 tot l) (fun x y ->
synth_bitfield_injective' cl 0 tot l x y;
BF.get_bitfield_full (cl.v x);
BF.get_bitfield_full (cl.v y);
assert (cl.uint_to_t (cl.v x) == cl.uint_to_t (cl.v y)))
#push-options "--z3rlimit 128"
let rec synth_bitfield_ext (#tot: pos) (#t: Type) (cl: uint_t tot t) (lo: nat) (hi: nat { lo <= hi /\ hi <= tot }) (l: list nat { valid_bitfield_widths lo hi l }) (x y: t) : Lemma
(requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y)) | false | false | LowParse.Spec.BitFields.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 128,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val synth_bitfield_ext
(#tot: pos)
(#t: Type)
(cl: uint_t tot t)
(lo: nat)
(hi: nat{lo <= hi /\ hi <= tot})
(l: list nat {valid_bitfield_widths lo hi l})
(x y: t)
: Lemma (requires (BF.get_bitfield (cl.v x) lo hi == BF.get_bitfield (cl.v y) lo hi))
(ensures (synth_bitfield cl lo hi l x == synth_bitfield cl lo hi l y))
(decreases l) | [
"recursion"
] | LowParse.Spec.BitFields.synth_bitfield_ext | {
"file_name": "src/lowparse/LowParse.Spec.BitFields.fst",
"git_rev": "446a08ce38df905547cf20f28c43776b22b8087a",
"git_url": "https://github.com/project-everest/everparse.git",
"project_name": "everparse"
} |
cl: LowParse.BitFields.uint_t tot t ->
lo: Prims.nat ->
hi: Prims.nat{lo <= hi /\ hi <= tot} ->
l: Prims.list Prims.nat {LowParse.Spec.BitFields.valid_bitfield_widths lo hi l} ->
x: t ->
y: t
-> FStar.Pervasives.Lemma
(requires
LowParse.BitFields.get_bitfield (Mkuint_t?.v cl x) lo hi ==
LowParse.BitFields.get_bitfield (Mkuint_t?.v cl y) lo hi)
(ensures
LowParse.Spec.BitFields.synth_bitfield cl lo hi l x ==
LowParse.Spec.BitFields.synth_bitfield cl lo hi l y)
(decreases l) | {
"end_col": 71,
"end_line": 88,
"start_col": 2,
"start_line": 76
} |
FStar.All.ML | val test: Prims.unit -> FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test () : FStar.All.ML bool =
let t0 : bool = test_secret_to_public test2_sk test2_pk in
let t1 : bool = test_verify test1_pk test1_msg test1_sgnt in
let t2 : bool = test_sign_and_verify test2_sk test2_pk test2_nonce test2_msgHash test2_sgnt in
let t3 : bool = test_public_key_compressed test2_pk in
let t4 : bool = test_public_key_uncompressed test2_pk in
if t0 && t1 && t2 && t3 && t4
then begin IO.print_string "Test K256 ecdsa: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa: Failure :(\n"; false end | val test: Prims.unit -> FStar.All.ML bool
let test () : FStar.All.ML bool = | true | null | false | let t0:bool = test_secret_to_public test2_sk test2_pk in
let t1:bool = test_verify test1_pk test1_msg test1_sgnt in
let t2:bool = test_sign_and_verify test2_sk test2_pk test2_nonce test2_msgHash test2_sgnt in
let t3:bool = test_public_key_compressed test2_pk in
let t4:bool = test_public_key_uncompressed test2_pk in
if t0 && t1 && t2 && t3 && t4
then
(IO.print_string "Test K256 ecdsa: Success!\n";
true)
else
(IO.print_string "Test K256 ecdsa: Failure :(\n";
false) | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Prims.unit",
"Prims.op_AmpAmp",
"Prims.bool",
"FStar.IO.print_string",
"Spec.K256.Test.test_public_key_uncompressed",
"Spec.K256.Test.test2_pk",
"Spec.K256.Test.test_public_key_compressed",
"Spec.K256.Test.test_sign_and_verify",
"Spec.K256.Test.test2_sk",
"Spec.K256.Test.test2_nonce",
"Spec.K256.Test.test2_msgHash",
"Spec.K256.Test.test2_sgnt",
"Spec.K256.Test.test_verify",
"Spec.K256.Test.test1_pk",
"Spec.K256.Test.test1_msg",
"Spec.K256.Test.test1_sgnt",
"Spec.K256.Test.test_secret_to_public"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid
val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_verify pk msg sgnt =
let verify : bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then begin IO.print_string "Test K256 ecdsa verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa verification: Failure :(\n"; false end
val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_sign_and_verify sk pk nonce msgHash sgnt =
let signature = ecdsa_sign_hashed_msg msgHash sk nonce in
let is_sgnt_valid =
match signature with
| Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x
| None -> false in
let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in
if verify_sgnt && is_sgnt_valid
then begin IO.print_string "Test K256 ecdsa signature and verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa signature and verification: Failure :(\n"; false end
let test_public_key_compressed (pk_raw:lbytes 64) : FStar.All.ML bool =
let pk_c = pk_compressed_from_raw pk_raw in
let pk_raw_c = pk_compressed_to_raw pk_c in
match pk_raw_c with
| Some pk_raw_c ->
let is_pk_c_valid =
for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_c pk_raw in
if not is_pk_c_valid then IO.print_string "Test K256 pk_compressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_compressed: Success!\n";
is_pk_c_valid
| None ->
begin IO.print_string "Test K256 pk_compressed (None): Failure :(\n"; false end
let test_public_key_uncompressed (pk_raw:lbytes 64) : FStar.All.ML bool =
let pk_u = pk_uncompressed_from_raw pk_raw in
let pk_raw_u = pk_uncompressed_to_raw pk_u in
match pk_raw_u with
| Some pk_raw_u ->
let is_pk_u_valid =
for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_u pk_raw in
if not is_pk_u_valid then IO.print_string "Test K256 pk_uncompressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_uncompressed: Success!\n";
is_pk_u_valid
| None ->
begin IO.print_string "Test K256 pk_uncompressed (None): Failure :(\n"; false end
#set-options "--ifuel 2" | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"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": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test: Prims.unit -> FStar.All.ML bool | [] | Spec.K256.Test.test | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit -> FStar.All.ML Prims.bool | {
"end_col": 71,
"end_line": 207,
"start_col": 34,
"start_line": 198
} |
Prims.Tot | val test1_msg:lbytes 6 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l | val test1_msg:lbytes 6
let test1_msg:lbytes 6 = | false | null | false | let l = List.Tot.map u8_from_UInt8 [0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy] in
assert_norm (List.Tot.length l == 6);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test1_msg:lbytes 6 | [] | Spec.K256.Test.test1_msg | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 6 | {
"end_col": 11,
"end_line": 35,
"start_col": 26,
"start_line": 30
} |
FStar.All.ML | val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test_verify pk msg sgnt =
let verify : bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then begin IO.print_string "Test K256 ecdsa verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa verification: Failure :(\n"; false end | val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_verify pk msg sgnt = | true | null | false | let verify:bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then
(IO.print_string "Test K256 ecdsa verification: Success!\n";
true)
else
(IO.print_string "Test K256 ecdsa verification: Failure :(\n";
false) | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Lib.ByteSequence.lbytes",
"Lib.ByteSequence.bytes",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Lib.Sequence.length",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.IntTypes.max_size_t",
"Prims.bool",
"Prims.unit",
"FStar.IO.print_string",
"Spec.K256.ecdsa_verify_sha256"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid
val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool | [] | Spec.K256.Test.test_verify | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
pk: Lib.ByteSequence.lbytes 64 ->
msg: Lib.ByteSequence.bytes{Lib.Sequence.length msg <= Lib.IntTypes.max_size_t} ->
sgnt: Lib.ByteSequence.lbytes 64
-> FStar.All.ML Prims.bool | {
"end_col": 84,
"end_line": 141,
"start_col": 29,
"start_line": 137
} |
FStar.All.ML | val test_public_key_uncompressed (pk_raw: lbytes 64) : FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test_public_key_uncompressed (pk_raw:lbytes 64) : FStar.All.ML bool =
let pk_u = pk_uncompressed_from_raw pk_raw in
let pk_raw_u = pk_uncompressed_to_raw pk_u in
match pk_raw_u with
| Some pk_raw_u ->
let is_pk_u_valid =
for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_u pk_raw in
if not is_pk_u_valid then IO.print_string "Test K256 pk_uncompressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_uncompressed: Success!\n";
is_pk_u_valid
| None ->
begin IO.print_string "Test K256 pk_uncompressed (None): Failure :(\n"; false end | val test_public_key_uncompressed (pk_raw: lbytes 64) : FStar.All.ML bool
let test_public_key_uncompressed (pk_raw: lbytes 64) : FStar.All.ML bool = | true | null | false | let pk_u = pk_uncompressed_from_raw pk_raw in
let pk_raw_u = pk_uncompressed_to_raw pk_u in
match pk_raw_u with
| Some pk_raw_u ->
let is_pk_u_valid = for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_u pk_raw in
if not is_pk_u_valid
then IO.print_string "Test K256 pk_uncompressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_uncompressed: Success!\n";
is_pk_u_valid
| None ->
IO.print_string "Test K256 pk_uncompressed (None): Failure :(\n";
false | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Lib.ByteSequence.lbytes",
"Prims.bool",
"Prims.unit",
"Prims.op_Negation",
"FStar.IO.print_string",
"Lib.Sequence.for_all2",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.nat",
"Prims.l_or",
"Prims.b2t",
"Prims.int",
"Prims.op_GreaterThanOrEqual",
"Lib.IntTypes.range",
"Lib.IntTypes.uint_v",
"Lib.RawIntTypes.uint_to_nat",
"FStar.Pervasives.Native.option",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.K256.pk_uncompressed_to_raw",
"Spec.K256.pk_uncompressed_from_raw"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid
val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_verify pk msg sgnt =
let verify : bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then begin IO.print_string "Test K256 ecdsa verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa verification: Failure :(\n"; false end
val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_sign_and_verify sk pk nonce msgHash sgnt =
let signature = ecdsa_sign_hashed_msg msgHash sk nonce in
let is_sgnt_valid =
match signature with
| Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x
| None -> false in
let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in
if verify_sgnt && is_sgnt_valid
then begin IO.print_string "Test K256 ecdsa signature and verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa signature and verification: Failure :(\n"; false end
let test_public_key_compressed (pk_raw:lbytes 64) : FStar.All.ML bool =
let pk_c = pk_compressed_from_raw pk_raw in
let pk_raw_c = pk_compressed_to_raw pk_c in
match pk_raw_c with
| Some pk_raw_c ->
let is_pk_c_valid =
for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_c pk_raw in
if not is_pk_c_valid then IO.print_string "Test K256 pk_compressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_compressed: Success!\n";
is_pk_c_valid
| None ->
begin IO.print_string "Test K256 pk_compressed (None): Failure :(\n"; false end | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test_public_key_uncompressed (pk_raw: lbytes 64) : FStar.All.ML bool | [] | Spec.K256.Test.test_public_key_uncompressed | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | pk_raw: Lib.ByteSequence.lbytes 64 -> FStar.All.ML Prims.bool | {
"end_col": 85,
"end_line": 194,
"start_col": 73,
"start_line": 182
} |
FStar.All.ML | val test_public_key_compressed (pk_raw: lbytes 64) : FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test_public_key_compressed (pk_raw:lbytes 64) : FStar.All.ML bool =
let pk_c = pk_compressed_from_raw pk_raw in
let pk_raw_c = pk_compressed_to_raw pk_c in
match pk_raw_c with
| Some pk_raw_c ->
let is_pk_c_valid =
for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_c pk_raw in
if not is_pk_c_valid then IO.print_string "Test K256 pk_compressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_compressed: Success!\n";
is_pk_c_valid
| None ->
begin IO.print_string "Test K256 pk_compressed (None): Failure :(\n"; false end | val test_public_key_compressed (pk_raw: lbytes 64) : FStar.All.ML bool
let test_public_key_compressed (pk_raw: lbytes 64) : FStar.All.ML bool = | true | null | false | let pk_c = pk_compressed_from_raw pk_raw in
let pk_raw_c = pk_compressed_to_raw pk_c in
match pk_raw_c with
| Some pk_raw_c ->
let is_pk_c_valid = for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_raw_c pk_raw in
if not is_pk_c_valid
then IO.print_string "Test K256 pk_compressed (Some): Failure :(\n"
else IO.print_string "Test K256 pk_compressed: Success!\n";
is_pk_c_valid
| None ->
IO.print_string "Test K256 pk_compressed (None): Failure :(\n";
false | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Lib.ByteSequence.lbytes",
"Prims.bool",
"Prims.unit",
"Prims.op_Negation",
"FStar.IO.print_string",
"Lib.Sequence.for_all2",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.nat",
"Prims.l_or",
"Prims.b2t",
"Prims.int",
"Prims.op_GreaterThanOrEqual",
"Lib.IntTypes.range",
"Lib.IntTypes.uint_v",
"Lib.RawIntTypes.uint_to_nat",
"FStar.Pervasives.Native.option",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.K256.pk_compressed_to_raw",
"Spec.K256.pk_compressed_from_raw"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid
val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_verify pk msg sgnt =
let verify : bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then begin IO.print_string "Test K256 ecdsa verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa verification: Failure :(\n"; false end
val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_sign_and_verify sk pk nonce msgHash sgnt =
let signature = ecdsa_sign_hashed_msg msgHash sk nonce in
let is_sgnt_valid =
match signature with
| Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x
| None -> false in
let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in
if verify_sgnt && is_sgnt_valid
then begin IO.print_string "Test K256 ecdsa signature and verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa signature and verification: Failure :(\n"; false end | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test_public_key_compressed (pk_raw: lbytes 64) : FStar.All.ML bool | [] | Spec.K256.Test.test_public_key_compressed | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | pk_raw: Lib.ByteSequence.lbytes 64 -> FStar.All.ML Prims.bool | {
"end_col": 83,
"end_line": 179,
"start_col": 71,
"start_line": 167
} |
FStar.All.ML | val test_secret_to_public (sk: lbytes 32) (pk_expected: lbytes 64) : FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid | val test_secret_to_public (sk: lbytes 32) (pk_expected: lbytes 64) : FStar.All.ML bool
let test_secret_to_public (sk: lbytes 32) (pk_expected: lbytes 64) : FStar.All.ML bool = | true | null | false | let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false
in
if is_pk_valid
then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Lib.ByteSequence.lbytes",
"Prims.bool",
"Prims.unit",
"FStar.IO.print_string",
"Lib.Sequence.for_all2",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.nat",
"Prims.l_or",
"Prims.b2t",
"Prims.int",
"Prims.op_GreaterThanOrEqual",
"Lib.IntTypes.range",
"Lib.IntTypes.uint_v",
"Lib.RawIntTypes.uint_to_nat",
"FStar.Pervasives.Native.option",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.K256.secret_to_public"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test_secret_to_public (sk: lbytes 32) (pk_expected: lbytes 64) : FStar.All.ML bool | [] | Spec.K256.Test.test_secret_to_public | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | sk: Lib.ByteSequence.lbytes 32 -> pk_expected: Lib.ByteSequence.lbytes 64 -> FStar.All.ML Prims.bool | {
"end_col": 13,
"end_line": 128,
"start_col": 86,
"start_line": 118
} |
FStar.All.ML | val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test_sign_and_verify sk pk nonce msgHash sgnt =
let signature = ecdsa_sign_hashed_msg msgHash sk nonce in
let is_sgnt_valid =
match signature with
| Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x
| None -> false in
let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in
if verify_sgnt && is_sgnt_valid
then begin IO.print_string "Test K256 ecdsa signature and verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa signature and verification: Failure :(\n"; false end | val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_sign_and_verify sk pk nonce msgHash sgnt = | true | null | false | let signature = ecdsa_sign_hashed_msg msgHash sk nonce in
let is_sgnt_valid =
match signature with
| Some x -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) sgnt x
| None -> false
in
let verify_sgnt = ecdsa_verify_hashed_msg msgHash pk sgnt in
if verify_sgnt && is_sgnt_valid
then
(IO.print_string "Test K256 ecdsa signature and verification: Success!\n";
true)
else
(IO.print_string "Test K256 ecdsa signature and verification: Failure :(\n";
false) | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"ml"
] | [
"Lib.ByteSequence.lbytes",
"Prims.op_AmpAmp",
"Prims.bool",
"Prims.unit",
"FStar.IO.print_string",
"Spec.K256.ecdsa_verify_hashed_msg",
"Lib.Sequence.for_all2",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.nat",
"Prims.l_or",
"Prims.b2t",
"Prims.int",
"Prims.op_GreaterThanOrEqual",
"Lib.IntTypes.range",
"Lib.IntTypes.uint_v",
"Lib.RawIntTypes.uint_to_nat",
"FStar.Pervasives.Native.option",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.K256.ecdsa_sign_hashed_msg"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test_secret_to_public (sk:lbytes 32) (pk_expected:lbytes 64) : FStar.All.ML bool =
let pk = secret_to_public sk in
let is_pk_valid =
match pk with
| Some pk -> for_all2 (fun a b -> uint_to_nat #U8 a = uint_to_nat #U8 b) pk_expected pk
| None -> false in
if is_pk_valid then IO.print_string "Test K256 secret_to_public: Success!\n"
else IO.print_string "Test K256 secret_to_public: Failure :(\n";
is_pk_valid
val test_verify:
pk:lbytes 64
-> msg:bytes{length msg <= max_size_t}
-> sgnt:lbytes 64 ->
FStar.All.ML bool
let test_verify pk msg sgnt =
let verify : bool = ecdsa_verify_sha256 (length msg) msg pk sgnt in
if verify
then begin IO.print_string "Test K256 ecdsa verification: Success!\n"; true end
else begin IO.print_string "Test K256 ecdsa verification: Failure :(\n"; false end
val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test_sign_and_verify:
sk:lbytes 32
-> pk:lbytes 64
-> nonce:lbytes 32
-> msgHash:lbytes 32
-> sgnt:lbytes 64 ->
FStar.All.ML bool | [] | Spec.K256.Test.test_sign_and_verify | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
sk: Lib.ByteSequence.lbytes 32 ->
pk: Lib.ByteSequence.lbytes 64 ->
nonce: Lib.ByteSequence.lbytes 32 ->
msgHash: Lib.ByteSequence.lbytes 32 ->
sgnt: Lib.ByteSequence.lbytes 64
-> FStar.All.ML Prims.bool | {
"end_col": 98,
"end_line": 164,
"start_col": 51,
"start_line": 152
} |
Prims.Tot | val test2_nonce:lbytes 32 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l | val test2_nonce:lbytes 32
let test2_nonce:lbytes 32 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy; 0x0duy; 0x07uy; 0x21uy; 0xd7uy;
0x28uy; 0x04uy; 0xbeuy; 0xfduy; 0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
]
in
assert_norm (List.Tot.length l == 32);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test2_nonce:lbytes 32 | [] | Spec.K256.Test.test2_nonce | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 32 | {
"end_col": 11,
"end_line": 89,
"start_col": 29,
"start_line": 81
} |
Prims.Tot | val test2_sk:lbytes 32 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l | val test2_sk:lbytes 32
let test2_sk:lbytes 32 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy; 0x0auy; 0x28uy; 0xacuy; 0x82uy;
0xf6uy; 0xbduy; 0xf9uy; 0x7buy; 0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
]
in
assert_norm (List.Tot.length l == 32);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2 | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test2_sk:lbytes 32 | [] | Spec.K256.Test.test2_sk | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 32 | {
"end_col": 11,
"end_line": 63,
"start_col": 26,
"start_line": 55
} |
Prims.Tot | val test2_msgHash:lbytes 32 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l | val test2_msgHash:lbytes 32
let test2_msgHash:lbytes 32 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy; 0x41uy; 0xdduy; 0xb1uy; 0x6fuy;
0xf0uy; 0xa1uy; 0x84uy; 0x2duy; 0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
]
in
assert_norm (List.Tot.length l == 32);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test2_msgHash:lbytes 32 | [] | Spec.K256.Test.test2_msgHash | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 32 | {
"end_col": 11,
"end_line": 100,
"start_col": 31,
"start_line": 92
} |
Prims.Tot | val test1_sgnt:lbytes 64 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l | val test1_sgnt:lbytes 64
let test1_sgnt:lbytes 64 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy; 0xf7uy; 0xbauy; 0x80uy; 0x5fuy;
0x0euy; 0x47uy; 0x85uy; 0x84uy; 0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy; 0x6fuy; 0xf1uy; 0x8auy; 0x52uy;
0xdcuy; 0xc0uy; 0x33uy; 0x6fuy; 0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy; 0xd6uy; 0xf6uy; 0x13uy; 0xa5uy;
0x56uy; 0xebuy; 0x31uy; 0xbauy
]
in
assert_norm (List.Tot.length l == 64);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test1_sgnt:lbytes 64 | [] | Spec.K256.Test.test1_sgnt | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 64 | {
"end_col": 11,
"end_line": 50,
"start_col": 28,
"start_line": 38
} |
Prims.Tot | val test2_sgnt:lbytes 64 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test2_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy;
0x14uy; 0x5cuy; 0x89uy; 0x61uy; 0xdbuy; 0xdfuy; 0x10uy; 0xc3uy;
0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy;
0x02uy; 0x10uy; 0x06uy; 0xb7uy; 0x83uy; 0x86uy; 0x09uy; 0x33uy;
0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy;
0xc7uy; 0x95uy; 0x5duy; 0xfbuy; 0x01uy; 0xf3uy; 0xcauy; 0x0euy
] in
assert_norm (List.Tot.length l == 64);
of_list l | val test2_sgnt:lbytes 64
let test2_sgnt:lbytes 64 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0x24uy; 0x10uy; 0x97uy; 0xefuy; 0xbfuy; 0x8buy; 0x63uy; 0xbfuy; 0x14uy; 0x5cuy; 0x89uy; 0x61uy;
0xdbuy; 0xdfuy; 0x10uy; 0xc3uy; 0x10uy; 0xefuy; 0xbbuy; 0x3buy; 0x26uy; 0x76uy; 0xbbuy; 0xc0uy;
0xf8uy; 0xb0uy; 0x85uy; 0x05uy; 0xc9uy; 0xe2uy; 0xf7uy; 0x95uy; 0x02uy; 0x10uy; 0x06uy; 0xb7uy;
0x83uy; 0x86uy; 0x09uy; 0x33uy; 0x9euy; 0x8buy; 0x41uy; 0x5auy; 0x7fuy; 0x9auy; 0xcbuy; 0x1buy;
0x66uy; 0x18uy; 0x28uy; 0x13uy; 0x1auy; 0xefuy; 0x1euy; 0xcbuy; 0xc7uy; 0x95uy; 0x5duy; 0xfbuy;
0x01uy; 0xf3uy; 0xcauy; 0x0euy
]
in
assert_norm (List.Tot.length l == 64);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test2_nonce : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x49uy; 0xa0uy; 0xd7uy; 0xb7uy; 0x86uy; 0xecuy; 0x9cuy; 0xdeuy;
0x0duy; 0x07uy; 0x21uy; 0xd7uy; 0x28uy; 0x04uy; 0xbeuy; 0xfduy;
0x06uy; 0x57uy; 0x1cuy; 0x97uy; 0x4buy; 0x19uy; 0x1euy; 0xfbuy;
0x42uy; 0xecuy; 0xf3uy; 0x22uy; 0xbauy; 0x9duy; 0xdduy; 0x9auy
] in
assert_norm (List.Tot.length l == 32);
of_list l
let test2_msgHash : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0x4buy; 0x68uy; 0x8duy; 0xf4uy; 0x0buy; 0xceuy; 0xdbuy; 0xe6uy;
0x41uy; 0xdduy; 0xb1uy; 0x6fuy; 0xf0uy; 0xa1uy; 0x84uy; 0x2duy;
0x9cuy; 0x67uy; 0xeauy; 0x1cuy; 0x3buy; 0xf6uy; 0x3fuy; 0x3euy;
0x04uy; 0x71uy; 0xbauy; 0xa6uy; 0x64uy; 0x53uy; 0x1duy; 0x1auy
] in
assert_norm (List.Tot.length l == 32);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test2_sgnt:lbytes 64 | [] | Spec.K256.Test.test2_sgnt | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 64 | {
"end_col": 11,
"end_line": 115,
"start_col": 28,
"start_line": 103
} |
Prims.Tot | val test2_pk:lbytes 64 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test2_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy;
0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy; 0x1duy; 0x82uy; 0xd4uy; 0x33uy;
0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy;
0xe9uy; 0x4buy; 0x72uy; 0x4auy; 0x55uy; 0x5buy; 0x6duy; 0x01uy;
0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy;
0x75uy; 0xc9uy; 0x23uy; 0x7buy; 0x91uy; 0x7duy; 0x42uy; 0x6fuy
] in
assert_norm (List.Tot.length l == 64);
of_list l | val test2_pk:lbytes 64
let test2_pk:lbytes 64 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0x77uy; 0x9duy; 0xd1uy; 0x97uy; 0xa5uy; 0xdfuy; 0x97uy; 0x7euy; 0xd2uy; 0xcfuy; 0x6cuy; 0xb3uy;
0x1duy; 0x82uy; 0xd4uy; 0x33uy; 0x28uy; 0xb7uy; 0x90uy; 0xdcuy; 0x6buy; 0x3buy; 0x7duy; 0x44uy;
0x37uy; 0xa4uy; 0x27uy; 0xbduy; 0x58uy; 0x47uy; 0xdfuy; 0xcduy; 0xe9uy; 0x4buy; 0x72uy; 0x4auy;
0x55uy; 0x5buy; 0x6duy; 0x01uy; 0x7buy; 0xb7uy; 0x60uy; 0x7cuy; 0x3euy; 0x32uy; 0x81uy; 0xdauy;
0xf5uy; 0xb1uy; 0x69uy; 0x9duy; 0x6euy; 0xf4uy; 0x12uy; 0x49uy; 0x75uy; 0xc9uy; 0x23uy; 0x7buy;
0x91uy; 0x7duy; 0x42uy; 0x6fuy
]
in
assert_norm (List.Tot.length l == 64);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1
let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l
let test1_msg : lbytes 6 =
let l = List.Tot.map u8_from_UInt8 [
0x31uy; 0x32uy; 0x33uy; 0x34uy; 0x30uy; 0x30uy
] in
assert_norm (List.Tot.length l == 6);
of_list l
let test1_sgnt : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0x81uy; 0x3euy; 0xf7uy; 0x9cuy; 0xceuy; 0xfauy; 0x9auy; 0x56uy;
0xf7uy; 0xbauy; 0x80uy; 0x5fuy; 0x0euy; 0x47uy; 0x85uy; 0x84uy;
0xfeuy; 0x5fuy; 0x0duy; 0xd5uy; 0xf5uy; 0x67uy; 0xbcuy; 0x09uy;
0xb5uy; 0x12uy; 0x3cuy; 0xcbuy; 0xc9uy; 0x83uy; 0x23uy; 0x65uy;
0x6fuy; 0xf1uy; 0x8auy; 0x52uy; 0xdcuy; 0xc0uy; 0x33uy; 0x6fuy;
0x7auy; 0xf6uy; 0x24uy; 0x00uy; 0xa6uy; 0xdduy; 0x9buy; 0x81uy;
0x07uy; 0x32uy; 0xbauy; 0xf1uy; 0xffuy; 0x75uy; 0x80uy; 0x00uy;
0xd6uy; 0xf6uy; 0x13uy; 0xa5uy; 0x56uy; 0xebuy; 0x31uy; 0xbauy
] in
assert_norm (List.Tot.length l == 64);
of_list l
/// Test 2
let test2_sk : lbytes 32 =
let l = List.Tot.map u8_from_UInt8 [
0xebuy; 0xb2uy; 0xc0uy; 0x82uy; 0xfduy; 0x77uy; 0x27uy; 0x89uy;
0x0auy; 0x28uy; 0xacuy; 0x82uy; 0xf6uy; 0xbduy; 0xf9uy; 0x7buy;
0xaduy; 0x8duy; 0xe9uy; 0xf5uy; 0xd7uy; 0xc9uy; 0x02uy; 0x86uy;
0x92uy; 0xdeuy; 0x1auy; 0x25uy; 0x5cuy; 0xaduy; 0x3euy; 0x0fuy
] in
assert_norm (List.Tot.length l == 32);
of_list l | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test2_pk:lbytes 64 | [] | Spec.K256.Test.test2_pk | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 64 | {
"end_col": 11,
"end_line": 78,
"start_col": 26,
"start_line": 66
} |
Prims.Tot | val test1_pk:lbytes 64 | [
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.K256",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let test1_pk : lbytes 64 =
let l = List.Tot.map u8_from_UInt8 [
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy;
0xf2uy; 0x11uy; 0x89uy; 0xd0uy; 0x76uy; 0x60uy; 0x82uy; 0xfcuy;
0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy;
0xf0uy; 0xc9uy; 0xd7uy; 0x5buy; 0xfbuy; 0xa7uy; 0xb3uy; 0x1auy;
0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy;
0xb1uy; 0xbauy; 0xdauy; 0xa0uy; 0xb2uy; 0x18uy; 0x32uy; 0xe9uy
] in
assert_norm (List.Tot.length l == 64);
of_list l | val test1_pk:lbytes 64
let test1_pk:lbytes 64 = | false | null | false | let l =
List.Tot.map u8_from_UInt8
[
0xb8uy; 0x38uy; 0xffuy; 0x44uy; 0xe5uy; 0xbcuy; 0x17uy; 0x7buy; 0xf2uy; 0x11uy; 0x89uy; 0xd0uy;
0x76uy; 0x60uy; 0x82uy; 0xfcuy; 0x9duy; 0x84uy; 0x32uy; 0x26uy; 0x88uy; 0x7fuy; 0xc9uy; 0x76uy;
0x03uy; 0x71uy; 0x10uy; 0x0buy; 0x7euy; 0xe2uy; 0x0auy; 0x6fuy; 0xf0uy; 0xc9uy; 0xd7uy; 0x5buy;
0xfbuy; 0xa7uy; 0xb3uy; 0x1auy; 0x6buy; 0xcauy; 0x19uy; 0x74uy; 0x49uy; 0x6euy; 0xebuy; 0x56uy;
0xdeuy; 0x35uy; 0x70uy; 0x71uy; 0x95uy; 0x5duy; 0x83uy; 0xc4uy; 0xb1uy; 0xbauy; 0xdauy; 0xa0uy;
0xb2uy; 0x18uy; 0x32uy; 0xe9uy
]
in
assert_norm (List.Tot.length l == 64);
of_list l | {
"checked_file": "Spec.K256.Test.fst.checked",
"dependencies": [
"Spec.K256.fst.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt8.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.List.Tot.fst.checked",
"FStar.IO.fst.checked",
"FStar.All.fst.checked"
],
"interface_file": false,
"source_file": "Spec.K256.Test.fst"
} | [
"total"
] | [
"Lib.Sequence.of_list",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"FStar.List.Tot.Base.length",
"Prims.list",
"FStar.List.Tot.Base.map",
"FStar.UInt8.t",
"Lib.RawIntTypes.u8_from_UInt8",
"Prims.Cons",
"FStar.UInt8.__uint_to_t",
"Prims.Nil"
] | [] | module Spec.K256.Test
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
open Spec.K256
#set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
/// Test 1 | false | false | Spec.K256.Test.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val test1_pk:lbytes 64 | [] | Spec.K256.Test.test1_pk | {
"file_name": "specs/tests/Spec.K256.Test.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 64 | {
"end_col": 11,
"end_line": 27,
"start_col": 26,
"start_line": 15
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let natN = Vale.Def.Words_s.natN | let natN = | false | null | false | Vale.Def.Words_s.natN | {
"checked_file": "Vale.Def.TypesNative_s.fst.checked",
"dependencies": [
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": false,
"source_file": "Vale.Def.TypesNative_s.fst"
} | [
"total"
] | [
"Vale.Def.Words_s.natN"
] | [] | module Vale.Def.TypesNative_s
open FStar.Mul | false | true | Vale.Def.TypesNative_s.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val natN : n: Prims.nat -> Type0 | [] | Vale.Def.TypesNative_s.natN | {
"file_name": "vale/specs/defs/Vale.Def.TypesNative_s.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | n: Prims.nat -> Type0 | {
"end_col": 39,
"end_line": 4,
"start_col": 18,
"start_line": 4
} |
|
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let pow2_norm = Vale.Def.Words_s.pow2_norm | let pow2_norm = | false | null | false | Vale.Def.Words_s.pow2_norm | {
"checked_file": "Vale.Def.TypesNative_s.fst.checked",
"dependencies": [
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.Types_s.fst.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": false,
"source_file": "Vale.Def.TypesNative_s.fst"
} | [
"total"
] | [
"Vale.Def.Words_s.pow2_norm"
] | [] | module Vale.Def.TypesNative_s
open FStar.Mul | false | true | Vale.Def.TypesNative_s.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val pow2_norm : n: Prims.nat -> Prims.pos | [] | Vale.Def.TypesNative_s.pow2_norm | {
"file_name": "vale/specs/defs/Vale.Def.TypesNative_s.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | n: Prims.nat -> Prims.pos | {
"end_col": 49,
"end_line": 5,
"start_col": 23,
"start_line": 5
} |
|
Prims.Tot | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let op_Plus_At #f e1 e2 = fadd #f e1 e2 | let op_Plus_At #f e1 e2 = | false | null | false | fadd #f e1 e2 | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Spec.GaloisField.fadd"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e) | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val op_Plus_At : e1: Spec.GaloisField.felem f -> e2: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | [] | Spec.GaloisField.op_Plus_At | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | e1: Spec.GaloisField.felem f -> e2: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 39,
"end_line": 34,
"start_col": 26,
"start_line": 34
} |
|
Prims.Tot | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let op_Star_At #f e1 e2 = fmul #f e1 e2 | let op_Star_At #f e1 e2 = | false | null | false | fmul #f e1 e2 | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Spec.GaloisField.fmul"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val op_Star_At : e1: Spec.GaloisField.felem f -> e2: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | [] | Spec.GaloisField.op_Star_At | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | e1: Spec.GaloisField.felem f -> e2: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 39,
"end_line": 51,
"start_col": 26,
"start_line": 51
} |
|
Prims.Tot | val fadd (#f: field) (a b: felem f) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b | val fadd (#f: field) (a b: felem f) : felem f
let fadd (#f: field) (a b: felem f) : felem f = | false | null | false | a ^. b | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Lib.IntTypes.op_Hat_Dot",
"Spec.GaloisField.__proj__GF__item__t",
"Lib.IntTypes.SEC"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e) | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fadd (#f: field) (a b: felem f) : felem f | [] | Spec.GaloisField.fadd | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Spec.GaloisField.felem f -> b: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 62,
"end_line": 33,
"start_col": 56,
"start_line": 33
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let op_Star_Star_At #f e1 e2 = fexp #f e1 e2 | let op_Star_Star_At #f e1 e2 = | false | null | false | fexp #f e1 e2 | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"Spec.GaloisField.fexp"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p
let op_Star_At #f e1 e2 = fmul #f e1 e2
val get_ith_bit: #f:field -> x:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{v r == v x / pow2 (bits f.t - 1 - i) % 2})
let get_ith_bit #f x i =
logand_mask (x >>. size (bits f.t - 1 - i)) one 1;
(x >>. size (bits f.t - 1 - i)) &. one
val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)})
let mask_add #f x y res i =
logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one)
val mask_shift_right_mod: #f:field -> y:felem f ->
Tot (r:felem f{r == (if v (get_ith_bit y (bits f.t - 1)) = 1 then (y >>. 1ul) `fadd` f.irred else (y >>. 1ul))})
let mask_shift_right_mod #f y =
logxor_lemma (y >>. 1ul) zero;
(y >>. 1ul) `fadd` (f.irred &. eq_mask #f.t (get_ith_bit y (bits f.t - 1)) one)
val fmul_be_f: #f:field -> x:felem f -> i:nat{i < bits f.t} -> res_y:tuple2 (felem f) (felem f) -> felem f & felem f
let fmul_be_f #f x i (res, y) =
let res = mask_add x y res i in
let y = mask_shift_right_mod y in
(res, y)
let fmul_be (#f:field) (x:felem f) (y:felem f) : felem f =
let (res, y) = repeati (bits f.t) (fmul_be_f x) (zero, y) in
res
val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n)
let rec fexp #f a x =
if x = 1 then a else
if x = 2 then fmul #f a a else
let r = fexp #f a (x / 2) in
let r' = fmul #f r r in
if (x % 2) = 0 then r' | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val op_Star_Star_At : e1: Spec.GaloisField.felem f -> e2: n: Prims.nat{n >= 1} -> Spec.GaloisField.felem f | [] | Spec.GaloisField.op_Star_Star_At | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | e1: Spec.GaloisField.felem f -> e2: n: Prims.nat{n >= 1} -> Spec.GaloisField.felem f | {
"end_col": 44,
"end_line": 91,
"start_col": 31,
"start_line": 91
} |
|
Prims.Tot | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let gf t irred = GF t irred | let gf t irred = | false | null | false | GF t irred | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Lib.IntTypes.inttype",
"Prims.l_and",
"Prims.b2t",
"Lib.IntTypes.unsigned",
"Prims.op_disEquality",
"Lib.IntTypes.U1",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.SEC",
"Spec.GaloisField.GF",
"Spec.GaloisField.field"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val gf : t: Lib.IntTypes.inttype{Lib.IntTypes.unsigned t /\ t <> Lib.IntTypes.U1} ->
irred: Lib.IntTypes.uint_t t Lib.IntTypes.SEC
-> Spec.GaloisField.field | [] | Spec.GaloisField.gf | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
t: Lib.IntTypes.inttype{Lib.IntTypes.unsigned t /\ t <> Lib.IntTypes.U1} ->
irred: Lib.IntTypes.uint_t t Lib.IntTypes.SEC
-> Spec.GaloisField.field | {
"end_col": 27,
"end_line": 15,
"start_col": 17,
"start_line": 15
} |
|
Prims.Tot | val to_felem (#f: field) (n: nat{n <= maxint f.t}) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n | val to_felem (#f: field) (n: nat{n <= maxint f.t}) : felem f
let to_felem (#f: field) (n: nat{n <= maxint f.t}) : felem f = | false | null | false | uint #f.t #SEC n | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.maxint",
"Spec.GaloisField.__proj__GF__item__t",
"Lib.IntTypes.uint",
"Lib.IntTypes.SEC",
"Spec.GaloisField.felem"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val to_felem (#f: field) (n: nat{n <= maxint f.t}) : felem f | [] | Spec.GaloisField.to_felem | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | n: Prims.nat{n <= Lib.IntTypes.maxint (GF?.t f)} -> Spec.GaloisField.felem f | {
"end_col": 77,
"end_line": 17,
"start_col": 61,
"start_line": 17
} |
Prims.Tot | val from_felem (#f: field) (e: felem f) : n: nat{n <= maxint f.t} | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e | val from_felem (#f: field) (e: felem f) : n: nat{n <= maxint f.t}
let from_felem (#f: field) (e: felem f) : n: nat{n <= maxint f.t} = | false | null | false | uint_v #f.t #SEC e | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Lib.IntTypes.uint_v",
"Spec.GaloisField.__proj__GF__item__t",
"Lib.IntTypes.SEC",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Lib.IntTypes.maxint"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val from_felem (#f: field) (e: felem f) : n: nat{n <= maxint f.t} | [] | Spec.GaloisField.from_felem | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | e: Spec.GaloisField.felem f -> n: Prims.nat{n <= Lib.IntTypes.maxint (GF?.t f)} | {
"end_col": 83,
"end_line": 18,
"start_col": 65,
"start_line": 18
} |
Prims.Tot | val zero (#f: field) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let zero (#f:field) : felem f = to_felem 0 | val zero (#f: field) : felem f
let zero (#f: field) : felem f = | false | null | false | to_felem 0 | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.to_felem",
"Spec.GaloisField.felem"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val zero (#f: field) : felem f | [] | Spec.GaloisField.zero | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Spec.GaloisField.felem f | {
"end_col": 42,
"end_line": 20,
"start_col": 32,
"start_line": 20
} |
Prims.Tot | val one (#f: field) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let one (#f:field) : felem f = to_felem 1 | val one (#f: field) : felem f
let one (#f: field) : felem f = | false | null | false | to_felem 1 | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.to_felem",
"Spec.GaloisField.felem"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val one (#f: field) : felem f | [] | Spec.GaloisField.one | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Spec.GaloisField.felem f | {
"end_col": 41,
"end_line": 21,
"start_col": 31,
"start_line": 21
} |
Prims.Tot | val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n) | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec fexp #f a x =
if x = 1 then a else
if x = 2 then fmul #f a a else
let r = fexp #f a (x / 2) in
let r' = fmul #f r r in
if (x % 2) = 0 then r'
else fmul #f a r' | val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n)
let rec fexp #f a x = | false | null | false | if x = 1
then a
else
if x = 2
then fmul #f a a
else
let r = fexp #f a (x / 2) in
let r' = fmul #f r r in
if (x % 2) = 0 then r' else fmul #f a r' | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total",
""
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"Prims.op_Equality",
"Prims.int",
"Prims.bool",
"Spec.GaloisField.fmul",
"Prims.op_Modulus",
"Spec.GaloisField.fexp",
"Prims.op_Division"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p
let op_Star_At #f e1 e2 = fmul #f e1 e2
val get_ith_bit: #f:field -> x:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{v r == v x / pow2 (bits f.t - 1 - i) % 2})
let get_ith_bit #f x i =
logand_mask (x >>. size (bits f.t - 1 - i)) one 1;
(x >>. size (bits f.t - 1 - i)) &. one
val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)})
let mask_add #f x y res i =
logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one)
val mask_shift_right_mod: #f:field -> y:felem f ->
Tot (r:felem f{r == (if v (get_ith_bit y (bits f.t - 1)) = 1 then (y >>. 1ul) `fadd` f.irred else (y >>. 1ul))})
let mask_shift_right_mod #f y =
logxor_lemma (y >>. 1ul) zero;
(y >>. 1ul) `fadd` (f.irred &. eq_mask #f.t (get_ith_bit y (bits f.t - 1)) one)
val fmul_be_f: #f:field -> x:felem f -> i:nat{i < bits f.t} -> res_y:tuple2 (felem f) (felem f) -> felem f & felem f
let fmul_be_f #f x i (res, y) =
let res = mask_add x y res i in
let y = mask_shift_right_mod y in
(res, y)
let fmul_be (#f:field) (x:felem f) (y:felem f) : felem f =
let (res, y) = repeati (bits f.t) (fmul_be_f x) (zero, y) in
res
val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n) | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n) | [
"recursion"
] | Spec.GaloisField.fexp | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Spec.GaloisField.felem f -> n: Prims.nat{n >= 1} -> Prims.Tot (Spec.GaloisField.felem f) | {
"end_col": 19,
"end_line": 90,
"start_col": 2,
"start_line": 85
} |
Prims.Tot | val fmul_be (#f: field) (x y: felem f) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let fmul_be (#f:field) (x:felem f) (y:felem f) : felem f =
let (res, y) = repeati (bits f.t) (fmul_be_f x) (zero, y) in
res | val fmul_be (#f: field) (x y: felem f) : felem f
let fmul_be (#f: field) (x y: felem f) : felem f = | false | null | false | let res, y = repeati (bits f.t) (fmul_be_f x) (zero, y) in
res | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"FStar.Pervasives.Native.tuple2",
"Lib.LoopCombinators.repeati",
"Lib.IntTypes.bits",
"Spec.GaloisField.__proj__GF__item__t",
"Spec.GaloisField.fmul_be_f",
"FStar.Pervasives.Native.Mktuple2",
"Spec.GaloisField.zero"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p
let op_Star_At #f e1 e2 = fmul #f e1 e2
val get_ith_bit: #f:field -> x:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{v r == v x / pow2 (bits f.t - 1 - i) % 2})
let get_ith_bit #f x i =
logand_mask (x >>. size (bits f.t - 1 - i)) one 1;
(x >>. size (bits f.t - 1 - i)) &. one
val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)})
let mask_add #f x y res i =
logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one)
val mask_shift_right_mod: #f:field -> y:felem f ->
Tot (r:felem f{r == (if v (get_ith_bit y (bits f.t - 1)) = 1 then (y >>. 1ul) `fadd` f.irred else (y >>. 1ul))})
let mask_shift_right_mod #f y =
logxor_lemma (y >>. 1ul) zero;
(y >>. 1ul) `fadd` (f.irred &. eq_mask #f.t (get_ith_bit y (bits f.t - 1)) one)
val fmul_be_f: #f:field -> x:felem f -> i:nat{i < bits f.t} -> res_y:tuple2 (felem f) (felem f) -> felem f & felem f
let fmul_be_f #f x i (res, y) =
let res = mask_add x y res i in
let y = mask_shift_right_mod y in
(res, y) | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fmul_be (#f: field) (x y: felem f) : felem f | [] | Spec.GaloisField.fmul_be | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | x: Spec.GaloisField.felem f -> y: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 5,
"end_line": 81,
"start_col": 58,
"start_line": 79
} |
Prims.Tot | val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)}) | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mask_add #f x y res i =
logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one) | val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)})
let mask_add #f x y res i = | false | null | false | logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one) | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.bits",
"Spec.GaloisField.__proj__GF__item__t",
"Spec.GaloisField.fadd",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.SEC",
"Lib.IntTypes.eq_mask",
"Spec.GaloisField.get_ith_bit",
"Spec.GaloisField.one",
"Prims.unit",
"Lib.IntTypes.logxor_lemma",
"Spec.GaloisField.zero",
"Prims.eq2",
"Prims.op_Equality",
"Prims.int",
"Lib.IntTypes.v",
"Prims.bool"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p
let op_Star_At #f e1 e2 = fmul #f e1 e2
val get_ith_bit: #f:field -> x:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{v r == v x / pow2 (bits f.t - 1 - i) % 2})
let get_ith_bit #f x i =
logand_mask (x >>. size (bits f.t - 1 - i)) one 1;
(x >>. size (bits f.t - 1 - i)) &. one
val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)}) | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)}) | [] | Spec.GaloisField.mask_add | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
x: Spec.GaloisField.felem f ->
y: Spec.GaloisField.felem f ->
res: Spec.GaloisField.felem f ->
i: Prims.nat{i < Lib.IntTypes.bits (GF?.t f)}
-> r:
Spec.GaloisField.felem f
{ r ==
(match Lib.IntTypes.v (Spec.GaloisField.get_ith_bit x i) = 1 with
| true -> Spec.GaloisField.fadd res y
| _ -> res) } | {
"end_col": 54,
"end_line": 63,
"start_col": 2,
"start_line": 62
} |
Prims.Tot | val reverse (#t: inttype{unsigned t}) (a: uint_t t SEC) : uint_t t SEC | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0) | val reverse (#t: inttype{unsigned t}) (a: uint_t t SEC) : uint_t t SEC
let reverse (#t: inttype{unsigned t}) (a: uint_t t SEC) : uint_t t SEC = | false | null | false | repeati (bits t)
(fun i u -> u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i))))
(uint #t #SEC 0) | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Lib.IntTypes.inttype",
"Prims.b2t",
"Lib.IntTypes.unsigned",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.SEC",
"Lib.LoopCombinators.repeati",
"Lib.IntTypes.int_t",
"Lib.IntTypes.bits",
"Prims.nat",
"Prims.op_LessThan",
"Lib.IntTypes.op_Bar_Dot",
"Lib.IntTypes.op_Less_Less_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.size",
"Lib.IntTypes.uint",
"Prims.op_Subtraction"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val reverse (#t: inttype{unsigned t}) (a: uint_t t SEC) : uint_t t SEC | [] | Spec.GaloisField.reverse | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Lib.IntTypes.uint_t t Lib.IntTypes.SEC -> Lib.IntTypes.uint_t t Lib.IntTypes.SEC | {
"end_col": 91,
"end_line": 28,
"start_col": 2,
"start_line": 27
} |
Prims.Tot | val finv (#f: field) (a: felem f) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let finv (#f:field) (a:felem f) : felem f =
fexp #f a (maxint f.t - 1) | val finv (#f: field) (a: felem f) : felem f
let finv (#f: field) (a: felem f) : felem f = | false | null | false | fexp #f a (maxint f.t - 1) | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Spec.GaloisField.fexp",
"Prims.op_Subtraction",
"Lib.IntTypes.maxint",
"Spec.GaloisField.__proj__GF__item__t"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2
let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p
let op_Star_At #f e1 e2 = fmul #f e1 e2
val get_ith_bit: #f:field -> x:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{v r == v x / pow2 (bits f.t - 1 - i) % 2})
let get_ith_bit #f x i =
logand_mask (x >>. size (bits f.t - 1 - i)) one 1;
(x >>. size (bits f.t - 1 - i)) &. one
val mask_add: #f:field -> x:felem f -> y:felem f -> res:felem f -> i:nat{i < bits f.t} ->
Tot (r:felem f{r == (if v (get_ith_bit x i) = 1 then res `fadd` y else res)})
let mask_add #f x y res i =
logxor_lemma res zero;
res `fadd` (y &. eq_mask #f.t (get_ith_bit x i) one)
val mask_shift_right_mod: #f:field -> y:felem f ->
Tot (r:felem f{r == (if v (get_ith_bit y (bits f.t - 1)) = 1 then (y >>. 1ul) `fadd` f.irred else (y >>. 1ul))})
let mask_shift_right_mod #f y =
logxor_lemma (y >>. 1ul) zero;
(y >>. 1ul) `fadd` (f.irred &. eq_mask #f.t (get_ith_bit y (bits f.t - 1)) one)
val fmul_be_f: #f:field -> x:felem f -> i:nat{i < bits f.t} -> res_y:tuple2 (felem f) (felem f) -> felem f & felem f
let fmul_be_f #f x i (res, y) =
let res = mask_add x y res i in
let y = mask_shift_right_mod y in
(res, y)
let fmul_be (#f:field) (x:felem f) (y:felem f) : felem f =
let (res, y) = repeati (bits f.t) (fmul_be_f x) (zero, y) in
res
val fexp: #f:field -> a:felem f -> n:nat{n >= 1} -> Tot (felem f) (decreases n)
let rec fexp #f a x =
if x = 1 then a else
if x = 2 then fmul #f a a else
let r = fexp #f a (x / 2) in
let r' = fmul #f r r in
if (x % 2) = 0 then r'
else fmul #f a r'
let op_Star_Star_At #f e1 e2 = fexp #f e1 e2 | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val finv (#f: field) (a: felem f) : felem f | [] | Spec.GaloisField.finv | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 28,
"end_line": 94,
"start_col": 2,
"start_line": 94
} |
Prims.Tot | val fmul (#f: field) (a b: felem f) : felem f | [
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.LoopCombinators",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let fmul (#f:field) (a:felem f) (b:felem f) : felem f =
let one = one #f in
let zero = zero #f in
let (p,a,b) =
repeati (bits f.t - 1) (fun i (p,a,b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p,a,b)) (zero,a,b) in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p | val fmul (#f: field) (a b: felem f) : felem f
let fmul (#f: field) (a b: felem f) : felem f = | false | null | false | let one = one #f in
let zero = zero #f in
let p, a, b =
repeati (bits f.t - 1)
(fun i (p, a, b) ->
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
let carry_mask = eq_mask #f.t (a >>. size (bits f.t - 1)) one in
let a = a <<. size 1 in
let a = a ^. (carry_mask &. f.irred) in
let b = b >>. size 1 in
(p, a, b))
(zero, a, b)
in
let b0 = eq_mask #f.t (b &. one) one in
let p = p ^. (b0 &. a) in
p | {
"checked_file": "Spec.GaloisField.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.LoopCombinators.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "Spec.GaloisField.fst"
} | [
"total"
] | [
"Spec.GaloisField.field",
"Spec.GaloisField.felem",
"Lib.IntTypes.int_t",
"Spec.GaloisField.__proj__GF__item__t",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Hat_Dot",
"Lib.IntTypes.op_Amp_Dot",
"Lib.IntTypes.eq_mask",
"FStar.Pervasives.Native.tuple3",
"Lib.LoopCombinators.repeati",
"Prims.op_Subtraction",
"Lib.IntTypes.bits",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Pervasives.Native.Mktuple3",
"Lib.IntTypes.op_Greater_Greater_Dot",
"Lib.IntTypes.size",
"Spec.GaloisField.__proj__GF__item__irred",
"Lib.IntTypes.op_Less_Less_Dot",
"Spec.GaloisField.zero",
"Spec.GaloisField.one"
] | [] | module Spec.GaloisField
open Lib.IntTypes
open Lib.Sequence
open Lib.LoopCombinators
open Lib.ByteSequence
(* We represent GF(2^n) by uint_t along with some irreducible polynomial also of type uint_t *)
(* Consequently this module is specialized for GF(8/16/32/64/128) but can be generalized to other sizes if needed *)
#set-options "--z3rlimit 30 --max_fuel 0 --max_ifuel 0"
noeq type field =
| GF: t:inttype{unsigned t /\ t <> U1} -> irred: uint_t t SEC -> field
let gf t irred = GF t irred
type felem (f:field) = uint_t f.t SEC
let to_felem (#f:field) (n:nat{n <= maxint f.t}) : felem f = uint #f.t #SEC n
let from_felem (#f:field) (e:felem f) : n:nat{n <= maxint f.t} = uint_v #f.t #SEC e
let zero (#f:field) : felem f = to_felem 0
let one (#f:field) : felem f = to_felem 1
let load_felem_be (#f:field) (b:lbytes (numbytes f.t)) : felem f = uint_from_bytes_be #f.t #SEC b
let store_felem_be (#f:field) (e:felem f): lbytes (numbytes f.t) = uint_to_bytes_be #f.t #SEC e
let reverse (#t:inttype{unsigned t}) (a:uint_t t SEC) : uint_t t SEC =
repeati (bits t) (fun i u ->
u |. (((a >>. size i) &. uint #t #SEC 1) <<. (size (bits t - 1 - i)))) (uint #t #SEC 0)
let load_felem_le (#f:field) (b:lbytes (numbytes f.t)) : felem f = reverse #f.t (load_felem_be #f b)
let store_felem_le (#f:field) (e:felem f) : lbytes (numbytes f.t) = store_felem_be #f (reverse #f.t e)
let fadd (#f:field) (a:felem f) (b:felem f) : felem f = a ^. b
let op_Plus_At #f e1 e2 = fadd #f e1 e2 | false | false | Spec.GaloisField.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 30,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fmul (#f: field) (a b: felem f) : felem f | [] | Spec.GaloisField.fmul | {
"file_name": "specs/Spec.GaloisField.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | a: Spec.GaloisField.felem f -> b: Spec.GaloisField.felem f -> Spec.GaloisField.felem f | {
"end_col": 3,
"end_line": 50,
"start_col": 55,
"start_line": 36
} |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.