From ce583d76bdb8f15148fc4222d8bdec096547682a Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Fri, 1 Feb 2019 18:50:00 -0500 Subject: Use Preconditions: Postconditions:, rather than /\ and -> --- p224_64.c | 109 +++++++++++++++++++++++++++++++++++++++++--------------------- 1 file changed, 73 insertions(+), 36 deletions(-) (limited to 'p224_64.c') diff --git a/p224_64.c b/p224_64.c index 540ddb245..0dd8edb1c 100644 --- a/p224_64.c +++ b/p224_64.c @@ -20,8 +20,10 @@ typedef unsigned __int128 fiat_p224_uint128; /* * The function fiat_p224_addcarryx_u64 is an addition with carry. - * out1 = (arg1 + arg2 + arg3) mod 2^64 - * ∧ out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ + * Postconditions: + * out1 = (arg1 + arg2 + arg3) mod 2^64 + * out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] @@ -40,8 +42,10 @@ static void fiat_p224_addcarryx_u64(uint64_t* out1, fiat_p224_uint1* out2, fiat_ /* * The function fiat_p224_subborrowx_u64 is a subtraction with borrow. - * out1 = (-arg1 + arg2 + -arg3) mod 2^64 - * ∧ out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ + * Postconditions: + * out1 = (-arg1 + arg2 + -arg3) mod 2^64 + * out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] @@ -60,8 +64,10 @@ static void fiat_p224_subborrowx_u64(uint64_t* out1, fiat_p224_uint1* out2, fiat /* * The function fiat_p224_mulx_u64 is a multiplication, returning the full double-width result. - * out1 = (arg1 * arg2) mod 2^64 - * ∧ out2 = ⌊arg1 * arg2 / 2^64⌋ + * Postconditions: + * out1 = (arg1 * arg2) mod 2^64 + * out2 = ⌊arg1 * arg2 / 2^64⌋ + * * Input Bounds: * arg1: [0x0 ~> 0xffffffffffffffff] * arg2: [0x0 ~> 0xffffffffffffffff] @@ -79,7 +85,9 @@ static void fiat_p224_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, ui /* * The function fiat_p224_cmovznz_u64 is a single-word conditional move. - * out1 = (if arg1 = 0 then arg2 else arg3) + * Postconditions: + * out1 = (if arg1 = 0 then arg2 else arg3) + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffffffffffff] @@ -96,10 +104,13 @@ static void fiat_p224_cmovznz_u64(uint64_t* out1, fiat_p224_uint1 arg1, uint64_t /* * The function fiat_p224_mul multiplies two field elements in the Montgomery domain. - * 0 ≤ eval arg1 < m → - * 0 ≤ eval arg2 < m → - * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * 0 ≤ eval arg2 < m + * Postconditions: + * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] @@ -439,9 +450,12 @@ static void fiat_p224_mul(uint64_t out1[4], const uint64_t arg1[4], const uint64 /* * The function fiat_p224_square squares a field element in the Montgomery domain. - * 0 ≤ eval arg1 < m → - * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: @@ -780,10 +794,13 @@ static void fiat_p224_square(uint64_t out1[4], const uint64_t arg1[4]) { /* * The function fiat_p224_add adds two field elements in the Montgomery domain. - * 0 ≤ eval arg1 < m → - * 0 ≤ eval arg2 < m → - * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * 0 ≤ eval arg2 < m + * Postconditions: + * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] @@ -834,10 +851,13 @@ static void fiat_p224_add(uint64_t out1[4], const uint64_t arg1[4], const uint64 /* * The function fiat_p224_sub subtracts two field elements in the Montgomery domain. - * 0 ≤ eval arg1 < m → - * 0 ≤ eval arg2 < m → - * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * 0 ≤ eval arg2 < m + * Postconditions: + * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] @@ -879,9 +899,12 @@ static void fiat_p224_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64 /* * The function fiat_p224_opp negates a field element in the Montgomery domain. - * 0 ≤ eval arg1 < m → - * eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: @@ -922,9 +945,12 @@ static void fiat_p224_opp(uint64_t out1[4], const uint64_t arg1[4]) { /* * The function fiat_p224_from_montgomery translates a field element out of the Montgomery domain. - * 0 ≤ eval arg1 < m → - * eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: @@ -1143,8 +1169,11 @@ static void fiat_p224_from_montgomery(uint64_t out1[4], const uint64_t arg1[4]) /* * The function fiat_p224_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. - * 0 ≤ eval arg1 < m → - * out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0 + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0 + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] * Output Bounds: @@ -1157,7 +1186,9 @@ static void fiat_p224_nonzero(uint64_t* out1, const uint64_t arg1[4]) { /* * The function fiat_p224_selectznz is a multi-limb conditional select. - * eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) + * Postconditions: + * eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] @@ -1182,8 +1213,11 @@ static void fiat_p224_selectznz(uint64_t out1[4], fiat_p224_uint1 arg1, const ui /* * The function fiat_p224_to_bytes serializes a field element in the Montgomery domain to bytes in little-endian order. - * 0 ≤ eval arg1 < m → - * out1 = map (λ x, ⌊(eval arg1 mod m) mod 2^(8 * (x + 1)) / 2^(8 * x)⌋) [0..31] + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31] + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -1282,9 +1316,12 @@ static void fiat_p224_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) { /* * The function fiat_p224_from_bytes deserializes a field element in the Montgomery domain from bytes in little-endian order. - * 0 ≤ bytes_eval arg1 < m → - * eval out1 mod m = bytes_eval arg1 mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ bytes_eval arg1 < m + * Postconditions: + * eval out1 mod m = bytes_eval arg1 mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0], [0x0 ~> 0x0]] * Output Bounds: -- cgit v1.2.3