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 -> --- p256_32.c | 109 +++++++++++++++++++++++++++++++++++++++++--------------------- 1 file changed, 73 insertions(+), 36 deletions(-) (limited to 'p256_32.c') diff --git a/p256_32.c b/p256_32.c index b4742b2dd..010d78a14 100644 --- a/p256_32.c +++ b/p256_32.c @@ -18,8 +18,10 @@ typedef signed char fiat_p256_int1; /* * The function fiat_p256_addcarryx_u32 is an addition with carry. - * out1 = (arg1 + arg2 + arg3) mod 2^32 - * ∧ out2 = ⌊(arg1 + arg2 + arg3) / 2^32⌋ + * Postconditions: + * out1 = (arg1 + arg2 + arg3) mod 2^32 + * out2 = ⌊(arg1 + arg2 + arg3) / 2^32⌋ + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffff] @@ -38,8 +40,10 @@ static void fiat_p256_addcarryx_u32(uint32_t* out1, fiat_p256_uint1* out2, fiat_ /* * The function fiat_p256_subborrowx_u32 is a subtraction with borrow. - * out1 = (-arg1 + arg2 + -arg3) mod 2^32 - * ∧ out2 = -⌊(-arg1 + arg2 + -arg3) / 2^32⌋ + * Postconditions: + * out1 = (-arg1 + arg2 + -arg3) mod 2^32 + * out2 = -⌊(-arg1 + arg2 + -arg3) / 2^32⌋ + * * Input Bounds: * arg1: [0x0 ~> 0x1] * arg2: [0x0 ~> 0xffffffff] @@ -58,8 +62,10 @@ static void fiat_p256_subborrowx_u32(uint32_t* out1, fiat_p256_uint1* out2, fiat /* * The function fiat_p256_mulx_u32 is a multiplication, returning the full double-width result. - * out1 = (arg1 * arg2) mod 2^32 - * ∧ out2 = ⌊arg1 * arg2 / 2^32⌋ + * Postconditions: + * out1 = (arg1 * arg2) mod 2^32 + * out2 = ⌊arg1 * arg2 / 2^32⌋ + * * Input Bounds: * arg1: [0x0 ~> 0xffffffff] * arg2: [0x0 ~> 0xffffffff] @@ -77,7 +83,9 @@ static void fiat_p256_mulx_u32(uint32_t* out1, uint32_t* out2, uint32_t arg1, ui /* * The function fiat_p256_cmovznz_u32 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 ~> 0xffffffff] @@ -94,10 +102,13 @@ static void fiat_p256_cmovznz_u32(uint32_t* out1, fiat_p256_uint1 arg1, uint32_t /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * arg2: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] @@ -1149,9 +1160,12 @@ static void fiat_p256_mul(uint32_t out1[8], const uint32_t arg1[8], const uint32 /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -2202,10 +2216,13 @@ static void fiat_p256_square(uint32_t out1[8], const uint32_t arg1[8]) { /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * arg2: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] @@ -2292,10 +2309,13 @@ static void fiat_p256_add(uint32_t out1[8], const uint32_t arg1[8], const uint32 /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * arg2: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] @@ -2365,9 +2385,12 @@ static void fiat_p256_sub(uint32_t out1[8], const uint32_t arg1[8], const uint32 /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -2436,9 +2459,12 @@ static void fiat_p256_opp(uint32_t out1[8], const uint32_t arg1[8]) { /* * The function fiat_p256_from_montgomery translates a field element out of the Montgomery domain. - * 0 ≤ eval arg1 < m → - * eval out1 mod m = (eval arg1 * ((2^32)⁻¹ mod m)^8) mod m - * ∧ 0 ≤ eval out1 < m + * Preconditions: + * 0 ≤ eval arg1 < m + * Postconditions: + * eval out1 mod m = (eval arg1 * ((2^32)⁻¹ mod m)^8) mod m + * 0 ≤ eval out1 < m + * * Input Bounds: * arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -3044,8 +3070,11 @@ static void fiat_p256_from_montgomery(uint32_t out1[8], const uint32_t arg1[8]) /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -3058,7 +3087,9 @@ static void fiat_p256_nonzero(uint32_t* out1, const uint32_t arg1[8]) { /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] @@ -3095,8 +3126,11 @@ static void fiat_p256_selectznz(uint32_t out1[8], fiat_p256_uint1 arg1, const ui /* * The function fiat_p256_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 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]] * Output Bounds: @@ -3202,9 +3236,12 @@ static void fiat_p256_to_bytes(uint8_t out1[32], const uint32_t arg1[8]) { /* * The function fiat_p256_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 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] * Output Bounds: -- cgit v1.2.3