Drop `map λ` bits in docstrings

They are redundant with the bounds pre- and post-conditions in WBW
montgomery.

Also drop the fiat_p... prefix from the `from_montgomery` bits in most
of the docstrings, under the assumption that shorter strings with less
repetition are more readable.

1 files changed, 18 insertions, 25 deletions

diff --git a/p256_32.c b/p256_32.c
index 27c1983df..1bfabfaa7 100644
--- a/p256_32.c
+++ b/p256_32.c
@@ -94,10 +94,9 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p256_from_montgomery out1) mod m = (eval (fiat_p256_from_montgomery arg1) * eval (fiat_p256_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
+ * 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
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -1150,9 +1149,8 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p256_from_montgomery out1) mod m = (eval (fiat_p256_from_montgomery arg1) * eval (fiat_p256_from_montgomery arg1)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
+ * 0 ≤ eval arg1 < m →
+ * 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]]
@@ -2204,10 +2202,9 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p256_from_montgomery out1) mod m = (eval (fiat_p256_from_montgomery arg1) + eval (fiat_p256_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
+ * 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
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -2295,10 +2292,9 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p256_from_montgomery out1) mod m = (eval (fiat_p256_from_montgomery arg1) - eval (fiat_p256_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
+ * 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
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -2369,9 +2365,8 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p256_from_montgomery out1) mod m = -eval (fiat_p256_from_montgomery arg1) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
+ * 0 ≤ eval arg1 < m →
+ * 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]]
@@ -2441,9 +2436,8 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
+ * 0 ≤ eval arg1 < m →
  * eval out1 mod m = (eval arg1 * ((2^32)⁻¹ mod m)^8) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
  * ∧ 0 ≤ eval out1 < m
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -3050,8 +3044,8 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
- * out1 = 0 ↔ eval (fiat_p256_from_montgomery arg1) mod m = 0
+ * 0 ≤ eval arg1 < m →
+ * 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:
@@ -3101,7 +3095,7 @@ 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7] ∧ 0 ≤ eval arg1 < m →
+ * 0 ≤ eval arg1 < m →
  * 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]]
@@ -3208,9 +3202,8 @@ 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.
- * arg1 = map (λ x, ⌊bytes_eval arg1 mod 2^(8 * (x + 1)) / 2^(8 * x)⌋) [0..31] ∧ 0 ≤ bytes_eval arg1 < m →
+ * 0 ≤ bytes_eval arg1 < m →
  * eval out1 mod m = bytes_eval arg1 mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..7]
  * ∧ 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]]