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/p224_32.c b/p224_32.c
index 2cae5b631..bf1df313d 100644
--- a/p224_32.c
+++ b/p224_32.c
@@ -94,10 +94,9 @@ static void fiat_p224_cmovznz_u32(uint32_t* out1, fiat_p224_uint1 arg1, uint32_t
 
 /*
  * The function fiat_p224_mul multiplies two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p224_from_montgomery out1) mod m = (eval (fiat_p224_from_montgomery arg1) * eval (fiat_p224_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
+ * 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]]
@@ -978,9 +977,8 @@ static void fiat_p224_mul(uint32_t out1[7], const uint32_t arg1[7], const uint32
 
 /*
  * The function fiat_p224_square squares a field element in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p224_from_montgomery out1) mod m = (eval (fiat_p224_from_montgomery arg1) * eval (fiat_p224_from_montgomery arg1)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
+ * 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]]
@@ -1860,10 +1858,9 @@ static void fiat_p224_square(uint32_t out1[7], const uint32_t arg1[7]) {
 
 /*
  * The function fiat_p224_add adds two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p224_from_montgomery out1) mod m = (eval (fiat_p224_from_montgomery arg1) + eval (fiat_p224_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
+ * 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]]
@@ -1942,10 +1939,9 @@ static void fiat_p224_add(uint32_t out1[7], const uint32_t arg1[7], const uint32
 
 /*
  * The function fiat_p224_sub subtracts two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p224_from_montgomery out1) mod m = (eval (fiat_p224_from_montgomery arg1) - eval (fiat_p224_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
+ * 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]]
@@ -2009,9 +2005,8 @@ static void fiat_p224_sub(uint32_t out1[7], const uint32_t arg1[7], const uint32
 
 /*
  * The function fiat_p224_opp negates a field element in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p224_from_montgomery out1) mod m = -eval (fiat_p224_from_montgomery arg1) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
+ * 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]]
@@ -2074,9 +2069,8 @@ static void fiat_p224_opp(uint32_t out1[7], const uint32_t arg1[7]) {
 
 /*
  * The function fiat_p224_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..6] ∧ 0 ≤ eval arg1 < m →
+ * 0 ≤ eval arg1 < m →
  * eval out1 mod m = (eval arg1 * ((2^32)⁻¹ mod m)^7) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6]
  * ∧ 0 ≤ eval out1 < m
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -2614,8 +2608,8 @@ static void fiat_p224_from_montgomery(uint32_t out1[7], const uint32_t arg1[7])
 
 /*
  * The function fiat_p224_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..6] ∧ 0 ≤ eval arg1 < m →
- * out1 = 0 ↔ eval (fiat_p224_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]]
  * Output Bounds:
@@ -2662,7 +2656,7 @@ static void fiat_p224_selectznz(uint32_t out1[7], 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.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(32 * (x + 1)) / 2^(32 * x)⌋) [0..6] ∧ 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..27]
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff], [0x0 ~> 0xffffffff]]
@@ -2757,9 +2751,8 @@ static void fiat_p224_to_bytes(uint8_t out1[28], const uint32_t arg1[7]) {
 
 /*
  * The function fiat_p224_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..27] ∧ 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..6]
  * ∧ 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]]