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/p484_64.c b/p484_64.c
index 41c1a0c90..33c12b7e8 100644
--- a/p484_64.c
+++ b/p484_64.c
@@ -96,10 +96,9 @@ static void fiat_p484_cmovznz_u64(uint64_t* out1, fiat_p484_uint1 arg1, uint64_t
 
 /*
  * The function fiat_p484_mul multiplies two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p484_from_montgomery out1) mod m = (eval (fiat_p484_from_montgomery arg1) * eval (fiat_p484_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -1085,9 +1084,8 @@ static void fiat_p484_mul(uint64_t out1[7], const uint64_t arg1[7], const uint64
 
 /*
  * The function fiat_p484_square squares a field element in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p484_from_montgomery out1) mod m = (eval (fiat_p484_from_montgomery arg1) * eval (fiat_p484_from_montgomery arg1)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -2072,10 +2070,9 @@ static void fiat_p484_square(uint64_t out1[7], const uint64_t arg1[7]) {
 
 /*
  * The function fiat_p484_add adds two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p484_from_montgomery out1) mod m = (eval (fiat_p484_from_montgomery arg1) + eval (fiat_p484_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -2154,10 +2151,9 @@ static void fiat_p484_add(uint64_t out1[7], const uint64_t arg1[7], const uint64
 
 /*
  * The function fiat_p484_sub subtracts two field elements in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * arg2 = map (λ x, ⌊eval arg2 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg2 < m →
- * eval (fiat_p484_from_montgomery out1) mod m = (eval (fiat_p484_from_montgomery arg1) - eval (fiat_p484_from_montgomery arg2)) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -2221,9 +2217,8 @@ static void fiat_p484_sub(uint64_t out1[7], const uint64_t arg1[7], const uint64
 
 /*
  * The function fiat_p484_opp negates a field element in the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * eval (fiat_p484_from_montgomery out1) mod m = -eval (fiat_p484_from_montgomery arg1) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * 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 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -2286,9 +2281,8 @@ static void fiat_p484_opp(uint64_t out1[7], const uint64_t arg1[7]) {
 
 /*
  * The function fiat_p484_from_montgomery translates a field element out of the Montgomery domain.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
+ * 0 ≤ eval arg1 < m →
  * eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^7) mod m
- * ∧ out1 = map (λ x, ⌊eval out1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6]
  * ∧ 0 ≤ eval out1 < m
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
@@ -2934,8 +2928,8 @@ static void fiat_p484_from_montgomery(uint64_t out1[7], const uint64_t arg1[7])
 
 /*
  * The function fiat_p484_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * x)⌋) [0..6] ∧ 0 ≤ eval arg1 < m →
- * out1 = 0 ↔ eval (fiat_p484_from_montgomery arg1) mod m = 0
+ * 0 ≤ eval arg1 < m →
+ * out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
  * Output Bounds:
@@ -2982,7 +2976,7 @@ static void fiat_p484_selectznz(uint64_t out1[7], fiat_p484_uint1 arg1, const ui
 
 /*
  * The function fiat_p484_to_bytes serializes a field element in the Montgomery domain to bytes in little-endian order.
- * arg1 = map (λ x, ⌊eval arg1 mod 2^(64 * (x + 1)) / 2^(64 * 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..55]
  * Input Bounds:
  *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x3ffffffffffff]]
@@ -3160,9 +3154,8 @@ static void fiat_p484_to_bytes(uint8_t out1[56], const uint64_t arg1[7]) {
 
 /*
  * The function fiat_p484_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..55] ∧ 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^(64 * (x + 1)) / 2^(64 * 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], [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 ~> 0x3], [0x0 ~> 0x0]]