From ce583d76bdb8f15148fc4222d8bdec096547682a Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Fri, 1 Feb 2019 18:50:00 -0500
Subject: Use Preconditions: Postconditions:, rather than /\ and ->

---
 secp256k1_32.c | 109 ++++++++++++++++++++++++++++++++++++++-------------------
 1 file changed, 73 insertions(+), 36 deletions(-)

(limited to 'secp256k1_32.c')

diff --git a/secp256k1_32.c b/secp256k1_32.c
index 354338e62..cfa8e76f8 100644
--- a/secp256k1_32.c
+++ b/secp256k1_32.c
@@ -18,8 +18,10 @@ typedef signed char fiat_secp256k1_int1;
 
 /*
  * The function fiat_secp256k1_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_secp256k1_addcarryx_u32(uint32_t* out1, fiat_secp256k1_uint1* o
 
 /*
  * The function fiat_secp256k1_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_secp256k1_subborrowx_u32(uint32_t* out1, fiat_secp256k1_uint1*
 
 /*
  * The function fiat_secp256k1_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_secp256k1_mulx_u32(uint32_t* out1, uint32_t* out2, uint32_t arg
 
 /*
  * The function fiat_secp256k1_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_secp256k1_cmovznz_u32(uint32_t* out1, fiat_secp256k1_uint1 arg1
 
 /*
  * The function fiat_secp256k1_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]]
@@ -1389,9 +1400,12 @@ static void fiat_secp256k1_mul(uint32_t out1[8], const uint32_t arg1[8], const u
 
 /*
  * The function fiat_secp256k1_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:
@@ -2682,10 +2696,13 @@ static void fiat_secp256k1_square(uint32_t out1[8], const uint32_t arg1[8]) {
 
 /*
  * The function fiat_secp256k1_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]]
@@ -2772,10 +2789,13 @@ static void fiat_secp256k1_add(uint32_t out1[8], const uint32_t arg1[8], const u
 
 /*
  * The function fiat_secp256k1_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]]
@@ -2845,9 +2865,12 @@ static void fiat_secp256k1_sub(uint32_t out1[8], const uint32_t arg1[8], const u
 
 /*
  * The function fiat_secp256k1_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:
@@ -2916,9 +2939,12 @@ static void fiat_secp256k1_opp(uint32_t out1[8], const uint32_t arg1[8]) {
 
 /*
  * The function fiat_secp256k1_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:
@@ -3818,8 +3844,11 @@ static void fiat_secp256k1_from_montgomery(uint32_t out1[8], const uint32_t arg1
 
 /*
  * The function fiat_secp256k1_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:
@@ -3832,7 +3861,9 @@ static void fiat_secp256k1_nonzero(uint32_t* out1, const uint32_t arg1[8]) {
 
 /*
  * The function fiat_secp256k1_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]]
@@ -3869,8 +3900,11 @@ static void fiat_secp256k1_selectznz(uint32_t out1[8], fiat_secp256k1_uint1 arg1
 
 /*
  * The function fiat_secp256k1_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:
@@ -3976,9 +4010,12 @@ static void fiat_secp256k1_to_bytes(uint8_t out1[32], const uint32_t arg1[8]) {
 
 /*
  * The function fiat_secp256k1_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:
-- 
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