From 17cfae66550de1bd3ff2620e728d8400f322d8e0 Mon Sep 17 00:00:00 2001
From: Dmitry Vagner <dmitry.vagner@gmail.com>
Date: Sat, 21 Jan 2023 16:15:27 +0700
Subject: [PATCH] reorg

---
 evm/src/bn254_pairing.rs | 43 ++++++++++++++++++++--------------------
 1 file changed, 22 insertions(+), 21 deletions(-)

diff --git a/evm/src/bn254_pairing.rs b/evm/src/bn254_pairing.rs
index 8c0b501a..d368162e 100644
--- a/evm/src/bn254_pairing.rs
+++ b/evm/src/bn254_pairing.rs
@@ -13,7 +13,8 @@ pub struct Curve {
     y: Fp,
 }
 
-/// Standard addition formula for elliptic curves, source:
+/// Standard addition formula for elliptic curves, restricted to the cases  
+/// where neither inputs nor output would ever be the identity O. source:
 /// https://en.wikipedia.org/wiki/Elliptic_curve#Algebraic_interpretation
 impl Add for Curve {
     type Output = Self;
@@ -79,6 +80,26 @@ pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 {
     acc
 }
 
+pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 {
+    let cx = -Fp::new(3) * p.x * p.x;
+    let cy = Fp::new(2) * p.y;
+    sparse_embed(
+        p.y * p.y - Fp::new(9),
+        mul_fp_fp2(cx, q.x),
+        mul_fp_fp2(cy, q.y),
+    )
+}
+
+pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
+    let cx = p2.y - p1.y;
+    let cy = p1.x - p2.x;
+    sparse_embed(
+        p1.y * p2.x - p2.y * p1.x,
+        mul_fp_fp2(cx, q.x),
+        mul_fp_fp2(cy, q.y),
+    )
+}
+
 pub fn power(f: Fp12) -> Fp12 {
     const EXPS4: [(usize, usize, usize); 64] = [
         (1, 1, 0),
@@ -268,26 +289,6 @@ pub fn power(f: Fp12) -> Fp12 {
     y4 * y2 * y0
 }
 
-pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 {
-    let cx = -Fp::new(3) * p.x * p.x;
-    let cy = Fp::new(2) * p.y;
-    sparse_embed(
-        p.y * p.y - Fp::new(9),
-        mul_fp_fp2(cx, q.x),
-        mul_fp_fp2(cy, q.y),
-    )
-}
-
-pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
-    let cx = p2.y - p1.y;
-    let cy = p1.x - p2.x;
-    sparse_embed(
-        p1.y * p2.x - p2.y * p1.x,
-        mul_fp_fp2(cx, q.x),
-        mul_fp_fp2(cy, q.y),
-    )
-}
-
 // The curve is cyclic with generator (1, 2)
 pub const CURVE_GENERATOR: Curve = {
     Curve {