From a11d2ed36be044162fa3bf8fda7208dbda51ac92 Mon Sep 17 00:00:00 2001
From: wborgeaud <williamborgeaud@gmail.com>
Date: Mon, 24 May 2021 22:04:06 +0200
Subject: [PATCH] Fixes based on PR comments

---
 src/field/extension_field/mod.rs       | 10 +++++++++-
 src/field/extension_field/quadratic.rs |  8 +++-----
 src/field/extension_field/quartic.rs   | 12 ++++++------
 src/field/extension_field/target.rs    |  4 ++--
 4 files changed, 20 insertions(+), 14 deletions(-)

diff --git a/src/field/extension_field/mod.rs b/src/field/extension_field/mod.rs
index 89263916..46c99f11 100644
--- a/src/field/extension_field/mod.rs
+++ b/src/field/extension_field/mod.rs
@@ -28,8 +28,16 @@ pub trait OEF<const D: usize>: FieldExtension<D> {
     }
 }
 
+impl<F: Field> OEF<1> for F {
+    const W: Self::BaseField = F::ZERO;
+}
+
 pub trait Extendable<const D: usize>: Sized {
-    type Extension: Field + FieldExtension<D, BaseField = Self> + OEF<D> + From<Self>;
+    type Extension: Field + OEF<D, BaseField = Self> + From<Self>;
+}
+
+impl<F: Field> Extendable<1> for F {
+    type Extension = F;
 }
 
 pub trait FieldExtension<const D: usize>: Field {
diff --git a/src/field/extension_field/quadratic.rs b/src/field/extension_field/quadratic.rs
index ac910278..fc74ec88 100644
--- a/src/field/extension_field/quadratic.rs
+++ b/src/field/extension_field/quadratic.rs
@@ -1,8 +1,6 @@
-use crate::circuit_builder::CircuitBuilder;
 use crate::field::crandall_field::CrandallField;
 use crate::field::extension_field::{FieldExtension, OEF};
 use crate::field::field::Field;
-use crate::target::Target;
 use rand::Rng;
 use std::fmt::{Debug, Display, Formatter};
 use std::hash::{Hash, Hasher};
@@ -82,7 +80,7 @@ impl Field for QuadraticCrandallField {
             return None;
         }
 
-        let a_pow_r_minus_1 = self.frobenius();
+        let a_pow_r_minus_1 = OEF::<2>::frobenius(self);
         let a_pow_r = a_pow_r_minus_1 * *self;
         debug_assert!(FieldExtension::<2>::is_in_basefield(&a_pow_r));
 
@@ -171,7 +169,7 @@ impl Mul for QuadraticCrandallField {
         let Self([a0, a1]) = self;
         let Self([b0, b1]) = rhs;
 
-        let c0 = a0 * b0 + Self::W * a1 * b1;
+        let c0 = a0 * b0 + <Self as OEF<2>>::W * a1 * b1;
         let c1 = a0 * b1 + a1 * b0;
 
         Self([c0, c1])
@@ -250,7 +248,7 @@ mod tests {
         let x = F::rand();
         assert_eq!(
             x.exp(<F as FieldExtension<2>>::BaseField::ORDER),
-            x.frobenius()
+            OEF::<2>::frobenius(&x)
         );
     }
 
diff --git a/src/field/extension_field/quartic.rs b/src/field/extension_field/quartic.rs
index c69e365d..f1791d0e 100644
--- a/src/field/extension_field/quartic.rs
+++ b/src/field/extension_field/quartic.rs
@@ -106,9 +106,9 @@ impl Field for QuarticCrandallField {
             return None;
         }
 
-        let a_pow_p = self.frobenius();
+        let a_pow_p = OEF::<4>::frobenius(self);
         let a_pow_p_plus_1 = a_pow_p * *self;
-        let a_pow_p3_plus_p2 = a_pow_p_plus_1.frobenius().frobenius();
+        let a_pow_p3_plus_p2 = OEF::<4>::frobenius(&OEF::<4>::frobenius(&a_pow_p_plus_1));
         let a_pow_r_minus_1 = a_pow_p3_plus_p2 * a_pow_p;
         let a_pow_r = a_pow_r_minus_1 * *self;
         debug_assert!(FieldExtension::<4>::is_in_basefield(&a_pow_r));
@@ -214,9 +214,9 @@ impl Mul for QuarticCrandallField {
         let Self([a0, a1, a2, a3]) = self;
         let Self([b0, b1, b2, b3]) = rhs;
 
-        let c0 = a0 * b0 + Self::W * (a1 * b3 + a2 * b2 + a3 * b1);
-        let c1 = a0 * b1 + a1 * b0 + Self::W * (a2 * b3 + a3 * b2);
-        let c2 = a0 * b2 + a1 * b1 + a2 * b0 + Self::W * a3 * b3;
+        let c0 = a0 * b0 + <Self as OEF<4>>::W * (a1 * b3 + a2 * b2 + a3 * b1);
+        let c1 = a0 * b1 + a1 * b0 + <Self as OEF<4>>::W * (a2 * b3 + a3 * b2);
+        let c2 = a0 * b2 + a1 * b1 + a2 * b0 + <Self as OEF<4>>::W * a3 * b3;
         let c3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
 
         Self([c0, c1, c2, c3])
@@ -308,7 +308,7 @@ mod tests {
         let x = F::rand();
         assert_eq!(
             exp_naive(x, <F as FieldExtension<4>>::BaseField::ORDER as u128),
-            x.frobenius()
+            OEF::<4>::frobenius(&x)
         );
     }
 
diff --git a/src/field/extension_field/target.rs b/src/field/extension_field/target.rs
index 861baaf5..1927e0d1 100644
--- a/src/field/extension_field/target.rs
+++ b/src/field/extension_field/target.rs
@@ -63,8 +63,8 @@ impl<F: Field> CircuitBuilder<F> {
                 res[(i + j) % D] = if i + j < D {
                     self.mul_add(a.0[i], b.0[j], res[(i + j) % D])
                 } else {
-                    let tmp = self.mul_add(a.0[i], b.0[j], res[(i + j) % D]);
-                    self.mul(w, tmp)
+                    let tmp = self.mul(a.0[i], b.0[j]);
+                    self.mul_add(w, tmp, res[(i + j) % D])
                 }
             }
         }