Remove Frobeniable trait

src/field/crandall_field.rs

@@ -6,7 +6,7 @@ use num::Integer;
 
 use crate::field::extension_field::quadratic::QuadraticCrandallField;
 use crate::field::extension_field::quartic::QuarticCrandallField;
-use crate::field::extension_field::{Extendable, Frobeniable};
+use crate::field::extension_field::{Extendable, Frobenius};
 use crate::field::field::Field;
 use std::hash::{Hash, Hasher};
 use std::iter::{Product, Sum};
@@ -444,16 +444,7 @@ fn split(x: u128) -> (u64, u64) {
     (x as u64, (x >> 64) as u64)
 }
 
-impl Frobeniable for CrandallField {
-    const FROBENIUS_CONSTANTS_2: [u64; 1] = [9223372035646816256];
-    /// Placeholder since there's no OEF of degree 3 for `CrandallField`.
-    const FROBENIUS_CONSTANTS_3: [u64; 2] = [0, 0];
-    const FROBENIUS_CONSTANTS_4: [u64; 3] = [
-        4611686017823408128,
-        9223372035646816256,
-        13835058053470224384,
-    ];
-}
+impl Frobenius<1> for CrandallField {}
 
 #[cfg(test)]
 mod tests {

src/field/extension_field/mod.rs

@@ -19,59 +19,36 @@ impl<F: Field> OEF<1> for F {
     const W: Self::BaseField = F::ZERO;
 }
 
-pub trait Frobenius<BF: Frobeniable, const D: usize>: OEF<D, BaseField = BF> {
+pub trait Frobenius<const D: usize>: OEF<D> {
     /// FrobeniusField automorphisms: x -> x^p, where p is the order of BaseField.
     fn frobenius(&self) -> Self {
         self.repeated_frobenius(1)
     }
 
     /// Repeated Frobenius automorphisms: x -> x^(p^k).
-    fn repeated_frobenius(&self, k: usize) -> Self {
-        if k == 0 {
+    fn repeated_frobenius(&self, count: usize) -> Self {
+        if count == 0 {
             return *self;
-        } else if k >= D {
-            return self.repeated_frobenius(k % D);
+        } else if count >= D {
+            return self.repeated_frobenius(count % D);
         }
         let arr = self.to_basefield_array();
-        let z0 = match D {
-            2 => Self::W.exp(BF::FROBENIUS_CONSTANTS_2[k - 1]),
-            3 => Self::W.exp(BF::FROBENIUS_CONSTANTS_3[k - 1]),
-            4 => Self::W.exp(BF::FROBENIUS_CONSTANTS_4[k - 1]),
-            _ => unimplemented!("Only extensions of degree 2, 3, or 4 are allowed for now."),
-        };
-        let mut z = Self::BaseField::ONE;
+        let k = (Self::BaseField::ORDER - 1) / (D as u64);
+        let z0 = Self::W.exp(k * count as u64);
         let mut res = [Self::BaseField::ZERO; D];
-        for i in 0..D {
+        for (i, z) in z0.powers().take(D).enumerate() {
             res[i] = arr[i] * z;
-            z *= z0;
         }
 
         Self::from_basefield_array(res)
     }
 }
 
-impl<F: Frobeniable> Frobenius<F, 1> for F {
-    fn frobenius(&self) -> Self {
-        *self
-    }
-    fn repeated_frobenius(&self, _k: usize) -> Self {
-        *self
-    }
+pub trait Extendable<const D: usize>: Field + Sized {
+    type Extension: Field + OEF<D, BaseField = Self> + Frobenius<D> + From<Self>;
 }
 
-/// Trait to hardcode constants used in the Frobenius automorphism.
-pub trait Frobeniable: Field {
-    //! `FROBENIUS_CONSTANTS_D[i-1] = floor( p^i / D) mod p-1`
-    const FROBENIUS_CONSTANTS_2: [u64; 1];
-    const FROBENIUS_CONSTANTS_3: [u64; 2];
-    const FROBENIUS_CONSTANTS_4: [u64; 3];
-}
-
-pub trait Extendable<const D: usize>: Frobeniable + Sized {
-    type Extension: Field + OEF<D, BaseField = Self> + Frobenius<Self, D> + From<Self>;
-}
-
-impl<F: Frobeniable + Frobenius<F, 1>> Extendable<1> for F {
+impl<F: Frobenius<1> + FieldExtension<1, BaseField = F>> Extendable<1> for F {
     type Extension = F;
 }
 

src/field/extension_field/quadratic.rs

@@ -16,7 +16,7 @@ impl OEF<2> for QuadraticCrandallField {
     const W: CrandallField = CrandallField(3);
 }
 
-impl Frobenius<CrandallField, 2> for QuadraticCrandallField {}
+impl Frobenius<2> for QuadraticCrandallField {}
 
 impl FieldExtension<2> for QuadraticCrandallField {
     type BaseField = CrandallField;

src/field/extension_field/quartic.rs

@@ -20,7 +20,7 @@ impl OEF<4> for QuarticCrandallField {
     const W: CrandallField = CrandallField(3);
 }
 
-impl Frobenius<CrandallField, 4> for QuarticCrandallField {}
+impl Frobenius<4> for QuarticCrandallField {}
 
 impl FieldExtension<4> for QuarticCrandallField {
     type BaseField = CrandallField;
@@ -294,16 +294,18 @@ mod tests {
     #[test]
     fn test_frobenius() {
         type F = QuarticCrandallField;
+        const D: usize = 4;
         let x = F::rand();
         assert_eq!(
-            exp_naive(x, <F as FieldExtension<4>>::BaseField::ORDER as u128),
+            exp_naive(x, <F as FieldExtension<D>>::BaseField::ORDER as u128),
             x.frobenius()
         );
-        assert_eq!(x.repeated_frobenius(2), x.frobenius().frobenius());
-        assert_eq!(
-            x.repeated_frobenius(3),
-            x.frobenius().frobenius().frobenius()
-        );
+        for count in 2..D {
+            assert_eq!(
+                x.repeated_frobenius(count),
+                (0..count).fold(x, |acc, _| acc.frobenius())
+            );
+        }
     }
 
     #[test]

src/field/extension_field/target.rs

@@ -34,16 +34,17 @@ impl<const D: usize> ExtensionTarget<D> {
 
     pub fn repeated_frobenius<F: Extendable<D>>(
         &self,
-        k: usize,
+        count: usize,
         builder: &mut CircuitBuilder<F, D>,
     ) -> Self {
+        if count == 0 {
+            return *self;
+        } else if count >= D {
+            return self.repeated_frobenius(count % D, builder);
+        }
         let arr = self.to_target_array();
-        let z0 = match D {
-            2 => F::Extension::W.exp(F::FROBENIUS_CONSTANTS_2[k - 1]),
-            3 => F::Extension::W.exp(F::FROBENIUS_CONSTANTS_3[k - 1]),
-            4 => F::Extension::W.exp(F::FROBENIUS_CONSTANTS_4[k - 1]),
-            _ => unimplemented!("Only extensions of degree 2, 3, or 4 are allowed for now."),
-        };
+        let k = (F::ORDER - 1) / (D as u64);
+        let z0 = F::W.exp(k * count as u64);
         let zs = z0
             .powers()
             .take(D)

src/field/field.rs

@@ -7,7 +7,7 @@ use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssi
 use num::Integer;
 use rand::Rng;
 
-use crate::field::extension_field::{Extendable, FieldExtension, Frobeniable, Frobenius, OEF};
+use crate::field::extension_field::{Extendable, FieldExtension, Frobenius, OEF};
 use crate::util::bits_u64;
 
 /// A finite field with prime order less than 2^64.
@@ -287,9 +287,9 @@ impl<F: Field> Iterator for Powers<F> {
 
 impl<F: Field> Powers<F> {
     /// Apply the Frobenius automorphism `k` times.
-    pub fn repeated_frobenius<BF: Frobeniable, const D: usize>(self, k: usize) -> Self
+    pub fn repeated_frobenius<const D: usize>(self, k: usize) -> Self
     where
-        F: Frobenius<BF, D>,
+        F: Frobenius<D>,
     {
         let Self { base, current } = self;
         Self {

src/gadgets/rotate.rs

@@ -119,7 +119,7 @@ mod tests {
 
     #[test]
     fn test_rotate() {
-        for len_log in 1..4 {
+        for len_log in 1..3 {
             test_rotate_given_len(len_log);
         }
     }