working

src/field/extension_field/quadratic.rs

@@ -50,8 +50,6 @@ impl<F: Extendable<2>> From<F> for QuadraticExtension<F> {
 }
 
 impl<F: Extendable<2>> Field for QuadraticExtension<F> {
-    type PrimeField = F;
-
     const ZERO: Self = Self([F::ZERO; 2]);
     const ONE: Self = Self([F::ONE, F::ZERO]);
     const TWO: Self = Self([F::TWO, F::ZERO]);
@@ -63,6 +61,7 @@ impl<F: Extendable<2>> Field for QuadraticExtension<F> {
     // long as `F::TWO_ADICITY >= 2`, `p` can be written as `4n + 1`, so `p + 1` can be written as
     // `2(2n + 1)`, which has a 2-adicity of 1.
     const TWO_ADICITY: usize = F::TWO_ADICITY + 1;
+    const CHARACTERISTIC_TWO_ADICITY: usize = F::CHARACTERISTIC_TWO_ADICITY;
 
     const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(F::EXT_MULTIPLICATIVE_GROUP_GENERATOR);
     const POWER_OF_TWO_GENERATOR: Self = Self(F::EXT_POWER_OF_TWO_GENERATOR);

src/field/extension_field/quartic.rs

@@ -51,8 +51,6 @@ impl<F: Extendable<4>> From<F> for QuarticExtension<F> {
 }
 
 impl<F: Extendable<4>> Field for QuarticExtension<F> {
-    type PrimeField = F;
-
     const ZERO: Self = Self([F::ZERO; 4]);
     const ONE: Self = Self([F::ONE, F::ZERO, F::ZERO, F::ZERO]);
     const TWO: Self = Self([F::TWO, F::ZERO, F::ZERO, F::ZERO]);
@@ -65,6 +63,7 @@ impl<F: Extendable<4>> Field for QuarticExtension<F> {
     // `2(2n + 1)`, which has a 2-adicity of 1. A similar argument can show that `p^2 + 1` also has
     // a 2-adicity of 1.
     const TWO_ADICITY: usize = F::TWO_ADICITY + 2;
+    const CHARACTERISTIC_TWO_ADICITY: usize = F::CHARACTERISTIC_TWO_ADICITY;
 
     const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(F::EXT_MULTIPLICATIVE_GROUP_GENERATOR);
     const POWER_OF_TWO_GENERATOR: Self = Self(F::EXT_POWER_OF_TWO_GENERATOR);

src/field/field_types.rs

@@ -42,8 +42,6 @@ pub trait Field:
     + Serialize
     + DeserializeOwned
 {
-    type PrimeField: PrimeField;
-
     const ZERO: Self;
     const ONE: Self;
     const TWO: Self;
@@ -54,6 +52,9 @@ pub trait Field:
     /// The 2-adicity of this field's multiplicative group.
     const TWO_ADICITY: usize;
 
+    /// The 2-adicity of this field's multiplicative group.
+    const CHARACTERISTIC_TWO_ADICITY: usize;
+
     /// Generator of the entire multiplicative group, i.e. all non-zero elements.
     const MULTIPLICATIVE_GROUP_GENERATOR: Self;
     /// Generator of a multiplicative subgroup of order `2^TWO_ADICITY`.
@@ -212,17 +213,17 @@ pub trait Field:
         // TWO_ADICITY. Can remove the branch and simplify if that
         // saving isn't worth it.
 
-        if exp > Self::PrimeField::TWO_ADICITY {
+        if exp > Self::CHARACTERISTIC_TWO_ADICITY {
             // NB: This should be a compile-time constant
             let inverse_2_pow_adicity: Self =
-                Self::from_canonical_u64(p - ((p - 1) >> Self::PrimeField::TWO_ADICITY));
+                Self::from_canonical_u64(p - ((p - 1) >> Self::CHARACTERISTIC_TWO_ADICITY));
 
             let mut res = inverse_2_pow_adicity;
-            let mut e = exp - Self::PrimeField::TWO_ADICITY;
+            let mut e = exp - Self::CHARACTERISTIC_TWO_ADICITY;
 
-            while e > Self::PrimeField::TWO_ADICITY {
+            while e > Self::CHARACTERISTIC_TWO_ADICITY {
                 res *= inverse_2_pow_adicity;
-                e -= Self::PrimeField::TWO_ADICITY;
+                e -= Self::CHARACTERISTIC_TWO_ADICITY;
             }
             res * Self::from_canonical_u64(p - ((p - 1) >> e))
         } else {
@@ -404,7 +405,7 @@ pub trait Field:
 }
 
 /// A finite field of prime order less than 2^64.
-pub trait PrimeField: Field<PrimeField = Self> {
+pub trait PrimeField: Field {
     const ORDER: u64;
 
     /// The number of bits required to encode any field element.
@@ -449,6 +450,15 @@ pub trait PrimeField: Field<PrimeField = Self> {
     }
 }
 
+pub trait SmallCharacteristicField: Field {
+    const SMALLCHAR: u64;
+
+    #[inline]
+    fn inverse_2exp(exp: usize) -> Self {
+        todo!()
+    }
+}
+
 /// An iterator over the powers of a certain base element `b`: `b^0, b^1, b^2, ...`.
 #[derive(Clone)]
 pub struct Powers<F: Field> {

src/field/goldilocks_field.rs

@@ -62,8 +62,6 @@ impl Debug for GoldilocksField {
 }
 
 impl Field for GoldilocksField {
-    type PrimeField = Self;
-
     const ZERO: Self = Self(0);
     const ONE: Self = Self(1);
     const TWO: Self = Self(2);
@@ -71,6 +69,7 @@ impl Field for GoldilocksField {
     const CHARACTERISTIC: u64 = Self::ORDER;
 
     const TWO_ADICITY: usize = 32;
+    const CHARACTERISTIC_TWO_ADICITY: usize = Self::TWO_ADICITY;
 
     // Sage: `g = GF(p).multiplicative_generator()`
     const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(7);

src/field/packed_field.rs

@@ -39,7 +39,6 @@ where
     Self::Scalar: Sub<Self, Output = Self>,
 {
     type Scalar: Field;
-    type PackedPrimeField: PackedField<Scalar = <Self::Scalar as Field>::PrimeField>;
 
     const WIDTH: usize;
     const ZERO: Self;
@@ -102,7 +101,6 @@ where
 
 unsafe impl<F: Field> PackedField for F {
     type Scalar = Self;
-    type PackedPrimeField = F::PrimeField;
 
     const WIDTH: usize = 1;
     const ZERO: Self = <F as Field>::ZERO;

src/field/secp256k1_base.rs

@@ -68,9 +68,6 @@ impl Debug for Secp256K1Base {
 }
 
 impl Field for Secp256K1Base {
-    // TODO: fix
-    type PrimeField = GoldilocksField;
-
     const ZERO: Self = Self([0; 4]);
     const ONE: Self = Self([1, 0, 0, 0]);
     const TWO: Self = Self([2, 0, 0, 0]);
@@ -84,6 +81,7 @@ impl Field for Secp256K1Base {
     // TODO: fix
     const CHARACTERISTIC: u64 = 0;
     const TWO_ADICITY: usize = 1;
+    const CHARACTERISTIC_TWO_ADICITY: usize = Self::TWO_ADICITY;
 
     // Sage: `g = GF(p).multiplicative_generator()`
     const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self([5, 0, 0, 0]);

src/field/secp256k1_scalar.rs

@@ -71,9 +71,6 @@ impl Debug for Secp256K1Scalar {
 }
 
 impl Field for Secp256K1Scalar {
-    // TODO: fix
-    type PrimeField = GoldilocksField;
-
     const ZERO: Self = Self([0; 4]);
     const ONE: Self = Self([1, 0, 0, 0]);
     const TWO: Self = Self([2, 0, 0, 0]);
@@ -88,6 +85,7 @@ impl Field for Secp256K1Scalar {
     const CHARACTERISTIC: u64 = 0;
 
     const TWO_ADICITY: usize = 6;
+    const CHARACTERISTIC_TWO_ADICITY: usize = 6;
 
     // Sage: `g = GF(p).multiplicative_generator()`
     const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self([7, 0, 0, 0]);