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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| use std::{ | ||
| collections::BTreeMap, | ||
| iter::Sum, | ||
| ops::{Add, Mul, Sub}, | ||
| }; | ||
|
|
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| use num_traits::{One, Zero}; | ||
|
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| pub trait ExtensionField<T>: | ||
| Add<Output = Self> + Sub<Output = Self> + Mul<T, Output = Self> + Zero + One + Copy + Sum | ||
| { | ||
| fn get_challenge(challenges: &BTreeMap<u64, T>, index: u64) -> Self; | ||
| fn size() -> usize; | ||
| fn inverse(self) -> Self; | ||
| fn to_vec(self) -> Vec<T>; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,199 @@ | ||
| use std::{ | ||
| collections::BTreeMap, | ||
| iter::Sum, | ||
| ops::{Add, Div, Mul, Sub}, | ||
| }; | ||
|
|
||
| use num_traits::{One, Zero}; | ||
| use powdr_number::FieldElement; | ||
|
|
||
| use super::extension_field::ExtensionField; | ||
|
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| /// An implementation of Fp4, analogous to `std/math/fp4.asm`. | ||
| /// An Fp4 element. The tuple (a, b, c, d) represents the polynomial a + b * X + c * X^2 + d * X^3. | ||
| /// All computations are done modulo the irreducible polynomial X^4 - 11. | ||
| #[derive(Debug, Clone, Copy, PartialEq, Eq)] | ||
| pub struct Fp4<T>(pub T, pub T, pub T, pub T); | ||
|
|
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| impl<T: FieldElement> Fp4<T> { | ||
| pub fn new(a: T, b: T, c: T, d: T) -> Self { | ||
| Fp4(a, b, c, d) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Zero for Fp4<T> { | ||
| fn zero() -> Self { | ||
| Fp4(T::zero(), T::zero(), T::zero(), T::zero()) | ||
| } | ||
|
|
||
| fn is_zero(&self) -> bool { | ||
| self.0.is_zero() && self.1.is_zero() && self.2.is_zero() && self.3.is_zero() | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> One for Fp4<T> { | ||
| fn one() -> Self { | ||
| Fp4(T::one(), T::zero(), T::zero(), T::zero()) | ||
| } | ||
|
|
||
| fn is_one(&self) -> bool { | ||
| self.0.is_one() && self.1.is_zero() && self.2.is_zero() && self.3.is_zero() | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> From<T> for Fp4<T> { | ||
| fn from(a: T) -> Self { | ||
| Fp4(a, T::zero(), T::zero(), T::zero()) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Add for Fp4<T> { | ||
| type Output = Self; | ||
|
|
||
| fn add(self, other: Self) -> Self { | ||
| Fp4( | ||
| self.0 + other.0, | ||
| self.1 + other.1, | ||
| self.2 + other.2, | ||
| self.3 + other.3, | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Sum for Fp4<T> { | ||
| fn sum<I: Iterator<Item = Self>>(iter: I) -> Self { | ||
| iter.fold(Self::zero(), Add::add) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Sub for Fp4<T> { | ||
| type Output = Self; | ||
|
|
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| fn sub(self, other: Self) -> Self { | ||
| Fp4( | ||
| self.0 - other.0, | ||
| self.1 - other.1, | ||
| self.2 - other.2, | ||
| self.3 - other.3, | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Mul for Fp4<T> { | ||
| type Output = Self; | ||
|
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| fn mul(self, other: Self) -> Self { | ||
| Fp4( | ||
| self.0 * other.0 | ||
| + T::from(11) * (self.1 * other.3 + self.2 * other.2 + self.3 * other.1), | ||
| self.0 * other.1 | ||
| + self.1 * other.0 | ||
| + T::from(11) * (self.2 * other.3 + self.3 * other.2), | ||
| self.0 * other.2 + self.1 * other.1 + self.2 * other.0 + T::from(11) * self.3 * other.3, | ||
| self.0 * other.3 + self.1 * other.2 + self.2 * other.1 + self.3 * other.0, | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Mul<T> for Fp4<T> { | ||
| type Output = Self; | ||
|
|
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| fn mul(self, other: T) -> Self { | ||
| Fp4( | ||
| self.0 * other, | ||
| self.1 * other, | ||
| self.2 * other, | ||
| self.3 * other, | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Fp4<T> { | ||
| pub fn inverse(self) -> Self { | ||
| let b0 = self.0 * self.0 - T::from(11) * (self.1 * T::from(2) * self.3 - self.2 * self.2); | ||
| let b2 = T::from(2) * self.0 * self.2 - self.1 * self.1 - T::from(11) * self.3 * self.3; | ||
| let c = b0 * b0 - T::from(11) * b2 * b2; | ||
| let ic = T::from(1) / c; | ||
|
|
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| let b0_ic = b0 * ic; | ||
| let b2_ic = b2 * ic; | ||
|
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||
| Fp4( | ||
| self.0 * b0_ic - T::from(11) * self.2 * b2_ic, | ||
| -self.1 * b0_ic + T::from(11) * self.3 * b2_ic, | ||
| -self.0 * b2_ic + self.2 * b0_ic, | ||
| self.1 * b2_ic - self.3 * b0_ic, | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> Div for Fp4<T> { | ||
| type Output = Self; | ||
|
|
||
| #[allow(clippy::suspicious_arithmetic_impl)] | ||
| fn div(self, other: Self) -> Self { | ||
| self * other.inverse() | ||
| } | ||
| } | ||
|
|
||
| impl<T: FieldElement> ExtensionField<T> for Fp4<T> { | ||
| fn get_challenge(challenges: &BTreeMap<u64, T>, index: u64) -> Self { | ||
| Fp4::new( | ||
| challenges[&(index * 4 + 1)], | ||
| challenges[&(index * 4 + 2)], | ||
| challenges[&(index * 4 + 3)], | ||
| challenges[&(index * 4 + 4)], | ||
| ) | ||
| } | ||
| fn size() -> usize { | ||
| 4 | ||
| } | ||
| fn inverse(self) -> Self { | ||
| self.inverse() | ||
| } | ||
| fn to_vec(self) -> Vec<T> { | ||
| vec![self.0, self.1, self.2, self.3] | ||
| } | ||
| } | ||
|
|
||
| #[cfg(test)] | ||
| mod tests { | ||
| use powdr_number::GoldilocksField; | ||
|
|
||
| use super::*; | ||
|
|
||
| fn new(a: i64, b: i64, c: i64, d: i64) -> Fp4<GoldilocksField> { | ||
| Fp4( | ||
| GoldilocksField::from(a), | ||
| GoldilocksField::from(b), | ||
| GoldilocksField::from(c), | ||
| GoldilocksField::from(d), | ||
| ) | ||
| } | ||
|
|
||
| fn from_base(x: i64) -> Fp4<GoldilocksField> { | ||
| Fp4::from(GoldilocksField::from(x)) | ||
| } | ||
|
|
||
| #[test] | ||
| fn test_add() { | ||
| assert_eq!(from_base(0) + from_base(0), from_base(0)); | ||
| assert_eq!(new(1, 2, 3, 4) + new(5, 6, 7, 8), new(6, 8, 10, 12)); | ||
| } | ||
|
|
||
| #[test] | ||
| fn test_sub() { | ||
| assert_eq!(new(1, 2, 3, 4) - new(5, 6, 7, 8), new(-4, -4, -4, -4)); | ||
| } | ||
|
|
||
| #[test] | ||
| fn test_mul() { | ||
| assert_eq!(new(1, 2, 3, 4) * new(5, 6, 7, 8), new(676, 588, 386, 60)); | ||
| } | ||
|
|
||
| #[test] | ||
| fn test_inverse() { | ||
| let x = new(1, 2, 3, 4); | ||
| assert_eq!(x * x.inverse(), Fp4::one()); | ||
| } | ||
| } |
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