use core::fmt::{self, Debug, Display, Formatter};
use core::iter::{Product, Sum};
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use num::bigint::BigUint;
use serde::{Deserialize, Serialize};
use crate::extension::{Extendable, FieldExtension, Frobenius, OEF};
use crate::ops::Square;
use crate::types::{Field, Sample};
#[derive(Copy, Clone, Eq, PartialEq, Hash, Serialize, Deserialize)]
#[serde(bound = "")]
pub struct QuadraticExtension<F: Extendable<2>>(pub [F; 2]);
impl<F: Extendable<2>> Default for QuadraticExtension<F> {
fn default() -> Self {
Self::ZERO
}
}
impl<F: Extendable<2>> OEF<2> for QuadraticExtension<F> {
const W: F = F::W;
const DTH_ROOT: F = F::DTH_ROOT;
}
impl<F: Extendable<2>> Frobenius<2> for QuadraticExtension<F> {}
impl<F: Extendable<2>> FieldExtension<2> for QuadraticExtension<F> {
type BaseField = F;
fn to_basefield_array(&self) -> [F; 2] {
self.0
}
fn from_basefield_array(arr: [F; 2]) -> Self {
Self(arr)
}
fn from_basefield(x: F) -> Self {
x.into()
}
}
impl<F: Extendable<2>> From<F> for QuadraticExtension<F> {
fn from(x: F) -> Self {
Self([x, F::ZERO])
}
}
impl<F: Extendable<2>> Sample for QuadraticExtension<F> {
#[inline]
fn sample<R>(rng: &mut R) -> Self
where
R: rand::RngCore + ?Sized,
{
Self([F::sample(rng), F::sample(rng)])
}
}
impl<F: Extendable<2>> Field for QuadraticExtension<F> {
const ZERO: Self = Self([F::ZERO; 2]);
const ONE: Self = Self([F::ONE, F::ZERO]);
const TWO: Self = Self([F::TWO, F::ZERO]);
const NEG_ONE: Self = Self([F::NEG_ONE, F::ZERO]);
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);
const BITS: usize = F::BITS * 2;
fn order() -> BigUint {
F::order() * F::order()
}
fn characteristic() -> BigUint {
F::characteristic()
}
fn try_inverse(&self) -> Option<Self> {
if self.is_zero() {
return None;
}
let a_pow_r_minus_1 = self.frobenius();
let a_pow_r = a_pow_r_minus_1 * *self;
debug_assert!(FieldExtension::<2>::is_in_basefield(&a_pow_r));
Some(FieldExtension::<2>::scalar_mul(
&a_pow_r_minus_1,
a_pow_r.0[0].inverse(),
))
}
fn from_noncanonical_biguint(n: BigUint) -> Self {
F::from_noncanonical_biguint(n).into()
}
fn from_canonical_u64(n: u64) -> Self {
F::from_canonical_u64(n).into()
}
fn from_noncanonical_u128(n: u128) -> Self {
F::from_noncanonical_u128(n).into()
}
}
impl<F: Extendable<2>> Display for QuadraticExtension<F> {
fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
write!(f, "{} + {}*a", self.0[0], self.0[1])
}
}
impl<F: Extendable<2>> Debug for QuadraticExtension<F> {
fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
Display::fmt(self, f)
}
}
impl<F: Extendable<2>> Neg for QuadraticExtension<F> {
type Output = Self;
#[inline]
fn neg(self) -> Self {
Self([-self.0[0], -self.0[1]])
}
}
impl<F: Extendable<2>> Add for QuadraticExtension<F> {
type Output = Self;
#[inline]
fn add(self, rhs: Self) -> Self {
Self([self.0[0] + rhs.0[0], self.0[1] + rhs.0[1]])
}
}
impl<F: Extendable<2>> AddAssign for QuadraticExtension<F> {
fn add_assign(&mut self, rhs: Self) {
*self = *self + rhs;
}
}
impl<F: Extendable<2>> Sum for QuadraticExtension<F> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::ZERO, |acc, x| acc + x)
}
}
impl<F: Extendable<2>> Sub for QuadraticExtension<F> {
type Output = Self;
#[inline]
fn sub(self, rhs: Self) -> Self {
Self([self.0[0] - rhs.0[0], self.0[1] - rhs.0[1]])
}
}
impl<F: Extendable<2>> SubAssign for QuadraticExtension<F> {
#[inline]
fn sub_assign(&mut self, rhs: Self) {
*self = *self - rhs;
}
}
impl<F: Extendable<2>> Mul for QuadraticExtension<F> {
type Output = Self;
#[inline]
default fn mul(self, rhs: Self) -> Self {
let Self([a0, a1]) = self;
let Self([b0, b1]) = rhs;
let c0 = a0 * b0 + <Self as OEF<2>>::W * a1 * b1;
let c1 = a0 * b1 + a1 * b0;
Self([c0, c1])
}
}
impl<F: Extendable<2>> MulAssign for QuadraticExtension<F> {
#[inline]
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}
impl<F: Extendable<2>> Square for QuadraticExtension<F> {
#[inline(always)]
fn square(&self) -> Self {
let Self([a0, a1]) = *self;
let c0 = a0.square() + <Self as OEF<2>>::W * a1.square();
let c1 = a0 * a1.double();
Self([c0, c1])
}
}
impl<F: Extendable<2>> Product for QuadraticExtension<F> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::ONE, |acc, x| acc * x)
}
}
impl<F: Extendable<2>> Div for QuadraticExtension<F> {
type Output = Self;
#[allow(clippy::suspicious_arithmetic_impl)]
fn div(self, rhs: Self) -> Self::Output {
self * rhs.inverse()
}
}
impl<F: Extendable<2>> DivAssign for QuadraticExtension<F> {
fn div_assign(&mut self, rhs: Self) {
*self = *self / rhs;
}
}
#[cfg(test)]
mod tests {
mod goldilocks {
use crate::{test_field_arithmetic, test_field_extension};
test_field_extension!(crate::goldilocks_field::GoldilocksField, 2);
test_field_arithmetic!(
crate::extension::quadratic::QuadraticExtension<
crate::goldilocks_field::GoldilocksField,
>
);
}
}