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Add quadratic and quartic extensions to Goldilocks

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This commit is contained in:
wborgeaud 2021-09-15 09:10:18 +02:00
parent 2ae9e34993
commit dc4062cde7
1 changed files with 33 additions and 1 deletions
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34
src/field/goldilocks_field.rs
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@ -8,7 +8,10 @@ use num::BigUint;
use rand::Rng;
use serde::{Deserialize, Serialize};
use crate::field::field_types::{Field, PrimeField};
use crate::field::extension_field::quadratic::QuadraticExtension;
use crate::field::extension_field::quartic::QuarticExtension;
use crate::field::extension_field::Extendable;
use crate::field::field_types::{Field, PrimeField, RichField};
use crate::field::inversion::try_inverse_u64;
const EPSILON: u64 = (1 << 32) - 1;
@ -213,6 +216,35 @@ impl DivAssign for GoldilocksField {
}
}
impl Extendable<2> for GoldilocksField {
type Extension = QuadraticExtension<Self>;
// Verifiable in Sage with
// `R.<x> = GF(p)[]; assert (x^2 - 7).is_irreducible()`.
const W: Self = Self(7);
const EXT_MULTIPLICATIVE_GROUP_GENERATOR: [Self; 2] =
[Self(18081566051660590251), Self(16121475356294670766)];
const EXT_POWER_OF_TWO_GENERATOR: [Self; 2] = [Self(0), Self(15659105665374529263)];
}
impl Extendable<4> for GoldilocksField {
type Extension = QuarticExtension<Self>;
const W: Self = Self(7);
const EXT_MULTIPLICATIVE_GROUP_GENERATOR: [Self; 4] = [
Self(5024755240244648895),
Self(13227474371289740625),
Self(3912887029498544536),
Self(3900057112666848848),
];
const EXT_POWER_OF_TWO_GENERATOR: [Self; 4] =
[Self(0), Self(0), Self(0), Self(12587610116473453104)];
}
/// Reduces to a 64-bit value. The result might not be in canonical form; it could be in between the
/// field order and `2^64`.
#[inline]