Trait halo2_proofs::arithmetic::FieldExt

pub trait FieldExt: SqrtRatio + From<bool> + Ord + Group<Scalar = Self> {
    const MODULUS: &'static str;
    const ROOT_OF_UNITY_INV: Self;
    const DELTA: Self;
    const TWO_INV: Self;
    const ZETA: Self;

    fn from_u128(v: u128) -> Self;
    fn from_bytes_wide(bytes: &[u8; 64]) -> Self;
    fn get_lower_128(&self) -> u128;

    fn pow(&self, by: &[u64; 4]) -> Self { ... }
}

This trait is a common interface for dealing with elements of a finite field.

Required Associated Constants

const MODULUS: &'static str

Modulus of the field written as a string for display purposes

const ROOT_OF_UNITY_INV: Self

Inverse of PrimeField::root_of_unity()

const DELTA: Self

Generator of the $t-order$ multiplicative subgroup

const TWO_INV: Self

Inverse of $2$ in the field.

const ZETA: Self

Element of multiplicative order $3$.

Required Methods

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn from_bytes_wide(bytes: &[u8; 64]) -> Self

Obtains a field element that is congruent to the provided little endian byte representation of an integer.

fn get_lower_128(&self) -> u128

Gets the lower 128 bits of this field element when expressed canonically.

Provided Methods

fn pow(&self, by: &[u64; 4]) -> Self

Exponentiates self by by, where by is a little-endian order integer exponent.

Implementations on Foreign Types

impl FieldExt for Fp

fn from_bytes_wide(bytes: &[u8; 64]) -> Fp

Converts a 512-bit little endian integer into a $field by reducing by the modulus.

const MODULUS: &'static str = MODULUS_STR

const TWO_INV: Fp = TWO_INV

const ROOT_OF_UNITY_INV: Fp = ROOT_OF_UNITY_INV

const DELTA: Fp = DELTA

const ZETA: Fp = ZETA

fn from_u128(v: u128) -> Fp

fn get_lower_128(&self) -> u128

impl FieldExt for Fq

fn from_bytes_wide(bytes: &[u8; 64]) -> Fq

Converts a 512-bit little endian integer into a $field by reducing by the modulus.

const MODULUS: &'static str = MODULUS_STR

const TWO_INV: Fq = TWO_INV

const ROOT_OF_UNITY_INV: Fq = ROOT_OF_UNITY_INV

const DELTA: Fq = DELTA

const ZETA: Fq = ZETA

fn from_u128(v: u128) -> Fq

fn get_lower_128(&self) -> u128

impl FieldExt for Fr

fn from_bytes_wide(bytes: &[u8; 64]) -> Fr

Converts a 512-bit little endian integer into a $field by reducing by the modulus.

const MODULUS: &'static str = MODULUS_STR

const TWO_INV: Fr = TWO_INV

const ROOT_OF_UNITY_INV: Fr = ROOT_OF_UNITY_INV

const DELTA: Fr = DELTA

const ZETA: Fr = ZETA

fn from_u128(v: u128) -> Fr

fn get_lower_128(&self) -> u128

impl FieldExt for Fq

fn from_bytes_wide(bytes: &[u8; 64]) -> Fq

Converts a 512-bit little endian integer into a $field by reducing by the modulus.

const MODULUS: &'static str = MODULUS_STR

const TWO_INV: Fq = TWO_INV

const ROOT_OF_UNITY_INV: Fq = ROOT_OF_UNITY_INV

const DELTA: Fq = DELTA

const ZETA: Fq = ZETA

fn from_u128(v: u128) -> Fq

fn get_lower_128(&self) -> u128

impl FieldExt for Fq2

fn from_bytes_wide(bytes: &[u8; 64]) -> Fq2

Converts a 512-bit little endian integer into a Fq by reducing by the modulus.

const MODULUS: &'static str = "0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47"

const ROOT_OF_UNITY_INV: Fq2 = Fq2{ c0: Fq::zero(), c1: Fq::zero(),}

const DELTA: Fq2 = Fq2{ c0: Fq::zero(), c1: Fq::zero(),}

const TWO_INV: Fq2 = Fq2{ c0: Fq::from_raw([11389680472494603940, 14681934109093717318, 15863968012492123182, 1743499133401485332]), c1: Fq([0, 0, 0, 0]),}

const ZETA: Fq2 = Fq2{ c0: Fq::zero(), c1: Fq::zero(),}

fn from_u128(v: u128) -> Fq2

fn get_lower_128(&self) -> u128

Implementors

impl FieldExt for Fp

const MODULUS: &'static str = "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001"

const ROOT_OF_UNITY_INV: Fp = Fp::from_raw([17345750844130103798, 9556816360606991983, 13037233058361039569, 3230532478545521500])

const DELTA: Fp = DELTA

const TWO_INV: Fp = Fp::from_raw([14742138064964943873, 1234914826957257869, 0, 2305843009213693952])

const ZETA: Fp = Fp::from_raw([2138469568173984441, 2098549686371430729, 3218620026049966512, 1354680253176199793])

impl FieldExt for Fq

const MODULUS: &'static str = "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001"

const ROOT_OF_UNITY_INV: Fq = Fq::from_raw([6336227815658842166, 5391806631710861324, 17638615478710601409, 2465124479527549238])

const DELTA: Fq = DELTA

const TWO_INV: Fq = Fq::from_raw([14277384507177828353, 1234914826959606894, 0, 2305843009213693952])

const ZETA: Fq = Fq::from_raw([3074220081524903503, 1147650983937979311, 5845026731688660826, 468825539646214798])