Trait ark_ff::fields::FpParameters

pub trait FpParameters: FftParameters {
    const MODULUS: Self::BigInt;
    const MODULUS_BITS: u32;
    const REPR_SHAVE_BITS: u32;
    const R: Self::BigInt;
    const R2: Self::BigInt;
    const INV: u64;
    const GENERATOR: Self::BigInt;
    const CAPACITY: u32;
    const T: Self::BigInt;
    const T_MINUS_ONE_DIV_TWO: Self::BigInt;
    const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInt;
}

A trait that defines parameters for a prime field.

Associated Constants

const MODULUS: Self::BigInt

The modulus of the field.

const MODULUS_BITS: u32

The number of bits needed to represent the Self::MODULUS.

const REPR_SHAVE_BITS: u32

The number of bits that must be shaved from the beginning of the representation when randomly sampling.

const R: Self::BigInt

Let M be the power of 2^64 nearest to Self::MODULUS_BITS. Then R = M % Self::MODULUS.

const R2: Self::BigInt

R2 = R^2 % Self::MODULUS

const INV: u64

INV = -MODULUS^{-1} mod 2^64

const GENERATOR: Self::BigInt

A multiplicative generator of the field. Self::GENERATOR is an element having multiplicative order Self::MODULUS - 1.

const CAPACITY: u32

The number of bits that can be reliably stored. (Should equal SELF::MODULUS_BITS - 1)

const T: Self::BigInt

t for 2^s * t = MODULUS - 1, and t coprime to 2.

const T_MINUS_ONE_DIV_TWO: Self::BigInt

(t - 1) / 2

const MODULUS_MINUS_ONE_DIV_TWO: Self::BigInt

(Self::MODULUS - 1) / 2

Implementors