Trait PrimeField 

pub trait PrimeField:
    Copy
    + Clone
    + Eq
    + PartialEq
    + Ord
    + PartialOrd
    + Debug {
    const MODULUS: u128;
    const BITS: u32;
    const ZERO: Self;
    const ONE: Self;

    // Required methods
    fn from_u64(v: u64) -> Self;
    fn to_u64(self) -> u64;
    fn add(self, rhs: Self) -> Self;
    fn sub(self, rhs: Self) -> Self;
    fn mul(self, rhs: Self) -> Self;
    fn neg(self) -> Self;

    // Provided methods
    fn inv(self) -> Option<Self> { ... }
    fn pow(self, exp: u64) -> Self { ... }
    fn pow_u128(self, exp: u128) -> Self { ... }
}

Trait for prime field arithmetic.

Warriors use this for field-generic hash functions, proof estimation, and verification. Trident provides concrete implementations; warriors call them without reimplementing the math.

Required Associated Constants

const MODULUS: u128

The field modulus as u128 (fits all supported primes).

const BITS: u32

Number of bits in the modulus.

const ZERO: Self

Additive identity.

const ONE: Self

Multiplicative identity.

Required Methods

fn from_u64(v: u64) -> Self

Construct from a u64 value (reduced mod p).

fn to_u64(self) -> u64

Extract the canonical u64 representative.

fn add(self, rhs: Self) -> Self

Field addition: (a + b) mod p.

fn sub(self, rhs: Self) -> Self

Field subtraction: (a - b) mod p.

fn mul(self, rhs: Self) -> Self

Field multiplication: (a * b) mod p.

fn neg(self) -> Self

Additive inverse: (-a) mod p.

Provided Methods

fn inv(self) -> Option<Self>

Multiplicative inverse via Fermat: a^(p-2) mod p. Returns None for zero.

fn pow(self, exp: u64) -> Self

Exponentiation: a^exp mod p (square-and-multiply, u64 exponent).

fn pow_u128(self, exp: u128) -> Self

Exponentiation with u128 exponent (for Fermat inversion).

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl PrimeField for BabyBear

const MODULUS: u128

const BITS: u32 = 31

const ZERO: Self

const ONE: Self

impl PrimeField for Goldilocks

const MODULUS: u128

const BITS: u32 = 64

const ZERO: Self

const ONE: Self

impl PrimeField for Mersenne31

const MODULUS: u128

const BITS: u32 = 31

const ZERO: Self

const ONE: Self