Struct BFieldElement 

pub struct BFieldElement(/* private fields */);

A field element in the Goldilocks prime field (mod 2^64 - 2^32 + 1).

Stored as a canonical u64 value in [0, p). Arithmetic promotes to u128 to avoid u64 overflow.

The name BFieldElement (Base Field Element) follows the convention from the Triton VM / twenty-first ecosystem. In the Plonky3 ecosystem the same field is called Goldilocks.

Examples

use field_cat::{BFieldElement, Field};

let a = BFieldElement::new(42);
let b = BFieldElement::new(7);

assert_eq!((a * b).value(), 294);

// Multiplicative inverse via Fermat's little theorem.
let a_inv = a.inv()?;
assert_eq!(a * a_inv, BFieldElement::one());

Implementations

impl BFieldElement

pub fn new(value: u64) -> Self

Create a new field element, reducing modulo p.

pub fn value(self) -> u64

The underlying integer value in [0, p).

Trait Implementations

impl Add for BFieldElement

type Output = BFieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for BFieldElement

fn clone(&self) -> BFieldElement

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BFieldElement

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for BFieldElement

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Field for BFieldElement

fn zero() -> Self

The additive identity.

fn one() -> Self

The multiplicative identity.

fn inv(&self) -> Result<Self, Error>

Multiplicative inverse.

impl FieldBytes for BFieldElement

fn to_le_bytes(&self) -> Vec<u8>

Serialize this element to little-endian bytes.

fn from_le_bytes(bytes: &[u8]) -> Result<Self, Error>

Deserialize from little-endian bytes.

impl Hash for BFieldElement

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for BFieldElement

type Output = BFieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Neg for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for BFieldElement

fn eq(&self, other: &BFieldElement) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Sub for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Copy for BFieldElement

impl Eq for BFieldElement

impl StructuralPartialEq for BFieldElement