Trait Field

pub trait Field: Sized {
    type Elem: Default + Clone + Copy + PartialEq + Debug;

    const ORDER: usize;

    // Required methods
    fn add(a: Self::Elem, b: Self::Elem) -> Self::Elem;
    fn mul(a: Self::Elem, b: Self::Elem) -> Self::Elem;
    fn div(a: Self::Elem, b: Self::Elem) -> Self::Elem;
    fn exp(a: Self::Elem, n: usize) -> Self::Elem;
    fn zero() -> Self::Elem;
    fn one() -> Self::Elem;
    fn nth_internal(n: usize) -> Self::Elem;

    // Provided methods
    fn nth(n: usize) -> Self::Elem { ... }
    fn mul_slice(elem: Self::Elem, input: &[Self::Elem], out: &mut [Self::Elem]) { ... }
    fn mul_slice_add(
        elem: Self::Elem,
        input: &[Self::Elem],
        out: &mut [Self::Elem],
    ) { ... }
}

A finite field to perform encoding over.

Required Associated Constants

const ORDER: usize

The order of the field. This is a limit on the number of shards in an encoding.

Required Associated Types

type Elem: Default + Clone + Copy + PartialEq + Debug

The representational type of the field.

Required Methods

fn add(a: Self::Elem, b: Self::Elem) -> Self::Elem

Add two elements together.

fn mul(a: Self::Elem, b: Self::Elem) -> Self::Elem

Multiply two elements together.

fn div(a: Self::Elem, b: Self::Elem) -> Self::Elem

Divide a by b. Panics is b is zero.

fn exp(a: Self::Elem, n: usize) -> Self::Elem

Raise a to the n’th power.

fn zero() -> Self::Elem

The “zero” element or additive identity.

fn one() -> Self::Elem

The “one” element or multiplicative identity.

fn nth_internal(n: usize) -> Self::Elem

Provided Methods

fn nth(n: usize) -> Self::Elem

Yield the nth element of the field. Panics if n >= ORDER. Assignment is arbitrary but must be unique to n.

fn mul_slice(elem: Self::Elem, input: &[Self::Elem], out: &mut [Self::Elem])

Multiply a slice of elements by another. Writes into the output slice.

Panics

Panics if the output slice does not have equal length to the input.

fn mul_slice_add(elem: Self::Elem, input: &[Self::Elem], out: &mut [Self::Elem])

Multiply a slice of elements by another, adding each result to the corresponding value in out.

Panics

Panics if the output slice does not have equal length to the input.

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 Field for reed_solomon_erasure::galois_8::Field

const ORDER: usize = 256usize

type Elem = u8

impl Field for reed_solomon_erasure::galois_16::Field

const ORDER: usize = 65_536usize

type Elem = [u8; 2]