Struct Field 

pub struct Field { /* private fields */ }

The Galois field $\mathrm{GF}(2^{m})$ by exponential and logarithm tables.

Implementations

impl Field

pub fn new(m: u32, poly: u32) -> Result<Field>

The field of degree m (2 to 20) generated by the primitive polynomial poly (bit $i$ the coefficient of $x^{i}$).

Errors

comnum_core::Error::Config for a degree outside 2 to 20, a polynomial of another degree, or one that is not primitive (its powers of $x$ do not run through every non-zero element).

pub fn m(&self) -> u32

The degree $m$.

pub fn order(&self) -> usize

The number of non-zero elements $2^{m} - 1$.

pub fn pow(&self, e: usize) -> u32

$\alpha^{e}$ for any non-negative exponent.

pub fn log(&self, a: u32) -> usize

The exponent $e$ of a non-zero element $\alpha^{e}$ (0 for the element 0).

pub fn mul(&self, a: u32, b: u32) -> u32

The product $ab$.

pub fn div(&self, a: u32, b: u32) -> u32

The quotient $a / b$ of a non-zero b ($0 / b = 0$).

Panics

In debug builds, for b = 0 (a division by zero is a broken invariant of the caller: release builds return a meaningless element instead of checking it in the inner loops of the decoders).

pub fn inv(&self, a: u32) -> u32

The inverse $a^{-1}$ of a non-zero element.

Panics

In debug builds, for a = 0 (as Field::div).

pub fn minimal_polynomial(&self, i: usize) -> Vec<u8>

The minimal polynomial of $\alpha^{i}$ (binary coefficients, lowest degree first).

Trait Implementations

impl Clone for Field

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Field

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

Formats the value using the given formatter.

impl Eq for Field

impl PartialEq for Field

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Field