Struct GF2 

pub struct GF2(/* private fields */);

Element of the Galois field GF(2) = {0, 1}.

The smallest finite field. Addition is XOR, multiplication is AND. Every nonzero element is its own inverse (both additive and multiplicative).

Implementations

impl GF2

pub const ZERO: Self

pub const ONE: Self

pub const fn new(value: u8) -> Self

Create from a u8 value (reduces mod 2).

pub const fn from_bool(value: bool) -> Self

Create from a bool.

pub const fn value(self) -> u8

The underlying value (0 or 1).

pub const fn is_zero_element(self) -> bool

Whether this is the zero element.

pub const fn is_one(self) -> bool

Whether this is the one (unity) element.

pub const fn inverse(self) -> Option<Self>

Multiplicative inverse. Returns None for zero.

Trait Implementations

impl Add for GF2

type Output = GF2

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for GF2

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for GF2

fn clone(&self) -> GF2

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GF2

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

Formats the value using the given formatter.

impl Default for GF2

fn default() -> GF2

Returns the “default value” for a type.

impl Display for GF2

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

Formats the value using the given formatter.

impl From<GF2> for bool

fn from(value: GF2) -> Self

Converts to this type from the input type.

impl From<GF2> for u8

fn from(value: GF2) -> Self

Converts to this type from the input type.

impl From<bool> for GF2

fn from(value: bool) -> Self

Converts to this type from the input type.

impl From<u8> for GF2

fn from(value: u8) -> Self

Converts to this type from the input type.

impl Hash for GF2

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 GF2

type Output = GF2

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign for GF2

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for GF2

type Output = GF2

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl One for GF2

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl PartialEq for GF2

fn eq(&self, other: &GF2) -> 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 GF2

type Output = GF2

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for GF2

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl Zero for GF2

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Copy for GF2

impl Eq for GF2

impl StructuralPartialEq for GF2