Struct guff::F16

pub struct F16 {
    pub full: u32,
    pub compact: u16,
}

A type implementing (default) maths in GF(2¹⁶)

Fields

full: u32

compact: u16

Trait Implementations

impl Debug for F16

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

Formats the value using the given formatter.

impl GaloisField for F16

type E = u16

Natural storage class (u8, u16, u32, etc.) for storing elements of the field.

type EE = u32

The next largest natural storage class, eg if E is u8, then EE should be U16. Used for:

type SEE = i32

As EE, but signed. Used internally to implement some lookup tables.

const ORDER: u16

Size of the field in bits, eg GF(2⁸) → 8

const POLY_BIT: u32

High bit of field polynomial, eg GF(2⁸) → 0x100

const FIELD_MASK: u16

Mask for selecting all bits of field value, eg GF(2⁸) → 0xff

const HIGH_BIT: u16

High bit of field values, eg GF(2⁸) → 0x80

fn poly(&self) -> u16

The field polynomial with (implicit) high bit stripped off.

fn full_poly(&self) -> u32

Field polynomial in full, with high poly bit set

fn add(&self, a: Self::E, b: Self::E) -> Self::E

Addition in Galois Fields GF(2^x) is simply XOR

fn sub(&self, a: Self::E, b: Self::E) -> Self::E

Subtraction is the same as addition in GF(2^x)

fn mul(&self, a: Self::E, b: Self::E) -> Self::E

Polynomial multiplication modulo the field polynomial

fn div(&self, a: Self::E, b: Self::E) -> Self::E

Division modulo to the field polynomial (default implementation calculated as a・b^-1)

fn inv(&self, a: Self::E) -> Self::E

Calculate polynomial a^-1 modulo the field polynomial (using Extended Euclidean method)

fn pow(&self, a: Self::E, b: Self::EE) -> Self::E where
    Self::E: Into<Self::EE>, 

Calculate polynomial a^b modulo the field polynomial

fn vec_sum_elements(&self, v: &[Self::E]) -> Self::E

fn vec_add_vec_in_place(&self, dest: &mut [Self::E], other: &[Self::E])

fn vec_add_vecs_giving_other(
    &self,
    dest: &mut [Self::E],
    a: &[Self::E],
    b: &[Self::E]
)

fn vec_cross_product(&self, dest: &mut [Self::E], a: &[Self::E], b: &[Self::E])

fn vec_dot_product(&self, a: &[Self::E], b: &[Self::E]) -> Self::E

fn vec_constant_scale_in_place(&self, dest: &mut [Self::E], a: Self::E)

fn vec_fma_in_place(&self, dest: &mut [Self::E], a: Self::E, b: Self::E)

fn high_bit(&self) -> Self::E

Access Self::HIGH_BIT as a method

fn order(&self) -> u16

Access Self::ORDER as a method

fn field_mask(&self) -> Self::E

Access Self::FIELD_MASK as a method