Struct Affine 

pub struct Affine {
    pub n: usize,
    pub matrix: Vec<u64>,
    pub translation: u64,
}

An affine map of the Boolean cube GF(2)ⁿ: x ↦ A x ⊕ b. matrix[i] is row i of A as a coefficient bitmask over the low n bits; translation is b. It is a bijection iff A ∈ GL(n,2).

Fields

n: usize

matrix: Vec<u64>

translation: u64

Implementations

impl Affine

pub fn identity(n: usize) -> Self

The identity x ↦ x (A = I, b = 0).

pub fn apply(&self, x: u64) -> u64

Apply the map to a point x (low n bits): output bit i is parity(row_i · x) ⊕ b_i.

pub fn compose(&self, other: &Affine) -> Affine

Composition self ∘ other: (self ∘ other)(x) = self(other(x)). The linear parts multiply over GF(2) and the translations combine as A_self · b_other ⊕ b_self.

pub fn is_bijection(&self) -> bool

Whether the linear part is invertible (so the map is a bijection of the cube).

Trait Implementations

impl Clone for Affine

fn clone(&self) -> Affine

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Affine

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

Formats the value using the given formatter.

impl PartialEq for Affine

fn eq(&self, other: &Affine) -> 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 Eq for Affine

impl StructuralPartialEq for Affine