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Hypercube

binius_math::multilinear::hypercube

Trait Hypercube 

Source 
pub trait Hypercube {
    // Required methods
    fn basis<F: FieldOps>(coord: &F) -> [F; 2];
    fn expand_var<F: FieldOps>(value: &F, coord: &F) -> [F; 2];
    fn contract_var<F: FieldOps>(lo: &mut F, hi: &F);

    // Provided method
    fn eq_one_var<F: FieldOps>(x: F, y: F) -> F { ... }
}
Expand description

A hypercube of coefficients for multilinear polynomials.

A cube is fixed by the two-element basis (b_0, b_1) that each of its variables contributes. That basis is a pair of linear polynomials, so a cube is a choice between two of them. Everything else is derived from that choice, and shared by every implementor.

Required Methods§

Source

fn basis<F: FieldOps>(coord: &F) -> [F; 2]

Evaluates the basis of one variable at a coordinate.

Returns (b_0(r), b_1(r)) for the coordinate r.

Source

fn expand_var<F: FieldOps>(value: &F, coord: &F) -> [F; 2]

Scales the basis of one variable by a value.

Returns (v * b_0(r), v * b_1(r)) for the value v and the coordinate r. This is the inner loop of every expansion. So an implementor beats the two multiplications that scaling the basis directly costs.

Source

fn contract_var<F: FieldOps>(lo: &mut F, hi: &F)

Strips one variable’s basis factor from the two halves of an expansion.

The halves hold v * b_0(r) and v * b_1(r) for the stripped variable’s coordinate r. The low half is overwritten with v.

Recovering v is one fixed linear combination of the two halves:

sum_i w_i * v * b_i(r) = v    where    sum_i w_i * b_i(X) = 1

Those weights are unique and free of r, so the same combination works at any coordinate.

Provided Methods§

Source

fn eq_one_var<F: FieldOps>(x: F, y: F) -> F

Evaluates the equality indicator of one variable.

eq(X, Y) = sum_i b_i(X) * b_i(Y)

An implementor overrides this with a cheaper closed form.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors§