Crate binius_math

Expand description

Mathematical primitives used in Binius, built atop the binius_field crate.

This crate provides a variety of mathematical primitives used in Binius, including:

Multilinear polynomials
Univariate polynomials
Matrix operations
Arithmetic expressions and evaluators

This crate is a dependency of binius_hal. When modules in binius_core need to be abstracted behind the HAL, this is one of the places they are often moved in order to avoid crate dependency cycles.

Structs§

BinarySubspace: An $F_2$-linear subspace of a binary field.
DefaultEvaluationDomainFactory
EvaluationDomain: A domain that univariate polynomials may be evaluated on.
InterpolationDomain: An extended version of EvaluationDomain that supports interpolation to monomial form. Takes longer to construct due to Vandermonde inversion, which has cubic complexity.
IsomorphicEvaluationDomainFactory
LinearNormalForm: A normal form for a linear expression.
MLEDirectAdapter: An adapter for MultilinearExtension that implements MultilinearPoly over the same packed field that the MultilinearExtension stores evaluations in.
MLEEmbeddingAdapter: An adapter for MultilinearExtension that implements MultilinearPoly over a packed extension field.
Matrix: A matrix over a field.
MultilinearExtension: A multilinear polynomial represented by its evaluations over the boolean hypercube.
MultilinearQuery: Tensor product expansion of sumcheck round challenges.
MultilinearQueryRef: Wraps MultilinearQuery to hide Data from the users.
PackingDeref: A wrapper for containers of underlier types that dereferences as packed field slices.

Enums§

ArithExpr: Arithmetic expressions that can be evaluated symbolically.
Error
EvaluationOrder: Sumcheck evaluation order.

Traits§

CompositionPoly: A multivariate polynomial that is used as a composition of several multilinear polynomials.
EvaluationDomainFactory: Wraps type information to enable instantiating EvaluationDomains.
MultilinearPoly: Represents a multilinear polynomial.

Functions§

eq_ind_partial_eval: Computes the partial evaluation of the equality indicator polynomial.
evaluate_piecewise_multilinear: Evaluate a piecewise multilinear polynomial at a point, given the evaluations of the pieces.
evaluate_univariate: Evaluate a univariate polynomial specified by its monomial coefficients.
extrapolate_line: Extrapolates lines through a pair of packed fields at a single point from a subfield.
extrapolate_line_scalar: Similar methods, but for scalar fields.
extrapolate_lines: Extrapolates lines through a pair of packed fields at a packed vector of points.
fold_left: Execute the left fold operation.
fold_left_lerp: Left linear interpolation (lerp, single variable) fold
fold_left_lerp_inplace: Inplace left linear interpolation (lerp, single variable) fold
fold_right: Execute the right fold operation.
fold_right_lerp: Specialized implementation for a single parameter right fold using linear interpolation instead of tensor expansion resulting in a single multiplication instead of two: f(r||w) = r * (f(1||w) - f(0||w)) + f(0||w).
tensor_prod_eq_ind: Tensor Product expansion of values with partial eq indicator evaluated at extra_query_coordinates

Type Aliases§