Crate p3_field

A framework for finite fields.

Modules

extension

Structs

FieldArray

Powers

An iterator which returns the powers of a base element b shifted by current c: c, c * b, c * b^2, ....

Traits

ExtensionField

Field

An element of a finite field.

FieldAlgebra

A commutative algebra over a finite field.

FieldExtensionAlgebra

A commutative algebra over an extension field.

Packable

A trait to constrain types that can be packed into a packed value.

PackedField

Safety

PackedFieldPow2

Safety

PackedValue

Safety

PrimeField

PrimeField32

A prime field of order less than 2^32.

PrimeField64

A prime field of order less than 2^64.

TwoAdicField

A field which supplies information like the two-adicity of its multiplicative group, and methods for obtaining two-adic generators.

Functions

add_scaled_slice_in_place

x += y * s, where s is a scalar.

add_vecs

batch_multiplicative_inverse

Batch multiplicative inverses with Montgomery’s trick This is Montgomery’s trick. At a high level, we invert the product of the given field elements, then derive the individual inverses from that via multiplication.

binomial_expand

Expand a product of binomials (x - roots[0])(x - roots[1]).. into polynomial coefficients.

cyclic_subgroup_coset_known_order

Computes a coset of a multiplicative subgroup whose order is known in advance.

cyclic_subgroup_known_order

Computes a multiplicative subgroup whose order is known in advance.

dot_product

Maximally generic dot product.

eval_poly

exp_1420470955

exp_1717986917

exp_1725656503

exp_10540996611094048183

exp_u64_by_squaring

field_to_array

Extend a field FA element x to an array of length D by filling zeros.

halve_u32

Given an element x from a 32 bit field F_P compute x/2.

halve_u64

Given an element x from a 64 bit field F_P compute x/2.

naive_poly_mul

Naive polynomial multiplication.

reduce_32

Given a slice of SF elements, reduce them to a TF element using a 2^32-base decomposition.

scale_slice_in_place

scale_vec

split_32

Given an SF element, split it to a vector of TF elements using a 2^64-base decomposition.

sum_vecs

two_adic_coset_zerofier

Computes Z_{sH}(x), where Z_{sH} is the zerofier of the given coset of a multiplicative subgroup of order 2^log_n.

two_adic_subgroup_zerofier

Computes Z_H(x), where Z_H is the zerofier of a multiplicative subgroup of order 2^log_n.