Crate p3_field

A framework for finite fields.

Modules

• extension

Structs

• FieldArray
• PackedPowers
  like Powers, but packed into PackedField elements
• Powers
  An iterator over the powers of a certain base element b: b^0, b^1, b^2, ....

Traits

• AbstractExtensionField
• AbstractField
  A generalization of Field which permits things like
• ExtensionField
• Field
  An element of a finite 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 AF 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.