package tezos-bls12-381-polynomial

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tezos-bls12-381-polynomial
- Bls12_381_polynomial
  - Carray
    
    Carray
    
    Stubs
  - Domain
    
    Domain_impl
    
    Domain_sig
    
    Domain_unsafe
    
    Domain_unsafe_sig
    
    Stubs
  - Evaluations_c
    
    Evaluations_c_impl
    
    Evaluations_c_sig
    
    Stubs
  - Fr_generation
    
    Make
    
    Scalar
  - Multivariate
    
    MultiPoly
    
    K
    
    MONOMIAL_MAP
    
    Monomial
    
    MonomialOperators
    
    MonomialMap
    
    Polynomial
    
    PolynomialOperators
    
    UPoly
    
    MultiPoly_sig
    
    MONOMIAL_MAP
    
    Monomial
    
    MonomialOperators
    
    MonomialMap
    
    Polynomial
    
    PolynomialOperators
    
    UPoly
    
    StringMap
  - Polynomial
    
    Domain
    
    Evaluations
    
    M
    
    Polynomial
    
    S
    
    Domain
    
    Evaluations
    
    Polynomial
    
    Srs
    
    Srs
  - Polynomial_c
    
    Polynomial_impl
    
    Polynomial_sig
    
    Polynomial_unsafe
    
    Polynomial_unsafe_sig
    
    Stubs
  - Srs
    
    M
    
    S
    
    Stubs
  - Univariate
    
    DomainEvaluation
    
    R
    
    Make
    
    R
    
    UNIVARIATE
    
    Utils

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module Fr = Bls12_381.Fr

module Stubs : sig ... end

module Polynomial_impl : sig ... end

module type Polynomial_sig = sig ... end

This library implements polynomials of Bls12_381.Fr as arrays of contiguous memory in C, allowing much better performances for algorithms that scan the polynomials.

module type Polynomial_unsafe_sig = sig ... end

module Polynomial_unsafe : 
  Polynomial_unsafe_sig with type scalar = Bls12_381.Fr.t

include Polynomial_sig
  with type scalar = Polynomial_unsafe.scalar
   and type t = Polynomial_unsafe.t

type scalar = Polynomial_unsafe.scalar

type t = Polynomial_unsafe.t

val encoding : t Data_encoding.t

val allocate : int -> t

allocate len creates a zero polynomial of size len

val erase : t -> unit

erase p overwrites a polynomial p with a zero polynomial of the same size as the polynomial p

val length : t -> int

length p returns the length of a C array where a polynomial p is stored

val generate_random_polynomial : int -> t

generate_random_polynomial n generates a polynomial with a maximum size n

Note: generates more often the zero polynomial and polynomials with zero coefficients

val degree : t -> int

degree p returns the degree of a polynomial p. Returns -1 for the zero polynomial

val get : t -> int -> scalar

get p i returns the i-th element of a given array p, a coefficient of X^i in p

val to_string : t -> string

to_string p returns the string representation of a polynomial p

val copy : ?offset:int -> ?len:int -> t -> t

copy p returns a copy of a polynomial p

val to_dense_coefficients : t -> scalar array

to_dense_coefficients p returns the dense representation of a polynomial p, i.e., it converts a C array to an OCaml array

val of_dense : scalar array -> t

of_dense p creates a value of type t from the dense representation of a polynomial p, i.e., it converts an OCaml array to a C array

val of_coefficients : (scalar * int) list -> t

of_coefficients p creates a value of type t from the sparse representation of a polynomial p, i.e., it converts an OCaml array to a C array

val equal : t -> t -> bool

equal a b checks whether a polynomial a is equal to a polynomial b

val is_zero : t -> bool

is_zero p checks whether a polynomial p is the zero polynomial

val zero : t

zero is the zero polynomial, the neutral element for polynomial addition

val one : t

one is the constant polynomial one, the neutral element for polynomial multiplication

val add : t -> t -> t

add computes polynomial addition

val add_inplace : t -> t -> t -> unit

add_inplace res a b computes polynomial addition of a and b and writes the result in res

Note: res can be equal to either a or b

val sub : t -> t -> t

sub computes polynomial subtraction

val sub_inplace : t -> t -> t -> unit

sub_inplace res a b computes polynomial subtraction of a and b and writes the result in res

Note: res can be equal to either a or b

val mul : t -> t -> t

mul computes polynomial multiplication

Note: naive quadratic algorithm, result's size is the sum of arguments' size

val mul_by_scalar : scalar -> t -> t

mul_by_scalar computes multiplication of a polynomial by a blst_fr element

val mul_by_scalar_inplace : t -> scalar -> t -> unit

mul_by_scalar_inplace res s p computes multiplication of a polynomial p by a blst_fr element s and stores it in res

val linear : t list -> scalar list -> t

linear p s computes sum (mul p.(i) s.(i))

val opposite : t -> t

opposite computes polynomial negation

val opposite_inplace : t -> unit

opposite_inplace p computes polynomial negation

Note: The argument p is overwritten

val evaluate : t -> scalar -> scalar

evaluate p x evaluates a polynomial p at x

exception Rest_not_null of string

val division_x_z : t -> scalar -> t

division_x_z p z returns the quotient of the division of p by (X - z)

requires: length of p >= 2
Does NOT raise an error if p is not divisible.

val division_zs : t -> int -> t

division_zs p n returns the quotient of the division of p by (X^n - 1)

requires: length of p >= 2*n
Does NOT raise an error if p is not divisible, it can be checked using mul_zs.

val mul_zs : t -> int -> t

mul_zs p n returns the product of p and (X^n - 1)

requires: length of p >= n

val derivative : t -> t

derivative p returns the formal derivative of p

val split : int -> int -> t -> t list

val (=) : t -> t -> bool

Infix operator for equal

val (+) : t -> t -> t

Infix operator for add

val (-) : t -> t -> t

Infix operator for sub

val (*) : t -> t -> t

Infix operator for mul

val constant : scalar -> t

constant s creates a value of type t from a blst_fr element s