nil::crypto3::math::arithmetic_sequence_domain< FieldType > Class Template Reference

#include <arithmetic_sequence_domain.hpp>

Inheritance diagram for nil::crypto3::math::arithmetic_sequence_domain< FieldType >:

Collaboration diagram for nil::crypto3::math::arithmetic_sequence_domain< FieldType >:

Public Types
typedef FieldType	field_type

Public Member Functions
void	add_poly_z (const value_type &coeff, std::vector< value_type > &H)
	arithmetic_sequence_domain (const std::size_t m)
value_type	compute_vanishing_polynomial (const value_type &t)
void	divide_by_z_on_coset (std::vector< value_type > &P)
void	do_precomputation ()
std::vector< value_type >	evaluate_all_lagrange_polynomials (const value_type &t)
void	fft (std::vector< value_type > &a)
value_type	get_domain_element (const std::size_t idx)
void	inverse_fft (std::vector< value_type > &a)

Public Attributes
value_type	arithmetic_generator
std::vector< value_type >	arithmetic_sequence
value_type	domain
value_type	domain_inverse
value_type	generator
value_type	generator_inverse
std::size_t	generator_size
std::size_t	log2_size
std::size_t	m
bool	precomputation_sentinel
value_type	root
value_type	root_inverse
std::vector< std::vector< std::vector< value_type > > >	subproduct_tree

Member Typedef Documentation

field_type

template<typename FieldType >

typedef FieldType nil::crypto3::math::arithmetic_sequence_domain< FieldType >::field_type

Constructor & Destructor Documentation

arithmetic_sequence_domain()

template<typename FieldType >

nil::crypto3::math::arithmetic_sequence_domain< FieldType >::arithmetic_sequence_domain ( const std::size_t  m )

inline

Member Function Documentation

add_poly_z()

template<typename FieldType >

void nil::crypto3::math::arithmetic_sequence_domain< FieldType >::add_poly_z ( const value_type &  coeff, std::vector< value_type > &  H  )

inlinevirtual

Add the coefficients of the vanishing polynomial of S to the coefficients of the polynomial H.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

compute_vanishing_polynomial()

template<typename FieldType >

value_type nil::crypto3::math::arithmetic_sequence_domain< FieldType >::compute_vanishing_polynomial ( const value_type &  t )

inlinevirtual

Evaluate the vanishing polynomial of S at the field element t.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

divide_by_z_on_coset()

template<typename FieldType >

void nil::crypto3::math::arithmetic_sequence_domain< FieldType >::divide_by_z_on_coset ( std::vector< value_type > &  P )

inlinevirtual

Multiply by the evaluation, on a coset of S, of the inverse of the vanishing polynomial of S.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

do_precomputation()

template<typename FieldType >

void nil::crypto3::math::arithmetic_sequence_domain< FieldType >::do_precomputation ( )

inline

evaluate_all_lagrange_polynomials()

template<typename FieldType >

std::vector<value_type> nil::crypto3::math::arithmetic_sequence_domain< FieldType >::evaluate_all_lagrange_polynomials ( const value_type &  t )

inlinevirtual

Evaluate all Lagrange polynomials.

The inputs are:

• an integer m
• an element t The output is a vector (b_{0},...,b_{m-1}) where b_{i} is the evaluation of L_{i,S}(z) at z = t.

If t equals one of the arithmetic progression values, then output 1 at the right place, and 0 elsewhere.

Otherwise, if t does not equal any of the arithmetic progression values, then compute each Lagrange coefficient.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

fft()

template<typename FieldType >

void nil::crypto3::math::arithmetic_sequence_domain< FieldType >::fft ( std::vector< value_type > &  a )

inlinevirtual

Compute the FFT, over the domain S, of the vector a.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

get_domain_element()

template<typename FieldType >

value_type nil::crypto3::math::arithmetic_sequence_domain< FieldType >::get_domain_element ( const std::size_t  idx )

inlinevirtual

Get the idx-th element in S.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

inverse_fft()

template<typename FieldType >

void nil::crypto3::math::arithmetic_sequence_domain< FieldType >::inverse_fft ( std::vector< value_type > &  a )

inlinevirtual

Compute the inverse FFT, over the domain S, of the vector a.

Implements nil::crypto3::math::evaluation_domain< FieldType >.

Member Data Documentation

arithmetic_generator

template<typename FieldType >

value_type nil::crypto3::math::arithmetic_sequence_domain< FieldType >::arithmetic_generator

arithmetic_sequence

template<typename FieldType >

std::vector<value_type> nil::crypto3::math::arithmetic_sequence_domain< FieldType >::arithmetic_sequence

domain

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::domain

inherited

domain_inverse

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::domain_inverse

inherited

generator

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::generator

inherited

generator_inverse

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::generator_inverse

inherited

generator_size

template<typename FieldType >

std::size_t nil::crypto3::math::evaluation_domain< FieldType >::generator_size

inherited

log2_size

template<typename FieldType >

std::size_t nil::crypto3::math::evaluation_domain< FieldType >::log2_size

inherited

m

template<typename FieldType >

std::size_t nil::crypto3::math::evaluation_domain< FieldType >::m

inherited

precomputation_sentinel

template<typename FieldType >

bool nil::crypto3::math::arithmetic_sequence_domain< FieldType >::precomputation_sentinel

root

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::root

inherited

root_inverse

template<typename FieldType >

value_type nil::crypto3::math::evaluation_domain< FieldType >::root_inverse

inherited

subproduct_tree

template<typename FieldType >

std::vector<std::vector<std::vector<value_type> > > nil::crypto3::math::arithmetic_sequence_domain< FieldType >::subproduct_tree

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The documentation for this class was generated from the following file:

• arithmetic_sequence_domain.hpp