#include <fp.hpp>

Collaboration diagram for libff::Fp_model< n, modulus >:

Public Member Functions
	Fp_model ()

	Fp_model (const bigint< n > &b)

	Fp_model (const long x, const bool is_unsigned=false)

void	set_ulong (const unsigned long x)

void	mul_reduce (const bigint< n > &other)

void	clear ()

bigint< n >	as_bigint () const

unsigned long	as_ulong () const

bool	operator== (const Fp_model &other) const

bool	operator!= (const Fp_model &other) const

bool	is_zero () const

void	print () const

Fp_model &	operator+= (const Fp_model &other)

Fp_model &	operator-= (const Fp_model &other)

Fp_model &	operator*= (const Fp_model &other)

Fp_model &	operator^= (const unsigned long pow)

template<mp_size_t m>
Fp_model &	operator^= (const bigint< m > &pow)

Fp_model	operator+ (const Fp_model &other) const

Fp_model	operator- (const Fp_model &other) const

Fp_model	operator* (const Fp_model &other) const

Fp_model	operator- () const

Fp_model	squared () const

Fp_model &	invert ()

Fp_model	inverse () const

Fp_model	sqrt () const

Fp_model	operator^ (const unsigned long pow) const

template<mp_size_t m>
Fp_model	operator^ (const bigint< m > &pow) const

Static Public Member Functions
static bool	modulus_is_valid ()

static size_t	size_in_bits ()

static size_t	capacity ()

static bigint< n >	field_char ()

static Fp_model< n, modulus >	zero ()

static Fp_model< n, modulus >	one ()

static Fp_model< n, modulus >	random_element ()

static Fp_model< n, modulus >	geometric_generator ()

static Fp_model< n, modulus >	arithmetic_generator ()

Public Attributes
bigint< n >	mont_repr

Static Public Attributes
static const mp_size_t	num_limbs = n

static const constexpr bigint< n > &	mod = modulus

static size_t	num_bits

static bigint< n >	euler

static size_t	s

static bigint< n >	t

static bigint< n >	t_minus_1_over_2

static Fp_model< n, modulus >	nqr

static Fp_model< n, modulus >	nqr_to_t

static Fp_model< n, modulus >	multiplicative_generator

static Fp_model< n, modulus >	root_of_unity

static mp_limb_t	inv

static bigint< n >	Rsquared

static bigint< n >	Rcubed

Friends
std::ostream &	operator (std::ostream &out, const Fp_model< n, modulus > &p)

std::istream &	operator>> (std::istream &in, Fp_model< n, modulus > &p)

Detailed Description

template<mp_size_t n, const bigint< n > & modulus>
class libff::Fp_model< n, modulus >

Arithmetic in the finite field F[p], for prime p of fixed length.

This class implements Fp-arithmetic, for a large prime p, using a fixed number of words. It is optimized for tight memory consumption, so the modulus p is passed as a template parameter, to avoid per-element overheads.

The implementation is mostly a wrapper around GMP's MPN (constant-size integers). But for the integer sizes of interest for libff (3 to 5 limbs of 64 bits each), we implement performance-critical routines, like addition and multiplication, using hand-optimzied assembly code.

Definition at line 40 of file fp.hpp.

Constructor & Destructor Documentation

◆ Fp_model() [1/3]

template<mp_size_t n, const bigint< n > & modulus>

libff::Fp_model< n, modulus >::Fp_model ( )

inline

Definition at line 68 of file fp.hpp.

68{};

◆ Fp_model() [2/3]

template<mp_size_t n, const bigint< n > & modulus>

libff::Fp_model< n, modulus >::Fp_model ( const bigint< n > & b )

◆ Fp_model() [3/3]

template<mp_size_t n, const bigint< n > & modulus>

libff::Fp_model< n, modulus >::Fp_model	(	const long	x,
		const bool	is_unsigned = false )

Member Function Documentation

◆ arithmetic_generator()

template<mp_size_t n, const bigint< n > & modulus>

static Fp_model< n, modulus > libff::Fp_model< n, modulus >::arithmetic_generator ( )

static

◆ as_bigint()

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::as_bigint ( ) const

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◆ as_ulong()

template<mp_size_t n, const bigint< n > & modulus>

unsigned long libff::Fp_model< n, modulus >::as_ulong ( ) const

◆ capacity()

template<mp_size_t n, const bigint< n > & modulus>

static size_t libff::Fp_model< n, modulus >::capacity ( )

inlinestatic

Definition at line 115 of file fp.hpp.

115{ return num_bits - 1; }

libff::Fp_model::num_bits

static size_t num_bits

Definition fp.hpp:53

◆ clear()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp_model< n, modulus >::clear ( )

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◆ field_char()

template<mp_size_t n, const bigint< n > & modulus>

static bigint< n > libff::Fp_model< n, modulus >::field_char ( )

inlinestatic

Definition at line 116 of file fp.hpp.

116{ return modulus; }

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◆ geometric_generator()

template<mp_size_t n, const bigint< n > & modulus>

static Fp_model< n, modulus > libff::Fp_model< n, modulus >::geometric_generator ( )

static

◆ inverse()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::inverse ( ) const

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◆ invert()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model & libff::Fp_model< n, modulus >::invert ( )

◆ is_zero()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp_model< n, modulus >::is_zero ( ) const

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◆ modulus_is_valid()

template<mp_size_t n, const bigint< n > & modulus>

static bool libff::Fp_model< n, modulus >::modulus_is_valid ( )

inlinestatic

Definition at line 66 of file fp.hpp.

66{ return modulus.data[n-1] != 0; } // mpn inverse assumes that highest limb is non-zero

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◆ mul_reduce()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp_model< n, modulus >::mul_reduce ( const bigint< n > & other )

◆ one()

template<mp_size_t n, const bigint< n > & modulus>

static Fp_model< n, modulus > libff::Fp_model< n, modulus >::one ( )

static

◆ operator!=()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp_model< n, modulus >::operator!= ( const Fp_model< n, modulus > & other ) const

◆ operator*()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::operator* ( const Fp_model< n, modulus > & other ) const

◆ operator*=()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model & libff::Fp_model< n, modulus >::operator*= ( const Fp_model< n, modulus > & other )

◆ operator+()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::operator+ ( const Fp_model< n, modulus > & other ) const

◆ operator+=()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model & libff::Fp_model< n, modulus >::operator+= ( const Fp_model< n, modulus > & other )

◆ operator-() [1/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::operator- ( ) const

◆ operator-() [2/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::operator- ( const Fp_model< n, modulus > & other ) const

◆ operator-=()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model & libff::Fp_model< n, modulus >::operator-= ( const Fp_model< n, modulus > & other )

◆ operator==()

template<mp_size_t n, const bigint< n > & modulus>

bool libff::Fp_model< n, modulus >::operator== ( const Fp_model< n, modulus > & other ) const

◆ operator^() [1/2]

template<mp_size_t n, const bigint< n > & modulus>

template<mp_size_t m>

Fp_model libff::Fp_model< n, modulus >::operator^ ( const bigint< m > & pow ) const

◆ operator^() [2/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::operator^ ( const unsigned long pow ) const

◆ operator^=() [1/2]

template<mp_size_t n, const bigint< n > & modulus>

template<mp_size_t m>

Fp_model & libff::Fp_model< n, modulus >::operator^= ( const bigint< m > & pow )

◆ operator^=() [2/2]

template<mp_size_t n, const bigint< n > & modulus>

Fp_model & libff::Fp_model< n, modulus >::operator^= ( const unsigned long pow )

◆ print()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp_model< n, modulus >::print ( ) const

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◆ random_element()

template<mp_size_t n, const bigint< n > & modulus>

static Fp_model< n, modulus > libff::Fp_model< n, modulus >::random_element ( )

static

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◆ set_ulong()

template<mp_size_t n, const bigint< n > & modulus>

void libff::Fp_model< n, modulus >::set_ulong ( const unsigned long x )

◆ size_in_bits()

template<mp_size_t n, const bigint< n > & modulus>

static size_t libff::Fp_model< n, modulus >::size_in_bits ( )

inlinestatic

Definition at line 114 of file fp.hpp.

114{ return num_bits; }

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◆ sqrt()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::sqrt ( ) const

◆ squared()

template<mp_size_t n, const bigint< n > & modulus>

Fp_model libff::Fp_model< n, modulus >::squared ( ) const

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◆ zero()

template<mp_size_t n, const bigint< n > & modulus>

static Fp_model< n, modulus > libff::Fp_model< n, modulus >::zero ( )

static

Friends And Related Symbol Documentation

◆ operator

template<mp_size_t n, const bigint< n > & modulus>

std::ostream & operator	(	std::ostream &	out,
		const Fp_model< n, modulus > &	p )

friend

◆ operator>>

template<mp_size_t n, const bigint< n > & modulus>

std::istream & operator>>	(	std::istream &	in,
		Fp_model< n, modulus > &	p )

friend

Member Data Documentation

◆ euler

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::euler

static

Definition at line 54 of file fp.hpp.

◆ inv

template<mp_size_t n, const bigint< n > & modulus>

mp_limb_t libff::Fp_model< n, modulus >::inv

static

Definition at line 62 of file fp.hpp.

◆ mod

template<mp_size_t n, const bigint< n > & modulus>

const constexpr bigint<n>& libff::Fp_model< n, modulus >::mod = modulus

staticconstexpr

Definition at line 45 of file fp.hpp.

◆ mont_repr

template<mp_size_t n, const bigint< n > & modulus>

bigint<n> libff::Fp_model< n, modulus >::mont_repr

Definition at line 42 of file fp.hpp.

◆ multiplicative_generator

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp_model< n, modulus >::multiplicative_generator

static

Definition at line 60 of file fp.hpp.

◆ nqr

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp_model< n, modulus >::nqr

static

Definition at line 58 of file fp.hpp.

◆ nqr_to_t

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp_model< n, modulus >::nqr_to_t

static

Definition at line 59 of file fp.hpp.

◆ num_bits

template<mp_size_t n, const bigint< n > & modulus>

size_t libff::Fp_model< n, modulus >::num_bits

static

Definition at line 53 of file fp.hpp.

◆ num_limbs

template<mp_size_t n, const bigint< n > & modulus>

const mp_size_t libff::Fp_model< n, modulus >::num_limbs = n

static

Definition at line 44 of file fp.hpp.

◆ Rcubed

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::Rcubed

static

Definition at line 64 of file fp.hpp.

◆ root_of_unity

template<mp_size_t n, const bigint< n > & modulus>

Fp_model< n, modulus > libff::Fp_model< n, modulus >::root_of_unity

static

Definition at line 61 of file fp.hpp.

◆ Rsquared

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::Rsquared

static

Definition at line 63 of file fp.hpp.

◆ s

template<mp_size_t n, const bigint< n > & modulus>

size_t libff::Fp_model< n, modulus >::s

static

Definition at line 55 of file fp.hpp.

◆ t

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::t

static

Definition at line 56 of file fp.hpp.

◆ t_minus_1_over_2

template<mp_size_t n, const bigint< n > & modulus>

bigint< n > libff::Fp_model< n, modulus >::t_minus_1_over_2

static

Definition at line 57 of file fp.hpp.

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

libraries/fc/libraries/ff/libff/algebra/fields/fp.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Fp_model() [1/3]

◆ Fp_model() [2/3]

◆ Fp_model() [3/3]

Member Function Documentation

◆ arithmetic_generator()

◆ as_bigint()

◆ as_ulong()

◆ capacity()

◆ clear()

◆ field_char()

◆ geometric_generator()

◆ inverse()

◆ invert()

◆ is_zero()

◆ modulus_is_valid()

◆ mul_reduce()

◆ one()

◆ operator!=()

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator==()

◆ operator^() [1/2]

◆ operator^() [2/2]

◆ operator^=() [1/2]

◆ operator^=() [2/2]

◆ print()

◆ random_element()

◆ set_ulong()

◆ size_in_bits()

◆ sqrt()

◆ squared()

◆ zero()

Friends And Related Symbol Documentation

◆ operator

◆ operator>>

Member Data Documentation

◆ euler

◆ inv

◆ mod

◆ mont_repr

◆ multiplicative_generator

◆ nqr

◆ nqr_to_t

◆ num_bits

◆ num_limbs

◆ Rcubed

◆ root_of_unity

◆ Rsquared

◆ s

◆ t

◆ t_minus_1_over_2