This class implements the standard arithmetic with Modulo Elements. More...

#include <montgomery-int32.h>

Public Types
enum	{ size_rep = sizeof(Residu_t) }

using	Self_t = Montgomery< int32_t >

using	Element = uint32_t

using	Element_ptr = Element *

using	ConstElement = const Element

using	ConstElement_ptr = const Element *

using	Residu_t = uint32_t

typedef ModularRandIter< Self_t >	RandIter

typedef GeneralRingNonZeroRandIter< Self_t >	NonZeroRandIter

Public Member Functions
	Montgomery ()

	Montgomery (Residu_t p, int=1)

	Montgomery (const Self_t &F)

Self_t &	operator= (const Self_t &F)

Element	minElement () const

Element	maxElement () const

Residu_t	residu () const

Residu_t	size () const

Residu_t	characteristic () const

Residu_t	cardinality () const

template<class T >
T &	characteristic (T &p) const

template<class T >
T &	cardinality (T &p) const

bool	isZero (const Element &a) const

bool	isOne (const Element &a) const

bool	isMOne (const Element &a) const

bool	isUnit (const Element &a) const

bool	areEqual (const Element &a, const Element &b) const

size_t	length (const Element a) const

bool	operator== (const Self_t &F) const

bool	operator!= (const Self_t &F) const

Element &	init (Element &x) const

Element &	init (Element &x, const double a) const

Element &	init (Element &x, const int64_t a) const

Element &	init (Element &x, const uint64_t a) const

Element &	init (Element &x, const Integer &a) const

template<typename T >
Element &	init (Element &r, const T &a) const

Element &	assign (Element &x, const Element &y) const

template<typename T >
T &	convert (T &r, const Element &a) const

Element &	reduce (Element &x, const Element &y) const

Element &	reduce (Element &x) const

Element &	mul (Element &r, const Element &a, const Element &b) const

Element &	div (Element &r, const Element &a, const Element &b) const

Element &	add (Element &r, const Element &a, const Element &b) const

Element &	sub (Element &r, const Element &a, const Element &b) const

Element &	neg (Element &r, const Element &a) const

Element &	inv (Element &r, const Element &a) const

Element &	mulin (Element &r, const Element &a) const

Element &	divin (Element &r, const Element &a) const

Element &	addin (Element &r, const Element &a) const

Element &	subin (Element &r, const Element &a) const

Element &	negin (Element &r) const

Element &	invin (Element &r) const

Element &	axpy (Element &r, const Element &a, const Element &x, const Element &y) const

Element &	axpyin (Element &r, const Element &a, const Element &x) const

Element &	axmy (Element &r, const Element &a, const Element &x, const Element &y) const

Element &	axmyin (Element &r, const Element &a, const Element &x) const

Element &	maxpy (Element &r, const Element &a, const Element &x, const Element &y) const

Element &	maxpyin (Element &r, const Element &a, const Element &x) const

template<class Random >
Element &	random (Random &g, Element &r) const

template<class Random >
Element &	nonzerorandom (Random &g, Element &a) const

std::ostream &	write (std::ostream &s) const

std::istream &	read (std::istream &s, Element &a) const

std::ostream &	write (std::ostream &s, const Element &a) const

Static Public Member Functions
static Residu_t	maxCardinality ()

static Residu_t	minCardinality ()

Data Fields
const Element	zero = 0

const Element	one

const Element	mOne

Protected Member Functions
Element &	redc (Element &, const Element) const

Element	redcal (const Element) const

Element	redcsal (const Element) const

Element &	redcin (Element &) const

Element &	redcs (Element &, const Element) const

Element &	redcsin (Element &) const

Protected Attributes
Residu_t	_p

Residu_t	_Bp

Residu_t	_B2p

Residu_t	_B3p

Residu_t	_nim

double	_dp

Detailed Description

This class implements the standard arithmetic with Modulo Elements.

Reduction is made through Montgomery's reduction. Representation of a is by storing (aB).

We must have gcd(p,2)=1
We must have , i.e. $2<p \leq 40504$ for .
m max is 40503
p max is 40499

Member Typedef Documentation

◆ Self_t

using Self_t = Montgomery<int32_t>

◆ Element

using Element = uint32_t

◆ Element_ptr

using Element_ptr = Element*

◆ ConstElement

using ConstElement = const Element

◆ ConstElement_ptr

using ConstElement_ptr = const Element*

◆ Residu_t

using Residu_t = uint32_t

◆ RandIter

typedef ModularRandIter<Self_t> RandIter

◆ NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
size_rep

Constructor & Destructor Documentation

◆ Montgomery() [1/3]

Montgomery ( )

inline

◆ Montgomery() [2/3]

Montgomery	(	Residu_t	p,
		int	= `1`
	)

inline

◆ Montgomery() [3/3]

Montgomery ( const Self_t & F )

inline

Member Function Documentation

◆ operator=()

Self_t& operator= ( const Self_t & F )

inline

◆ minElement()

Element minElement ( ) const

inline

◆ maxElement()

Element maxElement ( ) const

inline

◆ residu()

Residu_t residu ( ) const

inline

◆ size()

Residu_t size ( ) const

inline

◆ characteristic() [1/2]

Residu_t characteristic ( ) const

inline

◆ cardinality() [1/2]

Residu_t cardinality ( ) const

inline

◆ characteristic() [2/2]

T& characteristic ( T & p ) const

inline

◆ cardinality() [2/2]

T& cardinality ( T & p ) const

inline

◆ maxCardinality()

static Residu_t maxCardinality ( )

inlinestatic

◆ minCardinality()

static Residu_t minCardinality ( )

inlinestatic

◆ isZero()

bool isZero ( const Element & a ) const

inline

◆ isOne()

bool isOne ( const Element & a ) const

inline

◆ isMOne()

bool isMOne ( const Element & a ) const

inline

◆ isUnit()

bool isUnit ( const Element & a ) const

inline

◆ areEqual()

bool areEqual	(	const Element &	a,
		const Element &	b
	)		const

inline

◆ length()

size_t length ( const Element a ) const

inline

◆ operator==()

bool operator== ( const Self_t & F ) const

inline

◆ operator!=()

bool operator!= ( const Self_t & F ) const

inline

◆ init() [1/6]

Element& init ( Element & x ) const

inline

◆ init() [2/6]

Montgomery< int32_t >::Element & init	(	Element &	x,
		const double	a
	)		const

inline

◆ init() [3/6]

Montgomery< int32_t >::Element & init	(	Element &	x,
		const int64_t	a
	)		const

inline

◆ init() [4/6]

Montgomery< int32_t >::Element & init	(	Element &	x,
		const uint64_t	a
	)		const

inline

◆ init() [5/6]

Montgomery< int32_t >::Element & init	(	Element &	x,
		const Integer &	a
	)		const

inline

◆ init() [6/6]

Element& init	(	Element &	r,
		const T &	a
	)		const

inline

◆ assign()

Element& assign	(	Element &	x,
		const Element &	y
	)		const

inline

◆ convert()

T& convert	(	T &	r,
		const Element &	a
	)		const

inline

◆ reduce() [1/2]

Element& reduce	(	Element &	x,
		const Element &	y
	)		const

inline

◆ reduce() [2/2]

Element& reduce ( Element & x ) const

inline

◆ mul()

Montgomery< int32_t >::Element & mul	(	Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inline

◆ div()

Montgomery< int32_t >::Element & div	(	Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inline

◆ add()

Montgomery< int32_t >::Element & add	(	Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inline

◆ sub()

Montgomery< int32_t >::Element & sub	(	Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inline

◆ neg()

Montgomery< int32_t >::Element & neg	(	Element &	r,
		const Element &	a
	)		const

inline

◆ inv()

Montgomery< int32_t >::Element & inv	(	Element &	r,
		const Element &	a
	)		const

inline

◆ mulin()

Montgomery< int32_t >::Element & mulin	(	Element &	r,
		const Element &	a
	)		const

inline

◆ divin()

Montgomery< int32_t >::Element & divin	(	Element &	r,
		const Element &	a
	)		const

inline

◆ addin()

Montgomery< int32_t >::Element & addin	(	Element &	r,
		const Element &	a
	)		const

inline

◆ subin()

Montgomery< int32_t >::Element & subin	(	Element &	r,
		const Element &	a
	)		const

inline

◆ negin()

Montgomery< int32_t >::Element & negin ( Element & r ) const

inline

◆ invin()

Montgomery< int32_t >::Element & invin ( Element & r ) const

inline

◆ axpy()

Montgomery< int32_t >::Element & axpy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

◆ axpyin()

Montgomery< int32_t >::Element & axpyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

◆ axmy()

Montgomery< int32_t >::Element & axmy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

◆ axmyin()

Montgomery< int32_t >::Element & axmyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

◆ maxpy()

Montgomery< int32_t >::Element & maxpy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

◆ maxpyin()

Montgomery< int32_t >::Element & maxpyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

◆ random()

Element& random	(	Random &	g,
		Element &	r
	)		const

inline

◆ nonzerorandom()

Element& nonzerorandom	(	Random &	g,
		Element &	a
	)		const

inline

◆ write() [1/2]

std::ostream & write ( std::ostream & s ) const

inline

◆ read()

std::istream & read	(	std::istream &	s,
		Element &	a
	)		const

inline

◆ write() [2/2]

std::ostream & write	(	std::ostream &	s,
		const Element &	a
	)		const

inline

◆ redc()

Montgomery< int32_t >::Element & redc	(	Element &	r,
		const Element	c
	)		const

inlineprotected

◆ redcal()

Montgomery< int32_t >::Element redcal ( const Element c ) const

inlineprotected

◆ redcsal()

Montgomery< int32_t >::Element redcsal ( const Element c ) const

inlineprotected

◆ redcin()

Montgomery< int32_t >::Element & redcin ( Element & r ) const

inlineprotected

◆ redcs()

Montgomery< int32_t >::Element & redcs	(	Element &	r,
		const Element	c
	)		const

inlineprotected

◆ redcsin()

Montgomery< int32_t >::Element & redcsin ( Element & r ) const

inlineprotected

Field Documentation

◆ zero

const Element zero = 0

◆ one

const Element one

◆ mOne

const Element mOne

◆ _p

Residu_t _p

protected

◆ _Bp

Residu_t _Bp

protected

◆ _B2p

Residu_t _B2p

protected

◆ _B3p

Residu_t _B3p

protected

◆ _nim

Residu_t _nim

protected

◆ _dp

double _dp

protected

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

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Self_t

◆ Element

◆ Element_ptr

◆ ConstElement

◆ ConstElement_ptr

◆ Residu_t

◆ RandIter

◆ NonZeroRandIter

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Montgomery() [1/3]

◆ Montgomery() [2/3]

◆ Montgomery() [3/3]

Member Function Documentation

◆ operator=()

◆ minElement()

◆ maxElement()

◆ residu()

◆ size()

◆ characteristic() [1/2]

◆ cardinality() [1/2]

◆ characteristic() [2/2]

◆ cardinality() [2/2]

◆ maxCardinality()

◆ minCardinality()

◆ isZero()

◆ isOne()

◆ isMOne()

◆ isUnit()

◆ areEqual()

◆ length()

◆ operator==()

◆ operator!=()

◆ init() [1/6]

◆ init() [2/6]

◆ init() [3/6]

◆ init() [4/6]

◆ init() [5/6]

◆ init() [6/6]

◆ assign()

◆ convert()

◆ reduce() [1/2]

◆ reduce() [2/2]

◆ mul()

◆ div()

◆ add()

◆ sub()

◆ neg()

◆ inv()

◆ mulin()

◆ divin()

◆ addin()

◆ subin()

◆ negin()

◆ invin()

◆ axpy()

◆ axpyin()

◆ axmy()

◆ axmyin()

◆ maxpy()

◆ maxpyin()

◆ random()

◆ nonzerorandom()

◆ write() [1/2]

◆ read()

◆ write() [2/2]

◆ redc()

◆ redcal()

◆ redcsal()

◆ redcin()

◆ redcs()