ZpzDom< IntType > Class Template Reference

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

#include <givzpzGen.h>

Public Types
enum	{ size_rep = sizeof(Residu_t) }
typedef IntType	Residu_t
	type to store residue
typedef IntType	Rep
	Representation of Element of the domain ZpzDom.
typedef IntType	Element
typedef Rep *	Array
	Representation of vector of the Element.
typedef const Rep *	constArray
	Representation of vector of the Element.

Public Member Functions
ZpzDom< IntType > &	operator= (const ZpzDom< IntType > &F)
	Copy.
	ZpzDom ()
	Constructor.
	ZpzDom (Residu_t p)
	Constructor.
	ZpzDom (const ZpzDom< IntType > &F)
	Constructor.
int	operator== (const ZpzDom< IntType > &BC) const
	(in)Equality
int	operator!= (const ZpzDom< IntType > &BC) const
	(in)Equality
int	areEqual (const Rep &a, const Rep &b) const
	(in)Equality
Residu_t	residu () const
	Access to the modulus.
Residu_t	size () const
	Access to the modulus.
Rep	access (const Rep &a) const
	Access to the modulus.
Residu_t	characteristic () const
	Access to the modulus.
Residu_t	characteristic (Residu_t p) const
	Access to the modulus.
Residu_t	cardinality () const
	Access to the modulus.
Rep &	init (Rep &a) const
	Init a representation.
void	init (const size_t, Array a, constArray b) const
	Init a representation.
Rep &	init (Rep &r, const long int a) const
	Init a representation.
Rep &	init (Rep &r, const unsigned long int a) const
	Init a representation.
Rep &	init (Rep &a, const int i) const
	Init a representation.
Rep &	init (Rep &a, const unsigned int i) const
	Init a representation.
Rep &	init (Rep &a, const IntType &i) const
	Init a representation.
Rep &	init (Rep &a, const double i) const
	Init a representation.
Rep &	init (Rep &a, const float i) const
	Init a representation.
float &	convert (float &r, const Rep &a) const
	Conversion.
double &	convert (double &r, const Rep &a) const
	Conversion.
long int &	convert (long int &r, const Rep &a) const
	Conversion.
unsigned long int &	convert (unsigned long int &r, const Rep &a) const
	Conversion.
IntType &	convert (IntType &i, const Rep &a) const
	Conversion.
int	isZero (const Rep &a) const
	Misc methods.
int	isOne (const Rep &a) const
	Misc methods.
size_t	length (const Rep &a) const
	Misc methods.
Rep &	mul (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	div (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	add (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	sub (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	neg (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	inv (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	mulin (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	divin (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	addin (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	subin (Rep &r, const Rep &a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	negin (Rep &r) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	invin (Rep &r) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	mul (const size_t sz, Array r, constArray a, constArray b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	mul (const size_t sz, Array r, constArray a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	div (const size_t sz, Array r, constArray a, constArray b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	div (const size_t sz, Array r, constArray a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	add (const size_t sz, Array r, constArray a, constArray b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	add (const size_t sz, Array r, constArray a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	sub (const size_t sz, Array r, constArray a, constArray b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	sub (const size_t sz, Array r, constArray a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	neg (const size_t sz, Array r, constArray a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	inv (const size_t sz, Array r, constArray a) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	axpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	axpy (const size_t sz, Array r, constArray a, constArray x, constArray c) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	axpyin (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	axpyin (const size_t sz, Array r, constArray a, constArray x) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	axmy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	axmy (const size_t sz, Array r, constArray a, constArray x, constArray c) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	axmyin (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	maxpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
Rep &	maxpyin (Rep &r, const Rep &a, const Rep &b) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	maxpyin (const size_t sz, Array r, constArray a, constArray x) const
	Operations with reduction: r <- a op b mod p, r <- op a mod p.
void	assign (const size_t sz, Array r, constArray a) const
	Misc: r <- a mod p.
Rep &	assign (Rep &r, const Rep &a) const
	Misc: r <- a mod p.
Rep &	assign (Rep &r, const long a) const
	Misc: r <- a mod p.
Rep &	assign (Rep &r, const unsigned long a) const
	Misc: r <- a mod p.
Rep &	assign (Rep &r, const short a) const
	Misc: r <- a mod p.
Rep &	assign (Rep &r, const unsigned short a) const
	Misc: r <- a mod p.
Rep &	reduceadd (Rep &r, const size_t sz, constArray a) const
	Misc.
Rep &	reducemul (Rep &r, const size_t sz, constArray a) const
	Misc.
void	i2d (const size_t sz, double *r, constArray a) const
	Misc.
void	d2i (const size_t sz, Array r, const double *a) const
	Misc.
std::istream &	read (std::istream &s)
	IO methods.
std::ostream &	write (std::ostream &s) const
	IO methods.
std::istream &	read (std::istream &s, Rep &a) const
	IO methods.
std::ostream &	write (std::ostream &s, const Rep &a) const
	IO methods.

Data Fields
const Rep	zero
	Constantes.
const Rep	one
	1
const Rep	mOne
	-1

Static Protected Member Functions
static void	Init ()
static void	End ()

Protected Attributes
Residu_t	_p
	data representation of the domain:
typedef GIV_randIter< ZpzDom < IntType >, Rep >	randIter
	Random.
template<class RandIter >
Rep &	random (RandIter &, Rep &r) const
	Random.
template<class RandIter >
Rep &	random (RandIter &, Rep &r, long s) const
	Random.
template<class RandIter >
Rep &	random (RandIter &, Rep &r, const Rep &b) const
	Random.
template<class RandIter >
Rep &	nonzerorandom (RandIter &, Rep &r) const
	Random.
template<class RandIter >
Rep &	nonzerorandom (RandIter &, Rep &r, long s) const
	Random.
template<class RandIter >
Rep &	nonzerorandom (RandIter &, Rep &r, const Rep &b) const
	Random.

---

Detailed Description

template<typename IntType>
class Givaro::ZpzDom< IntType >

This class implement the standard arithmetic with Modulo Elements.

• The representation of an integer a in Zpz is the value a % p

---

Member Typedef Documentation

typedef IntType Residu_t

type to store residue

typedef IntType Rep

Representation of Element of the domain ZpzDom.

typedef IntType Element

typedef Rep* Array

Representation of vector of the Element.

typedef const Rep* constArray

Representation of vector of the Element.

typedef GIV_randIter< ZpzDom<IntType> , Rep > randIter

Random.

---

Member Enumeration Documentation

anonymous enum

Enumerator:

size_rep

---

Constructor & Destructor Documentation

ZpzDom ( )

inline

Constructor.

ZpzDom ( Residu_t  p )

inline

Constructor.

ZpzDom ( const ZpzDom< IntType > &  F )

inline

Constructor.

---

Member Function Documentation

ZpzDom<IntType>& operator= ( const ZpzDom< IntType > &  F )

inline

Copy.

int operator== ( const ZpzDom< IntType > &  BC ) const

inline

(in)Equality

int operator!= ( const ZpzDom< IntType > &  BC ) const

inline

(in)Equality

int areEqual ( const Rep &  a, const Rep &  b  ) const

inline

(in)Equality

ZpzDom< IntType >::Residu_t residu ( ) const

inline

Access to the modulus.

Residu_t size ( ) const

inline

Access to the modulus.

Rep access ( const Rep &  a ) const

inline

Access to the modulus.

Residu_t characteristic ( ) const

inline

Access to the modulus.

Residu_t characteristic ( Residu_t  p ) const

inline

Access to the modulus.

Residu_t cardinality ( ) const

inline

Access to the modulus.

ZpzDom< IntType >::Rep & init ( Rep &  a ) const

inline

Init a representation.

void init ( const size_t  sz, Array  a, constArray  b  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  r, const long int  a  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  r, const unsigned long int  a  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  a, const int  i  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  a, const unsigned int  i  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  a, const IntType &  i  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  a, const double  i  ) const

inline

Init a representation.

ZpzDom< IntType >::Rep & init ( Rep &  a, const float  i  ) const

inline

Init a representation.

float& convert ( float &  r, const Rep &  a  ) const

inline

Conversion.

double& convert ( double &  r, const Rep &  a  ) const

inline

Conversion.

long int& convert ( long int &  r, const Rep &  a  ) const

inline

Conversion.

unsigned long int& convert ( unsigned long int &  r, const Rep &  a  ) const

inline

Conversion.

IntType& convert ( IntType &  i, const Rep &  a  ) const

inline

Conversion.

int isZero ( const Rep &  a ) const

inline

Misc methods.

int isOne ( const Rep &  a ) const

inline

Misc methods.

size_t length ( const Rep &  a ) const

inline

Misc methods.

ZpzDom< IntType >::Rep & mul ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & div ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & add ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & sub ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & neg ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & inv ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & mulin ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & divin ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & addin ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & subin ( Rep &  r, const Rep &  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & negin ( Rep &  r ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & invin ( Rep &  r ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void mul ( const size_t  sz, Array  r, constArray  a, constArray  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void mul ( const size_t  sz, Array  r, constArray  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void div ( const size_t  sz, Array  r, constArray  a, constArray  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void div ( const size_t  sz, Array  r, constArray  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void add ( const size_t  sz, Array  r, constArray  a, constArray  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void add ( const size_t  sz, Array  r, constArray  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void sub ( const size_t  sz, Array  r, constArray  a, constArray  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void sub ( const size_t  sz, Array  r, constArray  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void neg ( const size_t  sz, Array  r, constArray  a  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void inv	(	const size_t	sz,
		Array	r,
		constArray	a
	)		const

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & axpy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void axpy ( const size_t  sz, Array  r, constArray  a, constArray  x, constArray  c  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & axpyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void axpyin ( const size_t  sz, Array  r, constArray  a, constArray  x  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & axmy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void axmy ( const size_t  sz, Array  r, constArray  a, constArray  x, constArray  c  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & axmyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & maxpy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

ZpzDom< IntType >::Rep & maxpyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void maxpyin ( const size_t  sz, Array  r, constArray  a, constArray  x  ) const

inline

Operations with reduction: r <- a op b mod p, r <- op a mod p.

void assign ( const size_t  sz, Array  r, constArray  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & assign ( Rep &  r, const Rep &  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & assign ( Rep &  r, const long  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & assign ( Rep &  r, const unsigned long  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & assign ( Rep &  r, const short  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & assign ( Rep &  r, const unsigned short  a  ) const

inline

Misc: r <- a mod p.

ZpzDom< IntType >::Rep & random ( RandIter &  g, Rep &  r  ) const

inline

Random.

ZpzDom< IntType >::Rep & random ( RandIter &  g, Rep &  r, long  s  ) const

inline

Random.

ZpzDom< IntType >::Rep & random ( RandIter &  g, Rep &  r, const Rep &  b  ) const

inline

Random.

ZpzDom< IntType >::Rep & nonzerorandom ( RandIter &  g, Rep &  r  ) const

inline

Random.

ZpzDom< IntType >::Rep & nonzerorandom ( RandIter &  g, Rep &  r, long  s  ) const

inline

Random.

ZpzDom< IntType >::Rep & nonzerorandom ( RandIter &  g, Rep &  r, const Rep &  b  ) const

inline

Random.

Rep& reduceadd	(	Rep &	r,
		const size_t	sz,
		constArray	a
	)		const

Misc.

Rep& reducemul	(	Rep &	r,
		const size_t	sz,
		constArray	a
	)		const

Misc.

void i2d ( const size_t  sz, double *  r, constArray  a  ) const

inline

Misc.

void d2i ( const size_t  sz, Array  r, const double *  a  ) const

inline

Misc.

std::istream & read ( std::istream &  s )

inline

IO methods.

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

inline

IO methods.

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

inline

IO methods.

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

inline

IO methods.

static void Init ( )

inlinestaticprotected

??

static void End ( )

inlinestaticprotected

??

---

Field Documentation

const Rep zero

Constantes.

0

const Rep one

1

const Rep mOne

-1

Residu_t _p

protected

data representation of the domain:

---

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

• givzpzGen.h
• givzpzGen.inl