Modular< IntType, _Compute_t, Enable > Class Template Reference

Forward declaration for Givaro::Modular. More...

#include <modular-inttype.h>

Inheritance diagram for Modular< IntType, _Compute_t, Enable >:

Public Types
using	Storage_t = IntType
using	Residu_t = IntType
using	Compute_t = _Compute_t
using	Self_t = Modular<Storage_t, Compute_t>
using	Parent_t = Modular_implem<Storage_t, Compute_t, Residu_t>
using	Element = Storage_t
typedef ModularRandIter< Self_t >	RandIter
typedef GeneralRingNonZeroRandIter< Self_t >	NonZeroRandIter
enum
using	Element_ptr
using	ConstElement
using	ConstElement_ptr
using	is_elt_integral
using	is_elt_floating_point

Public Member Functions
Element &	init (Element &x) const
Element &	init (Element &x, const Integer &y) const final
template<typename T>
Element &	init (Element &r, const T &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
Element	minElement () const
Element	maxElement () const
Residu_t	residu () const
Residu_t	size () const
Residu_t	characteristic () const
T &	characteristic (T &p) const
Residu_t	cardinality () const
T &	cardinality (T &p) const
bool	isZero (const Element &a) const
bool	isOne (const Element &a) const
bool	isMOne (const Element &a) const
bool	areEqual (const Element &a, const Element &b) const
bool	isUnit (const Element &a) const
size_t	length (const Element a) const
bool	operator== (const Self_t &F) const
bool	operator!= (const Self_t &F) const
Element &	assign (Element &x, const Element &y) const
T &	convert (T &r, const Element &a) const
std::ostream &	write (std::ostream &s, const Element &a) const
std::ostream &	write (std::ostream &s, const E &a) const
std::ostream &	write (std::ostream &s, const E &a) const
std::ostream &	write (std::ostream &s, const E &a) const
std::ostream &	write (std::ostream &s) const
std::ostream &	write (std::ostream &s) const
std::ostream &	write (std::ostream &s) const
std::istream &	read (std::istream &s)
std::istream &	read (std::istream &, Element &) const

Static Public Member Functions
static const std::string	type_string ()
static Residu_t	minCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()
static Residu_t	maxCardinality ()

Data Fields
Residu_t	_p
Compute_t	_pc
const Element	zero
const Element	one
const Element	mOne

Static Public Attributes
static constexpr bool	is_elt_integral_v
static constexpr bool	is_elt_floating_point_v

Detailed Description

template<typename IntType, typename _Compute_t, typename Enable>
class Givaro::Modular< IntType, _Compute_t, Enable >

Forward declaration for Givaro::Modular.

This class implement the standard arithmetic with Modulo Elements.

Elements will be stored in the storage type. While arithmetics will occur on the unsigned version of COMP type. Example: Modular<int32_t, uint64_t>

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

Examples

examples/FiniteField/all_field.C, examples/FiniteField/exponentiation.C, examples/FiniteField/ff_arith.C, examples/FiniteField/kronecker.C, examples/FiniteField/zpz_atomic.C, examples/Integer/ModularSquareRoot.C, examples/Integer/iexponentiation.C, examples/Polynomial/PolynomialCRT.C, and examples/Polynomial/interpolate.C.

Member Typedef Documentation

Storage_t

template<typename IntType, typename _Compute_t, typename Enable>

using Storage_t = IntType

Residu_t

template<typename IntType, typename _Compute_t, typename Enable>

using Residu_t = IntType

Compute_t

template<typename IntType, typename _Compute_t, typename Enable>

using Compute_t = _Compute_t

Self_t

template<typename IntType, typename _Compute_t, typename Enable>

using Self_t = Modular<Storage_t, Compute_t>

Parent_t

template<typename IntType, typename _Compute_t, typename Enable>

using Parent_t = Modular_implem<Storage_t, Compute_t, Residu_t>

Element

template<typename IntType, typename _Compute_t, typename Enable>

using Element = Storage_t

RandIter

template<typename IntType, typename _Compute_t, typename Enable>

typedef ModularRandIter<Self_t> RandIter

NonZeroRandIter

template<typename IntType, typename _Compute_t, typename Enable>

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

Element_ptr

using Element_ptr

inherited

ConstElement

using ConstElement

inherited

ConstElement_ptr

using ConstElement_ptr

inherited

is_elt_integral

using is_elt_integral

inherited

is_elt_floating_point

using is_elt_floating_point

inherited

Member Enumeration Documentation

anonymous enum

anonymous enum

inherited

Member Function Documentation

init() [1/3]

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< std::is_integral< Storage_t >::value &&std::is_integral< Compute_t >::value &&(sizeof(Storage_t)==sizeof(Compute_t)||2 *sizeof(Storage_t)==sizeof(Compute_t))>::type >::Element & init ( Element & x ) const

inline

Examples

examples/FiniteField/exponentiation.C, and examples/Integer/iexponentiation.C.

init() [2/3]

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< std::is_integral< Storage_t >::value &&std::is_integral< Compute_t >::value &&(sizeof(Storage_t)==sizeof(Compute_t)||2 *sizeof(Storage_t)==sizeof(Compute_t))>::type >::Element & init ( Element & x, const Integer & y ) const

inlinefinalvirtual

Implements Modular_implem< IntType, _Compute_t, IntType >.

init() [3/3]

template<typename IntType, typename _Compute_t, typename Enable>

template<typename T>

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

inline

reduce() [1/2]

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< std::is_integral< Storage_t >::value &&std::is_integral< Compute_t >::value &&(sizeof(Storage_t)==sizeof(Compute_t)||2 *sizeof(Storage_t)==sizeof(Compute_t))>::type >::Element & reduce ( Element & x, const Element & y ) const

inline

reduce() [2/2]

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< std::is_integral< Storage_t >::value &&std::is_integral< Compute_t >::value &&(sizeof(Storage_t)==sizeof(Compute_t)||2 *sizeof(Storage_t)==sizeof(Compute_t))>::type >::Element & reduce ( Element & x ) const

inline

mul()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & mul ( Element & r, const Element & a, const Element & b ) const

inline

div()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & div ( Element & r, const Element & a, const Element & b ) const

inline

add()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & add ( Element & r, const Element & a, const Element & b ) const

inline

sub()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & sub ( Element & r, const Element & a, const Element & b ) const

inline

neg()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & neg ( Element & r, const Element & a ) const

inline

inv()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & inv ( Element & r, const Element & a ) const

inline

mulin()

template<typename IntType, typename COMP, typename Enable>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & mulin ( Element & r, const Element & a ) const

inline

divin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & divin ( Element & r, const Element & a ) const

inline

addin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & addin ( Element & r, const Element & a ) const

inline

subin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & subin ( Element & r, const Element & a ) const

inline

negin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & negin ( Element & r ) const

inline

invin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & invin ( Element & r ) const

inline

axpy()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & axpy ( Element & r, const Element & a, const Element & x, const Element & y ) const

inline

axpyin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & axpyin ( Element & r, const Element & a, const Element & x ) const

inline

axmy()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & axmy ( Element & r, const Element & a, const Element & x, const Element & y ) const

inline

axmyin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & axmyin ( Element & r, const Element & a, const Element & x ) const

inline

maxpy()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & maxpy ( Element & r, const Element & a, const Element & x, const Element & y ) const

inline

maxpyin()

template<typename Storage_t, typename Compute_t>

Modular< Storage_t, Compute_t, typenamestd::enable_if< is_same_ruint< Storage_t, Compute_t >::value||is_smaller_ruint< Storage_t, Compute_t >::value||is_same_rint< Storage_t, Compute_t >::value||is_smaller_rint< Storage_t, Compute_t >::value >::type >::Element & maxpyin ( Element & r, const Element & a, const Element & x ) const

inline

type_string()

template<typename IntType, typename _Compute_t, typename Enable>

static const std::string type_string ( )

inlinestatic

random()

template<typename IntType, typename _Compute_t, typename Enable>

template<class Random>

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

inline

nonzerorandom()

template<typename IntType, typename _Compute_t, typename Enable>

template<class Random>

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

inline

minElement()

Element minElement ( ) const

inlineinherited

maxElement()

Element maxElement ( ) const

inlineinherited

residu()

Residu_t residu ( ) const

inlineinherited

size()

Residu_t size ( ) const

inlineinherited

characteristic() [1/2]

Residu_t characteristic ( ) const

inlineinherited

characteristic() [2/2]

T & characteristic ( T & p ) const

inlineinherited

cardinality() [1/2]

Residu_t cardinality ( ) const

inlineinherited

cardinality() [2/2]

T & cardinality ( T & p ) const

inlineinherited

minCardinality()

static Residu_t minCardinality ( )

inlinestaticinherited

maxCardinality() [1/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [2/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [3/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [4/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [5/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [6/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [7/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [8/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [9/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [10/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [11/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [12/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

maxCardinality() [13/13]

static Residu_t maxCardinality ( )

inlinestaticinherited

isZero()

bool isZero ( const Element & a ) const

inlineinherited

isOne()

bool isOne ( const Element & a ) const

inlineinherited

isMOne()

bool isMOne ( const Element & a ) const

inlineinherited

areEqual()

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

inlineinherited

isUnit()

bool isUnit ( const Element & a ) const

inlineinherited

length()

size_t length ( const Element a ) const

inlineinherited

operator==()

bool operator== ( const Self_t & F ) const

inlineinherited

operator!=()

bool operator!= ( const Self_t & F ) const

inlineinherited

assign()

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

inlineinherited

convert()

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

inlineinherited

write() [1/7]

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

inlineinherited

Examples

examples/FiniteField/exponentiation.C, examples/FiniteField/kronecker.C, and examples/Integer/iexponentiation.C.

write() [2/7]

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

inlineinherited

write() [3/7]

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

inlineinherited

write() [4/7]

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

inlineinherited

write() [5/7]

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

inlineinherited

write() [6/7]

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

inlineinherited

write() [7/7]

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

inlineinherited

read() [1/2]

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

inlineinherited

Examples

examples/Polynomial/interpolate.C.

read() [2/2]

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

inlineinherited

Field Documentation

_p

template<typename IntType, typename _Compute_t, typename Enable>

Residu_t _p

_pc

template<typename IntType, typename _Compute_t, typename Enable>

Compute_t _pc

zero

template<typename IntType, typename _Compute_t, typename Enable>

const Element zero

one

template<typename IntType, typename _Compute_t, typename Enable>

const Element one

mOne

template<typename IntType, typename _Compute_t, typename Enable>

const Element mOne

is_elt_integral_v

bool is_elt_integral_v

staticconstexprinherited

is_elt_floating_point_v

bool is_elt_floating_point_v

staticconstexprinherited

---

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

• modular-general.h
• modular-inttype.h
• modular-floating.inl
• modular-integer.inl
• modular-integral.inl
• modular-inttype.inl
• modular-log16.inl
• modular-ruint.inl