Namespace in which the whole Givaro library resides. More...

Namespaces
	AlgorithmType
	Information about the type of method.

Data Structures
struct	_perfArray0< T >
	defined by marco GIVARO_PERF_DEFCLASS. ref counting and stuff. More...

class	Array0
	NODOC. More...

class	ArrayAllocatort
	ArrayAllocator: class for allocation of arrays. More...

class	Array0Tag
	Array0Tag. More...

class	ArrayFixed
	ArrayFixed. More...

struct	__giv_map_less_ith
	Map opcode on all Elements less or requal that ith. More...

class	Bits
	Bits. More...

struct	ElemRef
	Elem Ref. More...

struct	ElemConstRef
	Elem const Ref. More...

struct	Pair
	Pair. More...

class	Key
	The class Key. More...

class	HashTable
	Hash table. More...

class	List0
	ListO. More...

class	Stack
	Stack. More...

struct	ChineseRemainder
	CRA. More...

struct	ChineseRemainder< Ring, Domain, false >
	CRA2. More...

class	GIV_ExtensionrandIter
	Extension rand iters. More...

class	Extension
	Extension. More...

class	GF2
	Integers modulo 2. More...

class	GFqDom
	class GFqDom More...

class	GFqExtFast
	GFq Ext. More...

class	GFqExt
	GFq Ext (other) More...

struct	GFqKronecker
	GFqKronecker. More...

class	Primes16
	class Primes16 More...

class	RNSsystem
	class RNSsystem. More...

class	RNSsystemFixed
	NO DOC. More...

class	QField< Rational >
	Rational Domain. More...

struct	StaticElement
	Static Element. More...

class	Integer
	This is the Integer class. More...

class	ZRing< Integer >
	Integer Domain, Specialization of ZRing. More...

class	IntFactorDom
	Integer Factor Domain. More...

class	IntNumTheoDom
	Num theory Domain. More...

class	FermatDom
	Fermat numbers. More...

class	IntPrimeDom
	Primality tests. More...

class	IntRNSsystem
	RNS system class. No doc. More...

class	IntRSADom
	RSA domain. More...

class	IntSqrtModDom
	Modular square roots. More...

class	RandomIntegerIterator
	Random Integer Iterator. More...

class	GivMMInfo
	Static informations of memory allocation. More...

class	BlocFreeList
	Data structure of a bloc. More...

class	GivMMFreeList
	Implementation of a memory manager with free-lists. More...

class	GivMMRefCount
	Memory management with reference counter on allocated data. More...

class	GivaroMM
	Memory manager that allocates array of object of type T for. More...

class	RefCountPtr
	Refcount Pointer. More...

class	RefCounter
	Ref counter. More...

class	Rational
	Rationals. No doc. More...

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

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

class	Modular< Integer >
	This class implement the standard arithmetic with Modulo Elements. More...

class	Modular< Log16 >
	This class implement the standard arithmetic with Modulo Elements. More...

class	Montgomery< int32_t >
	This class implements the standard arithmetic with Modulo Elements. More...

class	Montgomery< RecInt::ruint< K > >
	The recint-based Montgomery ring. More...

class	UnparametricZRing
	Generic Class ZRing. More...

class	Neutral
	Neutral type. More...

class	givNoInit
	Used to build no initialized object as static object. More...

class	givNoCopy
	Used to call cstor without copy. More...

class	givWithCopy
	Used to call cstor with copy. More...

class	GivError
	Base class for exeception handling in Givaro. More...

class	GivMathError
	Math error. More...

class	GivBadFormat
	Exception thrown in input of data structure. More...

class	GivMathDivZero
	Div by 0. More...

struct	__givdom_trait_name
	give a name for /read/write More...

class	BaseDomain
	Base Domain. More...

class	GivaroMain
	Initialisation of GIVARO . More...

class	GivaroAppli
	Main application class Could be not used. More...

class	GivaroNoInit
	GivaroNoInit. More...

class	InitAfter
	InitAfter. More...

class	GivModule
	GivModule. More...

class	ObjectInit
	GivModule. More...

struct	OMPTimer
	OMP timer. More...

class	GIV_randIter
	Random ring Element generator. More...

class	ModularRandIter
	Random ring Element generator. More...

class	GeneralRingRandIter
	UnparametricRandIter. More...

class	GeneralRingNonZeroRandIter
	Random iterator for nonzero random numbers. More...

class	GivRandom
	GivRandom. More...

class	BaseTimer
	base for class RealTimer; class SysTimer; class UserTimer; More...

class	RealTimer
	Real timer. More...

class	UserTimer
	User timer. More...

class	SysTimer
	Sys timer. More...

class	Timer
	Timer. More...

class	Degree
	Degree type for polynomials. More...

class	Indeter
	Indeterminate. More...

struct	Interpolation
	Interpolation. More...

struct	NewtonInterpGeomMultip
	Newton (multip) More...

struct	NewtonInterpGeom
	Newton. More...

class	Poly1CRT
	Poly1 CRT. More...

class	Poly1Dom< Domain, Dense >
	Class Poly1Dom. More...

class	Poly1FactorDom
	Poly1FactorDom. More...

class	Poly1PadicDom< Domain, Dense >
	Poly1 p-adic. More...

class	CyclotomicTable
	CyclotomicTable. More...

Typedefs
typedef BaseDomain< char >	CharDom
	char dom

typedef BaseDomain< short >	ShortDom
	short dom

typedef BaseDomain< int >	IntDom
	int dom

typedef BaseDomain< long >	LongDom
	long dom

typedef BaseDomain< float >	FloatDom
	float dom

typedef BaseDomain< double >	DoubleDom
	double dom

template<typename T , typename A = std::allocator<T>>
using	givvector = std::vector< T, A >
	givvector

Functions
template<class T1 , class T2 >
std::ostream &	operator<< (std::ostream &o, const Pair< T1, T2 > &p)
	IO.

template<class T1 , class T2 >
std::istream &	operator>> (std::istream &fin, Pair< T1, T2 > &p)
	IO.

template<class Rt >
Rt	FF_EXPONENT_MAX (const Rt p, const Rt maxe=21)
	XXX.

template<class Rt >
Rt	FF_SUBEXPONENT_MAX (const Rt p, const Rt e)
	XXX.

template<typename Field >
int64_t	Exponent_Trait (const Field &F)
	XXX.

template<>
int64_t	Exponent_Trait (const GFqDom< int64_t > &F)
	XXX.

template<typename BaseField >
int64_t	Exponent_Trait (const Extension< BaseField > &F)
	XXX.

Integer &	inv (Integer &u, const Integer &a, const Integer &b)
	Modular inverse. More...

Integer &	invin (Integer &u, const Integer &b)

Integer	gcd (const Integer &a, const Integer &b)

Integer	pp (const Integer &P, const Integer &Q)

Integer &	lcm (Integer &g, const Integer &a, const Integer &b)

Integer	lcm (const Integer &a, const Integer &b)

Integer &	pow (Integer &Res, const Integer &n, const int64_t l)

Integer	pow (const Integer &n, const int64_t l)

Integer	powmod (const Integer &n, const uint64_t e, const Integer &m)

int32_t	sign (const Integer &a)

int32_t	compare (const Integer &a, const Integer &b)

int32_t	absCompare (const Integer &a, const Integer &b)

int32_t	isZero (const Integer &a)

int32_t	nonZero (const Integer &a)

int32_t	isOne (const Integer &a)

Integer	fact (uint64_t l)

Integer	sqrt (const Integer &p)

Integer	sqrtrem (const Integer &p, Integer &rem)

Integer &	sqrt (Integer &r, const Integer &p)

Integer &	sqrtrem (Integer &r, const Integer &p, Integer &rem)

bool	root (Integer &q, const Integer &, uint32_t n)

int64_t	logp (const Integer &a, const Integer &p)

double	logtwo (const Integer &a)

double	naturallog (const Integer &a)

void	swap (Integer &, Integer &)

bool	isOdd (const Integer &a)
	Tests parity of an integer. More...

uint64_t	length (const Integer &a)

std::istream &	operator>> (std::istream &i, Integer &n)

std::ostream &	operator<< (std::ostream &o, const Integer &n)

std::ostream &	absOutput (std::ostream &o, const Integer &n)

Integer	operator+ (const int32_t l, const Integer &n)

int32_t	operator!= (uint32_t l, const Integer &n)

int32_t	operator== (uint32_t l, const Integer &n)

int32_t	operator> (uint32_t l, const Integer &n)

int32_t	operator< (uint32_t l, const Integer &n)

int32_t	operator>= (uint32_t l, const Integer &n)

int32_t	operator<= (uint32_t l, const Integer &n)

Integer	operator% (const int64_t l, const Integer &n)

Integer	operator* (const int32_t l, const Integer &n)

Integer	operator- (const int32_t l, const Integer &n)

std::ostream &	operator<< (std::ostream &o, const GivMMInfo &T)
	IO.

template<typename Storage_t >
Storage_t &	gcdext (Storage_t &d, Storage_t &u, Storage_t &v, const Storage_t a, const Storage_t b)
	Generalized extended GCD used by specialized Modular.

template<typename Storage_t >
std::enable_if< std::is_floating_point< Storage_t >::value, Storage_t & >::type	extended_euclid (Storage_t &x, Storage_t &d, const Storage_t a, const Storage_t b)
	Extended Euclidean algorithm computing only the Bezout coefficient for a.

template<typename Storage_t >
Storage_t &	invext (Storage_t &x, Storage_t &d, const Storage_t a, const Storage_t b)
	Generalized inversion used by specialized Modular.

template<typename T >
unsigned	GIVINTLOG (const T &a)
	Integer log.

template<class TT , class UU >
TT	power (const TT n, const UU l)
	Powering.

template<class D , class TT >
TT &	dom_power (TT &res, const TT &n, uint64_t l, const D &F)
	dom_power

std::ostream &	operator<< (std::ostream &o, const BaseTimer &BT)
	I/O.

std::ostream &	operator<< (std::ostream &o, const Timer &T)
	I/O.

int64_t	value (const Degree &d)
	value

int	operator== (const Indeter &i1, const Indeter &i2)

Detailed Description

Namespace in which the whole Givaro library resides.

Todo:: use NTL if available ?

Function Documentation

◆ inv()

Integer & inv	(	Integer &	u,
		const Integer &	a,
		const Integer &	b
	)

Modular inverse.

Inverse.

Parameters

	a
	b
[out]	u	is set to $a^{-1}$ modulo b

◆ invin()

Integer & invin	(	Integer &	u,
		const Integer &	b
	)

Parameters

u
b

◆ gcd()

Integer gcd	(	const Integer &	a,
		const Integer &	b
	)

Parameters

a,b integers

Returns: gcd(a,b)

Examples: examples/Integer/ProbLucas.C.

◆ pp()

Integer pp	(	const Integer &	P,
		const Integer &	Q
	)

Parameters

P,Q params

◆ lcm() [1/2]

Integer & lcm	(	Integer &	g,
		const Integer &	a,
		const Integer &	b
	)

Parameters

g,a,b

Returns: g=lcm(a,b)

◆ lcm() [2/2]

Integer lcm	(	const Integer &	a,
		const Integer &	b
	)

Parameters

a,b

◆ pow() [1/2]

Integer & pow	(	Integer &	Res,
		const Integer &	n,
		const int64_t	l
	)

return

Parameters

Res,n,l

Examples: examples/Integer/ProbLucas.C.

◆ pow() [2/2]

Integer pow	(	const Integer &	n,
		const int64_t	l
	)

return

Parameters

n,l

◆ powmod()

Integer powmod	(	const Integer &	n,
		const uint64_t	e,
		const Integer &	m
	)

return $n^e \mod m$ .

Parameters

n,e,m

◆ sign()

int32_t Givaro::sign ( const Integer & a )

Parameters

a

◆ compare()

int32_t compare	(	const Integer &	a,
		const Integer &	b
	)

Parameters

a	integer
b	integer

Returns: 1 if , 0 if and -1 otherwise.

◆ absCompare()

int32_t absCompare	(	const Integer &	a,
		const Integer &	b
	)

Parameters

a	integer
b	integer

Returns: 1 if , 0 if and -1 otherwise.

◆ isZero()

int32_t isZero ( const Integer & a )

Parameters

a

Examples: examples/Integer/ProbLucas.C.

◆ nonZero()

int32_t nonZero ( const Integer & a )

Parameters

a

◆ isOne()

int32_t isOne ( const Integer & a )

Parameters

a

Examples: examples/Integer/ProbLucas.C.

◆ fact()

Integer fact ( uint64_t l )

Parameters

l

◆ sqrt() [1/2]

Integer sqrt ( const Integer & p )

Parameters

p

Examples: examples/Integer/ProbLucas.C.

◆ sqrtrem() [1/2]

Integer sqrtrem	(	const Integer &	p,
		Integer &	rem
	)

Parameters

p,rem

◆ sqrt() [2/2]

Integer & sqrt	(	Integer &	r,
		const Integer &	p
	)

Parameters

r,p

◆ sqrtrem() [2/2]

Integer & sqrtrem	(	Integer &	r,
		const Integer &	p,
		Integer &	rem
	)

Parameters

r,p,rem

◆ root()

bool root	(	Integer &	q,
		const Integer &	a,
		uint32_t	n
	)

Parameters

q,a,n

Examples: examples/Integer/ModularSquareRoot.C, and examples/Integer/ProbLucas.C.

◆ logp()

int64_t logp	(	const Integer &	a,
		const Integer &	p
	)

Parameters

a,p

◆ logtwo()

double logtwo ( const Integer & a )

Parameters

a

Examples: examples/Integer/ProbLucas.C.

◆ naturallog()

double naturallog ( const Integer & a )

Parameters

a

◆ swap()

void swap	(	Integer &	a,
		Integer &	b
	)

swap

Parameters

a,b

◆ isOdd()

bool isOdd ( const Integer & a )

Tests parity of an integer.

parity of an integer

Parameters

a integer

Returns: 1 if odd, 0 if even

◆ length()

uint64_t length ( const Integer & a )

Parameters

a

Bug:: JGD 23.04.2012: shouldn't it be "mp_limb_t" instead of "uint64_t"?

Bug:: JGD 23.04.2012: shouldn't it be "mp_limb_t" instead of "uint64_t"?

◆ operator>>()

std::istream & operator>>	(	std::istream &	i,
		Integer &	n
	)

in operator.

Parameters

i	input stream
n	integer to be built

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	o,
		const Integer &	n
	)

Parameters

o	output stream
n	integer to be printed

◆ absOutput()

std::ostream & absOutput	(	std::ostream &	o,
		const Integer &	n
	)

Parameters

o	output
n	integer

◆ operator+()

Integer Givaro::operator+	(	const int32_t	l,
		const Integer &	n
	)

Parameters

l,n	to be added

◆ operator!=()

int32_t Givaro::operator!=	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n integer

Returns: 1 iff l == n

◆ operator==() [1/2]

int32_t Givaro::operator==	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n	integers to compare

◆ operator>()

int32_t Givaro::operator>	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n	integers to compare

◆ operator<()

int32_t Givaro::operator<	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n	integers to compare

◆ operator>=()

int32_t Givaro::operator>=	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n	integers to compare

◆ operator<=()

int32_t Givaro::operator<=	(	uint32_t	l,
		const Integer &	n
	)

Parameters

l,n	integers to compare

◆ operator%()

Integer Givaro::operator%	(	const int64_t	l,
		const Integer &	n
	)

Parameters

l
n

Returns: nl

◆ operator*()

Integer Givaro::operator*	(	const int32_t	l,
		const Integer &	n
	)

Parameters

l,n	to be multpct

◆ operator-()

Integer Givaro::operator-	(	const int32_t	l,
		const Integer &	n
	)

Parameters

l,n	to be substracted

◆ operator==() [2/2]

int Givaro::operator==	(	const Indeter &	i1,
		const Indeter &	i2
	)

inline

Bug:: put elsewere. Inline members functions :

Namespaces

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation

◆ inv()

◆ invin()

◆ gcd()

◆ pp()

◆ lcm() [1/2]

◆ lcm() [2/2]

◆ pow() [1/2]

◆ pow() [2/2]

◆ powmod()

◆ sign()

◆ compare()

◆ absCompare()

◆ isZero()

◆ nonZero()

◆ isOne()

◆ fact()

◆ sqrt() [1/2]

◆ sqrtrem() [1/2]

◆ sqrt() [2/2]

◆ sqrtrem() [2/2]

◆ root()

◆ logp()

◆ logtwo()

◆ naturallog()

◆ swap()

◆ isOdd()

◆ length()

◆ operator>>()

◆ operator<<()

◆ absOutput()

◆ operator+()

◆ operator!=()

◆ operator==() [1/2]

◆ operator>()

◆ operator<()

◆ operator>=()

◆ operator<=()

◆ operator%()

◆ operator*()

◆ operator-()

◆ operator==() [2/2]