This is the Integer class. More...

#include <gmp++_int.h>

Public Types
typedef std::vector< mp_limb_t >	vect_t
	vector of limbs (ie a gmp number).
Public Member Functions
Constructor/Destructors
	Integer (const std::vector< mp_limb_t > &vect_t)
	Integer (int n=0)
	Integer (long n)
	Integer (unsigned char n)
	Integer (unsigned int n)
	Integer (unsigned long n)
	Integer (double d)
	Integer (const char *s)
	Integer (const Integer &n)
	~Integer ()
Assignment and copy operators
Integer &	operator= (const Integer &n)
Integer &	logcpy (const Integer &n)
Integer &	copy (const Integer &n)
Bit logic
Integer	operator^ (const Integer &) const
Integer	operator\| (const Integer &) const
Integer	operator& (const Integer &) const
unsigned long	operator^ (const unsigned long &a) const
unsigned long	operator\| (const unsigned long &a) const
unsigned long	operator& (const unsigned long &a) const
Integer	operator~ () const
Integer &	operator^= (const Integer &)
Integer &	operator\|= (const Integer &)
Integer &	operator&= (const Integer &)
Integer	operator<< (int l) const
Integer	operator>> (int l) const
Integer	operator<< (long l) const
Integer	operator>> (long l) const
Integer	operator<< (unsigned int l) const
Integer	operator>> (unsigned int l) const
Integer	operator<< (unsigned long l) const
Integer	operator>> (unsigned long l) const
Integer &	operator<<= (int l)
Integer &	operator>>= (int l)
Integer &	operator<<= (long l)
Integer &	operator>>= (long l)
Integer &	operator<<= (unsigned int l)
Integer &	operator>>= (unsigned int l)
Integer &	operator<<= (unsigned long l)
Integer &	operator>>= (unsigned long l)
Static Public Member Functions
fused add-multiply
Groups a multiplication adn an addition/division is a single function. This is usually faster than doing the two operations separately.
static Integer &	axpy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	axpy `res = ax+y`.
static Integer &	axpy (Integer &res, const Integer &a, const unsigned long x, const Integer &y)
	axpy `res = ax+y`.
static Integer &	axpyin (Integer &res, const Integer &a, const Integer &x)
	axpyin (inplace) `res += ax`.
static Integer &	axpyin (Integer &res, const Integer &a, const unsigned long x)
	axpy `res = ax+y`.
static Integer &	maxpy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	maxpy `res = y - ax`.
static Integer &	maxpy (Integer &res, const Integer &a, const unsigned long x, const Integer &y)
	axpy `res = ax+y`.
static Integer &	maxpyin (Integer &res, const Integer &a, const Integer &x)
	maxpyin `res -= ax`.
static Integer &	maxpyin (Integer &res, const Integer &a, const unsigned long x)
	axpy `res = ax+y`.
static Integer &	axmy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	axmy `res = ax - y`.
static Integer &	axmy (Integer &res, const Integer &a, const unsigned long x, const Integer &y)
	axpy `res = ax+y`.
static Integer &	axmyin (Integer &res, const Integer &a, const Integer &x)
	axmyin (in place) `res = ax - res`.
static Integer &	axmyin (Integer &res, const Integer &a, const unsigned long x)
	axpy `res = ax+y`.
Random numbers functions
static void	seeding (unsigned long int s)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static void	seeding (Integer s)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static void	seeding ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
static __gmp_randstate_struct	intializerandstate ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
static __gmp_randstate_struct *	randstate ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
static bool	RandBool ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_lessthan (Integer &r, const Integer &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_lessthan (Integer &r, const Integer &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_lessthan_2exp (Integer &r, const unsigned long &m)
	returns a random integer `r` of at most `m` bits
static Integer &	random_lessthan_2exp (Integer &r, const unsigned long &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer	random_lessthan_2exp (const unsigned long &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	random_lessthan_2exp (const unsigned long &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_lessthan (Integer &r, const unsigned long &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_lessthan (Integer &r, const unsigned long &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer	random_lessthan (const T &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class T >
static Integer	random_lessthan (const T &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_exact (Integer &r, const Integer &s)
	returns a reference to a random number `r` of the size of `s`, exactly.
static Integer &	random_exact (Integer &r, const Integer &s)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_exact_2exp (Integer &r, const unsigned long int &m)
	returns a reference to a random number `r` of the size `m` bits, exactly.
static Integer &	random_exact_2exp (Integer &r, const unsigned long int &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer &	random_exact (Integer &r, const unsigned long int &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_exact (Integer &r, const unsigned long int &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer &	random_exact (Integer &r, const T &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class T >
static Integer &	random_exact (Integer &r, const T &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer	random_exact (const T &s)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class T >
static Integer	random_exact (const T &s)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_between (Integer &r, const Integer &m, const Integer &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	random_between (const Integer &m, const Integer &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_between_2exp (Integer &r, const unsigned long int &m, const unsigned long int &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer &	random_between (Integer &r, const unsigned long int &m, const unsigned long int &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	random_between_2exp (const unsigned long int &m, const unsigned long int &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	random_between (const unsigned long int &m, const unsigned long int &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class R >
static Integer	random_between (const R &m, const R &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class R >
static Integer &	random_between (Integer &r, const R &m, const R &M)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer &	random (Integer &r, const T &m)
	returns a random integer less than...
template<class T >
static Integer &	random (Integer &r, const T &m)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer	random (const T &sz)
	returns a random integer less than...
template<class T >
static Integer	random (const T &sz)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U>
static Integer	random ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	random ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer	nonzerorandom (const T &sz)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<bool U, class T >
static Integer &	nonzerorandom (Integer &r, const T &size)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class T >
static Integer	nonzerorandom (const T &sz)
	returns a random integer `r` in the intervall `[[0, m-1]]`
template<class T >
static Integer &	nonzerorandom (Integer &r, const T &size)
	returns a random integer `r` in the intervall `[[0, m-1]]`
static Integer	nonzerorandom ()
	returns a random integer `r` in the intervall `[[0, m-1]]`
Static Public Attributes
static const Integer	zero
	zero
static const Integer	one
	one
Friends
Arithmetic functions
Integer	gcd (const Integer &a, const Integer &b)
Integer	gcd (const Integer &a, const Integer &b, Integer &u, Integer &v)
Integer &	gcd (Integer &g, const Integer &a, const Integer &b)
Integer &	gcd (Integer &g, const Integer &a, const Integer &b, Integer &u, Integer &v)
Integer &	inv (Integer &u, const Integer &a, const Integer &b)
Integer &	invin (Integer &u, 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 long l)
Integer &	pow (Integer &Res, const unsigned long n, const unsigned long l)
Integer &	pow (Integer &Res, const Integer &n, const unsigned long l)
Integer &	pow (Integer &Res, const Integer &n, const int l)
Integer &	pow (Integer &Res, const Integer &n, const unsigned int l)
Integer	pow (const Integer &n, const long l)
Integer	pow (const Integer &n, const unsigned long l)
Integer	pow (const Integer &n, const int l)
Integer	pow (const Integer &n, const unsigned int l)
Integer &	powmod (Integer &Res, const Integer &n, const unsigned long e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const long e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const unsigned int e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const int e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const Integer &e, const Integer &m)
Integer	powmod (const Integer &n, const unsigned long e, const Integer &m)
Integer	powmod (const Integer &n, const long e, const Integer &m)
Integer	powmod (const Integer &n, const unsigned int e, const Integer &m)
Integer	powmod (const Integer &n, const int e, const Integer &m)
Integer	powmod (const Integer &n, const Integer &e, const Integer &m)
Integer	fact (unsigned long 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 &, unsigned int n)
long	logp (const Integer &a, const Integer &p)
double	logtwo (const Integer &a)
double	naturallog (const Integer &a)
(in)equality
int	operator!= (const int l) const
int	operator!= (const long l) const
int	operator!= (const unsigned long l) const
int	operator> (const int l) const
int	operator> (const long l) const
int	operator> (const unsigned long l) const
int	operator< (const int l) const
int	operator< (const long l) const
int	operator< (const unsigned long l) const
int	compare (const Integer &a, const Integer &b)
int	absCompare (const Integer &a, const Integer &b)
Addition, substraction, multiplication
Integer	operator+ (const Integer &n) const
	operator `+`.
Integer	operator+ (const unsigned long n) const
	operator `+`.
Integer	operator+ (const long n) const
	operator `+`.
Integer &	operator+= (const Integer &n)
	operator `+=` .
Integer &	operator+= (const unsigned long n)
	operator `+`.
Integer &	operator+= (const long n)
	operator `+`.
template<class XXX >
Integer &	operator+= (const XXX &n)
	operator `+`.
Integer	operator- (const Integer &n) const
	operator `-`.
Integer	operator- (const unsigned long n) const
	operator `+`.
Integer	operator- (const long n) const
	operator `+`.
Integer &	operator-= (const Integer &n)
	operator `-=` .
Integer &	operator-= (const unsigned long n)
	operator `+`.
Integer &	operator-= (const long n)
	operator `+`.
template<class XXX >
Integer &	operator-= (const XXX &n)
	operator `+`.
Integer	operator- () const
	Opposite.
Integer	operator* (const Integer &n) const
	operator `*`.
Integer	operator* (const unsigned long n) const
	operator `+`.
Integer	operator* (const long n) const
	operator `+`.
Integer &	operator*= (const Integer &n)
	operator `*=` .
Integer &	operator*= (const unsigned long n)
	operator `+`.
Integer &	operator*= (const long n)
	operator `+`.
template<class XXX >
Integer &	operator*= (const XXX &n)
	operator `+`.
static Integer &	addin (Integer &res, const Integer &n)
	Addition (inplace) `res+=n`.
static Integer &	addin (Integer &res, const long n)
	operator `+`.
static Integer &	addin (Integer &res, const unsigned long n)
	operator `+`.
static Integer &	add (Integer &res, const Integer &n1, const Integer &n2)
	Addition `res=n1+n2`.
static Integer &	add (Integer &res, const Integer &n1, const long n2)
	operator `+`.
static Integer &	add (Integer &res, const Integer &n1, const unsigned long n2)
	operator `+`.
static Integer &	subin (Integer &res, const Integer &n)
	Substraction (inplace) `res-=n`.
static Integer &	subin (Integer &res, const long n)
	operator `+`.
static Integer &	subin (Integer &res, const unsigned long n)
	operator `+`.
static Integer &	sub (Integer &res, const Integer &n1, const Integer &n2)
	Substraction `res=n1-n2`.
static Integer &	sub (Integer &res, const Integer &n1, const long n2)
	operator `+`.
static Integer &	sub (Integer &res, const Integer &n1, const unsigned long n2)
	operator `+`.
static Integer &	negin (Integer &res)
	Negation (inplace) `res=-res`.
static Integer &	neg (Integer &res, const Integer &n)
	Negation `res=-n`.
static Integer &	mulin (Integer &res, const Integer &n)
	Multiplication (inplace) `res*=n`.
static Integer &	mulin (Integer &res, const long n)
	operator `+`.
static Integer &	mulin (Integer &res, const unsigned long n)
	operator `+`.
static Integer &	mul (Integer &res, const Integer &n1, const Integer &n2)
	Multiplication `res=n1*n2`.
static Integer &	mul (Integer &res, const Integer &n1, const long n2)
	operator `+`.
static Integer &	mul (Integer &res, const Integer &n1, const unsigned long n2)
	operator `+`.
Division/euclidean division/modulo
The convention for rounding are the following : `q = a/b`, or equivalent operations with the name `div` or `divin`, return `q` rounded towards `0`, in the same manner as C's '/' (truncated division). `r = a % b` behaves like C %. The modulo function % rounds towards 0 and the sign of the dividend is preserved. This is : $a= b q + r, \text{with } \vert r\vert < \vert b\vert \text{ and } a r \geq 0$ `r = a mod b` or similar functions have the same behaviour as GMP `mpz_mod`, that is the remainder is always positive (>=0). This is the division algorithm convention that is used (see `divmod`). In a formula : $a= b q + r, \text{with } 0 \leq r < \vert b\vert$ Warning: if `q=a/b` and `r= a % b` then `a = b q + r` is always true (with in addition `0 <= \|r\| < \|b\|`). This is also true for `divmod(q,a,b,r)` (and `0<=r<\|b\|`). However, one should not mix the two conventions and expect equalities (except if a>=0).
Integer	operator/ (const Integer &d) const
	Division operator.
Integer	operator/ (const unsigned long d) const
	Division operator.
Integer	operator/ (const long d) const
	Division operator.
Integer &	operator/= (const Integer &d)
	Division operator (inplace).
Integer &	operator/= (const unsigned long d)
	Division operator.
Integer &	operator/= (const long d)
	Division operator.
template<class XXX >
Integer &	operator/= (const XXX &d)
	Division operator.
Integer	operator% (const Integer &n) const
	Modulo operator.
long	operator% (const unsigned long n) const
	Division operator.
long	operator% (const long n) const
	Division operator.
double	operator% (const double n) const
	Division operator.
short	operator% (const unsigned short n) const
	Division operator.
template<class XXX >
XXX	operator% (const XXX &n) const
	Division operator.
Integer &	operator%= (const Integer &n)
	Modulo operator (inplace).
Integer &	operator%= (const unsigned long n)
	Division operator.
Integer &	operator%= (const long n)
	Division operator.
template<class XXX >
Integer &	operator%= (const XXX &n)
	Division operator.
static Integer &	divin (Integer &q, const Integer &d)
	Division `q/=d`.
static Integer &	divin (Integer &q, const long d)
	Division operator.
static Integer &	divin (Integer &q, const unsigned long d)
	Division operator.
static Integer &	div (Integer &q, const Integer &n, const Integer &d)
	Division `q=n/d`.
static Integer &	div (Integer &q, const Integer &n, const long d)
	Division operator.
static Integer &	div (Integer &q, const Integer &n, const int d)
	Division operator.
static Integer &	div (Integer &q, const Integer &n, const unsigned long d)
	Division operator.
static Integer &	divexact (Integer &q, const Integer &n, const Integer &d)
	Division when `d` divides `n`.
static Integer	divexact (const Integer &n, const Integer &d)
	Division when `d` divides `n`.
static Integer &	modin (Integer &r, const Integer &n)
	Function `mod` (inplace).
static Integer &	modin (Integer &r, const long n)
	Division operator.
static Integer &	modin (Integer &r, const unsigned long n)
	Division operator.
static Integer &	mod (Integer &r, const Integer &n, const Integer &d)
	Function `mod`.
static Integer &	mod (Integer &r, const Integer &n, const long d)
	Division operator.
static Integer &	mod (Integer &r, const Integer &n, const unsigned long d)
	Division operator.
static Integer &	divmod (Integer &q, Integer &r, const Integer &n, const Integer &d)
	Euclidean division.
static Integer &	divmod (Integer &q, long &r, const Integer &n, const long d)
	Division operator.
static Integer &	divmod (Integer &q, unsigned long &r, const Integer &n, const unsigned long d)
	Division operator.
Miscellaneous.
Integer &	operator++ ()
Integer	operator++ (int)
Integer &	operator-- ()
Integer	operator-- (int)
size_t	size () const
size_t	size_in_base (int B) const
size_t	bitsize () const
unsigned long	operator[] (size_t i) const
	operator bool () const
	operator short () const
	operator unsigned short () const
	operator unsigned char () const
	operator unsigned int () const
	operator int () const
	operator signed char () const
	operator unsigned long () const
	operator long () const
	operator unsigned long long () const
	operator long long () const
	operator std::string () const
	operator float () const
	operator double () const
	operator vect_t () const
void	swap (Integer &, Integer &)
int	sign (const Integer &a)
int	isZero (const Integer &a)
int	isOne (const Integer &a)
int	isperfectpower (const Integer &)
Integer	abs (const Integer &n)
Integer &	prevprime (Integer &, const Integer &p)
Integer &	nextprime (Integer &, const Integer &p)
int	probab_prime (const Integer &p)
int	probab_prime (const Integer &p, int r)
int	jacobi (const Integer &u, const Integer &v)
int	legendre (const Integer &u, const Integer &v)
unsigned long	length (const Integer &a)
I/O
std::ostream &	print (std::ostream &o) const
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)
void	importWords (Integer &, size_t, int, int, int, size_t, const void *)

Detailed Description

This is the Integer class.

An Integer is represented as a GMP integer. This class provides arithmetic on Integers.

Examples:: examples/FiniteField/all_field.C, examples/FiniteField/domain_to_operatorstyle.C, examples/FiniteField/GF128.C, examples/FiniteField/Test_Extension.C, examples/Integer/iexponentiation.C, examples/Integer/ifactor.C, examples/Integer/ifactor_lenstra.C, examples/Integer/igcd.C, examples/Integer/igcdext.C, examples/Integer/ilcm.C, examples/Integer/ispower.C, examples/Integer/isprime.C, examples/Integer/isproot.C, examples/Integer/ModularSquareRoot.C, examples/Integer/nb_primes.C, examples/Integer/nextprime.C, examples/Integer/order.C, examples/Integer/prevprime.C, examples/Integer/primitiveroot.C, examples/Integer/ProbLucas.C, examples/Integer/RSA_breaking.C, examples/Integer/RSA_decipher.C, examples/Integer/RSA_encipher.C, examples/Polynomial/PolynomialCRT.C, examples/Rational/iratrecon.C, and examples/Rational/polydouble.C.

Member Function Documentation

Integer & addin	(	Integer &	res,
		const Integer &	n
	)		`[static]`

Addition (inplace) res+=n.

Parameters:

res	as in the formula
n	as in the formula

Integer & addin	(	Integer &	res,
		const long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & addin	(	Integer &	res,
		const unsigned long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & add	(	Integer &	res,
		const Integer &	n1,
		const Integer &	n2
	)		`[static]`

Addition res=n1+n2.

Parameters:

res	as in the formula
n1	as in the formula
n2	as in the formula

Integer & add	(	Integer &	res,
		const Integer &	n1,
		const long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & add	(	Integer &	res,
		const Integer &	n1,
		const unsigned long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & subin	(	Integer &	res,
		const Integer &	n
	)		`[static]`

Substraction (inplace) res-=n.

Parameters:

res	as in the formula
n	as in the formula

Integer & subin	(	Integer &	res,
		const long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & subin	(	Integer &	res,
		const unsigned long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & sub	(	Integer &	res,
		const Integer &	n1,
		const Integer &	n2
	)		`[static]`

Substraction res=n1-n2.

Parameters:

res	as in the formula
n1	as in the formula
n2	as in the formula

Examples:: examples/Integer/primitiveroot.C.

Integer & sub	(	Integer &	res,
		const Integer &	n1,
		const long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & sub	(	Integer &	res,
		const Integer &	n1,
		const unsigned long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & negin ( Integer & res ) [static]

Negation (inplace) res=-res.

Parameters:

res	as in the formula

Examples:: examples/Integer/ifactor.C, and examples/Integer/ifactor_lenstra.C.

Integer & neg	(	Integer &	res,
		const Integer &	n
	)		`[static]`

Negation res=-n.

Parameters:

n	as in the formula
res	as in the formula

Integer & mulin	(	Integer &	res,
		const Integer &	n
	)		`[static]`

Multiplication (inplace) res*=n.

Parameters:

res	as in the formula
n	as in the formula

Integer & mulin	(	Integer &	res,
		const long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & mulin	(	Integer &	res,
		const unsigned long	n
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & mul	(	Integer &	res,
		const Integer &	n1,
		const Integer &	n2
	)		`[static]`

Multiplication res=n1*n2.

Parameters:

res	as in the formula
n1	as in the formula
n2	as in the formula

Examples:: examples/Integer/ilcm.C.

Integer & mul	(	Integer &	res,
		const Integer &	n1,
		const long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & mul	(	Integer &	res,
		const Integer &	n1,
		const unsigned long	n2
	)		`[static]`

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator+ ( const Integer & n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator+ ( const unsigned long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator+ ( const long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator+= ( const Integer & n )

operator += .

Parameters:

n	as in the formula.

Returns:: (*this) += n.

Integer & operator+= ( const unsigned long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator+= ( const long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer& operator+= ( const XXX & n ) [inline]

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator- ( const Integer & n ) const

operator -.

Returns:: (*this)-n

Parameters:

n	as in the formula.

Integer operator- ( const unsigned long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator- ( const long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator-= ( const Integer & n )

operator -= .

Parameters:

n	as in the formula.

Returns:: (*this) -= n.

Integer & operator-= ( const unsigned long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator-= ( const long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer& operator-= ( const XXX & n ) [inline]

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator- ( ) const [inline]

Opposite.

Returns:: -(*this).

Integer operator* ( const Integer & n ) const

operator *.

Returns:: (*this)*n

Parameters:

n	as in the formula.

Integer operator* ( const unsigned long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer operator* ( const long n ) const

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator*= ( const Integer & n )

operator *= .

Parameters:

n	as in the formula.

Returns:: (*this) *= n.

Integer & operator*= ( const unsigned long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & operator*= ( const long n )

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer& operator*= ( const XXX & n ) [inline]

operator +.

Returns:: (*this)+n

Parameters:

n	as in the formula.

Integer & axpy	(	Integer &	res,
		const Integer &	a,
		const Integer &	x,
		const Integer &	y
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

static Integer& axpy	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x,
		const Integer &	y
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & axpyin	(	Integer &	res,
		const Integer &	a,
		const Integer &	x
	)		`[static]`

axpyin (inplace) res += ax.

Parameters:

res	Integers as in the formula.
a	Integers as in the formula.
x	Integers as in the formula.

static Integer& axpyin	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & maxpy	(	Integer &	res,
		const Integer &	a,
		const Integer &	x,
		const Integer &	y
	)		`[static]`

maxpy res = y - ax.

Parameters:

res	Integers as in the formula.
a	Integers as in the formula.
x	Integers as in the formula.
y	Integers as in the formula.

static Integer& maxpy	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x,
		const Integer &	y
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & maxpyin	(	Integer &	res,
		const Integer &	a,
		const Integer &	x
	)		`[static]`

maxpyin res -= ax.

Parameters:

res	Integers as in the formula.
a	Integers as in the formula.
x	Integers as in the formula.
y	Integers as in the formula.

Integer & maxpyin	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & axmy	(	Integer &	res,
		const Integer &	a,
		const Integer &	x,
		const Integer &	y
	)		`[static]`

axmy res = ax - y.

Parameters:

res	Integers as in the formula.
a	Integers as in the formula.
x	Integers as in the formula.
y	Integers as in the formula.

static Integer& axmy	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x,
		const Integer &	y
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & axmyin	(	Integer &	res,
		const Integer &	a,
		const Integer &	x
	)		`[static]`

axmyin (in place) res = ax - res.

Parameters:

res	Integers as in the formula.
a	Integers as in the formula.
x	Integers as in the formula.

Integer & axmyin	(	Integer &	res,
		const Integer &	a,
		const unsigned long	x
	)		`[static]`

axpy res = ax+y.

Parameters:

res	Integers as in the forumla
a	Integers as in the forumla
x	Integers as in the forumla
y	Integers as in the forumla

Integer & divin	(	Integer &	q,
		const Integer &	d
	)		`[static]`

Division q/=d.

Parameters:

q	quotient
d	divisor.

Returns:: q

Examples:: examples/Integer/ilcm.C.

Integer & divin	(	Integer &	q,
		const long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & divin	(	Integer &	q,
		const unsigned long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & div	(	Integer &	q,
		const Integer &	n,
		const Integer &	d
	)		`[static]`

Division q=n/d.

Parameters:

q	quotient
n	dividand.
d	divisor

Returns:: q

Integer & div	(	Integer &	q,
		const Integer &	n,
		const long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & div	(	Integer &	q,
		const Integer &	n,
		const int	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & div	(	Integer &	q,
		const Integer &	n,
		const unsigned long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & divexact	(	Integer &	q,
		const Integer &	n,
		const Integer &	d
	)		`[static]`

Division when d divides n.

Parameters:

q	exact quotient
n	dividend
d	divisor

Warning:: if quotient is not exact, the result is not predictable.

Integer divexact	(	const Integer &	n,
		const Integer &	d
	)		`[static]`

Division when d divides n.

Parameters:

n	dividend
d	divisor

Returns:: exact quotient n/d

Warning:: if quotient is not exact, the result is not predictable.

Integer operator/ ( const Integer & d ) const

Division operator.

Parameters:

d divisor

Integer operator/ ( const unsigned long d ) const

Division operator.

Parameters:

d divisor

Integer operator/ ( const long d ) const

Division operator.

Parameters:

d divisor

Integer & operator/= ( const Integer & d )

Division operator (inplace).

Parameters:

d divisor

Integer & operator/= ( const unsigned long d )

Division operator.

Parameters:

d divisor

Integer & operator/= ( const long d )

Division operator.

Parameters:

d divisor

Integer& operator/= ( const XXX & d ) [inline]

Division operator.

Parameters:

d divisor

Integer & modin	(	Integer &	r,
		const Integer &	n
	)		`[static]`

Function mod (inplace).

$r \gets r \mod n$

Parameters:

r	remainder
n	modulus

Integer & modin	(	Integer &	r,
		const long	n
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & modin	(	Integer &	r,
		const unsigned long	n
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & mod	(	Integer &	r,
		const Integer &	n,
		const Integer &	d
	)		`[static]`

Function mod.

$r \gets n \mod d$

Parameters:

r	remainder
n	integer
d	modulus

Integer & mod	(	Integer &	r,
		const Integer &	n,
		const long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & mod	(	Integer &	r,
		const Integer &	n,
		const unsigned long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & divmod	(	Integer &	q,
		Integer &	r,
		const Integer &	n,
		const Integer &	d
	)		`[static]`

Euclidean division.

n = d q + r .

Parameters:

q	as in the formula
r	as in the formula
n	as in the formula
d	as in the formula

Returns:: the quotient q

Integer & divmod	(	Integer &	q,
		long &	r,
		const Integer &	n,
		const long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer & divmod	(	Integer &	q,
		unsigned long &	r,
		const Integer &	n,
		const unsigned long	d
	)		`[static]`

Division operator.

Parameters:

d divisor

Integer operator% ( const Integer & n ) const

Modulo operator.

Parameters:

n modulus

Returns:: remainder (*this) mod n

long operator% ( const unsigned long n ) const

Division operator.

Parameters:

d divisor

long operator% ( const long n ) const

Division operator.

Parameters:

d divisor

double operator% ( const double n ) const

Division operator.

Parameters:

d divisor

short operator% ( const unsigned short n ) const [inline]

Division operator.

Parameters:

d divisor

XXX operator% ( const XXX & n ) const [inline]

Division operator.

Parameters:

d divisor

Integer & operator%= ( const Integer & n )

Modulo operator (inplace).

Parameters:

n modulus

Returns:: remainder (*this) <- (*this) mod n

Integer & operator%= ( const unsigned long n )

Division operator.

Parameters:

d divisor

Integer & operator%= ( const long n )

Division operator.

Parameters:

d divisor

Integer& operator%= ( const XXX & n ) [inline]

Division operator.

Parameters:

d divisor

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

gmp++_int.h
gmp++_int.inl
gmp++_int_add.C
gmp++_int_compare.C
gmp++_int_cstor.C
gmp++_int_div.C
gmp++_int_io.C
gmp++_int_misc.C
gmp++_int_mod.C
gmp++_int_mul.C
gmp++_int_sub.C

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

(in)equality

Addition, substraction, multiplication

Division/euclidean division/modulo

Miscellaneous.

I/O

Detailed Description

Member Function Documentation