Integer Class Reference

This is the Integer class. More...

#include <gmp++_int.h>

Inherited by SpyInteger::InHeritsInteger.

Public Types
typedef std::vector< mp_limb_t >	vect_t
	vector of limbs (ie a gmp number).

Public Member Functions
Constructor/Destructors.
Constructors and destructor for an Integer.
giv_all_inlined	Integer (int32_t n=0)
	Constructor form a known type.
giv_all_inlined	Integer (int64_t n)
	Constructor form a known type.
giv_all_inlined	Integer (unsigned char n)
	Constructor form a known type.
giv_all_inlined	Integer (uint32_t n)
	Constructor form a known type.
giv_all_inlined	Integer (uint64_t n)
	Constructor form a known type.
giv_all_inlined	Integer (double n)
	Constructor form a known type.
giv_all_inlined	Integer (const char *n)
	Constructor form a known type.
giv_all_inlined	Integer (const mpz_class &a)
	Constructor form a known type.
template<size_t K>
	Integer (const RecInt::ruint< K > &n)
	Constructor form a known type.
template<size_t K>
	Integer (const RecInt::rint< K > &n)
	Constructor form a known type.
giv_all_inlined	Integer (const Integer &n)
	Copy constructor.
giv_all_inlined	Integer (uint64_t *d, int64_t sz)
	Creates a new Integer from pointers.
giv_all_inlined	Integer (const vect_t &v)
	Creates a new Integers for a vector of limbs.
giv_all_inlined	~Integer ()
	destructor
Assignment and copy operators
giv_all_inlined Integer &	operator= (const Integer &n)
	copy from an integer.
giv_all_inlined Integer &	logcpy (const Integer &n)
	copy from an integer.
giv_all_inlined Integer &	copy (const Integer &n)
	copy from an integer.
Bit logic operators. <br>
giv_all_inlined Integer	operator^ (const Integer &a) const
	XOR (^)
giv_all_inlined Integer	operator^ (const uint64_t &a) const
	XOR (^)
giv_all_inlined Integer	operator^ (const uint32_t &a) const
	XOR (^)
giv_all_inlined Integer &	operator^= (const Integer &a)
	XOR inplace (^=)
giv_all_inlined Integer &	operator^= (const uint64_t &a)
	XOR (^)
giv_all_inlined Integer &	operator^= (const uint32_t &a)
	XOR (^)
giv_all_inlined Integer	operator| (const Integer &a) const
	OR (|)
giv_all_inlined Integer	operator| (const uint64_t &a) const
	XOR (^)
giv_all_inlined Integer	operator| (const uint32_t &a) const
	XOR (^)
giv_all_inlined Integer &	operator|= (const Integer &a)
	OR inplace (|=)
giv_all_inlined Integer &	operator|= (const uint64_t &a)
	XOR (^)
giv_all_inlined Integer &	operator|= (const uint32_t &a)
	XOR (^)
giv_all_inlined Integer	operator& (const Integer &a) const
	AND (&)
giv_all_inlined uint32_t	operator& (const uint32_t &a) const
	XOR (^)
giv_all_inlined uint64_t	operator& (const uint64_t &a) const
	XOR (^)
giv_all_inlined Integer &	operator&= (const Integer &a)
	AND inplace (&=)
giv_all_inlined Integer &	operator&= (const uint64_t &a)
	XOR (^)
giv_all_inlined Integer &	operator&= (const uint32_t &a)
	XOR (^)
giv_all_inlined Integer	operator~ () const
	complement to 1 (~)
giv_all_inlined Integer	operator<< (int32_t l) const
	left shift (<<)
giv_all_inlined Integer	operator<< (int64_t l) const
	XOR (^)
giv_all_inlined Integer	operator<< (uint32_t l) const
	XOR (^)
giv_all_inlined Integer	operator<< (uint64_t l) const
	XOR (^)
giv_all_inlined Integer &	operator<<= (int32_t l)
	left shift inplace (<<=)
giv_all_inlined Integer &	operator<<= (int64_t l)
	XOR (^)
giv_all_inlined Integer &	operator<<= (uint32_t l)
	XOR (^)
giv_all_inlined Integer &	operator<<= (uint64_t l)
	XOR (^)
giv_all_inlined Integer	operator>> (int32_t l) const
	right shift (>>)
giv_all_inlined Integer	operator>> (int64_t l) const
	XOR (^)
giv_all_inlined Integer	operator>> (uint32_t l) const
	XOR (^)
giv_all_inlined Integer	operator>> (uint64_t l) const
	XOR (^)
giv_all_inlined Integer &	operator>>= (int32_t l)
	right shift inplace (>>=)
giv_all_inlined Integer &	operator>>= (int64_t l)
	XOR (^)
giv_all_inlined Integer &	operator>>= (uint32_t l)
	XOR (^)
giv_all_inlined Integer &	operator>>= (uint64_t l)
	XOR (^)
Increment/Decrement operators
Integer &	operator++ ()
Integer	operator++ (int)
Integer &	operator-- ()
Integer	operator-- (int)
Cast operators.
Convert an Integer to a basic C++ type. Warning Cast towards unsigned consider only the absolute value
	operator bool () const
	operator int16_t () const
	operator uint16_t () const
	operator unsigned char () const
giv_all_inlined	operator uint32_t () const
giv_all_inlined	operator int32_t () const
	operator signed char () const
giv_all_inlined	operator uint64_t () const
giv_all_inlined	operator int64_t () const
giv_all_inlined	operator std::string () const
giv_all_inlined	operator float () const
giv_all_inlined	operator double () const
giv_all_inlined	operator vect_t () const
template<size_t K>
	operator RecInt::ruint< K > () const
template<size_t K>
	operator RecInt::rint< K > () const

Static Public Member Functions
Addition, substraction, multiplication
static giv_all_inlined Integer &	addin (Integer &res, const Integer &n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	addin (Integer &res, const int64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	addin (Integer &res, const uint64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	addin (Integer &res, const int32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	addin (Integer &res, const uint32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	add (Integer &res, const Integer &n1, const Integer &n2)
	Addition res=n1+n2.
static giv_all_inlined Integer &	add (Integer &res, const Integer &n1, const int64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	add (Integer &res, const Integer &n1, const uint64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	add (Integer &res, const Integer &n1, const int32_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	add (Integer &res, const Integer &n1, const uint32_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	subin (Integer &res, const Integer &n)
	Substraction (inplace) res-=n.
static giv_all_inlined Integer &	subin (Integer &res, const int64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	subin (Integer &res, const uint64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	subin (Integer &res, const int32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	subin (Integer &res, const uint32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	sub (Integer &res, const Integer &n1, const Integer &n2)
	Substraction res=n1-n2.
static giv_all_inlined Integer &	sub (Integer &res, const Integer &n1, const int64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	sub (Integer &res, const Integer &n1, const uint64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	sub (Integer &res, const Integer &n1, const int32_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	sub (Integer &res, const Integer &n1, const uint32_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	negin (Integer &res)
	Negation (inplace) res=-res.
static giv_all_inlined Integer &	neg (Integer &res, const Integer &n)
	Negation res=-n.
static giv_all_inlined Integer &	mulin (Integer &res, const Integer &n)
	Multiplication (inplace) res*=n.
static giv_all_inlined Integer &	mulin (Integer &res, const int64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mulin (Integer &res, const uint64_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mulin (Integer &res, const int32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mulin (Integer &res, const uint32_t n)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mul (Integer &res, const Integer &n1, const Integer &n2)
	Multiplication res=n1*n2.
static giv_all_inlined Integer &	mul (Integer &res, const Integer &n1, const int64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mul (Integer &res, const Integer &n1, const uint64_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mul (Integer &res, const Integer &n1, const int32_t n2)
	Addition (inplace) res+=n.
static giv_all_inlined Integer &	mul (Integer &res, const Integer &n1, const uint32_t n2)
	Addition (inplace) res+=n.
fused add-multiply
Groups a multiplication and an addition/division in a single function. This is usually faster than doing the two operations separately (and preferable to using operators).
static giv_all_inlined Integer &	axpy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	axpy res = ax+y.
static giv_all_inlined Integer &	axpy (Integer &res, const Integer &a, const uint64_t x, const Integer &y)
	axpy res = ax+y.
static giv_all_inlined Integer &	axpyin (Integer &res, const Integer &a, const Integer &x)
	axpyin (inplace) res += ax.
static giv_all_inlined Integer &	axpyin (Integer &res, const Integer &a, const uint64_t x)
	axpy res = ax+y.
static giv_all_inlined Integer &	maxpy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	maxpy res = y - ax.
static giv_all_inlined Integer &	maxpy (Integer &res, const Integer &a, const uint64_t x, const Integer &y)
	axpy res = ax+y.
static giv_all_inlined Integer &	maxpyin (Integer &res, const Integer &a, const Integer &x)
	maxpyin res -= ax.
static giv_all_inlined Integer &	maxpyin (Integer &res, const Integer &a, const uint64_t x)
	axpy res = ax+y.
static giv_all_inlined Integer &	axmy (Integer &res, const Integer &a, const Integer &x, const Integer &y)
	axmy res = ax - y.
static giv_all_inlined Integer &	axmy (Integer &res, const Integer &a, const uint64_t x, const Integer &y)
	axpy res = ax+y.
static giv_all_inlined Integer &	axmyin (Integer &res, const Integer &a, const Integer &x)
	axmyin (in place) res = ax - res.
static giv_all_inlined Integer &	axmyin (Integer &res, const Integer &a, const uint64_t x)
	axpy res = ax+y.
Random numbers functions
Other stuff gmp has (temporary)
static void	seeding (uint64_t s)
	Random numbers (no doc)
static void	seeding (const Integer &s)
	Random numbers (no doc)
static void	seeding ()
	Random numbers (no doc)
static bool	RandBool ()
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer &	random_lessthan (Integer &r, const Integer &m)
	returns a random integer r in the intervall [[x, m-1]] where x = 0 or -(m-1) according to ALWAYSPOSITIVE
static Integer &	random_lessthan (Integer &r, const Integer &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer &	random_lessthan_2exp (Integer &r, const uint64_t &m)
	returns a random integer r in the intervall [[x, 2^m-1]] where x = 0 or -(2^m-1) according to ALWAYSPOSITIVE returns a random integer r of at most m bits
static Integer &	random_lessthan_2exp (Integer &r, const uint64_t &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer	random_lessthan_2exp (const uint64_t &m)
	Random numbers (no doc)
static Integer	random_lessthan_2exp (const uint64_t &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer &	random_lessthan (Integer &r, const uint64_t &m)
	Random numbers (no doc)
static Integer &	random_lessthan (Integer &r, const uint64_t &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer	random_lessthan (const T &m)
	Random numbers (no doc)
template<class T >
static Integer	random_lessthan (const T &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer &	random_exact_2exp (Integer &r, const uint64_t &m)
	returns a reference to a random number r of the size m bits, exactly.
static Integer &	random_exact_2exp (Integer &r, const uint64_t &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
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)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer &	random_exact (Integer &r, const uint64_t &m)
	Random numbers (no doc)
static Integer &	random_exact (Integer &r, const uint64_t &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer &	random_exact (Integer &r, const T &m)
	Random numbers (no doc)
template<class T >
static Integer &	random_exact (Integer &r, const T &m)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer	random_exact (const T &s)
	Random numbers (no doc)
template<class T >
static Integer	random_exact (const T &s)
	Random numbers (no doc)
static Integer &	random_between (Integer &r, const Integer &m, const Integer &M)
	Random numbers (no doc)
static Integer	random_between (const Integer &m, const Integer &M)
	Random numbers (no doc)
static Integer &	random_between_2exp (Integer &r, const uint64_t &m, const uint64_t &M)
	Random numbers (no doc)
static Integer &	random_between (Integer &r, const uint64_t &m, const uint64_t &M)
	Random numbers (no doc)
static Integer	random_between_2exp (const uint64_t &m, const uint64_t &M)
	Random numbers (no doc)
static Integer	random_between (const uint64_t &m, const uint64_t &M)
	Random numbers (no doc)
template<class R >
static Integer	random_between (const R &m, const R &M)
	Random numbers (no doc)
template<class R >
static Integer &	random_between (Integer &r, const R &m, const R &M)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, 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)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer	random (const T &sz)
	returns a random integer less than...
template<class T >
static Integer	random (const T &sz)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE>
static Integer	random ()
	Random numbers (no doc)
static Integer	random ()
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer	nonzerorandom (const T &sz)
	Random numbers (no doc)
template<bool ALWAYSPOSITIVE, class T >
static Integer &	nonzerorandom (Integer &r, const T &size)
	Random numbers (no doc)
template<class T >
static Integer	nonzerorandom (const T &sz)
	Random numbers (no doc)
template<class T >
static Integer &	nonzerorandom (Integer &r, const T &size)
	Random numbers (no doc)
static Integer	nonzerorandom ()
	Random numbers (no doc)

Static Public Attributes
static const Integer	zero
	zero (0)
static const Integer	one
	one (1)
static const Integer	mOne
	minus one (-1)

Friends
giv_all_inlined Integer &	powmod (Integer &Res, const Integer &n, const uint64_t e, const Integer &m)
	modular pow. return .
giv_all_inlined Integer	powmod (const Integer &n, const uint64_t e, const Integer &m)
	modular pow.
giv_all_inlined Integer	fact (uint64_t l)
	fact
giv_all_inlined Integer	sqrt (const Integer &p)
	(square) roots
giv_all_inlined Integer &	sqrt (Integer &r, const Integer &p)
	(square) roots
giv_all_inlined Integer	sqrtrem (const Integer &p, Integer &rem)
	(square) roots
giv_all_inlined Integer &	sqrtrem (Integer &r, const Integer &p, Integer &rem)
	(square) roots
giv_all_inlined bool	root (Integer &q, const Integer &a, uint32_t n)
	(square) roots
giv_all_inlined int64_t	logp (const Integer &a, const Integer &p)
	logs
giv_all_inlined double	logtwo (const Integer &a)
	logs
giv_all_inlined double	naturallog (const Integer &a)
	logs
Arithmetic functions
giv_all_inlined Integer	gcd (const Integer &a, const Integer &b)
	gcd.
giv_all_inlined Integer	gcd (Integer &u, Integer &v, const Integer &a, const Integer &b)
	gcd.
giv_all_inlined Integer &	gcd (Integer &g, const Integer &a, const Integer &b)
	gcd.
giv_all_inlined Integer &	gcd (Integer &g, Integer &u, Integer &v, const Integer &a, const Integer &b)
	gcd.
giv_all_inlined Integer &	inv (Integer &u, const Integer &a, const Integer &b)
	Inverse.
giv_all_inlined Integer &	invin (Integer &u, const Integer &b)
	Compute the inverse inplace u = u/b.
giv_all_inlined Integer	pp (const Integer &P, const Integer &Q)
	pp
giv_all_inlined Integer &	lcm (Integer &g, const Integer &a, const Integer &b)
	lcm
giv_all_inlined Integer	lcm (const Integer &a, const Integer &b)
	lcm
giv_all_inlined Integer &	pow (Integer &Res, const Integer &n, const int64_t l)
	pow.
giv_all_inlined Integer &	pow (Integer &Res, const uint64_t n, const uint64_t l)
	gcd.
giv_all_inlined Integer &	pow (Integer &Res, const Integer &n, const uint64_t l)
	gcd.
giv_all_inlined Integer &	pow (Integer &Res, const Integer &n, const int32_t l)
	gcd.
giv_all_inlined Integer &	pow (Integer &Res, const Integer &n, const uint32_t l)
	gcd.
giv_all_inlined Integer	pow (const Integer &n, const int64_t l)
	pow.
giv_all_inlined Integer	pow (const Integer &n, const uint64_t l)
	gcd.
giv_all_inlined Integer	pow (const Integer &n, const int32_t l)
	gcd.
giv_all_inlined Integer	pow (const Integer &n, const uint32_t l)
	gcd.
primes
giv_all_inlined Integer &	Protected::prevprime (Integer &, const Integer &p)
giv_all_inlined Integer &	Protected::nextprime (Integer &, const Integer &p)
giv_all_inlined int32_t	Protected::probab_prime (const Integer &p, int32_t r)
giv_all_inlined int32_t	kronecker (const Integer &u, const Integer &v)
giv_all_inlined int32_t	jacobi (const Integer &u, const Integer &v)
giv_all_inlined int32_t	legendre (const Integer &u, const Integer &v)

Comparison operators.
Compare with operators.
giv_all_inlined int32_t	operator>= (const Integer &l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator>= (const float l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const Integer &l) const
	less or equal
giv_all_inlined int32_t	operator<= (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator<= (const float l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const Integer &l) const
	operator != (not equal)
giv_all_inlined int32_t	operator!= (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator!= (const float l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const Integer &l) const
	Equality.
giv_all_inlined int32_t	operator== (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator== (const float l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const Integer &l) const
	greater (strict)
giv_all_inlined int32_t	operator> (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator> (const float l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const Integer &l) const
	less (strict)
giv_all_inlined int32_t	operator< (const int32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const int64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const uint64_t l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const uint32_t l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const double l) const
	greater or equal.
giv_all_inlined int32_t	operator< (const float l) const
	greater or equal.
giv_all_inlined friend int32_t	operator>= (uint32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator>= (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator>= (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator>= (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator>= (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator>= (uint64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator<= (uint32_t l, const Integer &n)
	less or equal
giv_all_inlined friend int32_t	operator<= (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator<= (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator<= (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator<= (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator<= (uint64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator!= (uint32_t l, const Integer &n)
	operator != (not equal)
giv_all_inlined friend int32_t	operator!= (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator!= (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator!= (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator!= (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator!= (uint64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator== (uint32_t l, const Integer &n)
	Equality.
giv_all_inlined friend int32_t	operator== (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator== (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator== (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator== (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator== (uint64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator> (uint32_t l, const Integer &n)
	greater (strict)
giv_all_inlined friend int32_t	operator> (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator> (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator> (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator> (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator> (uint64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator< (uint32_t l, const Integer &n)
	less (strict)
giv_all_inlined friend int32_t	operator< (float l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator< (double l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator< (int32_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator< (int64_t l, const Integer &n)
	greater or equal.
giv_all_inlined friend int32_t	operator< (uint64_t l, const Integer &n)
	greater or equal.

Addition, substraction, multiplication operators
giv_all_inlined Integer	operator+ (const Integer &n) const
	operator +.
giv_all_inlined Integer	operator+ (const uint64_t n) const
	operator +.
giv_all_inlined Integer	operator+ (const int64_t n) const
	operator +.
giv_all_inlined Integer	operator+ (const uint32_t n) const
	operator +.
giv_all_inlined Integer	operator+ (const int32_t n) const
	operator +.
giv_all_inlined Integer &	operator+= (const Integer &n)
	operator += .
giv_all_inlined Integer &	operator+= (const uint64_t n)
	operator +.
giv_all_inlined Integer &	operator+= (const int64_t n)
	operator +.
giv_all_inlined Integer &	operator+= (const uint32_t n)
	operator +.
giv_all_inlined Integer &	operator+= (const int32_t n)
	operator +.
template<class XXX >
Integer &	operator+= (const XXX &n)
	operator +.
giv_all_inlined Integer	operator- (const Integer &n) const
	operator -.
giv_all_inlined Integer	operator- (const uint64_t n) const
	operator +.
giv_all_inlined Integer	operator- (const int64_t n) const
	operator +.
giv_all_inlined Integer	operator- (const uint32_t n) const
	operator +.
giv_all_inlined Integer	operator- (const int32_t n) const
	operator +.
giv_all_inlined Integer &	operator-= (const Integer &n)
	operator -= .
giv_all_inlined Integer &	operator-= (const uint64_t n)
	operator +.
giv_all_inlined Integer &	operator-= (const int64_t n)
	operator +.
giv_all_inlined Integer &	operator-= (const uint32_t n)
	operator +.
giv_all_inlined Integer &	operator-= (const int32_t n)
	operator +.
template<class XXX >
Integer &	operator-= (const XXX &n)
	operator +.
giv_all_inlined Integer	operator- () const
	Opposite.
giv_all_inlined Integer	operator* (const Integer &n) const
	operator *.
giv_all_inlined Integer	operator* (const uint64_t n) const
	operator +.
giv_all_inlined Integer	operator* (const int64_t n) const
	operator +.
giv_all_inlined Integer	operator* (const uint32_t n) const
	operator +.
giv_all_inlined Integer	operator* (const int32_t n) const
	operator +.
giv_all_inlined Integer &	operator*= (const Integer &n)
	operator *= .
giv_all_inlined Integer &	operator*= (const uint64_t n)
	operator +.
giv_all_inlined Integer &	operator*= (const int64_t n)
	operator +.
giv_all_inlined Integer &	operator*= (const uint32_t n)
	operator +.
giv_all_inlined Integer &	operator*= (const int32_t n)
	operator +.
template<class XXX >
Integer &	operator*= (const XXX &n)
	operator +.
giv_all_inlined Integer	operator+ (const int32_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator+ (const uint32_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator+ (const int64_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator+ (const uint64_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator- (const int32_t l, const Integer &n)
	operator -
giv_all_inlined Integer	operator- (const uint32_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator- (const int64_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator- (const uint64_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator* (const int32_t l, const Integer &n)
	operator *
giv_all_inlined Integer	operator* (const uint32_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator* (const int64_t l, const Integer &n)
	operator +.
giv_all_inlined Integer	operator* (const uint64_t l, const Integer &n)
	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 : 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 : 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).
giv_all_inlined Integer	operator/ (const Integer &d) const
	Division operator.
giv_all_inlined Integer	operator/ (const uint64_t d) const
	Division q/=d.
giv_all_inlined Integer	operator/ (const int64_t d) const
	Division q/=d.
giv_all_inlined Integer	operator/ (const uint32_t d) const
	Division q/=d.
giv_all_inlined Integer	operator/ (const int32_t d) const
	Division q/=d.
giv_all_inlined Integer &	operator/= (const Integer &d)
	Division operator (inplace).
giv_all_inlined Integer &	operator/= (const uint64_t d)
	Division q/=d.
giv_all_inlined Integer &	operator/= (const int64_t d)
	Division q/=d.
giv_all_inlined Integer &	operator/= (const uint32_t d)
	Division q/=d.
giv_all_inlined Integer &	operator/= (const int32_t d)
	Division q/=d.
template<class XXX >
Integer &	operator/= (const XXX &d)
	Division q/=d.
giv_all_inlined Integer	operator% (const Integer &n) const
	Modulo operator.
giv_all_inlined int64_t	operator% (const uint64_t n) const
	Division q/=d.
giv_all_inlined int64_t	operator% (const int64_t n) const
	Division q/=d.
giv_all_inlined int32_t	operator% (const uint32_t n) const
	Division q/=d.
giv_all_inlined int32_t	operator% (const int32_t n) const
	Division q/=d.
giv_all_inlined double	operator% (const double n) const
	Division q/=d.
int16_t	operator% (const uint16_t n) const
	Division q/=d.
template<class XXX >
XXX	operator% (const XXX &n) const
	Division q/=d.
giv_all_inlined Integer &	operator%= (const Integer &n)
	Modulo operator (inplace).
giv_all_inlined Integer &	operator%= (const uint64_t n)
	Division q/=d.
giv_all_inlined Integer &	operator%= (const int64_t n)
	Division q/=d.
giv_all_inlined Integer &	operator%= (const uint32_t n)
	Division q/=d.
giv_all_inlined Integer &	operator%= (const int32_t n)
	Division q/=d.
template<class XXX >
Integer &	operator%= (const XXX &n)
	Division q/=d.
static giv_all_inlined Integer &	divin (Integer &q, const Integer &d)
	Division q/=d.
static giv_all_inlined Integer &	divin (Integer &q, const int64_t d)
	Division q/=d.
static giv_all_inlined Integer &	divin (Integer &q, const uint64_t d)
	Division q/=d.
static giv_all_inlined Integer &	div (Integer &q, const Integer &n, const Integer &d)
	Division q=n/d.
static giv_all_inlined Integer &	div (Integer &q, const Integer &n, const int64_t d)
	Division q/=d.
static giv_all_inlined Integer &	div (Integer &q, const Integer &n, const int32_t d)
	Division q/=d.
static giv_all_inlined Integer &	div (Integer &q, const Integer &n, const uint64_t d)
	Division q/=d.
static giv_all_inlined Integer &	divexact (Integer &q, const Integer &n, const Integer &d)
	Division when d divides n.
static giv_all_inlined Integer &	divexact (Integer &q, const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined Integer &	divexact (Integer &q, const Integer &n, const int64_t &d)
	Division q/=d.
static giv_all_inlined Integer	divexact (const Integer &n, const Integer &d)
	Division when d divides n.
static giv_all_inlined Integer	divexact (const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined Integer	divexact (const Integer &n, const int64_t &d)
	Division q/=d.
static giv_all_inlined Integer &	trem (Integer &r, const Integer &n, const Integer &d)
	Stuff.
static giv_all_inlined Integer &	crem (Integer &r, const Integer &n, const Integer &d)
	Division q/=d.
static giv_all_inlined Integer &	frem (Integer &r, const Integer &n, const Integer &d)
	Division q/=d.
static giv_all_inlined Integer &	trem (Integer &r, const Integer &n, const uint64_t &d)
	Stuff.
static giv_all_inlined Integer &	crem (Integer &r, const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined Integer &	frem (Integer &r, const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined uint64_t	trem (const Integer &n, const uint64_t &d)
	Stuff.
static giv_all_inlined uint64_t	crem (const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined uint64_t	frem (const Integer &n, const uint64_t &d)
	Division q/=d.
static giv_all_inlined Integer &	modin (Integer &r, const Integer &n)
	Function mod (inplace).
static giv_all_inlined Integer &	modin (Integer &r, const int64_t n)
	Division q/=d.
static giv_all_inlined Integer &	modin (Integer &r, const uint64_t n)
	Division q/=d.
static giv_all_inlined Integer &	mod (Integer &r, const Integer &n, const Integer &d)
	Function mod.
static giv_all_inlined Integer &	mod (Integer &r, const Integer &n, const int64_t d)
	Division q/=d.
static giv_all_inlined Integer &	mod (Integer &r, const Integer &n, const uint64_t d)
	Division q/=d.
static giv_all_inlined Integer &	mod (Integer &r, const Integer &n, const int32_t d)
	Division q/=d.
static giv_all_inlined Integer &	mod (Integer &r, const Integer &n, const uint32_t d)
	Division q/=d.
static giv_all_inlined Integer &	divmod (Integer &q, Integer &r, const Integer &n, const Integer &d)
	Euclidean division.
static giv_all_inlined Integer &	divmod (Integer &q, int64_t &r, const Integer &n, const int64_t d)
	Division q/=d.
static giv_all_inlined Integer &	divmod (Integer &q, uint64_t &r, const Integer &n, const uint64_t d)
	Division q/=d.
static giv_all_inlined Integer &	ceil (Integer &res, const Integer &n, const Integer &d)
	rounding functions.
static giv_all_inlined Integer &	floor (Integer &res, const Integer &n, const Integer &d)
static giv_all_inlined Integer &	trunc (Integer &res, const Integer &n, const Integer &d)
static giv_all_inlined Integer	ceil (const Integer &n, const Integer &d)
	rounding functions.
static giv_all_inlined Integer	floor (const Integer &n, const Integer &d)
static giv_all_inlined Integer	trunc (const Integer &n, const Integer &d)
giv_all_inlined Integer	operator/ (const int32_t l, const Integer &n)
	operator /
giv_all_inlined Integer	operator/ (const int64_t l, const Integer &n)
	Division operator.
giv_all_inlined Integer	operator/ (const uint32_t l, const Integer &n)
	operator /
giv_all_inlined Integer	operator/ (const uint64_t l, const Integer &n)
	Division operator.
giv_all_inlined Integer	operator% (const int64_t l, const Integer &n)
	operator %
giv_all_inlined Integer	operator% (const uint64_t l, const Integer &n)
	Division operator.
giv_all_inlined Integer	operator% (const int32_t l, const Integer &n)
	Division operator.
giv_all_inlined Integer	operator% (const uint32_t l, const Integer &n)
	Division operator.

Miscellaneous.
int32_t	sign () const
	sign
int32_t	priv_sign () const
	private sign
giv_all_inlined void	swap (Integer &a, Integer &b)
int32_t	sign (const Integer &a)
	sign

representation
get representation
mpz_ptr	get_mpz ()
	get representation (constant)
mpz_srcptr	get_mpz () const
	get representation (constant)
mpz_srcptr	get_mpz_const () const
	get representation (constant)
giv_all_inlined size_t	size () const
	returns the number of machine words used to store *this
giv_all_inlined size_t	size_in_base (int32_t B) const
	returns ceil(log_BASE(*this)).
giv_all_inlined size_t	bitsize () const
	returns ceil(log_2(*this)) .
giv_all_inlined uint64_t	operator[] (size_t i) const
	return the i-th word of the integer.
giv_all_inlined uint64_t	length (const Integer &a)
	returns the number of bytes used to store *this
giv_all_inlined int32_t	isperfectpower (const Integer &n)
	perfect power
giv_all_inlined Integer	abs (const Integer &n)
	absolute value
giv_all_inlined bool	isOdd (const Integer &)
	parity of an integer

I/O
giv_all_inlined std::ostream &	print (std::ostream &o) const
	print32_t integer.
giv_all_inlined std::istream &	operator>> (std::istream &i, Integer &n)
	Input/Output of Integers.
giv_all_inlined std::ostream &	operator<< (std::ostream &o, const Integer &n)
	out operator.
giv_all_inlined std::ostream &	absOutput (std::ostream &o, const Integer &n)
	nodoc
giv_all_inlined void	Protected::importWords (Integer &x, size_t count, int32_t order, int32_t size, int32_t endian, size_t nails, const void *op)
	nodoc

Comparisons functions.
template<class A , class B >
static giv_all_inlined bool	isleq (const A &a, const B &b)
	isleq
giv_all_inlined friend int32_t	compare (const Integer &a, const Integer &b)
	Compares two integers.
giv_all_inlined friend int32_t	absCompare (const Integer &a, const Integer &b)
	Compare the norm of two integers.
giv_all_inlined friend int32_t	absCompare (const Integer &a, const double b)
	isleq
giv_all_inlined friend int32_t	absCompare (const Integer &a, const float b)
	isleq
giv_all_inlined friend int32_t	absCompare (const Integer &a, const uint64_t b)
	isleq
giv_all_inlined friend int32_t	absCompare (const Integer &a, const unsigned b)
	isleq
giv_all_inlined friend int32_t	absCompare (const Integer &a, const int64_t b)
	isleq
giv_all_inlined friend int32_t	absCompare (const Integer &a, const int32_t b)
	isleq
template<class T >
giv_all_inlined friend int32_t	absCompare (const T a, const Integer &b)
	isleq
giv_all_inlined int32_t	isOne (const Integer &a)
	name compare to 1 and 0
giv_all_inlined int32_t	isMOne (const Integer &a)
	isleq
giv_all_inlined int32_t	nonZero (const Integer &a)
	name compare to 1 and 0
giv_all_inlined int32_t	isZero (const Integer &a)
	name compare to 1 and 0
giv_all_inlined int32_t	isZero (const int16_t a)
	isleq
giv_all_inlined int32_t	isZero (const int32_t a)
	isleq
giv_all_inlined int32_t	isZero (const int64_t a)
	isleq
giv_all_inlined int32_t	isZero (const uint16_t a)
	isleq
giv_all_inlined int32_t	isZero (const uint32_t a)
	isleq
giv_all_inlined int32_t	isZero (const uint64_t a)
	isleq

Detailed Description

This is the Integer class.

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

Examples

examples/FiniteField/GF128.C, examples/FiniteField/Test_Extension.C, examples/FiniteField/all_field.C, examples/FiniteField/domain_to_operatorstyle.C, examples/FiniteField/kronecker.C, examples/Integer/Fibonacci.C, examples/Integer/ModularSquareRoot.C, examples/Integer/ProbLucas.C, examples/Integer/RSA_breaking.C, examples/Integer/RSA_decipher.C, examples/Integer/RSA_encipher.C, examples/Integer/givaro-ssh-keygen.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/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/nb_primes.C, examples/Integer/nextprime.C, examples/Integer/order.C, examples/Integer/phi.C, examples/Integer/prevprime.C, examples/Integer/primitiveelement.C, examples/Integer/primitiveroot.C, examples/Integer/probable_primroot.C, examples/Polynomial/PolynomialCRT.C, examples/Rational/iratrecon.C, and examples/Rational/polydouble.C.

Constructor & Destructor Documentation

Integer() [1/13]

Integer

(

int32_t

n = 0

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [2/13]

Integer

(

int64_t

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [3/13]

Integer

(

unsigned char

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [4/13]

Integer

(

uint32_t

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [5/13]

Integer

(

uint64_t

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [6/13]

Integer

(

double

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [7/13]

Integer

(

const char *

n

)

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [8/13]

giv_all_inlined Integer ( const mpz_class &  a )

inline

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [9/13]

Integer ( const RecInt::ruint< K > &  n )

inline

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [10/13]

Integer ( const RecInt::rint< K > &  n )

inline

Constructor form a known type.

Parameters

n	input to be constructed from

Integer() [11/13]

Integer

(

const Integer &

n

)

Copy constructor.

Parameters

n	input to be constructed from

Integer() [12/13]

giv_all_inlined Integer	(	uint64_t *	d,
		int64_t	sz
	)

Creates a new Integer from pointers.

Parameters

d	array
sz	size

Integer() [13/13]

Integer

(

const vect_t &

v

)

Creates a new Integers for a vector of limbs.

Parameters

v	vector of limbs

Member Function Documentation

operator=()

Integer & operator=

(

const Integer &

n

)

copy from an integer.

Parameters

n	integer to copy.

logcpy()

Integer & logcpy

(

const Integer &

n

)

copy from an integer.

Parameters

n	integer to copy.

copy()

Integer & copy

(

const Integer &

n

)

copy from an integer.

Parameters

n	integer to copy.

Examples

examples/Integer/ProbLucas.C.

isleq()

static giv_all_inlined bool isleq ( const A &  a, const B &  b  )

inlinestatic

isleq

Parameters

a,b

operator>=() [1/7]

int32_t operator>=

(

const Integer &

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [2/7]

int32_t operator>=

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [3/7]

int32_t operator>=

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [4/7]

int32_t operator>=

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [5/7]

int32_t operator>=

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [6/7]

int32_t operator>=

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>=() [7/7]

int32_t operator>=

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [1/7]

int32_t operator<=

(

const Integer &

l

)

const

less or equal

Parameters

l	integer to be compared to

operator<=() [2/7]

int32_t operator<=

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [3/7]

int32_t operator<=

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [4/7]

int32_t operator<=

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [5/7]

int32_t operator<=

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [6/7]

int32_t operator<=

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<=() [7/7]

int32_t operator<=

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [1/7]

int32_t operator!=

(

const Integer &

l

)

const

operator != (not equal)

Parameters

l

integer

Returns

1 iff l == this

operator!=() [2/7]

int32_t operator!=

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [3/7]

int32_t operator!=

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [4/7]

int32_t operator!=

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [5/7]

int32_t operator!=

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [6/7]

int32_t operator!=

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator!=() [7/7]

int32_t operator!=

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [1/7]

int32_t operator==

(

const Integer &

l

)

const

Equality.

Parameters

l	integer to be compared to

operator==() [2/7]

int32_t operator==

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [3/7]

int32_t operator==

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [4/7]

int32_t operator==

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [5/7]

int32_t operator==

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [6/7]

int32_t operator==

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator==() [7/7]

int32_t operator==

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [1/7]

int32_t operator>

(

const Integer &

l

)

const

greater (strict)

Parameters

l	integer to be compared to

operator>() [2/7]

int32_t operator>

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [3/7]

int32_t operator>

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [4/7]

int32_t operator>

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [5/7]

int32_t operator>

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [6/7]

int32_t operator>

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator>() [7/7]

int32_t operator>

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [1/7]

int32_t operator<

(

const Integer &

l

)

const

less (strict)

Parameters

l	integer to be compared to

operator<() [2/7]

int32_t operator<

(

const int32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [3/7]

int32_t operator<

(

const int64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [4/7]

int32_t operator<

(

const uint64_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [5/7]

int32_t operator<

(

const uint32_t

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [6/7]

int32_t operator<

(

const double

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator<() [7/7]

int32_t operator<

(

const float

l

)

const

greater or equal.

Parameters

l	integer to be compared to

operator^() [1/3]

Integer operator^

(

const Integer &

a

)

const

XOR (^)

Parameters

a

integer

operator^() [2/3]

Integer operator^

(

const uint64_t &

a

)

const

XOR (^)

Parameters

a

integer

operator^() [3/3]

Integer operator^

(

const uint32_t &

a

)

const

XOR (^)

Parameters

a

integer

operator^=() [1/3]

Integer & operator^=

(

const Integer &

a

)

XOR inplace (^=)

Parameters

a

integer

operator^=() [2/3]

Integer & operator^=

(

const uint64_t &

a

)

XOR (^)

Parameters

a

integer

operator^=() [3/3]

Integer & operator^=

(

const uint32_t &

a

)

XOR (^)

Parameters

a

integer

operator|() [1/3]

Integer operator|

(

const Integer &

a

)

const

OR (|)

Parameters

a

integer

operator|() [2/3]

Integer operator|

(

const uint64_t &

a

)

const

XOR (^)

Parameters

a

integer

operator|() [3/3]

Integer operator|

(

const uint32_t &

a

)

const

XOR (^)

Parameters

a

integer

operator|=() [1/3]

Integer & operator|=

(

const Integer &

a

)

OR inplace (|=)

Parameters

a

integer

operator|=() [2/3]

Integer & operator|=

(

const uint64_t &

a

)

XOR (^)

Parameters

a

integer

operator|=() [3/3]

Integer & operator|=

(

const uint32_t &

a

)

XOR (^)

Parameters

a

integer

operator&() [1/3]

Integer operator&

(

const Integer &

a

)

const

AND (&)

Parameters

a

integer

operator&() [2/3]

uint32_t operator&

(

const uint32_t &

a

)

const

XOR (^)

Parameters

a

integer

operator&() [3/3]

uint64_t operator&

(

const uint64_t &

a

)

const

XOR (^)

Parameters

a

integer

operator&=() [1/3]

Integer & operator&=

(

const Integer &

a

)

AND inplace (&=)

Parameters

a

integer

operator&=() [2/3]

Integer & operator&=

(

const uint64_t &

a

)

XOR (^)

Parameters

a

integer

operator&=() [3/3]

Integer & operator&=

(

const uint32_t &

a

)

XOR (^)

Parameters

a

integer

operator<<() [1/4]

Integer operator<<

(

int32_t

l

)

const

left shift (<<)

Parameters

l

shift

operator<<() [2/4]

Integer operator<<

(

int64_t

l

)

const

XOR (^)

Parameters

a

integer

operator<<() [3/4]

Integer operator<<

(

uint32_t

l

)

const

XOR (^)

Parameters

a

integer

operator<<() [4/4]

Integer operator<<

(

uint64_t

l

)

const

XOR (^)

Parameters

a

integer

operator<<=() [1/4]

Integer & operator<<=

(

int32_t

l

)

left shift inplace (<<=)

Parameters

l

shift

operator<<=() [2/4]

Integer & operator<<=

(

int64_t

l

)

XOR (^)

Parameters

a

integer

operator<<=() [3/4]

Integer & operator<<=

(

uint32_t

l

)

XOR (^)

Parameters

a

integer

operator<<=() [4/4]

Integer & operator<<=

(

uint64_t

l

)

XOR (^)

Parameters

a

integer

operator>>() [1/4]

Integer operator>>

(

int32_t

l

)

const

right shift (>>)

Parameters

l

shift

operator>>() [2/4]

Integer operator>>

(

int64_t

l

)

const

XOR (^)

Parameters

a

integer

operator>>() [3/4]

Integer operator>>

(

uint32_t

l

)

const

XOR (^)

Parameters

a

integer

operator>>() [4/4]

Integer operator>>

(

uint64_t

l

)

const

XOR (^)

Parameters

a

integer

operator>>=() [1/4]

Integer & operator>>=

(

int32_t

l

)

right shift inplace (>>=)

Parameters

l

shift

operator>>=() [2/4]

Integer & operator>>=

(

int64_t

l

)

XOR (^)

Parameters

a

integer

operator>>=() [3/4]

Integer & operator>>=

(

uint32_t

l

)

XOR (^)

Parameters

a

integer

operator>>=() [4/4]

Integer & operator>>=

(

uint64_t

l

)

XOR (^)

Parameters

a

integer

addin() [1/5]

Integer & addin ( Integer &  res, const Integer &  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

Examples

examples/Integer/givaro-ssh-keygen.C.

addin() [2/5]

Integer & addin ( Integer &  res, const int64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

addin() [3/5]

Integer & addin ( Integer &  res, const uint64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

addin() [4/5]

static giv_all_inlined Integer & addin ( Integer &  res, const int32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

addin() [5/5]

static giv_all_inlined Integer & addin ( Integer &  res, const uint32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

add() [1/5]

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

add() [2/5]

Integer & add ( Integer &  res, const Integer &  n1, const int64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

add() [3/5]

Integer & add ( Integer &  res, const Integer &  n1, const uint64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

add() [4/5]

static giv_all_inlined Integer & add ( Integer &  res, const Integer &  n1, const int32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

add() [5/5]

static giv_all_inlined Integer & add ( Integer &  res, const Integer &  n1, const uint32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

subin() [1/5]

Integer & subin ( Integer &  res, const Integer &  n  )

static

Substraction (inplace) res-=n.

Parameters

res	as in the formula
n	as in the formula

subin() [2/5]

Integer & subin ( Integer &  res, const int64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

subin() [3/5]

Integer & subin ( Integer &  res, const uint64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

subin() [4/5]

static giv_all_inlined Integer & subin ( Integer &  res, const int32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

subin() [5/5]

static giv_all_inlined Integer & subin ( Integer &  res, const uint32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

sub() [1/5]

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/Fibonacci.C.

sub() [2/5]

Integer & sub ( Integer &  res, const Integer &  n1, const int64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

sub() [3/5]

Integer & sub ( Integer &  res, const Integer &  n1, const uint64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

sub() [4/5]

static giv_all_inlined Integer & sub ( Integer &  res, const Integer &  n1, const int32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

sub() [5/5]

static giv_all_inlined Integer & sub ( Integer &  res, const Integer &  n1, const uint32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

negin()

Integer & negin ( Integer &  res )

static

Negation (inplace) res=-res.

Parameters

res	as in the formula

neg()

Integer & neg ( Integer &  res, const Integer &  n  )

static

Negation res=-n.

Parameters

n	as in the formula
res	as in the formula

mulin() [1/5]

Integer & mulin ( Integer &  res, const Integer &  n  )

static

Multiplication (inplace) res*=n.

Parameters

res	as in the formula
n	as in the formula

mulin() [2/5]

Integer & mulin ( Integer &  res, const int64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mulin() [3/5]

Integer & mulin ( Integer &  res, const uint64_t  n  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mulin() [4/5]

static giv_all_inlined Integer & mulin ( Integer &  res, const int32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mulin() [5/5]

static giv_all_inlined Integer & mulin ( Integer &  res, const uint32_t  n  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mul() [1/5]

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/givaro-ssh-keygen.C.

mul() [2/5]

Integer & mul ( Integer &  res, const Integer &  n1, const int64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mul() [3/5]

Integer & mul ( Integer &  res, const Integer &  n1, const uint64_t  n2  )

static

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mul() [4/5]

static giv_all_inlined Integer & mul ( Integer &  res, const Integer &  n1, const int32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

mul() [5/5]

static giv_all_inlined Integer & mul ( Integer &  res, const Integer &  n1, const uint32_t  n2  )

inlinestatic

Addition (inplace) res+=n.

Parameters

res	as in the formula
n	as in the formula

operator+() [1/5]

Integer operator+

(

const Integer &

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+() [2/5]

Integer operator+

(

const uint64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+() [3/5]

Integer operator+

(

const int64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+() [4/5]

giv_all_inlined Integer operator+ ( const uint32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+() [5/5]

giv_all_inlined Integer operator+ ( const int32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+=() [1/6]

Integer & operator+=

(

const Integer &

n

)

operator += .

Parameters

n	asfriend In the formula.

Returns

(*this) += n.

operator+=() [2/6]

Integer & operator+=

(

const uint64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+=() [3/6]

Integer & operator+=

(

const int64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+=() [4/6]

giv_all_inlined Integer & operator+= ( const uint32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+=() [5/6]

giv_all_inlined Integer & operator+= ( const int32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+=() [6/6]

Integer & operator+= ( const XXX &  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-() [1/6]

Integer operator-

(

const Integer &

n

)

const

operator -.

Returns

(*this)-n

Parameters

n	as in the formula.

operator-() [2/6]

Integer operator-

(

const uint64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-() [3/6]

Integer operator-

(

const int64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-() [4/6]

giv_all_inlined Integer operator- ( const uint32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-() [5/6]

giv_all_inlined Integer operator- ( const int32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-=() [1/6]

Integer & operator-=

(

const Integer &

n

)

operator -= .

Parameters

n	as in the formula.

Returns

(*this) -= n.

operator-=() [2/6]

Integer & operator-=

(

const uint64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-=() [3/6]

Integer & operator-=

(

const int64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-=() [4/6]

giv_all_inlined Integer & operator-= ( const uint32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-=() [5/6]

giv_all_inlined Integer & operator-= ( const int32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-=() [6/6]

Integer & operator-= ( const XXX &  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator-() [6/6]

Integer operator-

(

)

const

Opposite.

Returns

-(*this).

operator*() [1/5]

Integer operator*

(

const Integer &

n

)

const

operator *.

Returns

(*this)*n

Parameters

n	as in the formula.

operator*() [2/5]

Integer operator*

(

const uint64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*() [3/5]

Integer operator*

(

const int64_t

n

)

const

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*() [4/5]

giv_all_inlined Integer operator* ( const uint32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*() [5/5]

giv_all_inlined Integer operator* ( const int32_t  n ) const

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*=() [1/6]

Integer & operator*=

(

const Integer &

n

)

operator *= .

Parameters

n	as in the formula.

Returns

(*this) *= n.

operator*=() [2/6]

Integer & operator*=

(

const uint64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*=() [3/6]

Integer & operator*=

(

const int64_t

n

)

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*=() [4/6]

giv_all_inlined Integer & operator*= ( const uint32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*=() [5/6]

giv_all_inlined Integer & operator*= ( const int32_t  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator*=() [6/6]

Integer & operator*= ( const XXX &  n )

inline

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

axpy() [1/2]

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

axpy() [2/2]

Integer & axpy ( Integer &  res, const Integer &  a, const uint64_t  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

axpyin() [1/2]

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.

axpyin() [2/2]

Integer & axpyin ( Integer &  res, const Integer &  a, const uint64_t  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

maxpy() [1/2]

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.

maxpy() [2/2]

Integer & maxpy ( Integer &  res, const Integer &  a, const uint64_t  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

maxpyin() [1/2]

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.

maxpyin() [2/2]

Integer & maxpyin ( Integer &  res, const Integer &  a, const uint64_t  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

axmy() [1/2]

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.

axmy() [2/2]

Integer & axmy ( Integer &  res, const Integer &  a, const uint64_t  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

axmyin() [1/2]

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.

axmyin() [2/2]

Integer & axmyin ( Integer &  res, const Integer &  a, const uint64_t  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

divin() [1/3]

Integer & divin ( Integer &  q, const Integer &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divin() [2/3]

Integer & divin ( Integer &  q, const int64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divin() [3/3]

Integer & divin ( Integer &  q, const uint64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

div() [1/4]

Integer & div ( Integer &  q, const Integer &  n, const Integer &  d  )

static

Division q=n/d.

Parameters

q	quotient
n	dividand.
d	divisor

Returns

q

div() [2/4]

Integer & div ( Integer &  q, const Integer &  n, const int64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

div() [3/4]

Integer & div ( Integer &  q, const Integer &  n, const int32_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

div() [4/4]

Integer & div ( Integer &  q, const Integer &  n, const uint64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divexact() [1/6]

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.

divexact() [2/6]

Integer & divexact ( Integer &  q, const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divexact() [3/6]

Integer & divexact ( Integer &  q, const Integer &  n, const int64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divexact() [4/6]

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.

divexact() [5/6]

Integer divexact ( const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divexact() [6/6]

Integer divexact ( const Integer &  n, const int64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

crem() [1/3]

Integer & crem ( Integer &  r, const Integer &  n, const Integer &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

frem() [1/3]

Integer & frem ( Integer &  r, const Integer &  n, const Integer &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

crem() [2/3]

Integer & crem ( Integer &  r, const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

frem() [2/3]

Integer & frem ( Integer &  r, const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

crem() [3/3]

uint64_t crem ( const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

frem() [3/3]

uint64_t frem ( const Integer &  n, const uint64_t &  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/() [1/5]

Integer operator/

(

const Integer &

d

)

const

Division operator.

Parameters

d

divisor

operator/() [2/5]

Integer operator/

(

const uint64_t

d

)

const

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/() [3/5]

Integer operator/

(

const int64_t

d

)

const

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/() [4/5]

giv_all_inlined Integer operator/ ( const uint32_t  d ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/() [5/5]

giv_all_inlined Integer operator/ ( const int32_t  d ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/=() [1/6]

Integer & operator/=

(

const Integer &

d

)

Division operator (inplace).

Parameters

d

divisor

operator/=() [2/6]

Integer & operator/=

(

const uint64_t

d

)

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/=() [3/6]

Integer & operator/=

(

const int64_t

d

)

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/=() [4/6]

giv_all_inlined Integer & operator/= ( const uint32_t  d )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/=() [5/6]

giv_all_inlined Integer & operator/= ( const int32_t  d )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator/=() [6/6]

Integer & operator/= ( const XXX &  d )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

modin() [1/3]

Integer & modin ( Integer &  r, const Integer &  n  )

static

Function mod (inplace).

Parameters

r	remainder
n	modulus

Examples

examples/Integer/givaro-ssh-keygen.C.

modin() [2/3]

Integer & modin ( Integer &  r, const int64_t  n  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

modin() [3/3]

Integer & modin ( Integer &  r, const uint64_t  n  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

mod() [1/5]

Integer & mod ( Integer &  r, const Integer &  n, const Integer &  d  )

static

Function mod.

Parameters

r	remainder
n	integer
d	modulus

Examples

examples/Integer/givaro-ssh-keygen.C.

mod() [2/5]

Integer & mod ( Integer &  r, const Integer &  n, const int64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

mod() [3/5]

Integer & mod ( Integer &  r, const Integer &  n, const uint64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

mod() [4/5]

static giv_all_inlined Integer & mod ( Integer &  r, const Integer &  n, const int32_t  d  )

inlinestatic

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

mod() [5/5]

static giv_all_inlined Integer & mod ( Integer &  r, const Integer &  n, const uint32_t  d  )

inlinestatic

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divmod() [1/3]

Integer & divmod ( Integer &  q, Integer &  r, const Integer &  n, const Integer &  d  )

static

Euclidean division.

n = d q + r . Computes both the quotient and the residue (as in quorem).

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

divmod() [2/3]

Integer & divmod ( Integer &  q, int64_t &  r, const Integer &  n, const int64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

divmod() [3/3]

Integer & divmod ( Integer &  q, uint64_t &  r, const Integer &  n, const uint64_t  d  )

static

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

ceil() [1/2]

Integer & ceil ( Integer &  res, const Integer &  n, const Integer &  d  )

static

rounding functions.

these are the same as the STL ones, except for the signature.

Parameters

res	the result
n	the numerator
d	the demominator

same as std::ceil (n/d)

floor() [1/2]

Integer & floor ( Integer &  res, const Integer &  n, const Integer &  d  )

static

same as std::floor(n/d)

trunc() [1/2]

Integer & trunc ( Integer &  res, const Integer &  n, const Integer &  d  )

static

same as std::trunc(n/d)

ceil() [2/2]

Integer ceil ( const Integer &  n, const Integer &  d  )

static

rounding functions.

these are the same as the STL ones, except for the signature.

Parameters

n	the numerator
d	the demominator

Returns

n/d rounded.

same as std::ceil (n/d)

floor() [2/2]

Integer floor ( const Integer &  n, const Integer &  d  )

static

same as std::floor(n/d)

trunc() [2/2]

Integer trunc ( const Integer &  n, const Integer &  d  )

static

same as std::trunc(n/d)

operator%() [1/8]

Integer operator%

(

const Integer &

n

)

const

Modulo operator.

Parameters

n

modulus

Returns

remainder (*this) mod n

operator%() [2/8]

int64_t operator%

(

const uint64_t

n

)

const

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [3/8]

int64_t operator%

(

const int64_t

n

)

const

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [4/8]

giv_all_inlined int32_t operator% ( const uint32_t  n ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [5/8]

giv_all_inlined int32_t operator% ( const int32_t  n ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [6/8]

double operator%

(

const double

n

)

const

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [7/8]

int16_t operator% ( const uint16_t  n ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%() [8/8]

XXX operator% ( const XXX &  n ) const

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%=() [1/6]

Integer & operator%=

(

const Integer &

n

)

Modulo operator (inplace).

Parameters

n

modulus

Returns

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

operator%=() [2/6]

Integer & operator%=

(

const uint64_t

n

)

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%=() [3/6]

Integer & operator%=

(

const int64_t

n

)

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%=() [4/6]

giv_all_inlined Integer & operator%= ( const uint32_t  n )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%=() [5/6]

giv_all_inlined Integer & operator%= ( const int32_t  n )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

operator%=() [6/6]

Integer & operator%= ( const XXX &  n )

inline

Division q/=d.

Parameters

q	quotient
d	divisor.

Returns

q

size_in_base()

size_t size_in_base

(

int32_t

B

)

const

returns ceil(log_BASE(*this)).

bitsize()

size_t bitsize

(

)

const

returns ceil(log_2(*this)) .

operator[]()

uint64_t operator[]

(

size_t

i

)

const

return the i-th word of the integer.

Word 0 is lowest word.

random_lessthan()

Integer & random_lessthan ( Integer &  r, const Integer &  m  )

inlinestatic

returns a random integer r in the intervall [[x, m-1]] where x = 0 or -(m-1) according to ALWAYSPOSITIVE

Bug:

m has to be an integer here.

print()

std::ostream & print

(

std::ostream &

o

)

const

print32_t integer.

Parameters

o	output stream.

Friends And Related Function Documentation

compare

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

friend

Compares two integers.

Parameters

a	integer
b	integer

Returns

1 if , 0 if and -1 otherwise.

absCompare [1/8]

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

friend

Compare the norm of two integers.

Parameters

a	integer
b	integer

Returns

1 if , 0 if and -1 otherwise.

absCompare [2/8]

giv_all_inlined friend int32_t absCompare ( const Integer &  a, const double  b  )

friend

isleq

Parameters

a,b

absCompare [3/8]

giv_all_inlined friend int32_t absCompare ( const Integer &  a, const float  b  )

friend

isleq

Parameters

a,b

absCompare [4/8]

giv_all_inlined friend int32_t absCompare ( const Integer &  a, const uint64_t  b  )

friend

isleq

Parameters

a,b

absCompare [5/8]

giv_all_inlined friend int32_t absCompare ( const Integer &  a, const unsigned  b  )

friend

isleq

Parameters

a,b

absCompare [6/8]

giv_all_inlined friend int32_t absCompare ( const Integer &  a, const int64_t  b  )

friend

isleq

Parameters

a,b

absCompare [7/8]

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

friend

isleq

Parameters

a,b

absCompare [8/8]

giv_all_inlined friend int32_t absCompare ( const T  a, const Integer &  b  )

friend

isleq

Parameters

a,b

isOne

giv_all_inlined int32_t isOne ( const Integer &  a )

friend

name compare to 1 and 0

Parameters

a

isMOne

giv_all_inlined int32_t isMOne ( const Integer &  a )

friend

isleq

Parameters

a,b

nonZero

giv_all_inlined int32_t nonZero ( const Integer &  a )

friend

name compare to 1 and 0

Parameters

a

isZero [1/7]

giv_all_inlined int32_t isZero ( const Integer &  a )

friend

name compare to 1 and 0

Parameters

a

isZero [2/7]

giv_all_inlined int32_t isZero ( const int16_t  a )

friend

isleq

Parameters

a,b

isZero [3/7]

giv_all_inlined int32_t isZero ( const int32_t  a )

friend

isleq

Parameters

a,b

isZero [4/7]

giv_all_inlined int32_t isZero ( const int64_t  a )

friend

isleq

Parameters

a,b

isZero [5/7]

giv_all_inlined int32_t isZero ( const uint16_t  a )

friend

isleq

Parameters

a,b

isZero [6/7]

giv_all_inlined int32_t isZero ( const uint32_t  a )

friend

isleq

Parameters

a,b

isZero [7/7]

giv_all_inlined int32_t isZero ( const uint64_t  a )

friend

isleq

Parameters

a,b

operator>= [1/6]

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

friend

greater or equal.

Parameters

l,n	integers to compare

operator>= [2/6]

giv_all_inlined friend int32_t operator>= ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator>= [3/6]

giv_all_inlined friend int32_t operator>= ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator>= [4/6]

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

friend

greater or equal.

Parameters

l	integer to be compared to

operator>= [5/6]

giv_all_inlined friend int32_t operator>= ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator>= [6/6]

giv_all_inlined friend int32_t operator>= ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator<= [1/6]

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

friend

less or equal

Parameters

l,n	integers to compare

operator<= [2/6]

giv_all_inlined friend int32_t operator<= ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator<= [3/6]

giv_all_inlined friend int32_t operator<= ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator<= [4/6]

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

friend

greater or equal.

Parameters

l	integer to be compared to

operator<= [5/6]

giv_all_inlined friend int32_t operator<= ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator<= [6/6]

giv_all_inlined friend int32_t operator<= ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator!= [1/6]

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

friend

operator != (not equal)

Parameters

l,n

integer

Returns

1 iff l == n

operator!= [2/6]

giv_all_inlined friend int32_t operator!= ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator!= [3/6]

giv_all_inlined friend int32_t operator!= ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator!= [4/6]

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

friend

greater or equal.

Parameters

l	integer to be compared to

operator!= [5/6]

giv_all_inlined friend int32_t operator!= ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator!= [6/6]

giv_all_inlined friend int32_t operator!= ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator== [1/6]

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

friend

Equality.

Parameters

l,n	integers to compare

operator== [2/6]

giv_all_inlined friend int32_t operator== ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator== [3/6]

giv_all_inlined friend int32_t operator== ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator== [4/6]

giv_all_inlined friend int32_t operator== ( int32_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator== [5/6]

giv_all_inlined friend int32_t operator== ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator== [6/6]

giv_all_inlined friend int32_t operator== ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator> [1/6]

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

friend

greater (strict)

Parameters

l,n	integers to compare

operator> [2/6]

giv_all_inlined friend int32_t operator> ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator> [3/6]

giv_all_inlined friend int32_t operator> ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator> [4/6]

giv_all_inlined friend int32_t operator> ( int32_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator> [5/6]

giv_all_inlined friend int32_t operator> ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator> [6/6]

giv_all_inlined friend int32_t operator> ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator< [1/6]

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

friend

less (strict)

Parameters

l,n	integers to compare

operator< [2/6]

giv_all_inlined friend int32_t operator< ( float  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator< [3/6]

giv_all_inlined friend int32_t operator< ( double  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator< [4/6]

giv_all_inlined friend int32_t operator< ( int32_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator< [5/6]

giv_all_inlined friend int32_t operator< ( int64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator< [6/6]

giv_all_inlined friend int32_t operator< ( uint64_t  l, const Integer &  n  )

friend

greater or equal.

Parameters

l	integer to be compared to

operator+ [1/4]

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

friend

operator +.

Parameters

l,n	to be added

operator+ [2/4]

giv_all_inlined Integer operator+ ( const uint32_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+ [3/4]

giv_all_inlined Integer operator+ ( const int64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator+ [4/4]

giv_all_inlined Integer operator+ ( const uint64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator- [1/4]

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

friend

operator -

Parameters

l,n	to be substracted

operator- [2/4]

giv_all_inlined Integer operator- ( const uint32_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator- [3/4]

giv_all_inlined Integer operator- ( const int64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator- [4/4]

giv_all_inlined Integer operator- ( const uint64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator* [1/4]

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

friend

operator *

Parameters

l,n	to be multpct

operator* [2/4]

giv_all_inlined Integer operator* ( const uint32_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator* [3/4]

giv_all_inlined Integer operator* ( const int64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator* [4/4]

giv_all_inlined Integer operator* ( const uint64_t  l, const Integer &  n  )

friend

operator +.

Returns

(*this)+n

Parameters

n	as in the formula.

operator/ [1/2]

giv_all_inlined Integer operator/ ( const int64_t  l, const Integer &  n  )

friend

Division operator.

Parameters

d

divisor

operator/ [2/2]

giv_all_inlined Integer operator/ ( const uint64_t  l, const Integer &  n  )

friend

Division operator.

Parameters

d

divisor

operator% [1/4]

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

friend

operator %

Parameters

l
n

Returns

nl

operator% [2/4]

giv_all_inlined Integer operator% ( const uint64_t  l, const Integer &  n  )

friend

Division operator.

Parameters

d

divisor

operator% [3/4]

giv_all_inlined Integer operator% ( const int32_t  l, const Integer &  n  )

friend

Division operator.

Parameters

d

divisor

operator% [4/4]

giv_all_inlined Integer operator% ( const uint32_t  l, const Integer &  n  )

friend

Division operator.

Parameters

d

divisor

gcd [1/4]

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

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Examples

examples/Integer/givaro-ssh-keygen.C.

gcd [2/4]

giv_all_inlined Integer gcd ( Integer &  u, Integer &  v, const Integer &  a, const Integer &  b  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

gcd [3/4]

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

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

gcd [4/4]

giv_all_inlined Integer & gcd ( Integer &  g, Integer &  u, Integer &  v, const Integer &  a, const Integer &  b  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

inv

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

friend

Inverse.

Compute the inverse u = a/b.

Parameters

	u
	a
	b
	a
	b
[out]	u	is set to modulo b

invin

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

friend

Compute the inverse inplace u = u/b.

Parameters

u
b

pp

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

friend

pp

Parameters

P,Q

params

lcm [1/2]

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

friend

lcm

Parameters

g,a,b

Returns

g=lcm(a,b)

lcm [2/2]

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

friend

lcm

Parameters

a,b

pow [1/9]

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

friend

pow.

return

Parameters

Res,n,l

pow [2/9]

giv_all_inlined Integer & pow ( Integer &  Res, const uint64_t  n, const uint64_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [3/9]

giv_all_inlined Integer & pow ( Integer &  Res, const Integer &  n, const uint64_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [4/9]

giv_all_inlined Integer & pow ( Integer &  Res, const Integer &  n, const int32_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [5/9]

giv_all_inlined Integer & pow ( Integer &  Res, const Integer &  n, const uint32_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [6/9]

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

friend

pow.

return

Parameters

n,l

pow [7/9]

giv_all_inlined Integer pow ( const Integer &  n, const uint64_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [8/9]

giv_all_inlined Integer pow ( const Integer &  n, const int32_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

pow [9/9]

giv_all_inlined Integer pow ( const Integer &  n, const uint32_t  l  )

friend

gcd.

Parameters

a,b

integers

Returns

gcd(a,b)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

powmod

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

friend

modular pow.

return .

Parameters

n,e,m

fact

giv_all_inlined Integer fact ( uint64_t  l )

friend

fact

Parameters

l

sqrt [1/2]

giv_all_inlined Integer sqrt ( const Integer &  p )

friend

(square) roots

Parameters

p

sqrt [2/2]

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

friend

(square) roots

Parameters

r,p

sqrtrem [1/2]

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

friend

(square) roots

Parameters

p,rem

sqrtrem [2/2]

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

friend

(square) roots

Parameters

r,p,rem

root

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

friend

(square) roots

Parameters

q,a,n

logp

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

friend

logs

Parameters

a,p

logtwo

giv_all_inlined double logtwo ( const Integer &  a )

friend

logs

Parameters

a

naturallog

giv_all_inlined double naturallog ( const Integer &  a )

friend

logs

Parameters

a

swap

giv_all_inlined void swap ( Integer &  a, Integer &  b  )

friend

swap

Parameters

a,b

sign

int32_t sign ( const Integer &  a )

friend

sign

Parameters

a

length

giv_all_inlined uint64_t length ( const Integer &  a )

friend

returns the number of bytes used to store *this

Parameters

a

Bug:

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

isOdd

giv_all_inlined bool isOdd ( const Integer &  a )

friend

parity of an integer

Parameters

a

integer

Returns

1 if odd, 0 if even

operator>>

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

friend

Input/Output of Integers.

in operator.

Parameters

i	input stream
n	integer to be built

operator<<

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

friend

out operator.

Parameters

o	output stream
n	integer to be printed

absOutput

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

friend

nodoc

Parameters

o	output
n	integer

Protected::importWords

giv_all_inlined void Protected::importWords ( Integer &  x, size_t  count, int32_t  order, int32_t  size, int32_t  endian, size_t  nails, const void *  op  )

friend

nodoc

Parameters

x	x
count	x
order	x
size	x
endian	x
nails	x
op	x

---

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

• gmp++_int.h (4.2.0)
• gmp++_int_add.C (4.2.0)
• gmp++_int_compare.C (4.2.0)
• gmp++_int_cstor.C (4.2.0)
• gmp++_int_div.C (4.2.0)
• gmp++_int_io.C (4.2.0)
• gmp++_int_lib.C (4.2.0)
• gmp++_int_misc.C (4.2.0)
• gmp++_int_mod.C (4.2.0)
• gmp++_int_mul.C (4.2.0)
• gmp++_int_rand.inl (4.2.0)
• gmp++_int_sub.C (4.2.0)