Fixed some SVD issues.

Make the SVD's output unitary.
Improved unit tests.
Added an assert to the SVD ctor to check whether rows>=cols.

1 files changed, 3122 insertions, 3122 deletions

diff --git a/unsupported/test/mpreal.h b/unsupported/test/mpreal.h
index 29a0cf7ff..d8f315111 100644
--- a/unsupported/test/mpreal.h
+++ b/unsupported/test/mpreal.h
@@ -1,3122 +1,3122 @@
-/*

-	Multi-precision real number class. C++ wrapper fo MPFR library.

-	Project homepage: http://www.holoborodko.com/pavel/

-	Contact e-mail:   pavel@holoborodko.com

-

-	Copyright (c) 2008-2010 Pavel Holoborodko

-

-	This library is free software; you can redistribute it and/or

-	modify it under the terms of the GNU Lesser General Public

-	License as published by the Free Software Foundation; either

-	version 2.1 of the License, or (at your option) any later version.

-

-	This library is distributed in the hope that it will be useful,

-	but WITHOUT ANY WARRANTY; without even the implied warranty of

-	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

-	Lesser General Public License for more details.

-

-	You should have received a copy of the GNU Lesser General Public

-	License along with this library; if not, write to the Free Software

-	Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

-

-	Contributors:

-	Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, 

-	Heinz van Saanen, Pere Constans, Dmitriy Gubanov

-*/

-

-#ifndef __MP_REAL_H__

-#define __MP_REAL_H__

-

-#include <string>

-#include <iostream>

-#include <sstream>

-#include <stdexcept>

-#include <cfloat>

-#include <cmath>

-

-#include <mpfr.h>

-

-// Detect compiler using signatures from http://predef.sourceforge.net/

-#if defined(__GNUC__) && defined(__INTEL_COMPILER)

-	#define IsInf(x) isinf(x)                                // GNU C/C++ + Intel ICC compiler

-

-#elif defined(__GNUC__)

-	#define IsInf(x) std::isinf(x)                          // GNU C/C++ 

-

-#elif defined(_MSC_VER)		

-	#define IsInf(x) (!_finite(x))				// Microsoft Visual C++

-

-#else

-	#define IsInf(x) std::isinf(x)				// C99 conformance

-#endif

-

-namespace mpfr {

-

-class mpreal {

-private:

-	mpfr_t mp;

-

-public:

-	static mp_rnd_t		default_rnd;	

-	static mp_prec_t	default_prec;	

-	static int			default_base;

-	static int			double_bits;

-

-public:

-	// Constructors && type conversion

-	mpreal();

-	mpreal(const mpreal& u);

-

-	mpreal(const mpfr_t u);	

-	mpreal(const mpf_t u);	

-

-	mpreal(const mpz_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);	

-	mpreal(const mpq_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);	

-	mpreal(const double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const long double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const unsigned long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const unsigned int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);

-	mpreal(const char* s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);

-

-	~mpreal();                           

-

-	// Operations

-	// =

-	// +, -, *, /, ++, --, <<, >> 

-	// *=, +=, -=, /=,

-	// <, >, ==, <=, >=

-

-	// =

-	mpreal& operator=(const mpreal& v);

-	mpreal& operator=(const mpf_t v);

-	mpreal& operator=(const mpz_t v);

-	mpreal& operator=(const mpq_t v);

-	mpreal& operator=(const long double v);

-	mpreal& operator=(const double v);		

-	mpreal& operator=(const unsigned long int v);

-	mpreal& operator=(const unsigned int v);

-	mpreal& operator=(const long int v);

-	mpreal& operator=(const int v);

-	mpreal& operator=(const char* s);

-

-	// +

-	mpreal& operator+=(const mpreal& v);

-	mpreal& operator+=(const mpf_t v);

-	mpreal& operator+=(const mpz_t v);

-	mpreal& operator+=(const mpq_t v);

-	mpreal& operator+=(const long double u);

-	mpreal& operator+=(const double u);

-	mpreal& operator+=(const unsigned long int u);

-	mpreal& operator+=(const unsigned int u);

-	mpreal& operator+=(const long int u);

-	mpreal& operator+=(const int u);

-	const mpreal operator+() const;

-	mpreal& operator++ ();

-	const mpreal  operator++ (int); 

-

-	// -

-	mpreal& operator-=(const mpreal& v);

-	mpreal& operator-=(const mpz_t v);

-	mpreal& operator-=(const mpq_t v);

-	mpreal& operator-=(const long double u);

-	mpreal& operator-=(const double u);

-	mpreal& operator-=(const unsigned long int u);

-	mpreal& operator-=(const unsigned int u);

-	mpreal& operator-=(const long int u);

-	mpreal& operator-=(const int u);

-	const mpreal operator-() const;

-	friend const mpreal operator-(const unsigned long int b, const mpreal& a);

-	friend const mpreal operator-(const unsigned int b, const mpreal& a);

-	friend const mpreal operator-(const long int b, const mpreal& a);

-	friend const mpreal operator-(const int b, const mpreal& a);

-	friend const mpreal operator-(const double b, const mpreal& a);

-	mpreal& operator-- ();    

-	const mpreal  operator-- (int);

-

-	// *

-	mpreal& operator*=(const mpreal& v);

-	mpreal& operator*=(const mpz_t v);

-	mpreal& operator*=(const mpq_t v);

-	mpreal& operator*=(const long double v);

-	mpreal& operator*=(const double v);

-	mpreal& operator*=(const unsigned long int v);

-	mpreal& operator*=(const unsigned int v);

-	mpreal& operator*=(const long int v);

-	mpreal& operator*=(const int v);

-	

-	// /

-	mpreal& operator/=(const mpreal& v);

-	mpreal& operator/=(const mpz_t v);

-	mpreal& operator/=(const mpq_t v);

-	mpreal& operator/=(const long double v);

-	mpreal& operator/=(const double v);

-	mpreal& operator/=(const unsigned long int v);

-	mpreal& operator/=(const unsigned int v);

-	mpreal& operator/=(const long int v);

-	mpreal& operator/=(const int v);

-	friend const mpreal operator/(const unsigned long int b, const mpreal& a);

-	friend const mpreal operator/(const unsigned int b, const mpreal& a);

-	friend const mpreal operator/(const long int b, const mpreal& a);

-	friend const mpreal operator/(const int b, const mpreal& a);

-	friend const mpreal operator/(const double b, const mpreal& a);

-

-	//<<= Fast Multiplication by 2^u

-	mpreal& operator<<=(const unsigned long int u);

-	mpreal& operator<<=(const unsigned int u);

-	mpreal& operator<<=(const long int u);

-	mpreal& operator<<=(const int u);

-

-	//>>= Fast Division by 2^u

-	mpreal& operator>>=(const unsigned long int u);

-	mpreal& operator>>=(const unsigned int u);

-	mpreal& operator>>=(const long int u);

-	mpreal& operator>>=(const int u);

-

-	// Boolean Operators

-	friend bool operator >  (const mpreal& a, const mpreal& b);

-	friend bool operator >= (const mpreal& a, const mpreal& b);

-	friend bool operator <  (const mpreal& a, const mpreal& b);

-	friend bool operator <= (const mpreal& a, const mpreal& b);

-	friend bool operator == (const mpreal& a, const mpreal& b);

-	friend bool operator != (const mpreal& a, const mpreal& b);

-

-	// Type Conversion operators

-	inline operator long double() const;

-	inline operator double() const;

-	inline operator float() const;

-	inline operator unsigned long() const;

-	inline operator unsigned int() const;

-	inline operator long() const;

-	operator std::string() const;

-	inline operator mpfr_ptr();

-

-	// Math Functions

-	friend const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend int cmpabs(const mpreal& a,const mpreal& b);

-	

-	friend const mpreal log  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal exp  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-	friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-	friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-	friend const mpreal acos  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal asin  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal atan  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal cosh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sinh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal tanh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sech  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal csch  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal coth  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-	friend const mpreal acosh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal asinh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal atanh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal log1p  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal expm1  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal eint   (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-	friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-	friend const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-	friend const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-	friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend int sgn(const mpreal& v); // -1 or +1

-

-// MPFR 2.4.0 Specifics

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	friend int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-#endif

-

-// MPFR 3.0.0 Specifics

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))

-	friend const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-    friend const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode = mpreal::default_rnd); 	// use gmp_randinit_default() to init state, gmp_randclear() to clear

-	friend bool _isregular(const mpreal& v);

-#endif

-

-	// Exponent and mantissa manipulation

-	friend const mpreal frexp(const mpreal& v, mp_exp_t* exp);	

-	friend const mpreal ldexp(const mpreal& v, mp_exp_t exp);

-

-	// Splits mpreal value into fractional and integer parts.

-	// Returns fractional part and stores integer part in n.

-	friend const mpreal modf(const mpreal& v, mpreal& n);	

-

-	// Constants

-	// don't forget to call mpfr_free_cache() for every thread where you are using const-functions

-	friend const mpreal const_log2 (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal const_pi (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal const_euler (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal const_catalan (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	// returns +inf iff sign>=0 otherwise -inf

-	friend const mpreal const_infinity(int sign = 1, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-	// Output/ Input

-	friend std::ostream& operator<<(std::ostream& os, const mpreal& v);

-    friend std::istream& operator>>(std::istream& is, mpreal& v);

-

-	// Integer Related Functions

-	friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal ceil (const mpreal& v);

-	friend const mpreal floor(const mpreal& v);

-	friend const mpreal round(const mpreal& v);

-	friend const mpreal trunc(const mpreal& v);

-	friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);

-	

-	// Miscellaneous Functions

-	friend const mpreal nexttoward (const mpreal& x, const mpreal& y);

-	friend const mpreal nextabove  (const mpreal& x);

-	friend const mpreal nextbelow  (const mpreal& x);

-

-	// use gmp_randinit_default() to init state, gmp_randclear() to clear

-	friend const mpreal urandomb (gmp_randstate_t& state); 

-

-// MPFR < 2.4.2 Specifics

-#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))

-	friend const mpreal random2 (mp_size_t size, mp_exp_t exp);

-#endif

-

-	// Instance Checkers

-	friend bool _isnan(const mpreal& v);

-	friend bool _isinf(const mpreal& v);

-	friend bool _isnum(const mpreal& v);

-	friend bool _iszero(const mpreal& v);

-	friend bool _isint(const mpreal& v);

-

-	// Set/Get instance properties

-	inline mp_prec_t	get_prec() const;

-	inline void		set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = default_rnd);	// Change precision with rounding mode

-	

-	// Set mpreal to +-inf, NaN

-	void      set_inf(int sign = +1);	

-	void	  set_nan();

-

-	// sign = -1 or +1

-	void set_sign(int sign, mp_rnd_t rnd_mode = default_rnd);

-

-	//Exponent

-	mp_exp_t get_exp();

-	int set_exp(mp_exp_t e);

-	int check_range (int t, mp_rnd_t rnd_mode = default_rnd);

-	int subnormalize (int t,mp_rnd_t rnd_mode = default_rnd);

-

-	// Inexact conversion from float

-	inline bool fits_in_bits(double x, int n);

-

-	// Set/Get global properties

-	static void			set_default_prec(mp_prec_t prec);

-	static mp_prec_t	get_default_prec();

-	static void			set_default_base(int base);

-	static int			get_default_base();

-	static void			set_double_bits(int dbits);

-	static int			get_double_bits();

-	static void			set_default_rnd(mp_rnd_t rnd_mode);

-	static mp_rnd_t		get_default_rnd();

-	static mp_exp_t get_emin (void);

-	static mp_exp_t get_emax (void);

-	static mp_exp_t get_emin_min (void);

-	static mp_exp_t get_emin_max (void);

-	static mp_exp_t get_emax_min (void);

-	static mp_exp_t get_emax_max (void);

-	static int set_emin (mp_exp_t exp);

-	static int set_emax (mp_exp_t exp);

-

-	// Get/Set conversions

-	// Convert mpreal to string with n significant digits in base b

-	// n = 0 -> convert with the maximum available digits 

-	std::string to_string(size_t n = 0, int b = default_base, mp_rnd_t mode = default_rnd) const;

-	

-	// Efficient swapping of two mpreal values

-	friend void swap(mpreal& x, mpreal& y);

-	

-	//Min Max - macros is evil. Needed for systems which defines max and min globally as macros (e.g. Windows)

-	//Hope that globally defined macros use > < operations only

-	#ifndef max

-		friend const mpreal max(const mpreal& x, const mpreal& y);

-	#endif

-

-	#ifndef min

-		friend const mpreal min(const mpreal& x, const mpreal& y);

-	#endif

-};

-

-//////////////////////////////////////////////////////////////////////////

-// Exceptions

-class conversion_overflow : public std::exception {

-public:

-	std::string why() { return "inexact conversion from floating point"; }

-};

-

-//////////////////////////////////////////////////////////////////////////

-// + Addition

-const mpreal operator+(const mpreal& a, const mpreal& b);

-

-// + Fast specialized addition - implemented through fast += operations

-const mpreal operator+(const mpreal& a, const mpz_t b);

-const mpreal operator+(const mpreal& a, const mpq_t b);

-const mpreal operator+(const mpreal& a, const long double b);

-const mpreal operator+(const mpreal& a, const double b);

-const mpreal operator+(const mpreal& a, const unsigned long int b);

-const mpreal operator+(const mpreal& a, const unsigned int b);

-const mpreal operator+(const mpreal& a, const long int b);

-const mpreal operator+(const mpreal& a, const int b);

-const mpreal operator+(const mpreal& a, const char* b);

-const mpreal operator+(const char* a, const mpreal& b);

-const std::string operator+(const mpreal& a, const std::string b);

-const std::string operator+(const std::string a, const mpreal& b);

-

-const mpreal operator+(const mpz_t b, const mpreal& a);

-const mpreal operator+(const mpq_t b, const mpreal& a);

-const mpreal operator+(const long double b, const mpreal& a);

-const mpreal operator+(const double  b, const mpreal& a);

-const mpreal operator+(const unsigned long int b, const mpreal& a);

-const mpreal operator+(const unsigned int b, const mpreal& a);

-const mpreal operator+(const long int b, const mpreal& a);

-const mpreal operator+(const int b, const mpreal& a);

-

-//////////////////////////////////////////////////////////////////////////

-// - Subtraction

-const mpreal operator-(const mpreal& a, const mpreal& b);

-

-// - Fast specialized subtraction - implemented through fast -= operations

-const mpreal operator-(const mpreal& a, const mpz_t b);

-const mpreal operator-(const mpreal& a, const mpq_t b);

-const mpreal operator-(const mpreal& a, const long double b);

-const mpreal operator-(const mpreal& a, const double b);

-const mpreal operator-(const mpreal& a, const unsigned long int b);

-const mpreal operator-(const mpreal& a, const unsigned int b);

-const mpreal operator-(const mpreal& a, const long int b);

-const mpreal operator-(const mpreal& a, const int b);

-const mpreal operator-(const mpreal& a, const char* b);

-const mpreal operator-(const char* a, const mpreal& b);

-

-const mpreal operator-(const mpz_t b, const mpreal& a);

-const mpreal operator-(const mpq_t b, const mpreal& a);

-const mpreal operator-(const long double b, const mpreal& a);

-//const mpreal operator-(const double  b, const mpreal& a);

-

-//////////////////////////////////////////////////////////////////////////

-// * Multiplication

-const mpreal operator*(const mpreal& a, const mpreal& b);

-

-// * Fast specialized multiplication - implemented through fast *= operations

-const mpreal operator*(const mpreal& a, const mpz_t b);

-const mpreal operator*(const mpreal& a, const mpq_t b);

-const mpreal operator*(const mpreal& a, const long double b);

-const mpreal operator*(const mpreal& a, const double b);

-const mpreal operator*(const mpreal& a, const unsigned long int b);

-const mpreal operator*(const mpreal& a, const unsigned int b);

-const mpreal operator*(const mpreal& a, const long int b);

-const mpreal operator*(const mpreal& a, const int b);

-

-const mpreal operator*(const mpz_t b, const mpreal& a);

-const mpreal operator*(const mpq_t b, const mpreal& a);

-const mpreal operator*(const long double b, const mpreal& a);

-const mpreal operator*(const double  b, const mpreal& a);

-const mpreal operator*(const unsigned long int b, const mpreal& a);

-const mpreal operator*(const unsigned int b, const mpreal& a);

-const mpreal operator*(const long int b, const mpreal& a);

-const mpreal operator*(const int b, const mpreal& a);

-

-//////////////////////////////////////////////////////////////////////////

-// / Division

-const mpreal operator/(const mpreal& a, const mpreal& b);

-

-// / Fast specialized division - implemented through fast /= operations

-const mpreal operator/(const mpreal& a, const mpz_t b);

-const mpreal operator/(const mpreal& a, const mpq_t b);

-const mpreal operator/(const mpreal& a, const long double b);

-const mpreal operator/(const mpreal& a, const double b);

-const mpreal operator/(const mpreal& a, const unsigned long int b);

-const mpreal operator/(const mpreal& a, const unsigned int b);

-const mpreal operator/(const mpreal& a, const long int b);

-const mpreal operator/(const mpreal& a, const int b);

-

-const mpreal operator/(const long double b, const mpreal& a);

-

-//////////////////////////////////////////////////////////////////////////

-// Shifts operators - Multiplication/Division by a power of 2

-const mpreal operator<<(const mpreal& v, const unsigned long int k);

-const mpreal operator<<(const mpreal& v, const unsigned int k);

-const mpreal operator<<(const mpreal& v, const long int k);

-const mpreal operator<<(const mpreal& v, const int k);

-

-const mpreal operator>>(const mpreal& v, const unsigned long int k);

-const mpreal operator>>(const mpreal& v, const unsigned int k);

-const mpreal operator>>(const mpreal& v, const long int k);

-const mpreal operator>>(const mpreal& v, const int k);

-

-//////////////////////////////////////////////////////////////////////////

-// Boolean operators

-bool operator <  (const mpreal& a, const unsigned long int b);

-bool operator <  (const mpreal& a, const unsigned int b);

-bool operator <  (const mpreal& a, const long int b);

-bool operator <  (const mpreal& a, const int b);

-bool operator <  (const mpreal& a, const long double b);

-bool operator <  (const mpreal& a, const double b);

-

-bool operator <  (const unsigned long int a,const mpreal& b);

-bool operator <  (const unsigned int a,		const mpreal& b);

-bool operator <  (const long int a,			const mpreal& b);

-bool operator <  (const int a,				const mpreal& b);

-bool operator <  (const long double a,		const mpreal& b);

-bool operator <  (const double a,			const mpreal& b);

-

-bool operator >  (const mpreal& a, const unsigned long int b);

-bool operator >  (const mpreal& a, const unsigned int b);

-bool operator >  (const mpreal& a, const long int b);

-bool operator >  (const mpreal& a, const int b);

-bool operator >  (const mpreal& a, const long double b);

-bool operator >  (const mpreal& a, const double b);

-

-bool operator >  (const unsigned long int a,const mpreal& b);

-bool operator >  (const unsigned int a,		const mpreal& b);

-bool operator >  (const long int a,			const mpreal& b);

-bool operator >  (const int a,				const mpreal& b);

-bool operator >  (const long double a,		const mpreal& b);

-bool operator >  (const double a,			const mpreal& b);

-

-bool operator >=  (const mpreal& a, const unsigned long int b);

-bool operator >=  (const mpreal& a, const unsigned int b);

-bool operator >=  (const mpreal& a, const long int b);

-bool operator >=  (const mpreal& a, const int b);

-bool operator >=  (const mpreal& a, const long double b);

-bool operator >=  (const mpreal& a, const double b);

-

-bool operator >=  (const unsigned long int a,const mpreal& b);

-bool operator >=  (const unsigned int a,		const mpreal& b);

-bool operator >=  (const long int a,			const mpreal& b);

-bool operator >=  (const int a,				const mpreal& b);

-bool operator >=  (const long double a,		const mpreal& b);

-bool operator >=  (const double a,			const mpreal& b);

-

-bool operator <=  (const mpreal& a, const unsigned long int b);

-bool operator <=  (const mpreal& a, const unsigned int b);

-bool operator <=  (const mpreal& a, const long int b);

-bool operator <=  (const mpreal& a, const int b);

-bool operator <=  (const mpreal& a, const long double b);

-bool operator <=  (const mpreal& a, const double b);

-

-bool operator <=  (const unsigned long int a,const mpreal& b);

-bool operator <=  (const unsigned int a,		const mpreal& b);

-bool operator <=  (const long int a,			const mpreal& b);

-bool operator <=  (const int a,				const mpreal& b);

-bool operator <=  (const long double a,		const mpreal& b);

-bool operator <=  (const double a,			const mpreal& b);

-

-bool operator ==  (const mpreal& a, const unsigned long int b);

-bool operator ==  (const mpreal& a, const unsigned int b);

-bool operator ==  (const mpreal& a, const long int b);

-bool operator ==  (const mpreal& a, const int b);

-bool operator ==  (const mpreal& a, const long double b);

-bool operator ==  (const mpreal& a, const double b);

-

-bool operator ==  (const unsigned long int a,const mpreal& b);

-bool operator ==  (const unsigned int a,		const mpreal& b);

-bool operator ==  (const long int a,			const mpreal& b);

-bool operator ==  (const int a,				const mpreal& b);

-bool operator ==  (const long double a,		const mpreal& b);

-bool operator ==  (const double a,			const mpreal& b);

-

-bool operator !=  (const mpreal& a, const unsigned long int b);

-bool operator !=  (const mpreal& a, const unsigned int b);

-bool operator !=  (const mpreal& a, const long int b);

-bool operator !=  (const mpreal& a, const int b);

-bool operator !=  (const mpreal& a, const long double b);

-bool operator !=  (const mpreal& a, const double b);

-

-bool operator !=  (const unsigned long int a,const mpreal& b);

-bool operator !=  (const unsigned int a,		const mpreal& b);

-bool operator !=  (const long int a,			const mpreal& b);

-bool operator !=  (const int a,				const mpreal& b);

-bool operator !=  (const long double a,		const mpreal& b);

-bool operator !=  (const double a,			const mpreal& b);

-

-//////////////////////////////////////////////////////////////////////////

-// sqrt

-const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-//////////////////////////////////////////////////////////////////////////

-// pow

-const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd); 

-

-const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);	

-const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);	

-const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);

-

-//////////////////////////////////////////////////////////////////////////

-// Estimate machine epsilon for the given precision

-inline const mpreal machine_epsilon(mp_prec_t prec);

-inline const mpreal mpreal_min(mp_prec_t prec);

-inline const mpreal mpreal_max(mp_prec_t prec);

-

-//////////////////////////////////////////////////////////////////////////

-// Implementation of inline functions

-//////////////////////////////////////////////////////////////////////////

-

-//////////////////////////////////////////////////////////////////////////

-// Operators - Assignment

-inline mpreal& mpreal::operator=(const mpreal& v)

-{

-	if (this!= &v)	mpfr_set(mp,v.mp,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const mpf_t v)

-{

-	mpfr_set_f(mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const mpz_t v)

-{

-	mpfr_set_z(mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const mpq_t v)

-{

-	mpfr_set_q(mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const long double v)		

-{	

-    mpfr_set_ld(mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const double v)				

-{	

-    if(double_bits == -1 || fits_in_bits(v, double_bits))

-    {

-    	mpfr_set_d(mp,v,default_rnd);

-    }

-    else

-        throw conversion_overflow();

-

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const unsigned long int v)	

-{	

-	mpfr_set_ui(mp,v,default_rnd);	

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const unsigned int v)		

-{	

-	mpfr_set_ui(mp,v,default_rnd);	

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const long int v)			

-{	

-	mpfr_set_si(mp,v,default_rnd);	

-	return *this;

-}

-

-inline mpreal& mpreal::operator=(const int v)

-{	

-	mpfr_set_si(mp,v,default_rnd);	

-	return *this;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// + Addition

-inline mpreal& mpreal::operator+=(const mpreal& v)

-{

-	mpfr_add(mp,mp,v.mp,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const mpf_t u)

-{

-	*this += mpreal(u);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const mpz_t u)

-{

-	mpfr_add_z(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const mpq_t u)

-{

-	mpfr_add_q(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+= (const long double u)

-{

-	return *this += mpreal(u);	

-}

-

-inline mpreal& mpreal::operator+= (const double u)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpfr_add_d(mp,mp,u,default_rnd);

-	return *this;

-#else

-	return *this += mpreal(u);	

-#endif

-}

-

-inline mpreal& mpreal::operator+=(const unsigned long int u)

-{

-	mpfr_add_ui(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const unsigned int u)

-{

-	mpfr_add_ui(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const long int u)

-{

-	mpfr_add_si(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator+=(const int u)

-{

-	mpfr_add_si(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline const mpreal mpreal::operator+()const

-{

-	return mpreal(*this);

-}

-

-inline const mpreal operator+(const mpreal& a, const mpreal& b)

-{

-	// prec(a+b) = max(prec(a),prec(b))

-	if(a.get_prec()>b.get_prec()) return mpreal(a) += b;

-	else						  return mpreal(b) += a;

-}

-

-inline const std::string operator+(const mpreal& a, const std::string b)

-{

-	return (std::string)a+b;

-}

-

-inline const std::string operator+(const std::string a, const mpreal& b)

-{

-	return a+(std::string)b;

-}

-

-inline const mpreal operator+(const mpreal& a, const mpz_t b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const char* b)

-{

-	return a+mpreal(b);

-}

-

-inline const mpreal operator+(const char* a, const mpreal& b)

-{

-	return mpreal(a)+b;

-

-}

-

-inline const mpreal operator+(const mpreal& a, const mpq_t b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const long double b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const double b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const unsigned long int b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const unsigned int b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const long int b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpreal& a, const int b)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpz_t b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const mpq_t b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const long double b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const double  b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const unsigned long int b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const unsigned int b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const long int b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline const mpreal operator+(const int b, const mpreal& a)

-{

-	return mpreal(a) += b;

-}

-

-inline mpreal& mpreal::operator++() 

-{

-	*this += 1;

-	return *this;

-}

-

-inline const mpreal mpreal::operator++ (int)

-{

-	mpreal x(*this);

-	*this += 1;

-	return x;

-}

-

-inline mpreal& mpreal::operator--() 

-{

-	*this -= 1;

-	return *this;

-}

-

-inline const mpreal mpreal::operator-- (int)

-{

-	mpreal x(*this);

-	*this -= 1;

-	return x;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// - Subtraction

-inline mpreal& mpreal::operator-= (const mpreal& v)

-{

-	mpfr_sub(mp,mp,v.mp,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const mpz_t v)

-{

-	mpfr_sub_z(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const mpq_t v)

-{

-	mpfr_sub_q(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const long double v)

-{

-	return *this -= mpreal(v);	

-}

-

-inline mpreal& mpreal::operator-=(const double v)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpfr_sub_d(mp,mp,v,default_rnd);

-	return *this;

-#else

-	return *this -= mpreal(v);	

-#endif

-}

-

-inline mpreal& mpreal::operator-=(const unsigned long int v)

-{

-	mpfr_sub_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const unsigned int v)

-{

-	mpfr_sub_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const long int v)

-{

-	mpfr_sub_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator-=(const int v)

-{

-	mpfr_sub_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline const mpreal mpreal::operator-()const

-{

-	mpreal u(*this);

-	mpfr_neg(u.mp,u.mp,default_rnd);

-	return u;

-}

-

-inline const mpreal operator-(const mpreal& a, const mpreal& b)

-{

-	// prec(a-b) = max(prec(a),prec(b))

-	if(a.get_prec()>b.get_prec())	return   mpreal(a) -= b;

-	else							return -(mpreal(b) -= a);		

-}

-

-inline const mpreal operator-(const mpreal& a, const mpz_t b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const mpq_t b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const long double b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const double b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const unsigned long int b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const unsigned int b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const long int b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpreal& a, const int b)

-{

-	return mpreal(a) -= b;

-}

-

-inline const mpreal operator-(const mpz_t b, const mpreal& a)

-{

-	return -(mpreal(a) -= b);

-}

-

-inline const mpreal operator-(const mpq_t b, const mpreal& a)

-{

-	return -(mpreal(a) -= b);

-}

-

-inline const mpreal operator-(const long double b, const mpreal& a)

-{

-	return -(mpreal(a) -= b);

-}

-

-inline const mpreal operator-(const double  b, const mpreal& a)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpreal x(a);

-	mpfr_d_sub(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-#else

-	return -(mpreal(a) -= b);

-#endif

-}

-

-inline const mpreal operator-(const unsigned long int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator-(const unsigned int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator-(const long int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator-(const int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator-(const mpreal& a, const char* b)

-{

-	return a-mpreal(b);

-}

-

-inline const mpreal operator-(const char* a, const mpreal& b)

-{

-	return mpreal(a)-b;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// * Multiplication

-inline mpreal& mpreal::operator*= (const mpreal& v)

-{

-	mpfr_mul(mp,mp,v.mp,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const mpz_t v)

-{

-	mpfr_mul_z(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const mpq_t v)

-{

-	mpfr_mul_q(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const long double v)

-{

-	return *this *= mpreal(v);	

-}

-

-inline mpreal& mpreal::operator*=(const double v)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpfr_mul_d(mp,mp,v,default_rnd);

-	return *this;

-#else

-	return *this *= mpreal(v);	

-#endif

-}

-

-inline mpreal& mpreal::operator*=(const unsigned long int v)

-{

-	mpfr_mul_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const unsigned int v)

-{

-	mpfr_mul_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const long int v)

-{

-	mpfr_mul_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator*=(const int v)

-{

-	mpfr_mul_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline const mpreal operator*(const mpreal& a, const mpreal& b)

-{

-	// prec(a*b) = max(prec(a),prec(b))

-	if(a.get_prec()>b.get_prec())	return   mpreal(a) *= b;

-	else							return   mpreal(b) *= a;		

-}

-

-inline const mpreal operator*(const mpreal& a, const mpz_t b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const mpq_t b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const long double b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const double b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const unsigned long int b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const unsigned int b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const long int b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpreal& a, const int b)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpz_t b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const mpq_t b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const long double b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const double  b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const unsigned long int b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const unsigned int b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const long int b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-inline const mpreal operator*(const int b, const mpreal& a)

-{

-	return mpreal(a) *= b;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// / Division

-inline mpreal& mpreal::operator/=(const mpreal& v)

-{

-	mpfr_div(mp,mp,v.mp,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const mpz_t v)

-{

-	mpfr_div_z(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const mpq_t v)

-{

-	mpfr_div_q(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const long double v)

-{

-	return *this /= mpreal(v);	

-}

-

-inline mpreal& mpreal::operator/=(const double v)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpfr_div_d(mp,mp,v,default_rnd);

-	return *this;

-#else

-	return *this /= mpreal(v);	

-#endif

-}

-

-inline mpreal& mpreal::operator/=(const unsigned long int v)

-{

-	mpfr_div_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const unsigned int v)

-{

-	mpfr_div_ui(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const long int v)

-{

-	mpfr_div_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator/=(const int v)

-{

-	mpfr_div_si(mp,mp,v,default_rnd);

-	return *this;

-}

-

-inline const mpreal operator/(const mpreal& a, const mpreal& b)

-{

-	mpreal x(a);

-	mp_prec_t pb;

-	mp_prec_t pa;

-

-	// prec(a/b) = max(prec(a),prec(b))

-	pa = a.get_prec();

-	pb = b.get_prec();

-	if(pb>pa) x.set_prec(pb);

-

-	return   x /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const mpz_t b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const mpq_t b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const long double b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const double b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const unsigned long int b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const unsigned int b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const long int b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const mpreal& a, const int b)

-{

-	return mpreal(a) /= b;

-}

-

-inline const mpreal operator/(const unsigned long int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator/(const unsigned int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator/(const long int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator/(const int b, const mpreal& a)

-{

-	mpreal x(a);

-	mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-}

-

-inline const mpreal operator/(const long double b, const mpreal& a)

-{

-	mpreal x(b);

-	return x/a;

-}

-

-inline const mpreal operator/(const double  b, const mpreal& a)

-{

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-	mpreal x(a);

-	mpfr_d_div(x.mp,b,a.mp,mpreal::default_rnd);

-	return x;

-#else

-	mpreal x(b);

-	return x/a;

-#endif

-}

-

-//////////////////////////////////////////////////////////////////////////

-// Shifts operators - Multiplication/Division by power of 2

-inline mpreal& mpreal::operator<<=(const unsigned long int u)

-{

-	mpfr_mul_2ui(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator<<=(const unsigned int u)

-{

-	mpfr_mul_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator<<=(const long int u)

-{

-	mpfr_mul_2si(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator<<=(const int u)

-{

-	mpfr_mul_2si(mp,mp,static_cast<long int>(u),default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator>>=(const unsigned long int u)

-{

-	mpfr_div_2ui(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator>>=(const unsigned int u)

-{

-	mpfr_div_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator>>=(const long int u)

-{

-	mpfr_div_2si(mp,mp,u,default_rnd);

-	return *this;

-}

-

-inline mpreal& mpreal::operator>>=(const int u)

-{

-	mpfr_div_2si(mp,mp,static_cast<long int>(u),default_rnd);

-	return *this;

-}

-

-inline const mpreal operator<<(const mpreal& v, const unsigned long int k)

-{

-	return mul_2ui(v,k);

-}

-

-inline const mpreal operator<<(const mpreal& v, const unsigned int k)

-{

-	return mul_2ui(v,static_cast<unsigned long int>(k));

-}

-

-inline const mpreal operator<<(const mpreal& v, const long int k)

-{

-	return mul_2si(v,k);

-}

-

-inline const mpreal operator<<(const mpreal& v, const int k)

-{

-	return mul_2si(v,static_cast<long int>(k));

-}

-

-inline const mpreal operator>>(const mpreal& v, const unsigned long int k)

-{

-	return div_2ui(v,k);

-}

-

-inline const mpreal operator>>(const mpreal& v, const long int k)

-{

-	return div_2si(v,k);

-}

-

-inline const mpreal operator>>(const mpreal& v, const unsigned int k)

-{

-	return div_2ui(v,static_cast<unsigned long int>(k));

-}

-

-inline const mpreal operator>>(const mpreal& v, const int k)

-{

-	return div_2si(v,static_cast<long int>(k));

-}

-

-// mul_2ui

-inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_mul_2ui(x.mp,v.mp,k,rnd_mode);

-	return x;

-}

-

-// mul_2si

-inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_mul_2si(x.mp,v.mp,k,rnd_mode);

-	return x;

-}

-

-inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_div_2ui(x.mp,v.mp,k,rnd_mode);

-	return x;

-}

-

-inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_div_2si(x.mp,v.mp,k,rnd_mode);

-	return x;

-}

-

-//////////////////////////////////////////////////////////////////////////

-//Boolean operators

-inline bool operator > (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_greater_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator >  (const mpreal& a, const unsigned long int b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const mpreal& a, const unsigned int b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const mpreal& a, const long int b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const mpreal& a, const int b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const mpreal& a, const long double b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const mpreal& a, const double b)

-{

-	return a>mpreal(b);

-}

-

-inline bool operator >  (const unsigned long int a,	const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >  (const unsigned int a,		const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >  (const long int a,			const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >  (const int a,				const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >  (const long double a,		const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >  (const double a,			const mpreal& b)

-{

-	return mpreal(a)>b;

-}

-

-inline bool operator >= (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_greaterequal_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator >=  (const mpreal& a, const unsigned long int b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const mpreal& a, const unsigned int b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const mpreal& a, const long int b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const mpreal& a, const int b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const mpreal& a, const long double b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const mpreal& a, const double b)

-{

-	return a>=mpreal(b);

-}

-

-inline bool operator >=  (const unsigned long int a,const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator >=  (const unsigned int a,		const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator >=  (const long int a,			const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator >=  (const int a,				const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator >=  (const long double a,		const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator >=  (const double a,			const mpreal& b)

-{

-	return mpreal(a)>=b;

-}

-

-inline bool operator <  (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_less_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator <  (const mpreal& a, const unsigned long int b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const mpreal& a, const unsigned int b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const mpreal& a, const long int b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const mpreal& a, const int b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const mpreal& a, const long double b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const mpreal& a, const double b)

-{

-	return a<mpreal(b);

-}

-

-inline bool operator <  (const unsigned long int a,	const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <  (const unsigned int a,const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <  (const long int a,const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <  (const int a,const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <  (const long double a,const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <  (const double a,const mpreal& b)

-{

-	return mpreal(a)<b;

-}

-

-inline bool operator <= (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_lessequal_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator <=  (const mpreal& a, const unsigned long int b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const mpreal& a, const unsigned int b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const mpreal& a, const long int b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const mpreal& a, const int b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const mpreal& a, const long double b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const mpreal& a, const double b)

-{

-	return a<=mpreal(b);

-}

-

-inline bool operator <=  (const unsigned long int a,const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator <=  (const unsigned int a,		const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator <=  (const long int a,			const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator <=  (const int a,				const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator <=  (const long double a,		const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator <=  (const double a,			const mpreal& b)

-{

-	return mpreal(a)<=b;

-}

-

-inline bool operator == (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_equal_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator ==  (const mpreal& a, const unsigned long int b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const mpreal& a, const unsigned int b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const mpreal& a, const long int b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const mpreal& a, const int b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const mpreal& a, const long double b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const mpreal& a, const double b)

-{

-	return a==mpreal(b);

-}

-

-inline bool operator ==  (const unsigned long int a,const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator ==  (const unsigned int a,		const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator ==  (const long int a,			const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator ==  (const int a,				const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator ==  (const long double a,		const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator ==  (const double a,			const mpreal& b)

-{

-	return mpreal(a)==b;

-}

-

-inline bool operator != (const mpreal& a, const mpreal& b)

-{

-	return (mpfr_lessgreater_p(a.mp,b.mp)!=0);

-}

-

-inline bool operator !=  (const mpreal& a, const unsigned long int b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const mpreal& a, const unsigned int b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const mpreal& a, const long int b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const mpreal& a, const int b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const mpreal& a, const long double b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const mpreal& a, const double b)

-{

-	return a!=mpreal(b);

-}

-

-inline bool operator !=  (const unsigned long int a,const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool operator !=  (const unsigned int a,		const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool operator !=  (const long int a,			const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool operator !=  (const int a,				const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool operator !=  (const long double a,		const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool operator !=  (const double a,			const mpreal& b)

-{

-	return mpreal(a)!=b;

-}

-

-inline bool _isnan(const mpreal& v)

-{

-	return (mpfr_nan_p(v.mp)!=0);

-}

-

-inline bool _isinf(const mpreal& v)

-{

-	return (mpfr_inf_p(v.mp)!=0);

-}

-

-inline bool _isnum(const mpreal& v)

-{

-	return (mpfr_number_p(v.mp)!=0);

-}

-

-inline bool _iszero(const mpreal& v)

-{

-	return (mpfr_zero_p(v.mp)!=0);

-}

-

-inline bool _isint(const mpreal& v)

-{

-	return (mpfr_integer_p(v.mp)!=0);

-}

-

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))

-inline bool _isregular(const mpreal& v)

-{

-	return (mpfr_regular_p(v.mp));

-}

-#endif // MPFR 3.0.0 Specifics

-

-//////////////////////////////////////////////////////////////////////////

-// Type Converters

-inline mpreal::operator double() const

-{

-	return mpfr_get_d(mp,default_rnd);

-}

-

-inline mpreal::operator float() const

-{

-	return (float)mpfr_get_d(mp,default_rnd);

-}

-

-inline mpreal::operator long double() const

-{

-	return mpfr_get_ld(mp,default_rnd);

-}

-

-inline mpreal::operator unsigned long() const

-{

-	return mpfr_get_ui(mp,default_rnd);	

-}

-

-inline mpreal::operator unsigned int() const

-{

-	return static_cast<unsigned int>(mpfr_get_ui(mp,default_rnd));	

-}

-

-inline mpreal::operator long() const

-{

-	return mpfr_get_si(mp,default_rnd);	

-}

-

-inline mpreal::operator mpfr_ptr()

-{

-	return mp;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// Set/Get number properties

-inline int sgn(const mpreal& v)

-{

-	int r = mpfr_signbit(v.mp);

-	return (r>0?-1:1);

-}

-

-inline void mpreal::set_sign(int sign, mp_rnd_t rnd_mode)

-{

-	mpfr_setsign(mp,mp,(sign<0?1:0),rnd_mode);

-}

-

-inline mp_prec_t mpreal::get_prec() const

-{

-	return mpfr_get_prec(mp);

-}

-

-inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpfr_prec_round(mp,prec,rnd_mode);

-}

-

-inline void mpreal::set_inf(int sign) 

-{ 

-	mpfr_set_inf(mp,sign);

-}	

-

-inline void mpreal::set_nan() 

-{

-	mpfr_set_nan(mp);

-}

-

-inline mp_exp_t mpreal::get_exp ()

-{

-	return mpfr_get_exp(mp);

-}

-

-inline int mpreal::set_exp (mp_exp_t e)

-{

-	return mpfr_set_exp(mp,e);

-}

-

-inline const mpreal frexp(const mpreal& v, mp_exp_t* exp)

-{

-	mpreal x(v);

-	*exp = x.get_exp();

-	x.set_exp(0);

-	return x;

-}

-

-inline const mpreal ldexp(const mpreal& v, mp_exp_t exp)

-{

-	mpreal x(v);

-

-	// rounding is not important since we just increasing the exponent

-	mpfr_mul_2si(x.mp,x.mp,exp,mpreal::default_rnd); 

-	return x;

-}

-

-inline const mpreal machine_epsilon(mp_prec_t prec)

-{

-	// smallest eps such that 1.0+eps != 1.0

-	// depends (of cause) on the precision

-	mpreal x(1,prec); 

-	return nextabove(x)-x;

-}

-

-inline const mpreal mpreal_min(mp_prec_t prec)

-{

-	// min = 1/2*2^emin = 2^(emin-1)

-	

-	mpreal x(1,prec);

-	return x <<= mpreal::get_emin()-1;

-}

-

-inline const mpreal mpreal_max(mp_prec_t prec)

-{

-	// max = (1-eps)*2^emax, assume eps = 0?, 

-	// and use emax-1 to prevent value to be +inf

-	// max = 2^(emax-1)

-

-	mpreal x(1,prec);

-	return x <<= mpreal::get_emax()-1;

-}

-

-inline const mpreal modf(const mpreal& v, mpreal& n)

-{

-	mpreal frac(v);

-

-	// rounding is not important since we are using the same number

-	mpfr_frac(frac.mp,frac.mp,mpreal::default_rnd);	

-	mpfr_trunc(n.mp,v.mp);

-	return frac;

-}

-

-inline int mpreal::check_range (int t, mp_rnd_t rnd_mode)

-{

-	return mpfr_check_range(mp,t,rnd_mode);

-}

-

-inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode)

-{

-	return mpfr_subnormalize(mp,t,rnd_mode);

-}

-

-inline mp_exp_t mpreal::get_emin (void)

-{

-	return mpfr_get_emin();

-}

-

-inline int mpreal::set_emin (mp_exp_t exp)

-{

-	return mpfr_set_emin(exp);

-}

-

-inline mp_exp_t mpreal::get_emax (void)

-{

-	return mpfr_get_emax();

-}

-

-inline int mpreal::set_emax (mp_exp_t exp)

-{

-	return mpfr_set_emax(exp);

-}

-

-inline mp_exp_t mpreal::get_emin_min (void)

-{

-	return mpfr_get_emin_min();

-}

-

-inline mp_exp_t mpreal::get_emin_max (void)

-{

-	return mpfr_get_emin_max();

-}

-

-inline mp_exp_t mpreal::get_emax_min (void)

-{

-	return mpfr_get_emax_min();

-}

-

-inline mp_exp_t mpreal::get_emax_max (void)

-{

-	return mpfr_get_emax_max();

-}

-

-//////////////////////////////////////////////////////////////////////////

-// Mathematical Functions

-//////////////////////////////////////////////////////////////////////////

-inline const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sqr(x.mp,x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sqrt(x.mp,x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	mpfr_sqrt_ui(x.mp,v,rnd_mode);

-	return x;

-}

-

-inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode)

-{

-	return sqrt(static_cast<unsigned long int>(v),rnd_mode);

-}

-

-inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode)

-{

-	if (v>=0)	return sqrt(static_cast<unsigned long int>(v),rnd_mode);

-	else		return mpreal(); // NaN  

-}

-

-inline const mpreal sqrt(const int v, mp_rnd_t rnd_mode)

-{

-	if (v>=0)	return sqrt(static_cast<unsigned long int>(v),rnd_mode);

-	else		return mpreal(); // NaN

-}

-

-inline const mpreal sqrt(const long double v, mp_rnd_t rnd_mode)

-{

-	return sqrt(mpreal(v),rnd_mode);

-}

-

-inline const mpreal sqrt(const double v, mp_rnd_t rnd_mode)

-{

-	return sqrt(mpreal(v),rnd_mode);

-}

-

-inline const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_cbrt(x.mp,x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_root(x.mp,x.mp,k,rnd_mode);

-	return x;

-}

-

-inline const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_abs(x.mp,x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_abs(x.mp,x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_dim(x.mp,a.mp,b.mp,rnd_mode);

-	return x;

-}

-

-inline int cmpabs(const mpreal& a,const mpreal& b)

-{

-	return mpfr_cmpabs(a.mp,b.mp);

-}

-

-inline const mpreal log  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_log(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal log2(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_log2(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_log10(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal exp(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_exp(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal exp2(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_exp2(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_exp10(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_cos(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sin(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_tan(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sec(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_csc(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_cot(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)

-{

-	return mpfr_sin_cos(s.mp,c.mp,v.mp,rnd_mode);

-}

-

-inline const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_acos(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_asin(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_atan(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode)

-{

-	mpreal a;

-	mp_prec_t yp, xp;

-

-	yp = y.get_prec(); 

-	xp = x.get_prec(); 

-

-	a.set_prec(yp>xp?yp:xp);

-

-	mpfr_atan2(a.mp, y.mp, x.mp, rnd_mode);

-

-	return a;

-}

-

-inline const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_cosh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sinh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_tanh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_sech(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_csch(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_coth(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal acosh  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_acosh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal asinh  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_asinh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal atanh  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_atanh(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	mpfr_fac_ui(x.mp,v,rnd_mode);

-	return x;

-}

-

-inline const mpreal log1p  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_log1p(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal expm1  (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_expm1(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal eint   (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_eint(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_gamma(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_lngamma(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_lgamma(x.mp,signp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_zeta(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_erf(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_erfc(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_j0(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_j1(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_jn(x.mp,n,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_y0(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_y1(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_yn(x.mp,n,v.mp,rnd_mode);

-	return x;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// MPFR 2.4.0 Specifics

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))

-

-inline int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)

-{

-	return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode);

-}

-

-inline const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_li2(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)

-{

-	mpreal a;

-	mp_prec_t yp, xp;

-

-	yp = y.get_prec(); 

-	xp = x.get_prec(); 

-

-	a.set_prec(yp>xp?yp:xp);

-

-	mpfr_fmod(a.mp, x.mp, y.mp, rnd_mode);

-

-	return a;

-}

-

-inline const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rec_sqrt(x.mp,v.mp,rnd_mode);

-	return x;

-}

-#endif //  MPFR 2.4.0 Specifics

-

-//////////////////////////////////////////////////////////////////////////

-// MPFR 3.0.0 Specifics

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))

-inline const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_digamma(x.mp,v.mp,rnd_mode);

-	return x;

-}

-#endif // MPFR 3.0.0 Specifics

-

-//////////////////////////////////////////////////////////////////////////

-// Constants

-inline const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	x.set_prec(prec);

-	mpfr_const_log2(x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	x.set_prec(prec);

-	mpfr_const_pi(x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	x.set_prec(prec);

-	mpfr_const_euler(x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	x.set_prec(prec);

-	mpfr_const_catalan(x.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal const_infinity (int sign, mp_prec_t prec, mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	x.set_prec(prec,rnd_mode);

-	mpfr_set_inf(x.mp, sign);

-	return x;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// Integer Related Functions

-inline const mpreal rint(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rint(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal ceil(const mpreal& v)

-{

-	mpreal x(v);

-	mpfr_ceil(x.mp,v.mp);

-	return x;

-

-}

-

-inline const mpreal floor(const mpreal& v)

-{

-	mpreal x(v);

-	mpfr_floor(x.mp,v.mp);

-	return x;

-}

-

-inline const mpreal round(const mpreal& v)

-{

-	mpreal x(v);

-	mpfr_round(x.mp,v.mp);

-	return x;

-}

-

-inline const mpreal trunc(const mpreal& v)

-{

-	mpreal x(v);

-	mpfr_trunc(x.mp,v.mp);

-	return x;

-}

-

-inline const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rint_ceil(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rint_floor(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rint_round(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_rint_trunc(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode)

-{

-	mpreal x(v);

-	mpfr_frac(x.mp,v.mp,rnd_mode);

-	return x;

-}

-

-//////////////////////////////////////////////////////////////////////////

-// Miscellaneous Functions

-inline void swap(mpreal& a, mpreal& b) 

-{

-	mpfr_swap(a.mp,b.mp);

-}

-

-#ifndef max

-inline const mpreal max(const mpreal& x, const mpreal& y)

-{

-	return (x>y?x:y);

-}

-#endif

-

-#ifndef min

-inline const mpreal min(const mpreal& x, const mpreal& y)

-{

-	return (x<y?x:y);

-}

-#endif

-

-inline const mpreal nexttoward (const mpreal& x, const mpreal& y)

-{

-	mpreal a(x);

-	mpfr_nexttoward(a.mp,y.mp);

-	return a;

-}

-

-inline const mpreal nextabove  (const mpreal& x)

-{

-	mpreal a(x);

-	mpfr_nextabove(a.mp);

-	return a;

-}

-

-inline const mpreal nextbelow  (const mpreal& x)

-{

-	mpreal a(x);

-	mpfr_nextbelow(a.mp);

-	return a;

-}

-

-inline const mpreal urandomb (gmp_randstate_t& state)

-{

-	mpreal x;

-	mpfr_urandomb(x.mp,state);

-	return x;

-}

-

-#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))

-// use gmp_randinit_default() to init state, gmp_randclear() to clear

-inline const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode)

-{

-	mpreal x;

-	mpfr_urandom(x.mp,state,rnd_mode);

-	return x;

-}

-#endif 

-

-#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))

-inline const mpreal random2 (mp_size_t size, mp_exp_t exp)

-{

-	mpreal x;

-	mpfr_random2(x.mp,size,exp);

-	return x;

-}

-#endif

-

-//////////////////////////////////////////////////////////////////////////

-// Set/Get global properties

-inline void mpreal::set_default_prec(mp_prec_t prec)

-{ 

-	default_prec = prec;

-	mpfr_set_default_prec(prec); 

-}

-

-inline mp_prec_t mpreal::get_default_prec()

-{ 

-	return mpfr_get_default_prec();

-}

-

-inline void mpreal::set_default_base(int base)

-{ 

-	default_base = base;

-}

-

-inline int mpreal::get_default_base()

-{ 

-	return default_base;

-}

-

-inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode)

-{ 

-	default_rnd =  rnd_mode;

-	mpfr_set_default_rounding_mode(rnd_mode); 

-}

-

-inline mp_rnd_t mpreal::get_default_rnd()

-{ 

-	return mpfr_get_default_rounding_mode();

-}

-

-inline void mpreal::set_double_bits(int dbits)

-{ 

-	double_bits = dbits;

-}

-

-inline int mpreal::get_double_bits()

-{ 

-	return double_bits;

-}

-

-inline bool mpreal::fits_in_bits(double x, int n)

-{   

-	int i;

-	double t;

-	return IsInf(x) || (std::modf ( std::ldexp ( std::frexp ( x, &i ), n ), &t ) == 0.0);

-}

-

-inline const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_pow(x.mp,x.mp,b.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_pow_z(x.mp,x.mp,b,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_pow_ui(x.mp,x.mp,b,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	return pow(a,static_cast<unsigned long int>(b),rnd_mode);

-}

-

-inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_pow_si(x.mp,x.mp,b,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode)

-{

-	return pow(a,static_cast<long int>(b),rnd_mode);

-}

-

-inline const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode)

-{

-	return pow(a,mpreal(b),rnd_mode);

-}

-

-inline const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode)

-{

-	return pow(a,mpreal(b),rnd_mode);

-}

-

-inline const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_ui_pow(x.mp,a,b.mp,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	return pow(static_cast<unsigned long int>(a),b,rnd_mode);

-}

-

-inline const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),b,rnd_mode);

-	else		return pow(mpreal(a),b,rnd_mode);

-}

-

-inline const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),b,rnd_mode);

-	else		return pow(mpreal(a),b,rnd_mode);

-}

-

-inline const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode);

-}

-

-inline const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode);

-}

-

-// pow unsigned long int

-inline const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	mpreal x(a);

-	mpfr_ui_pow_ui(x.mp,a,b,rnd_mode);

-	return x;

-}

-

-inline const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-}

-

-inline const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode)

-{

-	if(b>0)	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-	else	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode)

-{

-	if(b>0)	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-	else	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode)

-{

-	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode)

-{

-	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-// pow unsigned int

-inline const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui

-}

-

-inline const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-}

-

-inline const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode)

-{

-	if(b>0)	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-	else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode)

-{

-	if(b>0)	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-	else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode)

-{

-	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-inline const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode)

-{

-	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-}

-

-// pow long int

-inline const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui

-	else	 return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui

-	else	 return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode)

-{

-	if (a>0)

-	{

-		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	}else{

-		return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si

-	}

-}

-

-inline const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode)

-{

-	if (a>0)

-	{

-		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	}else{

-		return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si

-	}

-}

-

-inline const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow

-}

-

-inline const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow

-}

-

-// pow int

-inline const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui

-	else	 return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui

-	else	 return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode)

-{

-	if (a>0)

-	{

-		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	}else{

-		return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si

-	}

-}

-

-inline const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode)

-{

-	if (a>0)

-	{

-		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui

-		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	}else{

-		return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si

-	}

-}

-

-inline const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow

-}

-

-inline const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode)

-{

-	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow

-	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow

-}

-

-// pow long double 

-inline const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),mpreal(b),rnd_mode);

-}

-

-inline const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui

-}

-

-inline const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si

-}

-

-inline const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si

-}

-

-inline const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),mpreal(b),rnd_mode);

-}

-

-inline const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_ui

-}

-

-inline const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); // mpfr_pow_ui

-}

-

-inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si

-}

-

-inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)

-{

-	return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si

-}

-}

-

-// Explicit specialization of std::swap for mpreal numbers

-// Thus standard algorithms will use efficient version of swap (due to Koenig lookup)

-// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap

-namespace std

-{

-	template <>

-	inline void swap(mpfr::mpreal& x, mpfr::mpreal& y) 

-	{ 

-		return mpfr::swap(x, y); 

-	}

-}

-

-#endif /* __MP_REAL_H__ */

+/*
+	Multi-precision real number class. C++ wrapper fo MPFR library.
+	Project homepage: http://www.holoborodko.com/pavel/
+	Contact e-mail:   pavel@holoborodko.com
+
+	Copyright (c) 2008-2010 Pavel Holoborodko
+
+	This library is free software; you can redistribute it and/or
+	modify it under the terms of the GNU Lesser General Public
+	License as published by the Free Software Foundation; either
+	version 2.1 of the License, or (at your option) any later version.
+
+	This library is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+	Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public
+	License along with this library; if not, write to the Free Software
+	Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+
+	Contributors:
+	Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, 
+	Heinz van Saanen, Pere Constans, Dmitriy Gubanov
+*/
+
+#ifndef __MP_REAL_H__
+#define __MP_REAL_H__
+
+#include <string>
+#include <iostream>
+#include <sstream>
+#include <stdexcept>
+#include <cfloat>
+#include <cmath>
+
+#include <mpfr.h>
+
+// Detect compiler using signatures from http://predef.sourceforge.net/
+#if defined(__GNUC__) && defined(__INTEL_COMPILER)
+	#define IsInf(x) isinf(x)                                // GNU C/C++ + Intel ICC compiler
+
+#elif defined(__GNUC__)
+	#define IsInf(x) std::isinf(x)                          // GNU C/C++ 
+
+#elif defined(_MSC_VER)		
+	#define IsInf(x) (!_finite(x))				// Microsoft Visual C++
+
+#else
+	#define IsInf(x) std::isinf(x)				// C99 conformance
+#endif
+
+namespace mpfr {
+
+class mpreal {
+private:
+	mpfr_t mp;
+
+public:
+	static mp_rnd_t		default_rnd;	
+	static mp_prec_t	default_prec;	
+	static int			default_base;
+	static int			double_bits;
+
+public:
+	// Constructors && type conversion
+	mpreal();
+	mpreal(const mpreal& u);
+
+	mpreal(const mpfr_t u);	
+	mpreal(const mpf_t u);	
+
+	mpreal(const mpz_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);	
+	mpreal(const mpq_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);	
+	mpreal(const double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const long double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const unsigned long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const unsigned int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+	mpreal(const char* s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
+
+	~mpreal();                           
+
+	// Operations
+	// =
+	// +, -, *, /, ++, --, <<, >> 
+	// *=, +=, -=, /=,
+	// <, >, ==, <=, >=
+
+	// =
+	mpreal& operator=(const mpreal& v);
+	mpreal& operator=(const mpf_t v);
+	mpreal& operator=(const mpz_t v);
+	mpreal& operator=(const mpq_t v);
+	mpreal& operator=(const long double v);
+	mpreal& operator=(const double v);		
+	mpreal& operator=(const unsigned long int v);
+	mpreal& operator=(const unsigned int v);
+	mpreal& operator=(const long int v);
+	mpreal& operator=(const int v);
+	mpreal& operator=(const char* s);
+
+	// +
+	mpreal& operator+=(const mpreal& v);
+	mpreal& operator+=(const mpf_t v);
+	mpreal& operator+=(const mpz_t v);
+	mpreal& operator+=(const mpq_t v);
+	mpreal& operator+=(const long double u);
+	mpreal& operator+=(const double u);
+	mpreal& operator+=(const unsigned long int u);
+	mpreal& operator+=(const unsigned int u);
+	mpreal& operator+=(const long int u);
+	mpreal& operator+=(const int u);
+	const mpreal operator+() const;
+	mpreal& operator++ ();
+	const mpreal  operator++ (int); 
+
+	// -
+	mpreal& operator-=(const mpreal& v);
+	mpreal& operator-=(const mpz_t v);
+	mpreal& operator-=(const mpq_t v);
+	mpreal& operator-=(const long double u);
+	mpreal& operator-=(const double u);
+	mpreal& operator-=(const unsigned long int u);
+	mpreal& operator-=(const unsigned int u);
+	mpreal& operator-=(const long int u);
+	mpreal& operator-=(const int u);
+	const mpreal operator-() const;
+	friend const mpreal operator-(const unsigned long int b, const mpreal& a);
+	friend const mpreal operator-(const unsigned int b, const mpreal& a);
+	friend const mpreal operator-(const long int b, const mpreal& a);
+	friend const mpreal operator-(const int b, const mpreal& a);
+	friend const mpreal operator-(const double b, const mpreal& a);
+	mpreal& operator-- ();    
+	const mpreal  operator-- (int);
+
+	// *
+	mpreal& operator*=(const mpreal& v);
+	mpreal& operator*=(const mpz_t v);
+	mpreal& operator*=(const mpq_t v);
+	mpreal& operator*=(const long double v);
+	mpreal& operator*=(const double v);
+	mpreal& operator*=(const unsigned long int v);
+	mpreal& operator*=(const unsigned int v);
+	mpreal& operator*=(const long int v);
+	mpreal& operator*=(const int v);
+	
+	// /
+	mpreal& operator/=(const mpreal& v);
+	mpreal& operator/=(const mpz_t v);
+	mpreal& operator/=(const mpq_t v);
+	mpreal& operator/=(const long double v);
+	mpreal& operator/=(const double v);
+	mpreal& operator/=(const unsigned long int v);
+	mpreal& operator/=(const unsigned int v);
+	mpreal& operator/=(const long int v);
+	mpreal& operator/=(const int v);
+	friend const mpreal operator/(const unsigned long int b, const mpreal& a);
+	friend const mpreal operator/(const unsigned int b, const mpreal& a);
+	friend const mpreal operator/(const long int b, const mpreal& a);
+	friend const mpreal operator/(const int b, const mpreal& a);
+	friend const mpreal operator/(const double b, const mpreal& a);
+
+	//<<= Fast Multiplication by 2^u
+	mpreal& operator<<=(const unsigned long int u);
+	mpreal& operator<<=(const unsigned int u);
+	mpreal& operator<<=(const long int u);
+	mpreal& operator<<=(const int u);
+
+	//>>= Fast Division by 2^u
+	mpreal& operator>>=(const unsigned long int u);
+	mpreal& operator>>=(const unsigned int u);
+	mpreal& operator>>=(const long int u);
+	mpreal& operator>>=(const int u);
+
+	// Boolean Operators
+	friend bool operator >  (const mpreal& a, const mpreal& b);
+	friend bool operator >= (const mpreal& a, const mpreal& b);
+	friend bool operator <  (const mpreal& a, const mpreal& b);
+	friend bool operator <= (const mpreal& a, const mpreal& b);
+	friend bool operator == (const mpreal& a, const mpreal& b);
+	friend bool operator != (const mpreal& a, const mpreal& b);
+
+	// Type Conversion operators
+	inline operator long double() const;
+	inline operator double() const;
+	inline operator float() const;
+	inline operator unsigned long() const;
+	inline operator unsigned int() const;
+	inline operator long() const;
+	operator std::string() const;
+	inline operator mpfr_ptr();
+
+	// Math Functions
+	friend const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend int cmpabs(const mpreal& a,const mpreal& b);
+	
+	friend const mpreal log  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal exp  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+	friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+	friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+	friend const mpreal acos  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal asin  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal atan  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal cosh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sinh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal tanh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sech  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal csch  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal coth  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+	friend const mpreal acosh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal asinh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal atanh  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal log1p  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal expm1  (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal eint   (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+	friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+	friend const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+	friend const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+	friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend int sgn(const mpreal& v); // -1 or +1
+
+// MPFR 2.4.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	friend int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+#endif
+
+// MPFR 3.0.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+	friend const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+    friend const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode = mpreal::default_rnd); 	// use gmp_randinit_default() to init state, gmp_randclear() to clear
+	friend bool _isregular(const mpreal& v);
+#endif
+
+	// Exponent and mantissa manipulation
+	friend const mpreal frexp(const mpreal& v, mp_exp_t* exp);	
+	friend const mpreal ldexp(const mpreal& v, mp_exp_t exp);
+
+	// Splits mpreal value into fractional and integer parts.
+	// Returns fractional part and stores integer part in n.
+	friend const mpreal modf(const mpreal& v, mpreal& n);	
+
+	// Constants
+	// don't forget to call mpfr_free_cache() for every thread where you are using const-functions
+	friend const mpreal const_log2 (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal const_pi (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal const_euler (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal const_catalan (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	// returns +inf iff sign>=0 otherwise -inf
+	friend const mpreal const_infinity(int sign = 1, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+	// Output/ Input
+	friend std::ostream& operator<<(std::ostream& os, const mpreal& v);
+    friend std::istream& operator>>(std::istream& is, mpreal& v);
+
+	// Integer Related Functions
+	friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal ceil (const mpreal& v);
+	friend const mpreal floor(const mpreal& v);
+	friend const mpreal round(const mpreal& v);
+	friend const mpreal trunc(const mpreal& v);
+	friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+	
+	// Miscellaneous Functions
+	friend const mpreal nexttoward (const mpreal& x, const mpreal& y);
+	friend const mpreal nextabove  (const mpreal& x);
+	friend const mpreal nextbelow  (const mpreal& x);
+
+	// use gmp_randinit_default() to init state, gmp_randclear() to clear
+	friend const mpreal urandomb (gmp_randstate_t& state); 
+
+// MPFR < 2.4.2 Specifics
+#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))
+	friend const mpreal random2 (mp_size_t size, mp_exp_t exp);
+#endif
+
+	// Instance Checkers
+	friend bool _isnan(const mpreal& v);
+	friend bool _isinf(const mpreal& v);
+	friend bool _isnum(const mpreal& v);
+	friend bool _iszero(const mpreal& v);
+	friend bool _isint(const mpreal& v);
+
+	// Set/Get instance properties
+	inline mp_prec_t	get_prec() const;
+	inline void		set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = default_rnd);	// Change precision with rounding mode
+	
+	// Set mpreal to +-inf, NaN
+	void      set_inf(int sign = +1);	
+	void	  set_nan();
+
+	// sign = -1 or +1
+	void set_sign(int sign, mp_rnd_t rnd_mode = default_rnd);
+
+	//Exponent
+	mp_exp_t get_exp();
+	int set_exp(mp_exp_t e);
+	int check_range (int t, mp_rnd_t rnd_mode = default_rnd);
+	int subnormalize (int t,mp_rnd_t rnd_mode = default_rnd);
+
+	// Inexact conversion from float
+	inline bool fits_in_bits(double x, int n);
+
+	// Set/Get global properties
+	static void			set_default_prec(mp_prec_t prec);
+	static mp_prec_t	get_default_prec();
+	static void			set_default_base(int base);
+	static int			get_default_base();
+	static void			set_double_bits(int dbits);
+	static int			get_double_bits();
+	static void			set_default_rnd(mp_rnd_t rnd_mode);
+	static mp_rnd_t		get_default_rnd();
+	static mp_exp_t get_emin (void);
+	static mp_exp_t get_emax (void);
+	static mp_exp_t get_emin_min (void);
+	static mp_exp_t get_emin_max (void);
+	static mp_exp_t get_emax_min (void);
+	static mp_exp_t get_emax_max (void);
+	static int set_emin (mp_exp_t exp);
+	static int set_emax (mp_exp_t exp);
+
+	// Get/Set conversions
+	// Convert mpreal to string with n significant digits in base b
+	// n = 0 -> convert with the maximum available digits 
+	std::string to_string(size_t n = 0, int b = default_base, mp_rnd_t mode = default_rnd) const;
+	
+	// Efficient swapping of two mpreal values
+	friend void swap(mpreal& x, mpreal& y);
+	
+	//Min Max - macros is evil. Needed for systems which defines max and min globally as macros (e.g. Windows)
+	//Hope that globally defined macros use > < operations only
+	#ifndef max
+		friend const mpreal max(const mpreal& x, const mpreal& y);
+	#endif
+
+	#ifndef min
+		friend const mpreal min(const mpreal& x, const mpreal& y);
+	#endif
+};
+
+//////////////////////////////////////////////////////////////////////////
+// Exceptions
+class conversion_overflow : public std::exception {
+public:
+	std::string why() { return "inexact conversion from floating point"; }
+};
+
+//////////////////////////////////////////////////////////////////////////
+// + Addition
+const mpreal operator+(const mpreal& a, const mpreal& b);
+
+// + Fast specialized addition - implemented through fast += operations
+const mpreal operator+(const mpreal& a, const mpz_t b);
+const mpreal operator+(const mpreal& a, const mpq_t b);
+const mpreal operator+(const mpreal& a, const long double b);
+const mpreal operator+(const mpreal& a, const double b);
+const mpreal operator+(const mpreal& a, const unsigned long int b);
+const mpreal operator+(const mpreal& a, const unsigned int b);
+const mpreal operator+(const mpreal& a, const long int b);
+const mpreal operator+(const mpreal& a, const int b);
+const mpreal operator+(const mpreal& a, const char* b);
+const mpreal operator+(const char* a, const mpreal& b);
+const std::string operator+(const mpreal& a, const std::string b);
+const std::string operator+(const std::string a, const mpreal& b);
+
+const mpreal operator+(const mpz_t b, const mpreal& a);
+const mpreal operator+(const mpq_t b, const mpreal& a);
+const mpreal operator+(const long double b, const mpreal& a);
+const mpreal operator+(const double  b, const mpreal& a);
+const mpreal operator+(const unsigned long int b, const mpreal& a);
+const mpreal operator+(const unsigned int b, const mpreal& a);
+const mpreal operator+(const long int b, const mpreal& a);
+const mpreal operator+(const int b, const mpreal& a);
+
+//////////////////////////////////////////////////////////////////////////
+// - Subtraction
+const mpreal operator-(const mpreal& a, const mpreal& b);
+
+// - Fast specialized subtraction - implemented through fast -= operations
+const mpreal operator-(const mpreal& a, const mpz_t b);
+const mpreal operator-(const mpreal& a, const mpq_t b);
+const mpreal operator-(const mpreal& a, const long double b);
+const mpreal operator-(const mpreal& a, const double b);
+const mpreal operator-(const mpreal& a, const unsigned long int b);
+const mpreal operator-(const mpreal& a, const unsigned int b);
+const mpreal operator-(const mpreal& a, const long int b);
+const mpreal operator-(const mpreal& a, const int b);
+const mpreal operator-(const mpreal& a, const char* b);
+const mpreal operator-(const char* a, const mpreal& b);
+
+const mpreal operator-(const mpz_t b, const mpreal& a);
+const mpreal operator-(const mpq_t b, const mpreal& a);
+const mpreal operator-(const long double b, const mpreal& a);
+//const mpreal operator-(const double  b, const mpreal& a);
+
+//////////////////////////////////////////////////////////////////////////
+// * Multiplication
+const mpreal operator*(const mpreal& a, const mpreal& b);
+
+// * Fast specialized multiplication - implemented through fast *= operations
+const mpreal operator*(const mpreal& a, const mpz_t b);
+const mpreal operator*(const mpreal& a, const mpq_t b);
+const mpreal operator*(const mpreal& a, const long double b);
+const mpreal operator*(const mpreal& a, const double b);
+const mpreal operator*(const mpreal& a, const unsigned long int b);
+const mpreal operator*(const mpreal& a, const unsigned int b);
+const mpreal operator*(const mpreal& a, const long int b);
+const mpreal operator*(const mpreal& a, const int b);
+
+const mpreal operator*(const mpz_t b, const mpreal& a);
+const mpreal operator*(const mpq_t b, const mpreal& a);
+const mpreal operator*(const long double b, const mpreal& a);
+const mpreal operator*(const double  b, const mpreal& a);
+const mpreal operator*(const unsigned long int b, const mpreal& a);
+const mpreal operator*(const unsigned int b, const mpreal& a);
+const mpreal operator*(const long int b, const mpreal& a);
+const mpreal operator*(const int b, const mpreal& a);
+
+//////////////////////////////////////////////////////////////////////////
+// / Division
+const mpreal operator/(const mpreal& a, const mpreal& b);
+
+// / Fast specialized division - implemented through fast /= operations
+const mpreal operator/(const mpreal& a, const mpz_t b);
+const mpreal operator/(const mpreal& a, const mpq_t b);
+const mpreal operator/(const mpreal& a, const long double b);
+const mpreal operator/(const mpreal& a, const double b);
+const mpreal operator/(const mpreal& a, const unsigned long int b);
+const mpreal operator/(const mpreal& a, const unsigned int b);
+const mpreal operator/(const mpreal& a, const long int b);
+const mpreal operator/(const mpreal& a, const int b);
+
+const mpreal operator/(const long double b, const mpreal& a);
+
+//////////////////////////////////////////////////////////////////////////
+// Shifts operators - Multiplication/Division by a power of 2
+const mpreal operator<<(const mpreal& v, const unsigned long int k);
+const mpreal operator<<(const mpreal& v, const unsigned int k);
+const mpreal operator<<(const mpreal& v, const long int k);
+const mpreal operator<<(const mpreal& v, const int k);
+
+const mpreal operator>>(const mpreal& v, const unsigned long int k);
+const mpreal operator>>(const mpreal& v, const unsigned int k);
+const mpreal operator>>(const mpreal& v, const long int k);
+const mpreal operator>>(const mpreal& v, const int k);
+
+//////////////////////////////////////////////////////////////////////////
+// Boolean operators
+bool operator <  (const mpreal& a, const unsigned long int b);
+bool operator <  (const mpreal& a, const unsigned int b);
+bool operator <  (const mpreal& a, const long int b);
+bool operator <  (const mpreal& a, const int b);
+bool operator <  (const mpreal& a, const long double b);
+bool operator <  (const mpreal& a, const double b);
+
+bool operator <  (const unsigned long int a,const mpreal& b);
+bool operator <  (const unsigned int a,		const mpreal& b);
+bool operator <  (const long int a,			const mpreal& b);
+bool operator <  (const int a,				const mpreal& b);
+bool operator <  (const long double a,		const mpreal& b);
+bool operator <  (const double a,			const mpreal& b);
+
+bool operator >  (const mpreal& a, const unsigned long int b);
+bool operator >  (const mpreal& a, const unsigned int b);
+bool operator >  (const mpreal& a, const long int b);
+bool operator >  (const mpreal& a, const int b);
+bool operator >  (const mpreal& a, const long double b);
+bool operator >  (const mpreal& a, const double b);
+
+bool operator >  (const unsigned long int a,const mpreal& b);
+bool operator >  (const unsigned int a,		const mpreal& b);
+bool operator >  (const long int a,			const mpreal& b);
+bool operator >  (const int a,				const mpreal& b);
+bool operator >  (const long double a,		const mpreal& b);
+bool operator >  (const double a,			const mpreal& b);
+
+bool operator >=  (const mpreal& a, const unsigned long int b);
+bool operator >=  (const mpreal& a, const unsigned int b);
+bool operator >=  (const mpreal& a, const long int b);
+bool operator >=  (const mpreal& a, const int b);
+bool operator >=  (const mpreal& a, const long double b);
+bool operator >=  (const mpreal& a, const double b);
+
+bool operator >=  (const unsigned long int a,const mpreal& b);
+bool operator >=  (const unsigned int a,		const mpreal& b);
+bool operator >=  (const long int a,			const mpreal& b);
+bool operator >=  (const int a,				const mpreal& b);
+bool operator >=  (const long double a,		const mpreal& b);
+bool operator >=  (const double a,			const mpreal& b);
+
+bool operator <=  (const mpreal& a, const unsigned long int b);
+bool operator <=  (const mpreal& a, const unsigned int b);
+bool operator <=  (const mpreal& a, const long int b);
+bool operator <=  (const mpreal& a, const int b);
+bool operator <=  (const mpreal& a, const long double b);
+bool operator <=  (const mpreal& a, const double b);
+
+bool operator <=  (const unsigned long int a,const mpreal& b);
+bool operator <=  (const unsigned int a,		const mpreal& b);
+bool operator <=  (const long int a,			const mpreal& b);
+bool operator <=  (const int a,				const mpreal& b);
+bool operator <=  (const long double a,		const mpreal& b);
+bool operator <=  (const double a,			const mpreal& b);
+
+bool operator ==  (const mpreal& a, const unsigned long int b);
+bool operator ==  (const mpreal& a, const unsigned int b);
+bool operator ==  (const mpreal& a, const long int b);
+bool operator ==  (const mpreal& a, const int b);
+bool operator ==  (const mpreal& a, const long double b);
+bool operator ==  (const mpreal& a, const double b);
+
+bool operator ==  (const unsigned long int a,const mpreal& b);
+bool operator ==  (const unsigned int a,		const mpreal& b);
+bool operator ==  (const long int a,			const mpreal& b);
+bool operator ==  (const int a,				const mpreal& b);
+bool operator ==  (const long double a,		const mpreal& b);
+bool operator ==  (const double a,			const mpreal& b);
+
+bool operator !=  (const mpreal& a, const unsigned long int b);
+bool operator !=  (const mpreal& a, const unsigned int b);
+bool operator !=  (const mpreal& a, const long int b);
+bool operator !=  (const mpreal& a, const int b);
+bool operator !=  (const mpreal& a, const long double b);
+bool operator !=  (const mpreal& a, const double b);
+
+bool operator !=  (const unsigned long int a,const mpreal& b);
+bool operator !=  (const unsigned int a,		const mpreal& b);
+bool operator !=  (const long int a,			const mpreal& b);
+bool operator !=  (const int a,				const mpreal& b);
+bool operator !=  (const long double a,		const mpreal& b);
+bool operator !=  (const double a,			const mpreal& b);
+
+//////////////////////////////////////////////////////////////////////////
+// sqrt
+const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+//////////////////////////////////////////////////////////////////////////
+// pow
+const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd); 
+
+const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);	
+const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);	
+const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+//////////////////////////////////////////////////////////////////////////
+// Estimate machine epsilon for the given precision
+inline const mpreal machine_epsilon(mp_prec_t prec);
+inline const mpreal mpreal_min(mp_prec_t prec);
+inline const mpreal mpreal_max(mp_prec_t prec);
+
+//////////////////////////////////////////////////////////////////////////
+// Implementation of inline functions
+//////////////////////////////////////////////////////////////////////////
+
+//////////////////////////////////////////////////////////////////////////
+// Operators - Assignment
+inline mpreal& mpreal::operator=(const mpreal& v)
+{
+	if (this!= &v)	mpfr_set(mp,v.mp,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpf_t v)
+{
+	mpfr_set_f(mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpz_t v)
+{
+	mpfr_set_z(mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpq_t v)
+{
+	mpfr_set_q(mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const long double v)		
+{	
+    mpfr_set_ld(mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const double v)				
+{	
+    if(double_bits == -1 || fits_in_bits(v, double_bits))
+    {
+    	mpfr_set_d(mp,v,default_rnd);
+    }
+    else
+        throw conversion_overflow();
+
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const unsigned long int v)	
+{	
+	mpfr_set_ui(mp,v,default_rnd);	
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const unsigned int v)		
+{	
+	mpfr_set_ui(mp,v,default_rnd);	
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const long int v)			
+{	
+	mpfr_set_si(mp,v,default_rnd);	
+	return *this;
+}
+
+inline mpreal& mpreal::operator=(const int v)
+{	
+	mpfr_set_si(mp,v,default_rnd);	
+	return *this;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// + Addition
+inline mpreal& mpreal::operator+=(const mpreal& v)
+{
+	mpfr_add(mp,mp,v.mp,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpf_t u)
+{
+	*this += mpreal(u);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpz_t u)
+{
+	mpfr_add_z(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpq_t u)
+{
+	mpfr_add_q(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+= (const long double u)
+{
+	return *this += mpreal(u);	
+}
+
+inline mpreal& mpreal::operator+= (const double u)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpfr_add_d(mp,mp,u,default_rnd);
+	return *this;
+#else
+	return *this += mpreal(u);	
+#endif
+}
+
+inline mpreal& mpreal::operator+=(const unsigned long int u)
+{
+	mpfr_add_ui(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const unsigned int u)
+{
+	mpfr_add_ui(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const long int u)
+{
+	mpfr_add_si(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator+=(const int u)
+{
+	mpfr_add_si(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline const mpreal mpreal::operator+()const
+{
+	return mpreal(*this);
+}
+
+inline const mpreal operator+(const mpreal& a, const mpreal& b)
+{
+	// prec(a+b) = max(prec(a),prec(b))
+	if(a.get_prec()>b.get_prec()) return mpreal(a) += b;
+	else						  return mpreal(b) += a;
+}
+
+inline const std::string operator+(const mpreal& a, const std::string b)
+{
+	return (std::string)a+b;
+}
+
+inline const std::string operator+(const std::string a, const mpreal& b)
+{
+	return a+(std::string)b;
+}
+
+inline const mpreal operator+(const mpreal& a, const mpz_t b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const char* b)
+{
+	return a+mpreal(b);
+}
+
+inline const mpreal operator+(const char* a, const mpreal& b)
+{
+	return mpreal(a)+b;
+
+}
+
+inline const mpreal operator+(const mpreal& a, const mpq_t b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const long double b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const double b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const unsigned long int b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const unsigned int b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const long int b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpreal& a, const int b)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpz_t b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const mpq_t b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const long double b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const double  b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const unsigned long int b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const unsigned int b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const long int b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline const mpreal operator+(const int b, const mpreal& a)
+{
+	return mpreal(a) += b;
+}
+
+inline mpreal& mpreal::operator++() 
+{
+	*this += 1;
+	return *this;
+}
+
+inline const mpreal mpreal::operator++ (int)
+{
+	mpreal x(*this);
+	*this += 1;
+	return x;
+}
+
+inline mpreal& mpreal::operator--() 
+{
+	*this -= 1;
+	return *this;
+}
+
+inline const mpreal mpreal::operator-- (int)
+{
+	mpreal x(*this);
+	*this -= 1;
+	return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// - Subtraction
+inline mpreal& mpreal::operator-= (const mpreal& v)
+{
+	mpfr_sub(mp,mp,v.mp,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const mpz_t v)
+{
+	mpfr_sub_z(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const mpq_t v)
+{
+	mpfr_sub_q(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const long double v)
+{
+	return *this -= mpreal(v);	
+}
+
+inline mpreal& mpreal::operator-=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpfr_sub_d(mp,mp,v,default_rnd);
+	return *this;
+#else
+	return *this -= mpreal(v);	
+#endif
+}
+
+inline mpreal& mpreal::operator-=(const unsigned long int v)
+{
+	mpfr_sub_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const unsigned int v)
+{
+	mpfr_sub_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const long int v)
+{
+	mpfr_sub_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator-=(const int v)
+{
+	mpfr_sub_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline const mpreal mpreal::operator-()const
+{
+	mpreal u(*this);
+	mpfr_neg(u.mp,u.mp,default_rnd);
+	return u;
+}
+
+inline const mpreal operator-(const mpreal& a, const mpreal& b)
+{
+	// prec(a-b) = max(prec(a),prec(b))
+	if(a.get_prec()>b.get_prec())	return   mpreal(a) -= b;
+	else							return -(mpreal(b) -= a);		
+}
+
+inline const mpreal operator-(const mpreal& a, const mpz_t b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const mpq_t b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const long double b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const double b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const unsigned long int b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const unsigned int b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const long int b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpreal& a, const int b)
+{
+	return mpreal(a) -= b;
+}
+
+inline const mpreal operator-(const mpz_t b, const mpreal& a)
+{
+	return -(mpreal(a) -= b);
+}
+
+inline const mpreal operator-(const mpq_t b, const mpreal& a)
+{
+	return -(mpreal(a) -= b);
+}
+
+inline const mpreal operator-(const long double b, const mpreal& a)
+{
+	return -(mpreal(a) -= b);
+}
+
+inline const mpreal operator-(const double  b, const mpreal& a)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpreal x(a);
+	mpfr_d_sub(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+#else
+	return -(mpreal(a) -= b);
+#endif
+}
+
+inline const mpreal operator-(const unsigned long int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator-(const unsigned int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator-(const long int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator-(const int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator-(const mpreal& a, const char* b)
+{
+	return a-mpreal(b);
+}
+
+inline const mpreal operator-(const char* a, const mpreal& b)
+{
+	return mpreal(a)-b;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// * Multiplication
+inline mpreal& mpreal::operator*= (const mpreal& v)
+{
+	mpfr_mul(mp,mp,v.mp,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const mpz_t v)
+{
+	mpfr_mul_z(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const mpq_t v)
+{
+	mpfr_mul_q(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const long double v)
+{
+	return *this *= mpreal(v);	
+}
+
+inline mpreal& mpreal::operator*=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpfr_mul_d(mp,mp,v,default_rnd);
+	return *this;
+#else
+	return *this *= mpreal(v);	
+#endif
+}
+
+inline mpreal& mpreal::operator*=(const unsigned long int v)
+{
+	mpfr_mul_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const unsigned int v)
+{
+	mpfr_mul_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const long int v)
+{
+	mpfr_mul_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator*=(const int v)
+{
+	mpfr_mul_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline const mpreal operator*(const mpreal& a, const mpreal& b)
+{
+	// prec(a*b) = max(prec(a),prec(b))
+	if(a.get_prec()>b.get_prec())	return   mpreal(a) *= b;
+	else							return   mpreal(b) *= a;		
+}
+
+inline const mpreal operator*(const mpreal& a, const mpz_t b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const mpq_t b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const long double b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const double b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const unsigned long int b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const unsigned int b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const long int b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpreal& a, const int b)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpz_t b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const mpq_t b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const long double b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const double  b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const unsigned long int b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const unsigned int b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const long int b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+inline const mpreal operator*(const int b, const mpreal& a)
+{
+	return mpreal(a) *= b;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// / Division
+inline mpreal& mpreal::operator/=(const mpreal& v)
+{
+	mpfr_div(mp,mp,v.mp,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const mpz_t v)
+{
+	mpfr_div_z(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const mpq_t v)
+{
+	mpfr_div_q(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const long double v)
+{
+	return *this /= mpreal(v);	
+}
+
+inline mpreal& mpreal::operator/=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpfr_div_d(mp,mp,v,default_rnd);
+	return *this;
+#else
+	return *this /= mpreal(v);	
+#endif
+}
+
+inline mpreal& mpreal::operator/=(const unsigned long int v)
+{
+	mpfr_div_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const unsigned int v)
+{
+	mpfr_div_ui(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const long int v)
+{
+	mpfr_div_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator/=(const int v)
+{
+	mpfr_div_si(mp,mp,v,default_rnd);
+	return *this;
+}
+
+inline const mpreal operator/(const mpreal& a, const mpreal& b)
+{
+	mpreal x(a);
+	mp_prec_t pb;
+	mp_prec_t pa;
+
+	// prec(a/b) = max(prec(a),prec(b))
+	pa = a.get_prec();
+	pb = b.get_prec();
+	if(pb>pa) x.set_prec(pb);
+
+	return   x /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const mpz_t b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const mpq_t b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const long double b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const double b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const unsigned long int b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const unsigned int b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const long int b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const mpreal& a, const int b)
+{
+	return mpreal(a) /= b;
+}
+
+inline const mpreal operator/(const unsigned long int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator/(const unsigned int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator/(const long int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator/(const int b, const mpreal& a)
+{
+	mpreal x(a);
+	mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+}
+
+inline const mpreal operator/(const long double b, const mpreal& a)
+{
+	mpreal x(b);
+	return x/a;
+}
+
+inline const mpreal operator/(const double  b, const mpreal& a)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+	mpreal x(a);
+	mpfr_d_div(x.mp,b,a.mp,mpreal::default_rnd);
+	return x;
+#else
+	mpreal x(b);
+	return x/a;
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Shifts operators - Multiplication/Division by power of 2
+inline mpreal& mpreal::operator<<=(const unsigned long int u)
+{
+	mpfr_mul_2ui(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const unsigned int u)
+{
+	mpfr_mul_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const long int u)
+{
+	mpfr_mul_2si(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const int u)
+{
+	mpfr_mul_2si(mp,mp,static_cast<long int>(u),default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const unsigned long int u)
+{
+	mpfr_div_2ui(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const unsigned int u)
+{
+	mpfr_div_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const long int u)
+{
+	mpfr_div_2si(mp,mp,u,default_rnd);
+	return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const int u)
+{
+	mpfr_div_2si(mp,mp,static_cast<long int>(u),default_rnd);
+	return *this;
+}
+
+inline const mpreal operator<<(const mpreal& v, const unsigned long int k)
+{
+	return mul_2ui(v,k);
+}
+
+inline const mpreal operator<<(const mpreal& v, const unsigned int k)
+{
+	return mul_2ui(v,static_cast<unsigned long int>(k));
+}
+
+inline const mpreal operator<<(const mpreal& v, const long int k)
+{
+	return mul_2si(v,k);
+}
+
+inline const mpreal operator<<(const mpreal& v, const int k)
+{
+	return mul_2si(v,static_cast<long int>(k));
+}
+
+inline const mpreal operator>>(const mpreal& v, const unsigned long int k)
+{
+	return div_2ui(v,k);
+}
+
+inline const mpreal operator>>(const mpreal& v, const long int k)
+{
+	return div_2si(v,k);
+}
+
+inline const mpreal operator>>(const mpreal& v, const unsigned int k)
+{
+	return div_2ui(v,static_cast<unsigned long int>(k));
+}
+
+inline const mpreal operator>>(const mpreal& v, const int k)
+{
+	return div_2si(v,static_cast<long int>(k));
+}
+
+// mul_2ui
+inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_mul_2ui(x.mp,v.mp,k,rnd_mode);
+	return x;
+}
+
+// mul_2si
+inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_mul_2si(x.mp,v.mp,k,rnd_mode);
+	return x;
+}
+
+inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_div_2ui(x.mp,v.mp,k,rnd_mode);
+	return x;
+}
+
+inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_div_2si(x.mp,v.mp,k,rnd_mode);
+	return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+//Boolean operators
+inline bool operator > (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_greater_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator >  (const mpreal& a, const unsigned long int b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const mpreal& a, const unsigned int b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const mpreal& a, const long int b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const mpreal& a, const int b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const mpreal& a, const long double b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const mpreal& a, const double b)
+{
+	return a>mpreal(b);
+}
+
+inline bool operator >  (const unsigned long int a,	const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >  (const unsigned int a,		const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >  (const long int a,			const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >  (const int a,				const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >  (const long double a,		const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >  (const double a,			const mpreal& b)
+{
+	return mpreal(a)>b;
+}
+
+inline bool operator >= (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_greaterequal_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator >=  (const mpreal& a, const unsigned long int b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const mpreal& a, const unsigned int b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const mpreal& a, const long int b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const mpreal& a, const int b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const mpreal& a, const long double b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const mpreal& a, const double b)
+{
+	return a>=mpreal(b);
+}
+
+inline bool operator >=  (const unsigned long int a,const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator >=  (const unsigned int a,		const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator >=  (const long int a,			const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator >=  (const int a,				const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator >=  (const long double a,		const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator >=  (const double a,			const mpreal& b)
+{
+	return mpreal(a)>=b;
+}
+
+inline bool operator <  (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_less_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator <  (const mpreal& a, const unsigned long int b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const mpreal& a, const unsigned int b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const mpreal& a, const long int b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const mpreal& a, const int b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const mpreal& a, const long double b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const mpreal& a, const double b)
+{
+	return a<mpreal(b);
+}
+
+inline bool operator <  (const unsigned long int a,	const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <  (const unsigned int a,const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <  (const long int a,const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <  (const int a,const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <  (const long double a,const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <  (const double a,const mpreal& b)
+{
+	return mpreal(a)<b;
+}
+
+inline bool operator <= (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_lessequal_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator <=  (const mpreal& a, const unsigned long int b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const mpreal& a, const unsigned int b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const mpreal& a, const long int b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const mpreal& a, const int b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const mpreal& a, const long double b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const mpreal& a, const double b)
+{
+	return a<=mpreal(b);
+}
+
+inline bool operator <=  (const unsigned long int a,const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator <=  (const unsigned int a,		const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator <=  (const long int a,			const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator <=  (const int a,				const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator <=  (const long double a,		const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator <=  (const double a,			const mpreal& b)
+{
+	return mpreal(a)<=b;
+}
+
+inline bool operator == (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_equal_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator ==  (const mpreal& a, const unsigned long int b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const mpreal& a, const unsigned int b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const mpreal& a, const long int b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const mpreal& a, const int b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const mpreal& a, const long double b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const mpreal& a, const double b)
+{
+	return a==mpreal(b);
+}
+
+inline bool operator ==  (const unsigned long int a,const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator ==  (const unsigned int a,		const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator ==  (const long int a,			const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator ==  (const int a,				const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator ==  (const long double a,		const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator ==  (const double a,			const mpreal& b)
+{
+	return mpreal(a)==b;
+}
+
+inline bool operator != (const mpreal& a, const mpreal& b)
+{
+	return (mpfr_lessgreater_p(a.mp,b.mp)!=0);
+}
+
+inline bool operator !=  (const mpreal& a, const unsigned long int b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const mpreal& a, const unsigned int b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const mpreal& a, const long int b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const mpreal& a, const int b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const mpreal& a, const long double b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const mpreal& a, const double b)
+{
+	return a!=mpreal(b);
+}
+
+inline bool operator !=  (const unsigned long int a,const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool operator !=  (const unsigned int a,		const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool operator !=  (const long int a,			const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool operator !=  (const int a,				const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool operator !=  (const long double a,		const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool operator !=  (const double a,			const mpreal& b)
+{
+	return mpreal(a)!=b;
+}
+
+inline bool _isnan(const mpreal& v)
+{
+	return (mpfr_nan_p(v.mp)!=0);
+}
+
+inline bool _isinf(const mpreal& v)
+{
+	return (mpfr_inf_p(v.mp)!=0);
+}
+
+inline bool _isnum(const mpreal& v)
+{
+	return (mpfr_number_p(v.mp)!=0);
+}
+
+inline bool _iszero(const mpreal& v)
+{
+	return (mpfr_zero_p(v.mp)!=0);
+}
+
+inline bool _isint(const mpreal& v)
+{
+	return (mpfr_integer_p(v.mp)!=0);
+}
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+inline bool _isregular(const mpreal& v)
+{
+	return (mpfr_regular_p(v.mp));
+}
+#endif // MPFR 3.0.0 Specifics
+
+//////////////////////////////////////////////////////////////////////////
+// Type Converters
+inline mpreal::operator double() const
+{
+	return mpfr_get_d(mp,default_rnd);
+}
+
+inline mpreal::operator float() const
+{
+	return (float)mpfr_get_d(mp,default_rnd);
+}
+
+inline mpreal::operator long double() const
+{
+	return mpfr_get_ld(mp,default_rnd);
+}
+
+inline mpreal::operator unsigned long() const
+{
+	return mpfr_get_ui(mp,default_rnd);	
+}
+
+inline mpreal::operator unsigned int() const
+{
+	return static_cast<unsigned int>(mpfr_get_ui(mp,default_rnd));	
+}
+
+inline mpreal::operator long() const
+{
+	return mpfr_get_si(mp,default_rnd);	
+}
+
+inline mpreal::operator mpfr_ptr()
+{
+	return mp;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Set/Get number properties
+inline int sgn(const mpreal& v)
+{
+	int r = mpfr_signbit(v.mp);
+	return (r>0?-1:1);
+}
+
+inline void mpreal::set_sign(int sign, mp_rnd_t rnd_mode)
+{
+	mpfr_setsign(mp,mp,(sign<0?1:0),rnd_mode);
+}
+
+inline mp_prec_t mpreal::get_prec() const
+{
+	return mpfr_get_prec(mp);
+}
+
+inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpfr_prec_round(mp,prec,rnd_mode);
+}
+
+inline void mpreal::set_inf(int sign) 
+{ 
+	mpfr_set_inf(mp,sign);
+}	
+
+inline void mpreal::set_nan() 
+{
+	mpfr_set_nan(mp);
+}
+
+inline mp_exp_t mpreal::get_exp ()
+{
+	return mpfr_get_exp(mp);
+}
+
+inline int mpreal::set_exp (mp_exp_t e)
+{
+	return mpfr_set_exp(mp,e);
+}
+
+inline const mpreal frexp(const mpreal& v, mp_exp_t* exp)
+{
+	mpreal x(v);
+	*exp = x.get_exp();
+	x.set_exp(0);
+	return x;
+}
+
+inline const mpreal ldexp(const mpreal& v, mp_exp_t exp)
+{
+	mpreal x(v);
+
+	// rounding is not important since we just increasing the exponent
+	mpfr_mul_2si(x.mp,x.mp,exp,mpreal::default_rnd); 
+	return x;
+}
+
+inline const mpreal machine_epsilon(mp_prec_t prec)
+{
+	// smallest eps such that 1.0+eps != 1.0
+	// depends (of cause) on the precision
+	mpreal x(1,prec); 
+	return nextabove(x)-x;
+}
+
+inline const mpreal mpreal_min(mp_prec_t prec)
+{
+	// min = 1/2*2^emin = 2^(emin-1)
+	
+	mpreal x(1,prec);
+	return x <<= mpreal::get_emin()-1;
+}
+
+inline const mpreal mpreal_max(mp_prec_t prec)
+{
+	// max = (1-eps)*2^emax, assume eps = 0?, 
+	// and use emax-1 to prevent value to be +inf
+	// max = 2^(emax-1)
+
+	mpreal x(1,prec);
+	return x <<= mpreal::get_emax()-1;
+}
+
+inline const mpreal modf(const mpreal& v, mpreal& n)
+{
+	mpreal frac(v);
+
+	// rounding is not important since we are using the same number
+	mpfr_frac(frac.mp,frac.mp,mpreal::default_rnd);	
+	mpfr_trunc(n.mp,v.mp);
+	return frac;
+}
+
+inline int mpreal::check_range (int t, mp_rnd_t rnd_mode)
+{
+	return mpfr_check_range(mp,t,rnd_mode);
+}
+
+inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode)
+{
+	return mpfr_subnormalize(mp,t,rnd_mode);
+}
+
+inline mp_exp_t mpreal::get_emin (void)
+{
+	return mpfr_get_emin();
+}
+
+inline int mpreal::set_emin (mp_exp_t exp)
+{
+	return mpfr_set_emin(exp);
+}
+
+inline mp_exp_t mpreal::get_emax (void)
+{
+	return mpfr_get_emax();
+}
+
+inline int mpreal::set_emax (mp_exp_t exp)
+{
+	return mpfr_set_emax(exp);
+}
+
+inline mp_exp_t mpreal::get_emin_min (void)
+{
+	return mpfr_get_emin_min();
+}
+
+inline mp_exp_t mpreal::get_emin_max (void)
+{
+	return mpfr_get_emin_max();
+}
+
+inline mp_exp_t mpreal::get_emax_min (void)
+{
+	return mpfr_get_emax_min();
+}
+
+inline mp_exp_t mpreal::get_emax_max (void)
+{
+	return mpfr_get_emax_max();
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Mathematical Functions
+//////////////////////////////////////////////////////////////////////////
+inline const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sqr(x.mp,x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sqrt(x.mp,x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	mpfr_sqrt_ui(x.mp,v,rnd_mode);
+	return x;
+}
+
+inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode)
+{
+	return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+}
+
+inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode)
+{
+	if (v>=0)	return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+	else		return mpreal(); // NaN  
+}
+
+inline const mpreal sqrt(const int v, mp_rnd_t rnd_mode)
+{
+	if (v>=0)	return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+	else		return mpreal(); // NaN
+}
+
+inline const mpreal sqrt(const long double v, mp_rnd_t rnd_mode)
+{
+	return sqrt(mpreal(v),rnd_mode);
+}
+
+inline const mpreal sqrt(const double v, mp_rnd_t rnd_mode)
+{
+	return sqrt(mpreal(v),rnd_mode);
+}
+
+inline const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_cbrt(x.mp,x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_root(x.mp,x.mp,k,rnd_mode);
+	return x;
+}
+
+inline const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_abs(x.mp,x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_abs(x.mp,x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_dim(x.mp,a.mp,b.mp,rnd_mode);
+	return x;
+}
+
+inline int cmpabs(const mpreal& a,const mpreal& b)
+{
+	return mpfr_cmpabs(a.mp,b.mp);
+}
+
+inline const mpreal log  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_log(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal log2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_log2(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_log10(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal exp(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_exp(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal exp2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_exp2(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_exp10(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_cos(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sin(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_tan(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sec(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_csc(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_cot(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
+{
+	return mpfr_sin_cos(s.mp,c.mp,v.mp,rnd_mode);
+}
+
+inline const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_acos(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_asin(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_atan(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode)
+{
+	mpreal a;
+	mp_prec_t yp, xp;
+
+	yp = y.get_prec(); 
+	xp = x.get_prec(); 
+
+	a.set_prec(yp>xp?yp:xp);
+
+	mpfr_atan2(a.mp, y.mp, x.mp, rnd_mode);
+
+	return a;
+}
+
+inline const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_cosh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sinh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_tanh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_sech(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_csch(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_coth(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal acosh  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_acosh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal asinh  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_asinh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal atanh  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_atanh(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	mpfr_fac_ui(x.mp,v,rnd_mode);
+	return x;
+}
+
+inline const mpreal log1p  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_log1p(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal expm1  (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_expm1(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal eint   (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_eint(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_gamma(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_lngamma(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_lgamma(x.mp,signp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_zeta(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_erf(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_erfc(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_j0(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_j1(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_jn(x.mp,n,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_y0(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_y1(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_yn(x.mp,n,v.mp,rnd_mode);
+	return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// MPFR 2.4.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+
+inline int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
+{
+	return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode);
+}
+
+inline const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_li2(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+	mpreal a;
+	mp_prec_t yp, xp;
+
+	yp = y.get_prec(); 
+	xp = x.get_prec(); 
+
+	a.set_prec(yp>xp?yp:xp);
+
+	mpfr_fmod(a.mp, x.mp, y.mp, rnd_mode);
+
+	return a;
+}
+
+inline const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rec_sqrt(x.mp,v.mp,rnd_mode);
+	return x;
+}
+#endif //  MPFR 2.4.0 Specifics
+
+//////////////////////////////////////////////////////////////////////////
+// MPFR 3.0.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+inline const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_digamma(x.mp,v.mp,rnd_mode);
+	return x;
+}
+#endif // MPFR 3.0.0 Specifics
+
+//////////////////////////////////////////////////////////////////////////
+// Constants
+inline const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	x.set_prec(prec);
+	mpfr_const_log2(x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	x.set_prec(prec);
+	mpfr_const_pi(x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	x.set_prec(prec);
+	mpfr_const_euler(x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	x.set_prec(prec);
+	mpfr_const_catalan(x.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal const_infinity (int sign, mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	x.set_prec(prec,rnd_mode);
+	mpfr_set_inf(x.mp, sign);
+	return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Integer Related Functions
+inline const mpreal rint(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rint(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal ceil(const mpreal& v)
+{
+	mpreal x(v);
+	mpfr_ceil(x.mp,v.mp);
+	return x;
+
+}
+
+inline const mpreal floor(const mpreal& v)
+{
+	mpreal x(v);
+	mpfr_floor(x.mp,v.mp);
+	return x;
+}
+
+inline const mpreal round(const mpreal& v)
+{
+	mpreal x(v);
+	mpfr_round(x.mp,v.mp);
+	return x;
+}
+
+inline const mpreal trunc(const mpreal& v)
+{
+	mpreal x(v);
+	mpfr_trunc(x.mp,v.mp);
+	return x;
+}
+
+inline const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rint_ceil(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rint_floor(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rint_round(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_rint_trunc(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode)
+{
+	mpreal x(v);
+	mpfr_frac(x.mp,v.mp,rnd_mode);
+	return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Miscellaneous Functions
+inline void swap(mpreal& a, mpreal& b) 
+{
+	mpfr_swap(a.mp,b.mp);
+}
+
+#ifndef max
+inline const mpreal max(const mpreal& x, const mpreal& y)
+{
+	return (x>y?x:y);
+}
+#endif
+
+#ifndef min
+inline const mpreal min(const mpreal& x, const mpreal& y)
+{
+	return (x<y?x:y);
+}
+#endif
+
+inline const mpreal nexttoward (const mpreal& x, const mpreal& y)
+{
+	mpreal a(x);
+	mpfr_nexttoward(a.mp,y.mp);
+	return a;
+}
+
+inline const mpreal nextabove  (const mpreal& x)
+{
+	mpreal a(x);
+	mpfr_nextabove(a.mp);
+	return a;
+}
+
+inline const mpreal nextbelow  (const mpreal& x)
+{
+	mpreal a(x);
+	mpfr_nextbelow(a.mp);
+	return a;
+}
+
+inline const mpreal urandomb (gmp_randstate_t& state)
+{
+	mpreal x;
+	mpfr_urandomb(x.mp,state);
+	return x;
+}
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+// use gmp_randinit_default() to init state, gmp_randclear() to clear
+inline const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode)
+{
+	mpreal x;
+	mpfr_urandom(x.mp,state,rnd_mode);
+	return x;
+}
+#endif 
+
+#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))
+inline const mpreal random2 (mp_size_t size, mp_exp_t exp)
+{
+	mpreal x;
+	mpfr_random2(x.mp,size,exp);
+	return x;
+}
+#endif
+
+//////////////////////////////////////////////////////////////////////////
+// Set/Get global properties
+inline void mpreal::set_default_prec(mp_prec_t prec)
+{ 
+	default_prec = prec;
+	mpfr_set_default_prec(prec); 
+}
+
+inline mp_prec_t mpreal::get_default_prec()
+{ 
+	return mpfr_get_default_prec();
+}
+
+inline void mpreal::set_default_base(int base)
+{ 
+	default_base = base;
+}
+
+inline int mpreal::get_default_base()
+{ 
+	return default_base;
+}
+
+inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode)
+{ 
+	default_rnd =  rnd_mode;
+	mpfr_set_default_rounding_mode(rnd_mode); 
+}
+
+inline mp_rnd_t mpreal::get_default_rnd()
+{ 
+	return mpfr_get_default_rounding_mode();
+}
+
+inline void mpreal::set_double_bits(int dbits)
+{ 
+	double_bits = dbits;
+}
+
+inline int mpreal::get_double_bits()
+{ 
+	return double_bits;
+}
+
+inline bool mpreal::fits_in_bits(double x, int n)
+{   
+	int i;
+	double t;
+	return IsInf(x) || (std::modf ( std::ldexp ( std::frexp ( x, &i ), n ), &t ) == 0.0);
+}
+
+inline const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_pow(x.mp,x.mp,b.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_pow_z(x.mp,x.mp,b,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_pow_ui(x.mp,x.mp,b,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	return pow(a,static_cast<unsigned long int>(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_pow_si(x.mp,x.mp,b,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode)
+{
+	return pow(a,static_cast<long int>(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode)
+{
+	return pow(a,mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode)
+{
+	return pow(a,mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_ui_pow(x.mp,a,b.mp,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+	else		return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+	else		return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode);
+}
+
+// pow unsigned long int
+inline const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	mpreal x(a);
+	mpfr_ui_pow_ui(x.mp,a,b,rnd_mode);
+	return x;
+}
+
+inline const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode)
+{
+	if(b>0)	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+	else	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode)
+{
+	if(b>0)	return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+	else	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode)
+{
+	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode)
+{
+	return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+// pow unsigned int
+inline const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode)
+{
+	if(b>0)	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+	else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode)
+{
+	if(b>0)	return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+	else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode)
+{
+	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode)
+{
+	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+// pow long int
+inline const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+	else	 return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui
+	else	 return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode)
+{
+	if (a>0)
+	{
+		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	}else{
+		return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+	}
+}
+
+inline const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode)
+{
+	if (a>0)
+	{
+		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	}else{
+		return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+	}
+}
+
+inline const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+inline const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+// pow int
+inline const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+	else	 return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui
+	else	 return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode)
+{
+	if (a>0)
+	{
+		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	}else{
+		return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+	}
+}
+
+inline const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode)
+{
+	if (a>0)
+	{
+		if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+		else	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	}else{
+		return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+	}
+}
+
+inline const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+inline const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode)
+{
+	if (a>=0) 	return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+	else		return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+// pow long double 
+inline const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_ui
+}
+
+inline const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); // mpfr_pow_ui
+}
+
+inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)
+{
+	return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+}
+}
+
+// Explicit specialization of std::swap for mpreal numbers
+// Thus standard algorithms will use efficient version of swap (due to Koenig lookup)
+// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap
+namespace std
+{
+	template <>
+	inline void swap(mpfr::mpreal& x, mpfr::mpreal& y) 
+	{ 
+		return mpfr::swap(x, y); 
+	}
+}
+
+#endif /* __MP_REAL_H__ */