diff options
| author |  Gael Guennebaud <g.gael@free.fr> | 2011-08-19 15:08:29 +0200 |
|---|---|---|
| committer | Gael Guennebaud <g.gael@free.fr> | 2011-08-19 15:08:29 +0200 |
| commit | ea4a1960f0cfd64ecccda5f52a6c43ede1e6c271 (patch) | |
| tree | 7d1ee46d4e522b15156cf0826604ed4328a47414 /unsupported/test/mpreal/mpreal.h | |
| parent | 79ad55a901434066e31523fcb47ce80cbc6897d5 (diff) | |
mv the mpreal copy in its own folder
Diffstat (limited to 'unsupported/test/mpreal/mpreal.h')
| -rw-r--r-- | unsupported/test/mpreal/mpreal.h | 3215 |
1 files changed, 3215 insertions, 0 deletions
diff --git a/unsupported/test/mpreal/mpreal.h b/unsupported/test/mpreal/mpreal.h new file mode 100644 index 000000000..96f474640 --- /dev/null +++ b/unsupported/test/mpreal/mpreal.h @@ -0,0 +1,3215 @@ +/*
+ Multi-precision real number class. C++ interface fo MPFR library.
+ Project homepage: http://www.holoborodko.com/pavel/
+ Contact e-mail: pavel@holoborodko.com
+
+ Copyright (c) 2008-2010 Pavel Holoborodko
+
+ Core Developers:
+ Pavel Holoborodko, Dmitriy Gubanov, Konstantin Holoborodko.
+
+ Contributors:
+ Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze,
+ Heinz van Saanen, Pere Constans, Peter van Hoof.
+
+ ****************************************************************************
+ 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
+
+ ****************************************************************************
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ 3. Redistributions of any form whatsoever must retain the following
+ acknowledgment:
+ "
+ This product includes software developed by Pavel Holoborodko
+ Web: http://www.holoborodko.com/pavel/
+ e-mail: pavel@holoborodko.com
+ "
+
+ 4. This software cannot be, by any means, used for any commercial
+ purpose without the prior permission of the copyright holder.
+
+ Any of the above conditions can be waived if you get permission from
+ the copyright holder.
+
+ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ SUCH DAMAGE.
+*/
+
+#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) // Intel ICC compiler on Linux
+
+#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) // Unknown compiler, just hope for 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(const std::string& 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;
+ inline operator int() 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 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 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 hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::default_prec, 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 = 0, 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 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 ai(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
+
+ friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);
+ friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);
+
+private:
+ // Optimized dynamic memory allocation/(re-)deallocation.
+ static bool is_custom_malloc;
+ static void *mpreal_allocate (size_t alloc_size);
+ static void *mpreal_reallocate (void *ptr, size_t old_size, size_t new_size);
+ static void mpreal_free (void *ptr, size_t size);
+ inline static void set_custom_malloc (void);
+};
+
+//////////////////////////////////////////////////////////////////////////
+// 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 = mpreal::default_prec);
+inline const mpreal mpreal_min(mp_prec_t prec = mpreal::default_prec);
+inline const mpreal mpreal_max(mp_prec_t prec = mpreal::default_prec);
+
+//////////////////////////////////////////////////////////////////////////
+// Implementation of inline functions
+//////////////////////////////////////////////////////////////////////////
+
+//////////////////////////////////////////////////////////////////////////
+// Operators - Assignment
+inline mpreal& mpreal::operator=(const mpreal& v)
+{
+ if (this!= &v)
+ {
+ mpfr_set_prec(mp,mpfr_get_prec(v.mp));
+ 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,GMP_RNDZ);
+}
+
+inline mpreal::operator unsigned int() const
+{
+ return static_cast<unsigned int>(mpfr_get_ui(mp,GMP_RNDZ));
+}
+
+inline mpreal::operator long() const
+{
+ return mpfr_get_si(mp,GMP_RNDZ);
+}
+
+inline mpreal::operator int() const
+{
+ return static_cast<int>(mpfr_get_si(mp,GMP_RNDZ));
+}
+
+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)
+{
+ // the 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_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x(0,prec);
+ 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);
+ int tsignp;
+
+ if(signp)
+ mpfr_lgamma(x.mp,signp,v.mp,rnd_mode);
+ else
+ mpfr_lgamma(x.mp,&tsignp,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;
+}
+
+inline const mpreal ai(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_ai(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);
+}
+
+
+inline const mpreal (max)(const mpreal& x, const mpreal& y)
+{
+ return (x>y?x:y);
+}
+
+inline const mpreal (min)(const mpreal& x, const mpreal& y)
+{
+ return (x<y?x:y);
+}
+
+inline const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mpfr_max(a.mp,x.mp,y.mp,rnd_mode);
+ return a;
+}
+
+inline const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mpfr_min(a.mp,x.mp,y.mp,rnd_mode);
+ return a;
+}
+
+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__ */
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