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mpreal.h
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mpreal.h
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/*
MPFR C++: Multi-precision floating point number class for C++.
Based on MPFR library: http://mpfr.org
Project homepage: http://www.holoborodko.com/pavel/mpfr
Contact e-mail: [email protected]
Copyright (c) 2008-2014 Pavel Holoborodko
Contributors:
Dmitriy Gubanov, Konstantin Holoborodko, Brian Gladman,
Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen,
Pere Constans, Peter van Hoof, Gael Guennebaud, Tsai Chia Cheng,
Alexei Zubanov, Jauhien Piatlicki, Victor Berger, John Westwood,
Petr Aleksandrov, Orion Poplawski.
Licensing:
(A) MPFR C++ is under GNU General Public License ("GPL").
(B) Non-free licenses may also be purchased from the author, for users who
do not want their programs protected by the GPL.
The non-free licenses are for users that wish to use MPFR C++ in
their products but are unwilling to release their software
under the GPL (which would require them to release source code
and allow free redistribution).
Such users can purchase an unlimited-use license from the author.
Contact us for more details.
GNU General Public License ("GPL") copyright permissions statement:
**************************************************************************
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef __MPREAL_H__
#define __MPREAL_H__
#include <string>
#include <iostream>
#include <sstream>
#include <stdexcept>
#include <cfloat>
#include <cmath>
#include <cstring>
#include <limits>
// Options
#define MPREAL_HAVE_INT64_SUPPORT // Enable int64_t support if possible. Available only for MSVC 2010 & GCC.
#define MPREAL_HAVE_MSVC_DEBUGVIEW // Enable Debugger Visualizer for "Debug" builds in MSVC.
// 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(_MSC_VER) // Microsoft Visual C++
#define IsInf(x) (!_finite(x))
#else
#define IsInf(x) std::isinf(x) // GNU C/C++ (and/or other compilers), just hope for C99 conformance
#endif
// Detect support for r-value references (move semantic). Borrowed from Eigen.
// A Clang feature extension to determine compiler features.
// We use it to determine 'cxx_rvalue_references'
#ifndef __has_feature
# define __has_feature(x) 0
#endif
#if (__has_feature(cxx_rvalue_references) || \
defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L || \
(defined(_MSC_VER) && _MSC_VER >= 1600))
#define MPREAL_HAVE_MOVE_SUPPORT
// Use fields in mpfr_t structure to check if it was initialized / set dummy initialization
#define mpfr_is_initialized(x) (0 != (x)->_mpfr_d)
#define mpfr_set_uninitialized(x) ((x)->_mpfr_d = 0 )
#endif
// Detect available 64-bit capabilities
#if defined(MPREAL_HAVE_INT64_SUPPORT)
#define MPFR_USE_INTMAX_T // Should be defined before mpfr.h
#if defined(_MSC_VER) // MSVC + Windows
#if (_MSC_VER >= 1600)
#include <stdint.h> // <stdint.h> is available only in msvc2010!
#else // MPFR relies on intmax_t which is available only in msvc2010
#undef MPREAL_HAVE_INT64_SUPPORT // Besides, MPFR & MPIR have to be compiled with msvc2010
#undef MPFR_USE_INTMAX_T // Since we cannot detect this, disable x64 by default
// Someone should change this manually if needed.
#endif
#elif defined (__GNUC__) && defined(__linux__)
#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__) || defined(__x86_64) || defined(__ia64) || defined(__itanium__) || defined(_M_IA64) || defined (__PPC64__)
#undef MPREAL_HAVE_INT64_SUPPORT // Remove all shaman dances for x64 builds since
#undef MPFR_USE_INTMAX_T // GCC already supports x64 as of "long int" is 64-bit integer, nothing left to do
#else
#include <stdint.h> // use int64_t, uint64_t otherwise
#endif
#else
#include <stdint.h> // rely on int64_t, uint64_t in all other cases, Mac OSX, etc.
#endif
#endif
#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG)
#define MPREAL_MSVC_DEBUGVIEW_CODE DebugView = toString();
#define MPREAL_MSVC_DEBUGVIEW_DATA std::string DebugView;
#else
#define MPREAL_MSVC_DEBUGVIEW_CODE
#define MPREAL_MSVC_DEBUGVIEW_DATA
#endif
#include <mpfr.h>
#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0))
#include <cstdlib> // Needed for random()
#endif
// Less important options
#define MPREAL_DOUBLE_BITS_OVERFLOW -1 // Triggers overflow exception during conversion to double if mpreal
// cannot fit in MPREAL_DOUBLE_BITS_OVERFLOW bits
// = -1 disables overflow checks (default)
#if defined(__GNUC__)
#define MPREAL_PERMISSIVE_EXPR __extension__
#else
#define MPREAL_PERMISSIVE_EXPR
#endif
namespace mpfr {
class mpreal {
private:
mpfr_t mp;
public:
// Get default rounding mode & precision
inline static mp_rnd_t get_default_rnd() { return (mp_rnd_t)(mpfr_get_default_rounding_mode()); }
inline static mp_prec_t get_default_prec() { return mpfr_get_default_prec(); }
// Constructors && type conversions
mpreal();
mpreal(const mpreal& u);
mpreal(const mpf_t u);
mpreal(const mpz_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const mpq_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const long double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const unsigned long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const unsigned int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
// Construct mpreal from mpfr_t structure.
// shared = true allows to avoid deep copy, so that mpreal and 'u' share the same data & pointers.
mpreal(const mpfr_t u, bool shared = false);
#if defined (MPREAL_HAVE_INT64_SUPPORT)
mpreal(const uint64_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const int64_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());
#endif
mpreal(const char* s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd());
mpreal(const std::string& s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd());
~mpreal();
#ifdef MPREAL_HAVE_MOVE_SUPPORT
mpreal& operator=(mpreal&& v);
mpreal(mpreal&& u);
#endif
// 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 std::string& 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);
#if defined (MPREAL_HAVE_INT64_SUPPORT)
mpreal& operator+=(const int64_t u);
mpreal& operator+=(const uint64_t u);
mpreal& operator-=(const int64_t u);
mpreal& operator-=(const uint64_t u);
mpreal& operator*=(const int64_t u);
mpreal& operator*=(const uint64_t u);
mpreal& operator/=(const int64_t u);
mpreal& operator/=(const uint64_t u);
#endif
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);
// Optimized specializations for boolean operators
friend bool operator == (const mpreal& a, const unsigned long int b);
friend bool operator == (const mpreal& a, const unsigned int b);
friend bool operator == (const mpreal& a, const long int b);
friend bool operator == (const mpreal& a, const int b);
friend bool operator == (const mpreal& a, const long double b);
friend bool operator == (const mpreal& a, const double b);
// Type Conversion operators
long toLong (mp_rnd_t mode = GMP_RNDZ) const;
unsigned long toULong (mp_rnd_t mode = GMP_RNDZ) const;
double toDouble (mp_rnd_t mode = GMP_RNDN) const;
long double toLDouble (mp_rnd_t mode = GMP_RNDN) const;
#if defined (MPREAL_HAVE_INT64_SUPPORT)
int64_t toInt64 (mp_rnd_t mode = GMP_RNDZ) const;
uint64_t toUInt64 (mp_rnd_t mode = GMP_RNDZ) const;
#endif
// Get raw pointers so that mpreal can be directly used in raw mpfr_* functions
::mpfr_ptr mpfr_ptr();
::mpfr_srcptr mpfr_ptr() const;
::mpfr_srcptr mpfr_srcptr() const;
// Convert mpreal to string with n significant digits in base b
// n = 0 -> convert with the maximum available digits
std::string toString(int n = 0, int b = 10, mp_rnd_t mode = mpreal::get_default_rnd()) const;
#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
std::string toString(const std::string& format) const;
#endif
// Math Functions
friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode);
friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);
friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode);
friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode);
friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode);
friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode);
friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode);
friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode);
friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode);
friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);
friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode);
friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);
friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode);
friend int cmpabs(const mpreal& a,const mpreal& b);
friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode);
friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode);
friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec, mp_rnd_t rnd_mode);
friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode);
friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode);
friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode);
friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode);
friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode);
friend int sgn(const mpreal& v); // returns -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);
friend const mpreal li2 (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
friend const mpreal rec_sqrt (const mpreal& v, mp_rnd_t rnd_mode);
// MATLAB's semantic equivalents
friend const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Remainder after division
friend const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Modulus after division
#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);
friend const mpreal ai (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear
friend const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear
friend const mpreal grandom (unsigned int seed);
#endif
// Uniformly distributed random number generation in [0,1] using
// Mersenne-Twister algorithm by default.
// Use parameter to setup seed, e.g.: random((unsigned)time(NULL))
// Check urandom() for more precise control.
friend const mpreal random(unsigned int seed);
// 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, mp_rnd_t rnd_mode);
friend const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode);
friend const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode);
friend const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode);
// returns +inf iff sign>=0 otherwise -inf
friend const mpreal const_infinity(int sign, mp_prec_t prec, mp_rnd_t rnd_mode);
// 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);
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);
friend const mpreal rint_floor (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal rint_round (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal rint_trunc (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode);
friend const mpreal remainder ( const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
// 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 isfinite (const mpreal& v);
friend bool isnum (const mpreal& v);
friend bool iszero (const mpreal& v);
friend bool isint (const mpreal& v);
#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
friend bool isregular(const mpreal& v);
#endif
// Set/Get instance properties
inline mp_prec_t get_prec() const;
inline void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = get_default_rnd()); // Change precision with rounding mode
// Aliases for get_prec(), set_prec() - needed for compatibility with std::complex<mpreal> interface
inline mpreal& setPrecision(int Precision, mp_rnd_t RoundingMode = get_default_rnd());
inline int getPrecision() const;
// Set mpreal to +/- inf, NaN, +/-0
mpreal& setInf (int Sign = +1);
mpreal& setNan ();
mpreal& setZero (int Sign = +1);
mpreal& setSign (int Sign, mp_rnd_t RoundingMode = get_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 = get_default_rnd());
int subnormalize (int t,mp_rnd_t rnd_mode = get_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 void set_default_rnd(mp_rnd_t rnd_mode);
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);
// Efficient swapping of two mpreal values - needed for std algorithms
friend void swap(mpreal& x, mpreal& y);
friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);
private:
// Human friendly Debug Preview in Visual Studio.
// Put one of these lines:
//
// mpfr::mpreal=<DebugView> ; Show value only
// mpfr::mpreal=<DebugView>, <mp[0]._mpfr_prec,u>bits ; Show value & precision
//
// at the beginning of
// [Visual Studio Installation Folder]\Common7\Packages\Debugger\autoexp.dat
MPREAL_MSVC_DEBUGVIEW_DATA
// "Smart" resources deallocation. Checks if instance initialized before deletion.
void clear(::mpfr_ptr);
};
//////////////////////////////////////////////////////////////////////////
// Exceptions
class conversion_overflow : public std::exception {
public:
std::string why() { return "inexact conversion from floating point"; }
};
//////////////////////////////////////////////////////////////////////////
// Constructors & converters
// Default constructor: creates mp number and initializes it to 0.
inline mpreal::mpreal()
{
mpfr_init2(mp,mpreal::get_default_prec());
mpfr_set_ui(mp,0,mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const mpreal& u)
{
mpfr_init2(mp,mpfr_get_prec(u.mp));
mpfr_set(mp,u.mp,mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
}
#ifdef MPREAL_HAVE_MOVE_SUPPORT
inline mpreal::mpreal(mpreal&& other)
{
mpfr_set_uninitialized(mpfr_ptr()); // make sure "other" holds no pinter to actual data
mpfr_swap(mpfr_ptr(), other.mpfr_ptr());
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal& mpreal::operator=(mpreal&& other)
{
mpfr_swap(mpfr_ptr(), other.mpfr_ptr());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
#endif
inline mpreal::mpreal(const mpfr_t u, bool shared)
{
if(shared)
{
std::memcpy(mp, u, sizeof(mpfr_t));
}
else
{
mpfr_init2(mp, mpfr_get_prec(u));
mpfr_set (mp, u, mpreal::get_default_rnd());
}
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const mpf_t u)
{
mpfr_init2(mp,(mp_prec_t) mpf_get_prec(u)); // (gmp: mp_bitcnt_t) unsigned long -> long (mpfr: mp_prec_t)
mpfr_set_f(mp,u,mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const mpz_t u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_z(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const mpq_t u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_q(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const double u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp, prec);
#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1)
if(fits_in_bits(u, MPREAL_DOUBLE_BITS_OVERFLOW))
{
mpfr_set_d(mp, u, mode);
}else
throw conversion_overflow();
#else
mpfr_set_d(mp, u, mode);
#endif
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const long double u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_ld(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const unsigned long int u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_ui(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const unsigned int u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_ui(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const long int u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_si(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const int u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_si(mp,u,mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
#if defined (MPREAL_HAVE_INT64_SUPPORT)
inline mpreal::mpreal(const uint64_t u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_uj(mp, u, mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const int64_t u, mp_prec_t prec, mp_rnd_t mode)
{
mpfr_init2(mp,prec);
mpfr_set_sj(mp, u, mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
#endif
inline mpreal::mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode)
{
mpfr_init2(mp, prec);
mpfr_set_str(mp, s, base, mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline mpreal::mpreal(const std::string& s, mp_prec_t prec, int base, mp_rnd_t mode)
{
mpfr_init2(mp, prec);
mpfr_set_str(mp, s.c_str(), base, mode);
MPREAL_MSVC_DEBUGVIEW_CODE;
}
inline void mpreal::clear(::mpfr_ptr x)
{
#ifdef MPREAL_HAVE_MOVE_SUPPORT
if(mpfr_is_initialized(x))
#endif
mpfr_clear(x);
}
inline mpreal::~mpreal()
{
clear(mpfr_ptr());
}
// internal namespace needed for template magic
namespace internal{
// Use SFINAE to restrict arithmetic operations instantiation only for numeric types
// This is needed for smooth integration with libraries based on expression templates, like Eigen.
// TODO: Do the same for boolean operators.
template <typename ArgumentType> struct result_type {};
template <> struct result_type<mpreal> {typedef mpreal type;};
template <> struct result_type<mpz_t> {typedef mpreal type;};
template <> struct result_type<mpq_t> {typedef mpreal type;};
template <> struct result_type<long double> {typedef mpreal type;};
template <> struct result_type<double> {typedef mpreal type;};
template <> struct result_type<unsigned long int> {typedef mpreal type;};
template <> struct result_type<unsigned int> {typedef mpreal type;};
template <> struct result_type<long int> {typedef mpreal type;};
template <> struct result_type<int> {typedef mpreal type;};
#if defined (MPREAL_HAVE_INT64_SUPPORT)
template <> struct result_type<int64_t > {typedef mpreal type;};
template <> struct result_type<uint64_t > {typedef mpreal type;};
#endif
}
// + Addition
template <typename Rhs>
inline const typename internal::result_type<Rhs>::type
operator+(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) += rhs; }
template <typename Lhs>
inline const typename internal::result_type<Lhs>::type
operator+(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) += lhs; }
// - Subtraction
template <typename Rhs>
inline const typename internal::result_type<Rhs>::type
operator-(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) -= rhs; }
template <typename Lhs>
inline const typename internal::result_type<Lhs>::type
operator-(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) -= rhs; }
// * Multiplication
template <typename Rhs>
inline const typename internal::result_type<Rhs>::type
operator*(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) *= rhs; }
template <typename Lhs>
inline const typename internal::result_type<Lhs>::type
operator*(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) *= lhs; }
// / Division
template <typename Rhs>
inline const typename internal::result_type<Rhs>::type
operator/(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) /= rhs; }
template <typename Lhs>
inline const typename internal::result_type<Lhs>::type
operator/(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) /= rhs; }
//////////////////////////////////////////////////////////////////////////
// sqrt
const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
// abs
inline const mpreal abs(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd());
//////////////////////////////////////////////////////////////////////////
// pow
const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());
//////////////////////////////////////////////////////////////////////////
// Estimate machine epsilon for the given precision
// Returns smallest eps such that 1.0 + eps != 1.0
inline mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec());
// Returns smallest eps such that x + eps != x (relative machine epsilon)
inline mpreal machine_epsilon(const mpreal& x);
// Gives max & min values for the required precision,
// minval is 'safe' meaning 1 / minval does not overflow
// maxval is 'safe' meaning 1 / maxval does not underflow
inline mpreal minval(mp_prec_t prec = mpreal::get_default_prec());
inline mpreal maxval(mp_prec_t prec = mpreal::get_default_prec());
// 'Dirty' equality check 1: |a-b| < min{|a|,|b|} * eps
inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps);
// 'Dirty' equality check 2: |a-b| < min{|a|,|b|} * eps( min{|a|,|b|} )
inline bool isEqualFuzzy(const mpreal& a, const mpreal& b);
// 'Bitwise' equality check
// maxUlps - a and b can be apart by maxUlps binary numbers.
inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps);
//////////////////////////////////////////////////////////////////////////
// Convert precision in 'bits' to decimal digits and vice versa.
// bits = ceil(digits*log[2](10))
// digits = floor(bits*log[10](2))
inline mp_prec_t digits2bits(int d);
inline int bits2digits(mp_prec_t b);
//////////////////////////////////////////////////////////////////////////
// min, max
const mpreal (max)(const mpreal& x, const mpreal& y);
const mpreal (min)(const mpreal& x, const mpreal& y);
//////////////////////////////////////////////////////////////////////////
// Implementation
//////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////
// Operators - Assignment
inline mpreal& mpreal::operator=(const mpreal& v)
{
if (this != &v)
{
mp_prec_t tp = mpfr_get_prec(mp);
mp_prec_t vp = mpfr_get_prec(v.mp);
if(tp != vp){
clear(mpfr_ptr());
mpfr_init2(mpfr_ptr(), vp);
}
mpfr_set(mp, v.mp, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
}
return *this;
}
inline mpreal& mpreal::operator=(const mpf_t v)
{
mpfr_set_f(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const mpz_t v)
{
mpfr_set_z(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const mpq_t v)
{
mpfr_set_q(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const long double v)
{
mpfr_set_ld(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const double v)
{
#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1)
if(fits_in_bits(v, MPREAL_DOUBLE_BITS_OVERFLOW))
{
mpfr_set_d(mp,v,mpreal::get_default_rnd());
}else
throw conversion_overflow();
#else
mpfr_set_d(mp,v,mpreal::get_default_rnd());
#endif
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const unsigned long int v)
{
mpfr_set_ui(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;
return *this;
}
inline mpreal& mpreal::operator=(const unsigned int v)
{
mpfr_set_ui(mp, v, mpreal::get_default_rnd());
MPREAL_MSVC_DEBUGVIEW_CODE;