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https://gitlab.com/libeigen/eigen.git
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2736 lines
81 KiB
C++
2736 lines
81 KiB
C++
/*
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Multi-precision real number class. C++ interface for MPFR library.
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Project homepage: http://www.holoborodko.com/pavel/
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Contact e-mail: pavel@holoborodko.com
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Copyright (c) 2008-2012 Pavel Holoborodko
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Core Developers:
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Pavel Holoborodko, Dmitriy Gubanov, Konstantin Holoborodko.
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Contributors:
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Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze,
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Heinz van Saanen, Pere Constans, Peter van Hoof, Gael Guennebaud,
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Tsai Chia Cheng, Alexei Zubanov.
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****************************************************************************
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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****************************************************************************
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The name of the author may be used to endorse or promote products
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derived from this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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SUCH DAMAGE.
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*/
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#ifndef __MPREAL_H__
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#define __MPREAL_H__
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#include <string>
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#include <iostream>
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#include <sstream>
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#include <stdexcept>
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#include <cfloat>
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#include <cmath>
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// Options
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#define MPREAL_HAVE_INT64_SUPPORT // int64_t support: available only for MSVC 2010 & GCC
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#define MPREAL_HAVE_MSVC_DEBUGVIEW // Enable Debugger Visualizer (valid only for MSVC in "Debug" builds)
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// Detect compiler using signatures from http://predef.sourceforge.net/
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#if defined(__GNUC__) && defined(__INTEL_COMPILER)
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#define IsInf(x) isinf(x) // Intel ICC compiler on Linux
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#elif defined(_MSC_VER) // Microsoft Visual C++
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#define IsInf(x) (!_finite(x))
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#elif defined(__GNUC__)
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#define IsInf(x) std::isinf(x) // GNU C/C++
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#else
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#define IsInf(x) std::isinf(x) // Unknown compiler, just hope for C99 conformance
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#endif
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#if defined(MPREAL_HAVE_INT64_SUPPORT)
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#define MPFR_USE_INTMAX_T // should be defined before mpfr.h
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#if defined(_MSC_VER) // <stdint.h> is available only in msvc2010!
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#if (_MSC_VER >= 1600)
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#include <stdint.h>
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#else // MPFR relies on intmax_t which is available only in msvc2010
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#undef MPREAL_HAVE_INT64_SUPPORT // Besides, MPFR - MPIR have to be compiled with msvc2010
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#undef MPFR_USE_INTMAX_T // Since we cannot detect this, disable x64 by default
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// Someone should change this manually if needed.
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#endif
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#endif
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#if defined (__MINGW32__) || defined(__MINGW64__)
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#include <stdint.h> // equivalent to msvc2010
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#elif defined (__GNUC__)
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#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__) || defined(__x86_64)
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#undef MPREAL_HAVE_INT64_SUPPORT // remove all shaman dances for x64 builds since
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#undef MPFR_USE_INTMAX_T // GCC already support x64 as of "long int" is 64-bit integer, nothing left to do
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#else
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#include <stdint.h> // use int64_t, uint64_t otherwise.
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#endif
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#endif
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#endif
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#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG)
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#define MPREAL_MSVC_DEBUGVIEW_CODE DebugView = toString()
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#define MPREAL_MSVC_DEBUGVIEW_DATA std::string DebugView
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#else
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#define MPREAL_MSVC_DEBUGVIEW_CODE
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#define MPREAL_MSVC_DEBUGVIEW_DATA
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#endif
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#include <mpfr.h>
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#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0))
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#include <cstdlib> // needed for random()
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#endif
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namespace mpfr {
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class mpreal {
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private:
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mpfr_t mp;
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public:
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static mp_rnd_t default_rnd;
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static mp_prec_t default_prec;
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static int default_base;
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static int double_bits;
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public:
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// Constructors && type conversion
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mpreal();
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mpreal(const mpreal& u);
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mpreal(const mpfr_t u);
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mpreal(const mpf_t u);
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mpreal(const mpz_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const mpq_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const long double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const unsigned long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const unsigned int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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#if defined (MPREAL_HAVE_INT64_SUPPORT)
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mpreal(const uint64_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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mpreal(const int64_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
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#endif
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mpreal(const char* s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
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mpreal(const std::string& s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
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~mpreal();
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// Operations
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// =
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// +, -, *, /, ++, --, <<, >>
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// *=, +=, -=, /=,
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// <, >, ==, <=, >=
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// =
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mpreal& operator=(const mpreal& v);
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mpreal& operator=(const mpf_t v);
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mpreal& operator=(const mpz_t v);
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mpreal& operator=(const mpq_t v);
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mpreal& operator=(const long double v);
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mpreal& operator=(const double v);
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mpreal& operator=(const unsigned long int v);
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mpreal& operator=(const unsigned int v);
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mpreal& operator=(const long int v);
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mpreal& operator=(const int v);
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mpreal& operator=(const char* s);
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// +
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mpreal& operator+=(const mpreal& v);
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mpreal& operator+=(const mpf_t v);
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mpreal& operator+=(const mpz_t v);
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mpreal& operator+=(const mpq_t v);
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mpreal& operator+=(const long double u);
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mpreal& operator+=(const double u);
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mpreal& operator+=(const unsigned long int u);
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mpreal& operator+=(const unsigned int u);
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mpreal& operator+=(const long int u);
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mpreal& operator+=(const int u);
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#if defined (MPREAL_HAVE_INT64_SUPPORT)
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mpreal& operator+=(const int64_t u);
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mpreal& operator+=(const uint64_t u);
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mpreal& operator-=(const int64_t u);
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mpreal& operator-=(const uint64_t u);
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mpreal& operator*=(const int64_t u);
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mpreal& operator*=(const uint64_t u);
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mpreal& operator/=(const int64_t u);
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mpreal& operator/=(const uint64_t u);
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#endif
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const mpreal operator+() const;
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mpreal& operator++ ();
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const mpreal operator++ (int);
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// -
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mpreal& operator-=(const mpreal& v);
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mpreal& operator-=(const mpz_t v);
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mpreal& operator-=(const mpq_t v);
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mpreal& operator-=(const long double u);
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mpreal& operator-=(const double u);
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mpreal& operator-=(const unsigned long int u);
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mpreal& operator-=(const unsigned int u);
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mpreal& operator-=(const long int u);
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mpreal& operator-=(const int u);
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const mpreal operator-() const;
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friend const mpreal operator-(const unsigned long int b, const mpreal& a);
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friend const mpreal operator-(const unsigned int b, const mpreal& a);
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friend const mpreal operator-(const long int b, const mpreal& a);
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friend const mpreal operator-(const int b, const mpreal& a);
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friend const mpreal operator-(const double b, const mpreal& a);
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mpreal& operator-- ();
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const mpreal operator-- (int);
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// *
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mpreal& operator*=(const mpreal& v);
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mpreal& operator*=(const mpz_t v);
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mpreal& operator*=(const mpq_t v);
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mpreal& operator*=(const long double v);
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mpreal& operator*=(const double v);
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mpreal& operator*=(const unsigned long int v);
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mpreal& operator*=(const unsigned int v);
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mpreal& operator*=(const long int v);
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mpreal& operator*=(const int v);
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// /
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mpreal& operator/=(const mpreal& v);
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mpreal& operator/=(const mpz_t v);
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mpreal& operator/=(const mpq_t v);
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mpreal& operator/=(const long double v);
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mpreal& operator/=(const double v);
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mpreal& operator/=(const unsigned long int v);
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mpreal& operator/=(const unsigned int v);
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mpreal& operator/=(const long int v);
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mpreal& operator/=(const int v);
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friend const mpreal operator/(const unsigned long int b, const mpreal& a);
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friend const mpreal operator/(const unsigned int b, const mpreal& a);
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friend const mpreal operator/(const long int b, const mpreal& a);
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friend const mpreal operator/(const int b, const mpreal& a);
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friend const mpreal operator/(const double b, const mpreal& a);
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//<<= Fast Multiplication by 2^u
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mpreal& operator<<=(const unsigned long int u);
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mpreal& operator<<=(const unsigned int u);
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mpreal& operator<<=(const long int u);
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mpreal& operator<<=(const int u);
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//>>= Fast Division by 2^u
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mpreal& operator>>=(const unsigned long int u);
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mpreal& operator>>=(const unsigned int u);
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mpreal& operator>>=(const long int u);
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mpreal& operator>>=(const int u);
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// Boolean Operators
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friend bool operator > (const mpreal& a, const mpreal& b);
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friend bool operator >= (const mpreal& a, const mpreal& b);
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friend bool operator < (const mpreal& a, const mpreal& b);
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friend bool operator <= (const mpreal& a, const mpreal& b);
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friend bool operator == (const mpreal& a, const mpreal& b);
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friend bool operator != (const mpreal& a, const mpreal& b);
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// Optimized specializations for boolean operators
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friend bool operator == (const mpreal& a, const unsigned long int b);
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friend bool operator == (const mpreal& a, const unsigned int b);
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friend bool operator == (const mpreal& a, const long int b);
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friend bool operator == (const mpreal& a, const int b);
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friend bool operator == (const mpreal& a, const long double b);
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friend bool operator == (const mpreal& a, const double b);
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// Type Conversion operators
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long toLong() const;
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unsigned long toULong() const;
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double toDouble() const;
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long double toLDouble() const;
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#if defined (MPREAL_HAVE_INT64_SUPPORT)
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int64_t toInt64() const;
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uint64_t toUInt64() const;
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#endif
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// Get raw pointers
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::mpfr_ptr mpfr_ptr();
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::mpfr_srcptr mpfr_srcptr() const;
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// Convert mpreal to string with n significant digits in base b
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// n = 0 -> convert with the maximum available digits
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std::string toString(int n = 0, int b = default_base, mp_rnd_t mode = default_rnd) const;
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#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
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std::string toString(const std::string& format) const;
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#endif
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// Math Functions
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friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend int cmpabs(const mpreal& a,const mpreal& b);
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friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
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friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
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|
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 besselj0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
|
|
friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
|
|
friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
|
|
friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
|
|
friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
|
|
friend const mpreal besselyn (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
|
|
|
|
// 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 = 0);
|
|
|
|
// 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 isfinite(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
|
|
|
|
// Aliases for get_prec(), set_prec() - needed for compatibility with std::complex<mpreal> interface
|
|
inline mpreal& setPrecision(int Precision, mp_rnd_t RoundingMode = (mpfr_get_default_rounding_mode)());
|
|
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 = (mpfr_get_default_rounding_mode)());
|
|
|
|
//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);
|
|
|
|
// 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
|
|
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);
|
|
|
|
#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
|
|
|
|
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);
|
|
|
|
#endif
|
|
|
|
|
|
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
|
|
};
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// Exceptions
|
|
class conversion_overflow : public std::exception {
|
|
public:
|
|
std::string why() { return "inexact conversion from floating point"; }
|
|
};
|
|
|
|
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
|
|
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::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
|
|
// Returns smallest eps such that 1.0 + eps != 1.0
|
|
inline const mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec());
|
|
|
|
// Returns the positive distance from abs(x) to the next larger in magnitude floating point number of the same precision as x
|
|
inline const mpreal machine_epsilon(const mpreal& x);
|
|
|
|
inline const mpreal mpreal_min(mp_prec_t prec = mpreal::get_default_prec());
|
|
inline const mpreal mpreal_max(mp_prec_t prec = mpreal::get_default_prec());
|
|
inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps);
|
|
inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps);
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// Bits - decimal digits relation
|
|
// 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)
|
|
{
|
|
mpfr_clear(mp);
|
|
mpfr_init2(mp,mpfr_get_prec(v.mp));
|
|
mpfr_set(mp,v.mp,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const mpf_t v)
|
|
{
|
|
mpfr_set_f(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const mpz_t v)
|
|
{
|
|
mpfr_set_z(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const mpq_t v)
|
|
{
|
|
mpfr_set_q(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const long double v)
|
|
{
|
|
mpfr_set_ld(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
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);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
}
|
|
else
|
|
throw conversion_overflow();
|
|
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const unsigned long int v)
|
|
{
|
|
mpfr_set_ui(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const unsigned int v)
|
|
{
|
|
mpfr_set_ui(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const long int v)
|
|
{
|
|
mpfr_set_si(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator=(const int v)
|
|
{
|
|
mpfr_set_si(mp,v,default_rnd);
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// + Addition
|
|
inline mpreal& mpreal::operator+=(const mpreal& v)
|
|
{
|
|
mpfr_add(mp,mp,v.mp,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const mpf_t u)
|
|
{
|
|
*this += mpreal(u);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const mpz_t u)
|
|
{
|
|
mpfr_add_z(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const mpq_t u)
|
|
{
|
|
mpfr_add_q(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+= (const long double u)
|
|
{
|
|
*this += mpreal(u);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+= (const double u)
|
|
{
|
|
#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
|
|
mpfr_add_d(mp,mp,u,default_rnd);
|
|
#else
|
|
*this += mpreal(u);
|
|
#endif
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const unsigned long int u)
|
|
{
|
|
mpfr_add_ui(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const unsigned int u)
|
|
{
|
|
mpfr_add_ui(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const long int u)
|
|
{
|
|
mpfr_add_si(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator+=(const int u)
|
|
{
|
|
mpfr_add_si(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
#if defined (MPREAL_HAVE_INT64_SUPPORT)
|
|
inline mpreal& mpreal::operator+=(const int64_t u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator+=(const uint64_t u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator-=(const int64_t u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator-=(const uint64_t u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator*=(const int64_t u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator*=(const uint64_t u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator/=(const int64_t u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
inline mpreal& mpreal::operator/=(const uint64_t u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
|
|
#endif
|
|
|
|
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 mpreal& mpreal::operator++()
|
|
{
|
|
return *this += 1;
|
|
}
|
|
|
|
inline const mpreal mpreal::operator++ (int)
|
|
{
|
|
mpreal x(*this);
|
|
*this += 1;
|
|
return x;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator--()
|
|
{
|
|
return *this -= 1;
|
|
}
|
|
|
|
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);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const mpz_t v)
|
|
{
|
|
mpfr_sub_z(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const mpq_t v)
|
|
{
|
|
mpfr_sub_q(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const long double v)
|
|
{
|
|
*this -= mpreal(v);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const double v)
|
|
{
|
|
#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
|
|
mpfr_sub_d(mp,mp,v,default_rnd);
|
|
#else
|
|
*this -= mpreal(v);
|
|
#endif
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const unsigned long int v)
|
|
{
|
|
mpfr_sub_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const unsigned int v)
|
|
{
|
|
mpfr_sub_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const long int v)
|
|
{
|
|
mpfr_sub_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator-=(const int v)
|
|
{
|
|
mpfr_sub_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
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.getPrecision() >= b.getPrecision())
|
|
{
|
|
return mpreal(a) -= b;
|
|
}else{
|
|
mpreal x(a);
|
|
x.setPrecision(b.getPrecision());
|
|
return x -= 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(b) -= a;
|
|
#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;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// * Multiplication
|
|
inline mpreal& mpreal::operator*= (const mpreal& v)
|
|
{
|
|
mpfr_mul(mp,mp,v.mp,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const mpz_t v)
|
|
{
|
|
mpfr_mul_z(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const mpq_t v)
|
|
{
|
|
mpfr_mul_q(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const long double v)
|
|
{
|
|
*this *= mpreal(v);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const double v)
|
|
{
|
|
#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
|
|
mpfr_mul_d(mp,mp,v,default_rnd);
|
|
#else
|
|
*this *= mpreal(v);
|
|
#endif
|
|
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const unsigned long int v)
|
|
{
|
|
mpfr_mul_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const unsigned int v)
|
|
{
|
|
mpfr_mul_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const long int v)
|
|
{
|
|
mpfr_mul_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator*=(const int v)
|
|
{
|
|
mpfr_mul_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline const mpreal operator*(const mpreal& a, const mpreal& b)
|
|
{
|
|
// prec(a*b) = max(prec(a),prec(b))
|
|
if(a.getPrecision() >= b.getPrecision()) return mpreal(a) *= b;
|
|
else return mpreal(b) *= a;
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// / Division
|
|
inline mpreal& mpreal::operator/=(const mpreal& v)
|
|
{
|
|
mpfr_div(mp,mp,v.mp,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const mpz_t v)
|
|
{
|
|
mpfr_div_z(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const mpq_t v)
|
|
{
|
|
mpfr_div_q(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const long double v)
|
|
{
|
|
*this /= mpreal(v);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const double v)
|
|
{
|
|
#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
|
|
mpfr_div_d(mp,mp,v,default_rnd);
|
|
#else
|
|
*this /= mpreal(v);
|
|
#endif
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const unsigned long int v)
|
|
{
|
|
mpfr_div_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const unsigned int v)
|
|
{
|
|
mpfr_div_ui(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const long int v)
|
|
{
|
|
mpfr_div_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator/=(const int v)
|
|
{
|
|
mpfr_div_si(mp,mp,v,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline const mpreal operator/(const mpreal& a, const mpreal& b)
|
|
{
|
|
// prec(a/b) = max(prec(a),prec(b))
|
|
if(a.getPrecision() >= b.getPrecision())
|
|
{
|
|
return mpreal(a) /= b;
|
|
}else{
|
|
|
|
mpreal x(a);
|
|
x.setPrecision(b.getPrecision());
|
|
return x /= 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 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
|
|
return mpreal(b) /= 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);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator<<=(const unsigned int u)
|
|
{
|
|
mpfr_mul_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator<<=(const long int u)
|
|
{
|
|
mpfr_mul_2si(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator<<=(const int u)
|
|
{
|
|
mpfr_mul_2si(mp,mp,static_cast<long int>(u),default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator>>=(const unsigned long int u)
|
|
{
|
|
mpfr_div_2ui(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator>>=(const unsigned int u)
|
|
{
|
|
mpfr_div_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator>>=(const long int u)
|
|
{
|
|
mpfr_div_2si(mp,mp,u,default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::operator>>=(const int u)
|
|
{
|
|
mpfr_div_2si(mp,mp,static_cast<long int>(u),default_rnd);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
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 mpreal& b){ return (mpfr_greaterequal_p(a.mp,b.mp) !=0); }
|
|
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 mpreal& b){ return (mpfr_lessequal_p(a.mp,b.mp) !=0); }
|
|
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 mpreal& b){ return (mpfr_lessgreater_p(a.mp,b.mp) !=0); }
|
|
|
|
inline bool operator == (const mpreal& a, const unsigned long int b ){ return (mpfr_cmp_ui(a.mp,b) == 0); }
|
|
inline bool operator == (const mpreal& a, const unsigned int b ){ return (mpfr_cmp_ui(a.mp,b) == 0); }
|
|
inline bool operator == (const mpreal& a, const long int b ){ return (mpfr_cmp_si(a.mp,b) == 0); }
|
|
inline bool operator == (const mpreal& a, const int b ){ return (mpfr_cmp_si(a.mp,b) == 0); }
|
|
inline bool operator == (const mpreal& a, const long double b ){ return (mpfr_cmp_ld(a.mp,b) == 0); }
|
|
inline bool operator == (const mpreal& a, const double b ){ return (mpfr_cmp_d(a.mp,b) == 0); }
|
|
|
|
|
|
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 isfinite(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
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// Type Converters
|
|
inline long mpreal::toLong() const { return mpfr_get_si(mp,GMP_RNDZ); }
|
|
inline unsigned long mpreal::toULong() const { return mpfr_get_ui(mp,GMP_RNDZ); }
|
|
inline double mpreal::toDouble() const { return mpfr_get_d(mp,default_rnd); }
|
|
inline long double mpreal::toLDouble() const { return mpfr_get_ld(mp,default_rnd); }
|
|
|
|
#if defined (MPREAL_HAVE_INT64_SUPPORT)
|
|
inline int64_t mpreal::toInt64() const{ return mpfr_get_sj(mp,GMP_RNDZ); }
|
|
inline uint64_t mpreal::toUInt64() const{ return mpfr_get_uj(mp,GMP_RNDZ); }
|
|
#endif
|
|
|
|
inline ::mpfr_ptr mpreal::mpfr_ptr() { return mp; }
|
|
inline ::mpfr_srcptr mpreal::mpfr_srcptr() const { return const_cast< ::mpfr_srcptr >(mp); }
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// Bits - decimal digits relation
|
|
// bits = ceil(digits*log[2](10))
|
|
// digits = floor(bits*log[10](2))
|
|
|
|
inline mp_prec_t digits2bits(int d)
|
|
{
|
|
const double LOG2_10 = 3.3219280948873624;
|
|
|
|
d = 10>d?10:d;
|
|
|
|
return (mp_prec_t)std::ceil((d)*LOG2_10);
|
|
}
|
|
|
|
inline int bits2digits(mp_prec_t b)
|
|
{
|
|
const double LOG10_2 = 0.30102999566398119;
|
|
|
|
b = 34>b?34:b;
|
|
|
|
return (int)std::floor((b)*LOG10_2);
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////
|
|
// Set/Get number properties
|
|
inline int sgn(const mpreal& v)
|
|
{
|
|
int r = mpfr_signbit(v.mp);
|
|
return (r>0?-1:1);
|
|
}
|
|
|
|
inline mpreal& mpreal::setSign(int sign, mp_rnd_t RoundingMode)
|
|
{
|
|
mpfr_setsign(mp,mp,(sign<0?1:0),RoundingMode);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline int mpreal::getPrecision() const
|
|
{
|
|
return mpfr_get_prec(mp);
|
|
}
|
|
|
|
inline mpreal& mpreal::setPrecision(int Precision, mp_rnd_t RoundingMode)
|
|
{
|
|
mpfr_prec_round(mp,Precision, RoundingMode);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::setInf(int sign)
|
|
{
|
|
mpfr_set_inf(mp,sign);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::setNan()
|
|
{
|
|
mpfr_set_nan(mp);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
inline mpreal& mpreal::setZero(int sign)
|
|
{
|
|
mpfr_set_zero(mp,sign);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return *this;
|
|
}
|
|
|
|
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);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
}
|
|
|
|
inline mp_exp_t mpreal::get_exp ()
|
|
{
|
|
return mpfr_get_exp(mp);
|
|
}
|
|
|
|
inline int mpreal::set_exp (mp_exp_t e)
|
|
{
|
|
int x = mpfr_set_exp(mp, e);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return x;
|
|
}
|
|
|
|
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
|
|
return machine_epsilon(mpreal(1,prec));
|
|
}
|
|
|
|
inline const mpreal machine_epsilon(const mpreal& x)
|
|
{
|
|
if( x < 0)
|
|
{
|
|
return nextabove(-x)+x;
|
|
}else{
|
|
return nextabove(x)-x;
|
|
}
|
|
}
|
|
|
|
inline const mpreal mpreal_min(mp_prec_t prec)
|
|
{
|
|
// min = 1/2*2^emin = 2^(emin-1)
|
|
|
|
return mpreal(1,prec) << 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)
|
|
|
|
return mpreal(1,prec) << mpreal::get_emax()-1;
|
|
}
|
|
|
|
inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps)
|
|
{
|
|
/*
|
|
maxUlps - a and b can be apart by maxUlps binary numbers.
|
|
*/
|
|
return abs(a - b) <= machine_epsilon((max)(abs(a), abs(b))) * maxUlps;
|
|
}
|
|
|
|
inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps)
|
|
{
|
|
return abs(a - b) <= (min)(abs(a), abs(b)) * eps;
|
|
}
|
|
|
|
inline bool isEqualFuzzy(const mpreal& a, const mpreal& b)
|
|
{
|
|
return isEqualFuzzy(a,b,machine_epsilon((std::min)(abs(a), abs(b))));
|
|
}
|
|
|
|
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)
|
|
{
|
|
int r = mpfr_subnormalize(mp,t,rnd_mode);
|
|
MPREAL_MSVC_DEBUGVIEW_CODE;
|
|
return r;
|
|
}
|
|
|
|
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().setNan(); // 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().setNan(); // 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 acot (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return atan(1/v, rnd_mode);
|
|
}
|
|
|
|
inline const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return acos(1/v, rnd_mode);
|
|
}
|
|
|
|
inline const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return asin(1/v, rnd_mode);
|
|
}
|
|
|
|
inline const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return atanh(1/v, rnd_mode);
|
|
}
|
|
|
|
inline const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return acosh(1/v, rnd_mode);
|
|
}
|
|
|
|
inline const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
return asinh(1/v, rnd_mode);
|
|
}
|
|
|
|
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 hypot (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_hypot(a.mp, x.mp, y.mp, rnd_mode);
|
|
|
|
return a;
|
|
}
|
|
|
|
inline const mpreal remainder (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_remainder(a.mp, x.mp, y.mp, rnd_mode);
|
|
|
|
return a;
|
|
}
|
|
|
|
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& x, mp_rnd_t rnd_mode)
|
|
{
|
|
mpreal FunctionValue(x);
|
|
|
|
// x < 0: gamma(-x) = -pi/(x * gamma(x) * sin(pi*x))
|
|
|
|
mpfr_gamma(FunctionValue.mp, x.mp, rnd_mode);
|
|
|
|
return FunctionValue;
|
|
}
|
|
|
|
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 besselj0 (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
mpreal x(v);
|
|
mpfr_j0(x.mp,v.mp,rnd_mode);
|
|
return x;
|
|
}
|
|
|
|
inline const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
mpreal x(v);
|
|
mpfr_j1(x.mp,v.mp,rnd_mode);
|
|
return x;
|
|
}
|
|
|
|
inline const mpreal besseljn (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 bessely0 (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
mpreal x(v);
|
|
mpfr_y0(x.mp,v.mp,rnd_mode);
|
|
return x;
|
|
}
|
|
|
|
inline const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode)
|
|
{
|
|
mpreal x(v);
|
|
mpfr_y1(x.mp,v.mp,rnd_mode);
|
|
return x;
|
|
}
|
|
|
|
inline const mpreal besselyn (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
|
|
|
|
// Uniformly distributed random number generation
|
|
// a = random(seed); <- initialization & first random number generation
|
|
// a = random(); <- next random numbers generation
|
|
// seed != 0
|
|
inline const mpreal random(unsigned int seed)
|
|
{
|
|
|
|
#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
|
|
static gmp_randstate_t state;
|
|
static bool isFirstTime = true;
|
|
|
|
if(isFirstTime)
|
|
{
|
|
gmp_randinit_default(state);
|
|
gmp_randseed_ui(state,0);
|
|
isFirstTime = false;
|
|
}
|
|
|
|
if(seed != 0) gmp_randseed_ui(state,seed);
|
|
|
|
return mpfr::urandom(state);
|
|
#else
|
|
if(seed != 0) std::srand(seed);
|
|
return mpfr::mpreal(std::rand()/(double)RAND_MAX);
|
|
#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 static_cast<mp_rnd_t>((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
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}
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inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)
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{
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return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
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}
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inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)
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{
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return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
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}
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} // End of mpfr namespace
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// Explicit specialization of std::swap for mpreal numbers
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// Thus standard algorithms will use efficient version of swap (due to Koenig lookup)
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// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap
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namespace std
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{
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template <>
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inline void swap(mpfr::mpreal& x, mpfr::mpreal& y)
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{
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return mpfr::swap(x, y);
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}
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}
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#endif /* __MPREAL_H__ */
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