From 5c22c7a7de55eeeafbf53e38711617238e61194a Mon Sep 17 00:00:00 2001 From: Aaron Franke Date: Sat, 21 Mar 2020 21:30:06 -0400 Subject: Make file formatting comply with POSIX and Unix standards UTF-8, LF, no BOM, and newlines at the end of files --- unsupported/test/cxx11_tensor_block_io.cpp | 2 +- unsupported/test/cxx11_tensor_trace.cpp | 2 +- unsupported/test/mpreal/mpreal.h | 6368 ++++++++++++++-------------- 3 files changed, 3186 insertions(+), 3186 deletions(-) (limited to 'unsupported/test') diff --git a/unsupported/test/cxx11_tensor_block_io.cpp b/unsupported/test/cxx11_tensor_block_io.cpp index b8600eaea..a6f7a44cd 100644 --- a/unsupported/test/cxx11_tensor_block_io.cpp +++ b/unsupported/test/cxx11_tensor_block_io.cpp @@ -434,4 +434,4 @@ EIGEN_DECLARE_TEST(cxx11_tensor_block_io) { CALL_SUBTEST(test_block_io_squeeze_ones()); CALL_SUBTEST(test_block_io_squeeze_ones()); // clang-format on -} \ No newline at end of file +} diff --git a/unsupported/test/cxx11_tensor_trace.cpp b/unsupported/test/cxx11_tensor_trace.cpp index 77e5dca20..009722895 100644 --- a/unsupported/test/cxx11_tensor_trace.cpp +++ b/unsupported/test/cxx11_tensor_trace.cpp @@ -169,4 +169,4 @@ EIGEN_DECLARE_TEST(cxx11_tensor_trace) { CALL_SUBTEST(test_simple_trace()); CALL_SUBTEST(test_trace_in_expr()); CALL_SUBTEST(test_trace_in_expr()); -} \ No newline at end of file +} diff --git a/unsupported/test/mpreal/mpreal.h b/unsupported/test/mpreal/mpreal.h index 2b4f8e80f..5cfd66a10 100644 --- a/unsupported/test/mpreal/mpreal.h +++ b/unsupported/test/mpreal/mpreal.h @@ -1,3184 +1,3184 @@ -/* - MPFR C++: Multi-precision floating point number class for C++. - Based on MPFR library: http://mpfr.org - - Project homepage: http://www.holoborodko.com/pavel/mpfr - Contact e-mail: pavel@holoborodko.com - - Copyright (c) 2008-2016 Pavel Holoborodko - - Contributors: - Dmitriy Gubanov, Konstantin Holoborodko, Brian Gladman, - Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen, - Pere Constans, Peter van Hoof, Gael Guennebaud, Tsai Chia Cheng, - Alexei Zubanov, Jauhien Piatlicki, Victor Berger, John Westwood, - Petr Aleksandrov, Orion Poplawski, Charles Karney, Arash Partow, - Rodney James, Jorge Leitao, Jerome Benoit. - - Licensing: - (A) MPFR C++ is under GNU General Public License ("GPL"). - - (B) Non-free licenses may also be purchased from the author, for users who - do not want their programs protected by the GPL. - - The non-free licenses are for users that wish to use MPFR C++ in - their products but are unwilling to release their software - under the GPL (which would require them to release source code - and allow free redistribution). - - Such users can purchase an unlimited-use license from the author. - Contact us for more details. - - GNU General Public License ("GPL") copyright permissions statement: - ************************************************************************** - This program is free software: you can redistribute it and/or modify - it under the terms of the GNU General Public License as published by - the Free Software Foundation, either version 3 of the License, or - (at your option) any later version. - - This program is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - GNU General Public License for more details. - - You should have received a copy of the GNU General Public License - along with this program. If not, see . -*/ - -#ifndef __MPREAL_H__ -#define __MPREAL_H__ - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - -// Options -#define MPREAL_HAVE_MSVC_DEBUGVIEW // Enable Debugger Visualizer for "Debug" builds in MSVC. -#define MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS // Enable extended std::numeric_limits specialization. - // Meaning that "digits", "round_style" and similar members are defined as functions, not constants. - // See std::numeric_limits at the end of the file for more information. - -// Library version -#define MPREAL_VERSION_MAJOR 3 -#define MPREAL_VERSION_MINOR 6 -#define MPREAL_VERSION_PATCHLEVEL 5 -#define MPREAL_VERSION_STRING "3.6.5" - -// Detect compiler using signatures from http://predef.sourceforge.net/ -#if defined(__GNUC__) && defined(__INTEL_COMPILER) - #define IsInf(x) isinf EIGEN_NOT_A_MACRO (x) // Intel ICC compiler on Linux - -#elif defined(_MSC_VER) // Microsoft Visual C++ - #define IsInf(x) (!_finite(x)) - -#else - #define IsInf(x) std::isinf EIGEN_NOT_A_MACRO (x) // GNU C/C++ (and/or other compilers), just hope for C99 conformance -#endif - -// A Clang feature extension to determine compiler features. -#ifndef __has_feature - #define __has_feature(x) 0 -#endif - -// Detect support for r-value references (move semantic). -// Move semantic should be enabled with great care in multi-threading environments, -// especially if MPFR uses custom memory allocators. -// Everything should be thread-safe and support passing ownership over thread boundary. -#if (__has_feature(cxx_rvalue_references) || \ - defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L || \ - (defined(_MSC_VER) && _MSC_VER >= 1600) && !defined(MPREAL_DISABLE_MOVE_SEMANTIC)) - - #define MPREAL_HAVE_MOVE_SUPPORT - - // Use fields in mpfr_t structure to check if it was initialized / set dummy initialization - #define mpfr_is_initialized(x) (0 != (x)->_mpfr_d) - #define mpfr_set_uninitialized(x) ((x)->_mpfr_d = 0 ) -#endif - -// Detect support for explicit converters. -#if (__has_feature(cxx_explicit_conversions) || \ - (defined(__GXX_EXPERIMENTAL_CXX0X__) && __GNUC_MINOR__ >= 5) || __cplusplus >= 201103L || \ - (defined(_MSC_VER) && _MSC_VER >= 1800) || \ - (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 1300)) - - #define MPREAL_HAVE_EXPLICIT_CONVERTERS -#endif - -#define MPFR_USE_INTMAX_T // Enable 64-bit integer types - should be defined before mpfr.h - -#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG) - #define MPREAL_MSVC_DEBUGVIEW_CODE DebugView = toString(); - #define MPREAL_MSVC_DEBUGVIEW_DATA std::string DebugView; -#else - #define MPREAL_MSVC_DEBUGVIEW_CODE - #define MPREAL_MSVC_DEBUGVIEW_DATA -#endif - -#include - -#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0)) - #include // Needed for random() -#endif - -// Less important options -#define MPREAL_DOUBLE_BITS_OVERFLOW -1 // Triggers overflow exception during conversion to double if mpreal - // cannot fit in MPREAL_DOUBLE_BITS_OVERFLOW bits - // = -1 disables overflow checks (default) - -// Fast replacement for mpfr_set_zero(x, +1): -// (a) uses low-level data members, might not be forward compatible -// (b) sign is not set, add (x)->_mpfr_sign = 1; -#define mpfr_set_zero_fast(x) ((x)->_mpfr_exp = __MPFR_EXP_ZERO) - -#if defined(__GNUC__) - #define MPREAL_PERMISSIVE_EXPR __extension__ -#else - #define MPREAL_PERMISSIVE_EXPR -#endif - -namespace mpfr { - -class mpreal { -private: - mpfr_t mp; - -public: - - // Get default rounding mode & precision - inline static mp_rnd_t get_default_rnd() { return (mp_rnd_t)(mpfr_get_default_rounding_mode()); } - inline static mp_prec_t get_default_prec() { return (mpfr_get_default_prec)(); } - - // Constructors && type conversions - mpreal(); - mpreal(const mpreal& u); - mpreal(const mpf_t u); - mpreal(const mpz_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const mpq_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const long double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const unsigned long long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const long long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const unsigned long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const unsigned int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); - - // Construct mpreal from mpfr_t structure. - // shared = true allows to avoid deep copy, so that mpreal and 'u' share the same data & pointers. - mpreal(const mpfr_t u, bool shared = false); - - mpreal(const char* s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd()); - mpreal(const std::string& s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd()); - - ~mpreal(); - -#ifdef MPREAL_HAVE_MOVE_SUPPORT - mpreal& operator=(mpreal&& v); - mpreal(mpreal&& u); -#endif - - // Operations - // = - // +, -, *, /, ++, --, <<, >> - // *=, +=, -=, /=, - // <, >, ==, <=, >= - - // = - mpreal& operator=(const mpreal& v); - mpreal& operator=(const mpf_t v); - mpreal& operator=(const mpz_t v); - mpreal& operator=(const mpq_t v); - mpreal& operator=(const long double v); - mpreal& operator=(const double v); - mpreal& operator=(const unsigned long int v); - mpreal& operator=(const unsigned long long int v); - mpreal& operator=(const long long int v); - mpreal& operator=(const unsigned int v); - mpreal& operator=(const long int v); - mpreal& operator=(const int v); - mpreal& operator=(const char* s); - mpreal& operator=(const std::string& s); - template mpreal& operator= (const std::complex& z); - - // + - mpreal& operator+=(const mpreal& v); - mpreal& operator+=(const mpf_t v); - mpreal& operator+=(const mpz_t v); - mpreal& operator+=(const mpq_t v); - mpreal& operator+=(const long double u); - mpreal& operator+=(const double u); - mpreal& operator+=(const unsigned long int u); - mpreal& operator+=(const unsigned int u); - mpreal& operator+=(const long int u); - mpreal& operator+=(const int u); - - mpreal& operator+=(const long long int u); - mpreal& operator+=(const unsigned long long int u); - mpreal& operator-=(const long long int u); - mpreal& operator-=(const unsigned long long int u); - mpreal& operator*=(const long long int u); - mpreal& operator*=(const unsigned long long int u); - mpreal& operator/=(const long long int u); - mpreal& operator/=(const unsigned long long int u); - - const mpreal operator+() const; - mpreal& operator++ (); - const mpreal operator++ (int); - - // - - mpreal& operator-=(const mpreal& v); - mpreal& operator-=(const mpz_t v); - mpreal& operator-=(const mpq_t v); - mpreal& operator-=(const long double u); - mpreal& operator-=(const double u); - mpreal& operator-=(const unsigned long int u); - mpreal& operator-=(const unsigned int u); - mpreal& operator-=(const long int u); - mpreal& operator-=(const int u); - const mpreal operator-() const; - friend const mpreal operator-(const unsigned long int b, const mpreal& a); - friend const mpreal operator-(const unsigned int b, const mpreal& a); - friend const mpreal operator-(const long int b, const mpreal& a); - friend const mpreal operator-(const int b, const mpreal& a); - friend const mpreal operator-(const double b, const mpreal& a); - mpreal& operator-- (); - const mpreal operator-- (int); - - // * - mpreal& operator*=(const mpreal& v); - mpreal& operator*=(const mpz_t v); - mpreal& operator*=(const mpq_t v); - mpreal& operator*=(const long double v); - mpreal& operator*=(const double v); - mpreal& operator*=(const unsigned long int v); - mpreal& operator*=(const unsigned int v); - mpreal& operator*=(const long int v); - mpreal& operator*=(const int v); - - // / - mpreal& operator/=(const mpreal& v); - mpreal& operator/=(const mpz_t v); - mpreal& operator/=(const mpq_t v); - mpreal& operator/=(const long double v); - mpreal& operator/=(const double v); - mpreal& operator/=(const unsigned long int v); - mpreal& operator/=(const unsigned int v); - mpreal& operator/=(const long int v); - mpreal& operator/=(const int v); - friend const mpreal operator/(const unsigned long int b, const mpreal& a); - friend const mpreal operator/(const unsigned int b, const mpreal& a); - friend const mpreal operator/(const long int b, const mpreal& a); - friend const mpreal operator/(const int b, const mpreal& a); - friend const mpreal operator/(const double b, const mpreal& a); - - //<<= Fast Multiplication by 2^u - mpreal& operator<<=(const unsigned long int u); - mpreal& operator<<=(const unsigned int u); - mpreal& operator<<=(const long int u); - mpreal& operator<<=(const int u); - - //>>= Fast Division by 2^u - mpreal& operator>>=(const unsigned long int u); - mpreal& operator>>=(const unsigned int u); - mpreal& operator>>=(const long int u); - mpreal& operator>>=(const int u); - - // Type Conversion operators - bool toBool ( ) const; - long toLong (mp_rnd_t mode = GMP_RNDZ) const; - unsigned long toULong (mp_rnd_t mode = GMP_RNDZ) const; - long long toLLong (mp_rnd_t mode = GMP_RNDZ) const; - unsigned long long toULLong (mp_rnd_t mode = GMP_RNDZ) const; - float toFloat (mp_rnd_t mode = GMP_RNDN) const; - double toDouble (mp_rnd_t mode = GMP_RNDN) const; - long double toLDouble (mp_rnd_t mode = GMP_RNDN) const; - -#if defined (MPREAL_HAVE_EXPLICIT_CONVERTERS) - explicit operator bool () const { return toBool(); } - explicit operator int () const { return int(toLong()); } - explicit operator long () const { return toLong(); } - explicit operator long long () const { return toLLong(); } - explicit operator unsigned () const { return unsigned(toULong()); } - explicit operator unsigned long () const { return toULong(); } - explicit operator unsigned long long () const { return toULLong(); } - explicit operator float () const { return toFloat(); } - explicit operator double () const { return toDouble(); } - explicit operator long double () const { return toLDouble(); } -#endif - - // Get raw pointers so that mpreal can be directly used in raw mpfr_* functions - ::mpfr_ptr mpfr_ptr(); - ::mpfr_srcptr mpfr_ptr() const; - ::mpfr_srcptr mpfr_srcptr() const; - - // Convert mpreal to string with n significant digits in base b - // n = -1 -> convert with the maximum available digits - std::string toString(int n = -1, int b = 10, mp_rnd_t mode = mpreal::get_default_rnd()) const; - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) - std::string toString(const std::string& format) const; -#endif - - std::ostream& output(std::ostream& os) const; - - // Math Functions - friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode); - friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); - friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode); - friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode); - friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode); - friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode); - friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode); - friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode); - friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode); - friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); - friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode); - friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); - friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode); - friend int cmpabs(const mpreal& a,const mpreal& b); - - friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal logb (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal nextpow2(const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode); - friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode); - friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - - friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec, mp_rnd_t rnd_mode); - friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode); - - friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal tgamma (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode); - friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode); - friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode); - friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode); - friend const mpreal sum (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t rnd_mode); - friend int sgn (const mpreal& v); - -// MPFR 2.4.0 Specifics -#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) - friend int sinh_cosh (mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal li2 (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - friend const mpreal rec_sqrt (const mpreal& v, mp_rnd_t rnd_mode); - - // MATLAB's semantic equivalents - friend const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Remainder after division - friend const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Modulus after division -#endif - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) - friend const mpreal digamma (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal ai (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear -#endif - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0)) - friend const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear - friend const mpreal grandom (unsigned int seed); -#endif - - // Uniformly distributed random number generation in [0,1] using - // Mersenne-Twister algorithm by default. - // Use parameter to setup seed, e.g.: random((unsigned)time(NULL)) - // Check urandom() for more precise control. - friend const mpreal random(unsigned int seed); - - // Splits mpreal value into fractional and integer parts. - // Returns fractional part and stores integer part in n. - friend const mpreal modf(const mpreal& v, mpreal& n); - - // Constants - // don't forget to call mpfr_free_cache() for every thread where you are using const-functions - friend const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode); - friend const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode); - friend const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode); - friend const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode); - - // returns +inf iff sign>=0 otherwise -inf - friend const mpreal const_infinity(int sign, mp_prec_t prec); - - // Output/ Input - friend std::ostream& operator<<(std::ostream& os, const mpreal& v); - friend std::istream& operator>>(std::istream& is, mpreal& v); - - // Integer Related Functions - friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal ceil (const mpreal& v); - friend const mpreal floor(const mpreal& v); - friend const mpreal round(const mpreal& v); - friend const mpreal trunc(const mpreal& v); - friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal rint_floor (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal rint_round (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal rint_trunc (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode); - friend const mpreal remainder ( const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - - // Miscellaneous Functions - friend const mpreal nexttoward (const mpreal& x, const mpreal& y); - friend const mpreal nextabove (const mpreal& x); - friend const mpreal nextbelow (const mpreal& x); - - // use gmp_randinit_default() to init state, gmp_randclear() to clear - friend const mpreal urandomb (gmp_randstate_t& state); - -// MPFR < 2.4.2 Specifics -#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2)) - friend const mpreal random2 (mp_size_t size, mp_exp_t exp); -#endif - - // Instance Checkers - friend bool isnan EIGEN_NOT_A_MACRO (const mpreal& v); - friend bool (isinf) (const mpreal& v); - friend bool (isfinite) (const mpreal& v); - - friend bool isnum (const mpreal& v); - friend bool iszero (const mpreal& v); - friend bool isint (const mpreal& v); - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) - friend bool isregular(const mpreal& v); -#endif - - // Set/Get instance properties - inline mp_prec_t get_prec() const; - inline void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = get_default_rnd()); // Change precision with rounding mode - - // Aliases for get_prec(), set_prec() - needed for compatibility with std::complex interface - inline mpreal& setPrecision(int Precision, mp_rnd_t RoundingMode = get_default_rnd()); - inline int getPrecision() const; - - // Set mpreal to +/- inf, NaN, +/-0 - mpreal& setInf (int Sign = +1); - mpreal& setNan (); - mpreal& setZero (int Sign = +1); - mpreal& setSign (int Sign, mp_rnd_t RoundingMode = get_default_rnd()); - - //Exponent - mp_exp_t get_exp() const; - int set_exp(mp_exp_t e); - int check_range (int t, mp_rnd_t rnd_mode = get_default_rnd()); - int subnormalize (int t, mp_rnd_t rnd_mode = get_default_rnd()); - - // Inexact conversion from float - inline bool fits_in_bits(double x, int n); - - // Set/Get global properties - static void set_default_prec(mp_prec_t prec); - static void set_default_rnd(mp_rnd_t rnd_mode); - - static mp_exp_t get_emin (void); - static mp_exp_t get_emax (void); - static mp_exp_t get_emin_min (void); - static mp_exp_t get_emin_max (void); - static mp_exp_t get_emax_min (void); - static mp_exp_t get_emax_max (void); - static int set_emin (mp_exp_t exp); - static int set_emax (mp_exp_t exp); - - // Efficient swapping of two mpreal values - needed for std algorithms - friend void swap(mpreal& x, mpreal& y); - - friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); - -private: - // Human friendly Debug Preview in Visual Studio. - // Put one of these lines: - // - // mpfr::mpreal= ; Show value only - // mpfr::mpreal=, bits ; Show value & precision - // - // at the beginning of - // [Visual Studio Installation Folder]\Common7\Packages\Debugger\autoexp.dat - MPREAL_MSVC_DEBUGVIEW_DATA - - // "Smart" resources deallocation. Checks if instance initialized before deletion. - void clear(::mpfr_ptr); -}; - -////////////////////////////////////////////////////////////////////////// -// Exceptions -class conversion_overflow : public std::exception { -public: - std::string why() { return "inexact conversion from floating point"; } -}; - -////////////////////////////////////////////////////////////////////////// -// Constructors & converters -// Default constructor: creates mp number and initializes it to 0. -inline mpreal::mpreal() -{ - mpfr_init2(mpfr_ptr(), mpreal::get_default_prec()); - mpfr_set_zero_fast(mpfr_ptr()); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const mpreal& u) -{ - mpfr_init2(mpfr_ptr(),mpfr_get_prec(u.mpfr_srcptr())); - mpfr_set (mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -#ifdef MPREAL_HAVE_MOVE_SUPPORT -inline mpreal::mpreal(mpreal&& other) -{ - mpfr_set_uninitialized(mpfr_ptr()); // make sure "other" holds null-pointer (in uninitialized state) - mpfr_swap(mpfr_ptr(), other.mpfr_ptr()); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal& mpreal::operator=(mpreal&& other) -{ - if (this != &other) - { - mpfr_swap(mpfr_ptr(), other.mpfr_ptr()); // destructor for "other" will be called just afterwards - MPREAL_MSVC_DEBUGVIEW_CODE; - } - return *this; -} -#endif - -inline mpreal::mpreal(const mpfr_t u, bool shared) -{ - if(shared) - { - std::memcpy(mpfr_ptr(), u, sizeof(mpfr_t)); - } - else - { - mpfr_init2(mpfr_ptr(), mpfr_get_prec(u)); - mpfr_set (mpfr_ptr(), u, mpreal::get_default_rnd()); - } - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const mpf_t u) -{ - mpfr_init2(mpfr_ptr(),(mp_prec_t) mpf_get_prec(u)); // (gmp: mp_bitcnt_t) unsigned long -> long (mpfr: mp_prec_t) - mpfr_set_f(mpfr_ptr(),u,mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const mpz_t u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2(mpfr_ptr(), prec); - mpfr_set_z(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const mpq_t u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2(mpfr_ptr(), prec); - mpfr_set_q(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const double u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2(mpfr_ptr(), prec); - -#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1) - if(fits_in_bits(u, MPREAL_DOUBLE_BITS_OVERFLOW)) - { - mpfr_set_d(mpfr_ptr(), u, mode); - }else - throw conversion_overflow(); -#else - mpfr_set_d(mpfr_ptr(), u, mode); -#endif - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const long double u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_ld(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const unsigned long long int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_uj(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const long long int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_sj(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const unsigned long int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_ui(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const unsigned int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_ui(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const long int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_si(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const int u, mp_prec_t prec, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_si(mpfr_ptr(), u, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_str(mpfr_ptr(), s, base, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mpreal::mpreal(const std::string& s, mp_prec_t prec, int base, mp_rnd_t mode) -{ - mpfr_init2 (mpfr_ptr(), prec); - mpfr_set_str(mpfr_ptr(), s.c_str(), base, mode); - - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline void mpreal::clear(::mpfr_ptr x) -{ -#ifdef MPREAL_HAVE_MOVE_SUPPORT - if(mpfr_is_initialized(x)) -#endif - mpfr_clear(x); -} - -inline mpreal::~mpreal() -{ - clear(mpfr_ptr()); -} - -// internal namespace needed for template magic -namespace internal{ - - // Use SFINAE to restrict arithmetic operations instantiation only for numeric types - // This is needed for smooth integration with libraries based on expression templates, like Eigen. - // TODO: Do the same for boolean operators. - template struct result_type {}; - - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; - template <> struct result_type {typedef mpreal type;}; -} - -// + Addition -template -inline const typename internal::result_type::type - operator+(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) += rhs; } - -template -inline const typename internal::result_type::type - operator+(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) += lhs; } - -// - Subtraction -template -inline const typename internal::result_type::type - operator-(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) -= rhs; } - -template -inline const typename internal::result_type::type - operator-(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) -= rhs; } - -// * Multiplication -template -inline const typename internal::result_type::type - operator*(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) *= rhs; } - -template -inline const typename internal::result_type::type - operator*(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) *= lhs; } - -// / Division -template -inline const typename internal::result_type::type - operator/(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) /= rhs; } - -template -inline const typename internal::result_type::type - operator/(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) /= rhs; } - -////////////////////////////////////////////////////////////////////////// -// sqrt -const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -// abs -inline const mpreal abs(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()); - -////////////////////////////////////////////////////////////////////////// -// pow -const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); -inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); - -////////////////////////////////////////////////////////////////////////// -// Estimate machine epsilon for the given precision -// Returns smallest eps such that 1.0 + eps != 1.0 -inline mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec()); - -// Returns smallest eps such that x + eps != x (relative machine epsilon) -inline mpreal machine_epsilon(const mpreal& x); - -// Gives max & min values for the required precision, -// minval is 'safe' meaning 1 / minval does not overflow -// maxval is 'safe' meaning 1 / maxval does not underflow -inline mpreal minval(mp_prec_t prec = mpreal::get_default_prec()); -inline mpreal maxval(mp_prec_t prec = mpreal::get_default_prec()); - -// 'Dirty' equality check 1: |a-b| < min{|a|,|b|} * eps -inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps); - -// 'Dirty' equality check 2: |a-b| < min{|a|,|b|} * eps( min{|a|,|b|} ) -inline bool isEqualFuzzy(const mpreal& a, const mpreal& b); - -// 'Bitwise' equality check -// maxUlps - a and b can be apart by maxUlps binary numbers. -inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps); - -////////////////////////////////////////////////////////////////////////// -// Convert precision in 'bits' to decimal digits and vice versa. -// bits = ceil(digits*log[2](10)) -// digits = floor(bits*log[10](2)) - -inline mp_prec_t digits2bits(int d); -inline int bits2digits(mp_prec_t b); - -////////////////////////////////////////////////////////////////////////// -// min, max -const mpreal (max)(const mpreal& x, const mpreal& y); -const mpreal (min)(const mpreal& x, const mpreal& y); - -////////////////////////////////////////////////////////////////////////// -// Implementation -////////////////////////////////////////////////////////////////////////// - -////////////////////////////////////////////////////////////////////////// -// Operators - Assignment -inline mpreal& mpreal::operator=(const mpreal& v) -{ - if (this != &v) - { - mp_prec_t tp = mpfr_get_prec( mpfr_srcptr()); - mp_prec_t vp = mpfr_get_prec(v.mpfr_srcptr()); - - if(tp != vp){ - clear(mpfr_ptr()); - mpfr_init2(mpfr_ptr(), vp); - } - - mpfr_set(mpfr_ptr(), v.mpfr_srcptr(), mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - } - return *this; -} - -inline mpreal& mpreal::operator=(const mpf_t v) -{ - mpfr_set_f(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const mpz_t v) -{ - mpfr_set_z(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const mpq_t v) -{ - mpfr_set_q(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const long double v) -{ - mpfr_set_ld(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const double v) -{ -#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1) - if(fits_in_bits(v, MPREAL_DOUBLE_BITS_OVERFLOW)) - { - mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd()); - }else - throw conversion_overflow(); -#else - mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd()); -#endif - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const unsigned long int v) -{ - mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const unsigned int v) -{ - mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const unsigned long long int v) -{ - mpfr_set_uj(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const long long int v) -{ - mpfr_set_sj(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const long int v) -{ - mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const int v) -{ - mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd()); - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator=(const char* s) -{ - // Use other converters for more precise control on base & precision & rounding: - // - // mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) - // mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode) - // - // Here we assume base = 10 and we use precision of target variable. - - mpfr_t t; - - mpfr_init2(t, mpfr_get_prec(mpfr_srcptr())); - - if(0 == mpfr_set_str(t, s, 10, mpreal::get_default_rnd())) - { - mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - } - - clear(t); - return *this; -} - -inline mpreal& mpreal::operator=(const std::string& s) -{ - // Use other converters for more precise control on base & precision & rounding: - // - // mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) - // mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode) - // - // Here we assume base = 10 and we use precision of target variable. - - mpfr_t t; - - mpfr_init2(t, mpfr_get_prec(mpfr_srcptr())); - - if(0 == mpfr_set_str(t, s.c_str(), 10, mpreal::get_default_rnd())) - { - mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - } - - clear(t); - return *this; -} - -template -inline mpreal& mpreal::operator= (const std::complex& z) -{ - return *this = z.real(); -} - -////////////////////////////////////////////////////////////////////////// -// + Addition -inline mpreal& mpreal::operator+=(const mpreal& v) -{ - mpfr_add(mpfr_ptr(), mpfr_srcptr(), v.mpfr_srcptr(), mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator+=(const mpq_t u) -{ - mpfr_add_q(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator+=(const unsigned int u) -{ - mpfr_add_ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator+=(const long int u) -{ - mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator+=(const int u) -{ - mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator+=(const long long int u) { *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator+=(const unsigned long long int u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator-=(const long long int u) { *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator-=(const unsigned long long int u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator*=(const long long int u) { *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator*=(const unsigned long long int u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator/=(const long long int u) { *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } -inline mpreal& mpreal::operator/=(const unsigned long long int u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } - -inline const mpreal mpreal::operator+()const { return mpreal(*this); } - -inline const mpreal operator+(const mpreal& a, const mpreal& b) -{ - mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); - mpfr_add(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); - return c; -} - -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(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator-=(const mpz_t v) -{ - mpfr_sub_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator-=(const mpq_t v) -{ - mpfr_sub_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator-=(const unsigned int v) -{ - mpfr_sub_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator-=(const long int v) -{ - mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator-=(const int v) -{ - mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline const mpreal mpreal::operator-()const -{ - mpreal u(*this); - mpfr_neg(u.mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd()); - return u; -} - -inline const mpreal operator-(const mpreal& a, const mpreal& b) -{ - mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); - mpfr_sub(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); - return c; -} - -inline const mpreal operator-(const double b, const mpreal& a) -{ -#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - mpfr_d_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -#else - mpreal x(b, mpfr_get_prec(a.mpfr_ptr())); - x -= a; - return x; -#endif -} - -inline const mpreal operator-(const unsigned long int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator-(const unsigned int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator-(const long int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator-(const int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -////////////////////////////////////////////////////////////////////////// -// * Multiplication -inline mpreal& mpreal::operator*= (const mpreal& v) -{ - mpfr_mul(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator*=(const mpz_t v) -{ - mpfr_mul_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator*=(const mpq_t v) -{ - mpfr_mul_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator*=(const unsigned int v) -{ - mpfr_mul_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator*=(const long int v) -{ - mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator*=(const int v) -{ - mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline const mpreal operator*(const mpreal& a, const mpreal& b) -{ - mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); - mpfr_mul(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); - return c; -} - -////////////////////////////////////////////////////////////////////////// -// / Division -inline mpreal& mpreal::operator/=(const mpreal& v) -{ - mpfr_div(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator/=(const mpz_t v) -{ - mpfr_div_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator/=(const mpq_t v) -{ - mpfr_div_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator/=(const unsigned int v) -{ - mpfr_div_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator/=(const long int v) -{ - mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator/=(const int v) -{ - mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline const mpreal operator/(const mpreal& a, const mpreal& b) -{ - mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_srcptr()), mpfr_get_prec(b.mpfr_srcptr()))); - mpfr_div(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); - return c; -} - -inline const mpreal operator/(const unsigned long int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator/(const unsigned int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator/(const long int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -} - -inline const mpreal operator/(const int b, const mpreal& a) -{ - mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_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(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_d_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); - return x; -#else - mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); - x /= a; - return x; -#endif -} - -////////////////////////////////////////////////////////////////////////// -// Shifts operators - Multiplication/Division by power of 2 -inline mpreal& mpreal::operator<<=(const unsigned long int u) -{ - mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator<<=(const unsigned int u) -{ - mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator<<=(const long int u) -{ - mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator<<=(const int u) -{ - mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator>>=(const unsigned long int u) -{ - mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator>>=(const unsigned int u) -{ - mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator>>=(const long int u) -{ - mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::operator>>=(const int u) -{ - mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_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(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(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(k)); -} - -inline const mpreal operator>>(const mpreal& v, const int k) -{ - return div_2si(v,static_cast(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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode); - return x; -} - -////////////////////////////////////////////////////////////////////////// -//Relational operators - -// WARNING: -// -// Please note that following checks for double-NaN are guaranteed to work only in IEEE math mode: -// -// isnan(b) = (b != b) -// isnan(b) = !(b == b) (we use in code below) -// -// Be cautions if you use compiler options which break strict IEEE compliance (e.g. -ffast-math in GCC). -// Use std::isnan instead (C++11). - -inline bool operator > (const mpreal& a, const mpreal& b ){ return (mpfr_greater_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } -inline bool operator > (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 ); } -inline bool operator > (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 ); } -inline bool operator > (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 ); } -inline bool operator > (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 ); } -inline bool operator > (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) > 0 ); } -inline bool operator > (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) > 0 ); } - -inline bool operator >= (const mpreal& a, const mpreal& b ){ return (mpfr_greaterequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } -inline bool operator >= (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 ); } -inline bool operator >= (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 ); } -inline bool operator >= (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 ); } -inline bool operator >= (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 ); } -inline bool operator >= (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) >= 0 ); } -inline bool operator >= (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) >= 0 ); } - -inline bool operator < (const mpreal& a, const mpreal& b ){ return (mpfr_less_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } -inline bool operator < (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 ); } -inline bool operator < (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 ); } -inline bool operator < (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 ); } -inline bool operator < (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 ); } -inline bool operator < (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) < 0 ); } -inline bool operator < (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) < 0 ); } - -inline bool operator <= (const mpreal& a, const mpreal& b ){ return (mpfr_lessequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } -inline bool operator <= (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 ); } -inline bool operator <= (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 ); } -inline bool operator <= (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 ); } -inline bool operator <= (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 ); } -inline bool operator <= (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) <= 0 ); } -inline bool operator <= (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) <= 0 ); } - -inline bool operator == (const mpreal& a, const mpreal& b ){ return (mpfr_equal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } -inline bool operator == (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 ); } -inline bool operator == (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 ); } -inline bool operator == (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 ); } -inline bool operator == (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 ); } -inline bool operator == (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) == 0 ); } -inline bool operator == (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) == 0 ); } - -inline bool operator != (const mpreal& a, const mpreal& b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const unsigned long int b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const unsigned int b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const long int b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const int b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const long double b ){ return !(a == b); } -inline bool operator != (const mpreal& a, const double b ){ return !(a == b); } - -inline bool isnan EIGEN_NOT_A_MACRO (const mpreal& op){ return (mpfr_nan_p (op.mpfr_srcptr()) != 0 ); } -inline bool (isinf) (const mpreal& op){ return (mpfr_inf_p (op.mpfr_srcptr()) != 0 ); } -inline bool (isfinite) (const mpreal& op){ return (mpfr_number_p (op.mpfr_srcptr()) != 0 ); } -inline bool iszero (const mpreal& op){ return (mpfr_zero_p (op.mpfr_srcptr()) != 0 ); } -inline bool isint (const mpreal& op){ return (mpfr_integer_p(op.mpfr_srcptr()) != 0 ); } - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) -inline bool isregular(const mpreal& op){ return (mpfr_regular_p(op.mpfr_srcptr()));} -#endif - -////////////////////////////////////////////////////////////////////////// -// Type Converters -inline bool mpreal::toBool ( ) const { return mpfr_zero_p (mpfr_srcptr()) == 0; } -inline long mpreal::toLong (mp_rnd_t mode) const { return mpfr_get_si (mpfr_srcptr(), mode); } -inline unsigned long mpreal::toULong (mp_rnd_t mode) const { return mpfr_get_ui (mpfr_srcptr(), mode); } -inline float mpreal::toFloat (mp_rnd_t mode) const { return mpfr_get_flt(mpfr_srcptr(), mode); } -inline double mpreal::toDouble (mp_rnd_t mode) const { return mpfr_get_d (mpfr_srcptr(), mode); } -inline long double mpreal::toLDouble(mp_rnd_t mode) const { return mpfr_get_ld (mpfr_srcptr(), mode); } -inline long long mpreal::toLLong (mp_rnd_t mode) const { return mpfr_get_sj (mpfr_srcptr(), mode); } -inline unsigned long long mpreal::toULLong (mp_rnd_t mode) const { return mpfr_get_uj (mpfr_srcptr(), mode); } - -inline ::mpfr_ptr mpreal::mpfr_ptr() { return mp; } -inline ::mpfr_srcptr mpreal::mpfr_ptr() const { return mp; } -inline ::mpfr_srcptr mpreal::mpfr_srcptr() const { return mp; } - -template -inline std::string toString(T t, std::ios_base & (*f)(std::ios_base&)) -{ - std::ostringstream oss; - oss << f << t; - return oss.str(); -} - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) - -inline std::string mpreal::toString(const std::string& format) const -{ - char *s = NULL; - std::string out; - - if( !format.empty() ) - { - if(!(mpfr_asprintf(&s, format.c_str(), mpfr_srcptr()) < 0)) - { - out = std::string(s); - - mpfr_free_str(s); - } - } - - return out; -} - -#endif - -inline std::string mpreal::toString(int n, int b, mp_rnd_t mode) const -{ - // TODO: Add extended format specification (f, e, rounding mode) as it done in output operator - (void)b; - (void)mode; - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) - - std::ostringstream format; - - int digits = (n >= 0) ? n : 2 + bits2digits(mpfr_get_prec(mpfr_srcptr())); - - format << "%." << digits << "RNg"; - - return toString(format.str()); - -#else - - char *s, *ns = NULL; - size_t slen, nslen; - mp_exp_t exp; - std::string out; - - if(mpfr_inf_p(mp)) - { - if(mpfr_sgn(mp)>0) return "+Inf"; - else return "-Inf"; - } - - if(mpfr_zero_p(mp)) return "0"; - if(mpfr_nan_p(mp)) return "NaN"; - - s = mpfr_get_str(NULL, &exp, b, 0, mp, mode); - ns = mpfr_get_str(NULL, &exp, b, (std::max)(0,n), mp, mode); - - if(s!=NULL && ns!=NULL) - { - slen = strlen(s); - nslen = strlen(ns); - if(nslen<=slen) - { - mpfr_free_str(s); - s = ns; - slen = nslen; - } - else { - mpfr_free_str(ns); - } - - // Make human eye-friendly formatting if possible - if (exp>0 && static_cast(exp)s+exp) ptr--; - - if(ptr==s+exp) out = std::string(s,exp+1); - else out = std::string(s,exp+1)+'.'+std::string(s+exp+1,ptr-(s+exp+1)+1); - - //out = string(s,exp+1)+'.'+string(s+exp+1); - } - else - { - // Remove zeros starting from right end - char* ptr = s+slen-1; - while (*ptr=='0' && ptr>s+exp-1) ptr--; - - if(ptr==s+exp-1) out = std::string(s,exp); - else out = std::string(s,exp)+'.'+std::string(s+exp,ptr-(s+exp)+1); - - //out = string(s,exp)+'.'+string(s+exp); - } - - }else{ // exp<0 || exp>slen - if(s[0]=='-') - { - // Remove zeros starting from right end - char* ptr = s+slen-1; - while (*ptr=='0' && ptr>s+1) ptr--; - - if(ptr==s+1) out = std::string(s,2); - else out = std::string(s,2)+'.'+std::string(s+2,ptr-(s+2)+1); - - //out = string(s,2)+'.'+string(s+2); - } - else - { - // Remove zeros starting from right end - char* ptr = s+slen-1; - while (*ptr=='0' && ptr>s) ptr--; - - if(ptr==s) out = std::string(s,1); - else out = std::string(s,1)+'.'+std::string(s+1,ptr-(s+1)+1); - - //out = string(s,1)+'.'+string(s+1); - } - - // Make final string - if(--exp) - { - if(exp>0) out += "e+"+mpfr::toString(exp,std::dec); - else out += "e"+mpfr::toString(exp,std::dec); - } - } - - mpfr_free_str(s); - return out; - }else{ - return "conversion error!"; - } -#endif -} - - -////////////////////////////////////////////////////////////////////////// -// I/O -inline std::ostream& mpreal::output(std::ostream& os) const -{ - std::ostringstream format; - const std::ios::fmtflags flags = os.flags(); - - format << ((flags & std::ios::showpos) ? "%+" : "%"); - if (os.precision() >= 0) - format << '.' << os.precision() << "R*" - << ((flags & std::ios::floatfield) == std::ios::fixed ? 'f' : - (flags & std::ios::floatfield) == std::ios::scientific ? 'e' : - 'g'); - else - format << "R*e"; - - char *s = NULL; - if(!(mpfr_asprintf(&s, format.str().c_str(), - mpfr::mpreal::get_default_rnd(), - mpfr_srcptr()) - < 0)) - { - os << std::string(s); - mpfr_free_str(s); - } - return os; -} - -inline std::ostream& operator<<(std::ostream& os, const mpreal& v) -{ - return v.output(os); -} - -inline std::istream& operator>>(std::istream &is, mpreal& v) -{ - // TODO: use cout::hexfloat and other flags to setup base - std::string tmp; - is >> tmp; - mpfr_set_str(v.mpfr_ptr(), tmp.c_str(), 10, mpreal::get_default_rnd()); - return is; -} - -////////////////////////////////////////////////////////////////////////// -// 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; - - return mp_prec_t(std::ceil( d * LOG2_10 )); -} - -inline int bits2digits(mp_prec_t b) -{ - const double LOG10_2 = 0.30102999566398119; - - return int(std::floor( b * LOG10_2 )); -} - -////////////////////////////////////////////////////////////////////////// -// Set/Get number properties -inline mpreal& mpreal::setSign(int sign, mp_rnd_t RoundingMode) -{ - mpfr_setsign(mpfr_ptr(), mpfr_srcptr(), sign < 0, RoundingMode); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline int mpreal::getPrecision() const -{ - return int(mpfr_get_prec(mpfr_srcptr())); -} - -inline mpreal& mpreal::setPrecision(int Precision, mp_rnd_t RoundingMode) -{ - mpfr_prec_round(mpfr_ptr(), Precision, RoundingMode); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::setInf(int sign) -{ - mpfr_set_inf(mpfr_ptr(), sign); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::setNan() -{ - mpfr_set_nan(mpfr_ptr()); - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mpreal& mpreal::setZero(int sign) -{ -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) - mpfr_set_zero(mpfr_ptr(), sign); -#else - mpfr_set_si(mpfr_ptr(), 0, (mpfr_get_default_rounding_mode)()); - setSign(sign); -#endif - - MPREAL_MSVC_DEBUGVIEW_CODE; - return *this; -} - -inline mp_prec_t mpreal::get_prec() const -{ - return mpfr_get_prec(mpfr_srcptr()); -} - -inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode) -{ - mpfr_prec_round(mpfr_ptr(),prec,rnd_mode); - MPREAL_MSVC_DEBUGVIEW_CODE; -} - -inline mp_exp_t mpreal::get_exp () const -{ - return mpfr_get_exp(mpfr_srcptr()); -} - -inline int mpreal::set_exp (mp_exp_t e) -{ - int x = mpfr_set_exp(mpfr_ptr(), e); - MPREAL_MSVC_DEBUGVIEW_CODE; - return x; -} - -inline const mpreal frexp(const mpreal& x, mp_exp_t* exp, mp_rnd_t mode = mpreal::get_default_rnd()) -{ - mpreal y(x); -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0)) - mpfr_frexp(exp,y.mpfr_ptr(),x.mpfr_srcptr(),mode); -#else - *exp = mpfr_get_exp(y.mpfr_srcptr()); - mpfr_set_exp(y.mpfr_ptr(),0); -#endif - return y; -} - -inline const mpreal ldexp(const mpreal& v, mp_exp_t exp) -{ - mpreal x(v); - - // rounding is not important since we are just increasing the exponent (= exact operation) - mpfr_mul_2si(x.mpfr_ptr(), x.mpfr_srcptr(), exp, mpreal::get_default_rnd()); - return x; -} - -inline const mpreal scalbn(const mpreal& v, mp_exp_t exp) -{ - return ldexp(v, exp); -} - -inline mpreal machine_epsilon(mp_prec_t prec) -{ - /* the smallest eps such that 1 + eps != 1 */ - return machine_epsilon(mpreal(1, prec)); -} - -inline mpreal machine_epsilon(const mpreal& x) -{ - /* the smallest eps such that x + eps != x */ - if( x < 0) - { - return nextabove(-x) + x; - }else{ - return nextabove( x) - x; - } -} - -// minval is 'safe' meaning 1 / minval does not overflow -inline mpreal minval(mp_prec_t prec) -{ - /* min = 1/2 * 2^emin = 2^(emin - 1) */ - return mpreal(1, prec) << mpreal::get_emin()-1; -} - -// maxval is 'safe' meaning 1 / maxval does not underflow -inline mpreal maxval(mp_prec_t prec) -{ - /* max = (1 - eps) * 2^emax, eps is machine epsilon */ - return (mpreal(1, prec) - machine_epsilon(prec)) << mpreal::get_emax(); -} - -inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps) -{ - 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) <= eps; -} - -inline bool isEqualFuzzy(const mpreal& a, const mpreal& b) -{ - return isEqualFuzzy(a, b, machine_epsilon((max)(1, (min)(abs(a), abs(b))))); -} - -////////////////////////////////////////////////////////////////////////// -// C++11 sign functions. -inline mpreal copysign(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal rop(0, mpfr_get_prec(x.mpfr_ptr())); - mpfr_setsign(rop.mpfr_ptr(), x.mpfr_srcptr(), mpfr_signbit(y.mpfr_srcptr()), rnd_mode); - return rop; -} - -inline bool signbit(const mpreal& x) -{ - return mpfr_signbit(x.mpfr_srcptr()); -} - -inline mpreal& setsignbit(mpreal& x, bool minus, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpfr_setsign(x.mpfr_ptr(), x.mpfr_srcptr(), minus, rnd_mode); - return x; -} - -inline const mpreal modf(const mpreal& v, mpreal& n) -{ - mpreal f(v); - - // rounding is not important since we are using the same number - mpfr_frac (f.mpfr_ptr(),f.mpfr_srcptr(),mpreal::get_default_rnd()); - mpfr_trunc(n.mpfr_ptr(),v.mpfr_srcptr()); - return f; -} - -inline int mpreal::check_range (int t, mp_rnd_t rnd_mode) -{ - return mpfr_check_range(mpfr_ptr(),t,rnd_mode); -} - -inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode) -{ - int r = mpfr_subnormalize(mpfr_ptr(),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 -////////////////////////////////////////////////////////////////////////// -#define MPREAL_UNARY_MATH_FUNCTION_BODY(f) \ - mpreal y(0, mpfr_get_prec(x.mpfr_srcptr())); \ - mpfr_##f(y.mpfr_ptr(), x.mpfr_srcptr(), r); \ - return y; - -inline const mpreal sqr (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ MPREAL_UNARY_MATH_FUNCTION_BODY(sqr ); } - -inline const mpreal sqrt (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ MPREAL_UNARY_MATH_FUNCTION_BODY(sqrt); } - -inline const mpreal sqrt(const unsigned long int x, mp_rnd_t r) -{ - mpreal y; - mpfr_sqrt_ui(y.mpfr_ptr(), x, r); - return y; -} - -inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode) -{ - return sqrt(static_cast(v),rnd_mode); -} - -inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode) -{ - if (v>=0) return sqrt(static_cast(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(v),rnd_mode); - else return mpreal().setNan(); // NaN -} - -inline const mpreal root(const mpreal& x, unsigned long int k, mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal y(0, mpfr_get_prec(x.mpfr_srcptr())); - #if (MPFR_VERSION >= MPFR_VERSION_NUM(4,0,0)) - mpfr_rootn_ui(y.mpfr_ptr(), x.mpfr_srcptr(), k, r); - #else - mpfr_root(y.mpfr_ptr(), x.mpfr_srcptr(), k, r); - #endif - return y; -} - -inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal y(0, mpfr_get_prec(a.mpfr_srcptr())); - mpfr_dim(y.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), r); - return y; -} - -inline int cmpabs(const mpreal& a,const mpreal& b) -{ - return mpfr_cmpabs(a.mpfr_ptr(), b.mpfr_srcptr()); -} - -inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - return mpfr_sin_cos(s.mpfr_ptr(), c.mpfr_ptr(), v.mpfr_srcptr(), rnd_mode); -} - -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& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cbrt ); } -inline const mpreal fabs (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(abs ); } -inline const mpreal abs (const mpreal& x, mp_rnd_t r) { MPREAL_UNARY_MATH_FUNCTION_BODY(abs ); } -inline const mpreal log (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log ); } -inline const mpreal log2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log2 ); } -inline const mpreal log10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log10); } -inline const mpreal exp (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp ); } -inline const mpreal exp2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp2 ); } -inline const mpreal exp10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp10); } -inline const mpreal cos (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cos ); } -inline const mpreal sin (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sin ); } -inline const mpreal tan (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(tan ); } -inline const mpreal sec (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sec ); } -inline const mpreal csc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(csc ); } -inline const mpreal cot (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cot ); } -inline const mpreal acos (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(acos ); } -inline const mpreal asin (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(asin ); } -inline const mpreal atan (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(atan ); } - -inline const mpreal logb (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { return log2 (abs(x),r); } - -inline const mpreal acot (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return atan (1/v, r); } -inline const mpreal asec (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return acos (1/v, r); } -inline const mpreal acsc (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return asin (1/v, r); } -inline const mpreal acoth (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return atanh(1/v, r); } -inline const mpreal asech (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return acosh(1/v, r); } -inline const mpreal acsch (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return asinh(1/v, r); } - -inline const mpreal cosh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cosh ); } -inline const mpreal sinh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sinh ); } -inline const mpreal tanh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(tanh ); } -inline const mpreal sech (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sech ); } -inline const mpreal csch (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(csch ); } -inline const mpreal coth (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(coth ); } -inline const mpreal acosh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(acosh); } -inline const mpreal asinh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(asinh); } -inline const mpreal atanh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(atanh); } - -inline const mpreal log1p (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log1p ); } -inline const mpreal expm1 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(expm1 ); } -inline const mpreal eint (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(eint ); } -inline const mpreal gamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(gamma ); } -inline const mpreal tgamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(gamma ); } -inline const mpreal lngamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(lngamma); } -inline const mpreal zeta (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(zeta ); } -inline const mpreal erf (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(erf ); } -inline const mpreal erfc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(erfc ); } -inline const mpreal besselj0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(j0 ); } -inline const mpreal besselj1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(j1 ); } -inline const mpreal bessely0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(y0 ); } -inline const mpreal bessely1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(y1 ); } - -inline const mpreal nextpow2(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal y(0, x.getPrecision()); - - if(!iszero(x)) - y = ceil(log2(abs(x,r),r)); - - return y; -} - -inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); - mpfr_atan2(a.mpfr_ptr(), y.mpfr_srcptr(), x.mpfr_srcptr(), rnd_mode); - return a; -} - -inline const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); - mpfr_hypot(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); - return a; -} - -inline const mpreal hypot(const mpreal& a, const mpreal& b, const mpreal& c) -{ - if(isnan EIGEN_NOT_A_MACRO (a) || isnan EIGEN_NOT_A_MACRO (b) || isnan EIGEN_NOT_A_MACRO(c)) return mpreal().setNan(); - else - { - mpreal absa = abs(a), absb = abs(b), absc = abs(c); - mpreal w = (std::max)(absa, (std::max)(absb, absc)); - mpreal r; - - if (!iszero(w)) - { - mpreal iw = 1/w; - r = w * sqrt(sqr(absa*iw) + sqr(absb*iw) + sqr(absc*iw)); - } - - return r; - } -} - -inline const mpreal hypot(const mpreal& a, const mpreal& b, const mpreal& c, const mpreal& d) -{ - if(isnan EIGEN_NOT_A_MACRO (a) || isnan EIGEN_NOT_A_MACRO (b) || isnan EIGEN_NOT_A_MACRO (c) || isnan EIGEN_NOT_A_MACRO (d)) return mpreal().setNan(); - else - { - mpreal absa = abs(a), absb = abs(b), absc = abs(c), absd = abs(d); - mpreal w = (std::max)(absa, (std::max)(absb, (std::max)(absc, absd))); - mpreal r; - - if (!iszero(w)) - { - mpreal iw = 1/w; - r = w * sqrt(sqr(absa*iw) + sqr(absb*iw) + sqr(absc*iw) + sqr(absd*iw)); - } - - return r; - } -} - -inline const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); - mpfr_remainder(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); - return a; -} - -inline const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); - mpfr_remquo(a.mpfr_ptr(),q, x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); - return a; -} - -inline const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::get_default_prec(), - mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal x(0, prec); - mpfr_fac_ui(x.mpfr_ptr(),v,rnd_mode); - return x; -} - - -inline const mpreal lgamma (const mpreal& v, int *signp = 0, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal x(v); - int tsignp; - - if(signp) mpfr_lgamma(x.mpfr_ptr(), signp,v.mpfr_srcptr(),rnd_mode); - else mpfr_lgamma(x.mpfr_ptr(),&tsignp,v.mpfr_srcptr(),rnd_mode); - - return x; -} - - -inline const mpreal besseljn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal y(0, x.getPrecision()); - mpfr_jn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r); - return y; -} - -inline const mpreal besselyn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal y(0, x.getPrecision()); - mpfr_yn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r); - return y; -} - -inline const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a; - mp_prec_t p1, p2, p3; - - p1 = v1.get_prec(); - p2 = v2.get_prec(); - p3 = v3.get_prec(); - - a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1)); - - mpfr_fma(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode); - return a; -} - -inline const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a; - mp_prec_t p1, p2, p3; - - p1 = v1.get_prec(); - p2 = v2.get_prec(); - p3 = v3.get_prec(); - - a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1)); - - mpfr_fms(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode); - return a; -} - -inline const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal a; - mp_prec_t p1, p2; - - p1 = v1.get_prec(); - p2 = v2.get_prec(); - - a.set_prec(p1>p2?p1:p2); - - mpfr_agm(a.mp, v1.mp, v2.mp, rnd_mode); - - return a; -} - -inline const mpreal sum (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t mode = mpreal::get_default_rnd()) -{ - mpfr_srcptr *p = new mpfr_srcptr[n]; - - for (unsigned long int i = 0; i < n; i++) - p[i] = tab[i].mpfr_srcptr(); - - mpreal x; - status = mpfr_sum(x.mpfr_ptr(), (mpfr_ptr*)p, n, mode); - - delete [] p; - 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 = mpreal::get_default_rnd()) -{ - return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode); -} - -inline const mpreal li2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) -{ - MPREAL_UNARY_MATH_FUNCTION_BODY(li2); -} - -inline const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - /* R = rem(X,Y) if Y != 0, returns X - n * Y where n = trunc(X/Y). */ - return fmod(x, y, rnd_mode); -} - -inline const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - (void)rnd_mode; - - /* - - m = mod(x,y) if y != 0, returns x - n*y where n = floor(x/y) - - The following are true by convention: - - mod(x,0) is x - - mod(x,x) is 0 - - mod(x,y) for x != y and y != 0 has the same sign as y. - - */ - - if(iszero(y)) return x; - if(x == y) return 0; - - mpreal m = x - floor(x / y) * y; - - return copysign(abs(m),y); // make sure result has the same sign as Y -} - -inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - 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::get_default_rnd()) -{ - 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& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(digamma); } -inline const mpreal ai (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(ai); } -#endif // MPFR 3.0.0 Specifics - -////////////////////////////////////////////////////////////////////////// -// Constants -inline const mpreal const_log2 (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal x(0, p); - mpfr_const_log2(x.mpfr_ptr(), r); - return x; -} - -inline const mpreal const_pi (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal x(0, p); - mpfr_const_pi(x.mpfr_ptr(), r); - return x; -} - -inline const mpreal const_euler (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal x(0, p); - mpfr_const_euler(x.mpfr_ptr(), r); - return x; -} - -inline const mpreal const_catalan (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) -{ - mpreal x(0, p); - mpfr_const_catalan(x.mpfr_ptr(), r); - return x; -} - -inline const mpreal const_infinity (int sign = 1, mp_prec_t p = mpreal::get_default_prec()) -{ - mpreal x(0, p); - mpfr_set_inf(x.mpfr_ptr(), sign); - return x; -} - -////////////////////////////////////////////////////////////////////////// -// Integer Related Functions -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 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint ); } -inline const mpreal rint_ceil (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_ceil ); } -inline const mpreal rint_floor (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_floor); } -inline const mpreal rint_round (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_round); } -inline const mpreal rint_trunc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_trunc); } -inline const mpreal frac (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(frac ); } - -////////////////////////////////////////////////////////////////////////// -// Miscellaneous Functions -inline int sgn(const mpreal& op) -{ - // Please note, this is classic signum function which ignores sign of zero. - // Use signbit if you need sign of zero. - return mpfr_sgn(op.mpfr_srcptr()); -} - -////////////////////////////////////////////////////////////////////////// -// Miscellaneous Functions -inline void swap (mpreal& a, mpreal& b) { mpfr_swap(a.mpfr_ptr(),b.mpfr_ptr()); } -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= MPFR_VERSION_NUM(3,0,0)) -inline const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal x; - mpfr_urandom(x.mpfr_ptr(), 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.mpfr_ptr(),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 = 0) -{ -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) - static gmp_randstate_t state; - static bool initialize = true; - - if(initialize) - { - gmp_randinit_default(state); - gmp_randseed_ui(state,0); - initialize = 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 - -} - -#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0) && MPFR_VERSION < MPFR_VERSION_NUM(4,0,0)) - -// TODO: -// Use mpfr_nrandom since mpfr_grandom is deprecated -#if defined(_MSC_VER) -#pragma warning( push ) -#pragma warning( disable : 1478) -#endif -inline const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - mpreal x; - mpfr_grandom(x.mpfr_ptr(), NULL, state, rnd_mode); - return x; -} -#if defined(_MSC_VER) -#pragma warning( pop ) -#endif - -inline const mpreal grandom(unsigned int seed = 0) -{ - static gmp_randstate_t state; - static bool initialize = true; - - if(initialize) - { - gmp_randinit_default(state); - gmp_randseed_ui(state,0); - initialize = false; - } - - if(seed != 0) gmp_randseed_ui(state,seed); - - return mpfr::grandom(state); -} -#endif - -////////////////////////////////////////////////////////////////////////// -// Set/Get global properties -inline void mpreal::set_default_prec(mp_prec_t prec) -{ - mpfr_set_default_prec(prec); -} - -inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode) -{ - mpfr_set_default_rounding_mode(rnd_mode); -} - -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::get_default_rnd()) -{ - 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::get_default_rnd()) -{ - 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::get_default_rnd()) -{ - 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(b),rnd_mode); -} - -inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) -{ - 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(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::get_default_rnd()) -{ - 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(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(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(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(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(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(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(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(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(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(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(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(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(mpreal(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(a),mpreal(b),rnd_mode); //mpfr_ui_pow - }else{ - return pow(mpreal(a),static_cast(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(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(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(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(mpreal(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui - else return pow(static_cast(a),mpreal(b),rnd_mode); //mpfr_ui_pow - }else{ - return pow(mpreal(a),static_cast(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(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(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(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(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(b),rnd_mode); // mpfr_pow_ui -} - -inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode) -{ - return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si -} - -inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode) -{ - return pow(mpreal(a),static_cast(b),rnd_mode); // mpfr_pow_si -} -} // End of mpfr namespace - -// Explicit specialization of std::swap for mpreal numbers -// Thus standard algorithms will use efficient version of swap (due to Koenig lookup) -// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap -namespace std -{ - // we are allowed to extend namespace std with specializations only - template <> - inline void swap(mpfr::mpreal& x, mpfr::mpreal& y) - { - return mpfr::swap(x, y); - } - - template<> - class numeric_limits - { - public: - static const bool is_specialized = true; - static const bool is_signed = true; - static const bool is_integer = false; - static const bool is_exact = false; - static const int radix = 2; - - static const bool has_infinity = true; - static const bool has_quiet_NaN = true; - static const bool has_signaling_NaN = true; - - static const bool is_iec559 = true; // = IEEE 754 - static const bool is_bounded = true; - static const bool is_modulo = false; - static const bool traps = true; - static const bool tinyness_before = true; - - static const float_denorm_style has_denorm = denorm_absent; - - inline static mpfr::mpreal (min) (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::minval(precision); } - inline static mpfr::mpreal (max) (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(precision); } - inline static mpfr::mpreal lowest (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(precision); } - - // Returns smallest eps such that 1 + eps != 1 (classic machine epsilon) - inline static mpfr::mpreal epsilon(mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(precision); } - - // Returns smallest eps such that x + eps != x (relative machine epsilon) - inline static mpfr::mpreal epsilon(const mpfr::mpreal& x) { return mpfr::machine_epsilon(x); } - - inline static mpfr::mpreal round_error(mp_prec_t precision = mpfr::mpreal::get_default_prec()) - { - mp_rnd_t r = mpfr::mpreal::get_default_rnd(); - - if(r == GMP_RNDN) return mpfr::mpreal(0.5, precision); - else return mpfr::mpreal(1.0, precision); - } - - inline static const mpfr::mpreal infinity() { return mpfr::const_infinity(); } - inline static const mpfr::mpreal quiet_NaN() { return mpfr::mpreal().setNan(); } - inline static const mpfr::mpreal signaling_NaN() { return mpfr::mpreal().setNan(); } - inline static const mpfr::mpreal denorm_min() { return (min)(); } - - // Please note, exponent range is not fixed in MPFR - static const int min_exponent = MPFR_EMIN_DEFAULT; - static const int max_exponent = MPFR_EMAX_DEFAULT; - MPREAL_PERMISSIVE_EXPR static const int min_exponent10 = (int) (MPFR_EMIN_DEFAULT * 0.3010299956639811); - MPREAL_PERMISSIVE_EXPR static const int max_exponent10 = (int) (MPFR_EMAX_DEFAULT * 0.3010299956639811); - -#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS - - // Following members should be constant according to standard, but they can be variable in MPFR - // So we define them as functions here. - // - // This is preferable way for std::numeric_limits specialization. - // But it is incompatible with standard std::numeric_limits and might not work with other libraries, e.g. boost. - // See below for compatible implementation. - inline static float_round_style round_style() - { - mp_rnd_t r = mpfr::mpreal::get_default_rnd(); - - switch (r) - { - case GMP_RNDN: return round_to_nearest; - case GMP_RNDZ: return round_toward_zero; - case GMP_RNDU: return round_toward_infinity; - case GMP_RNDD: return round_toward_neg_infinity; - default: return round_indeterminate; - } - } - - inline static int digits() { return int(mpfr::mpreal::get_default_prec()); } - inline static int digits(const mpfr::mpreal& x) { return x.getPrecision(); } - - inline static int digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec()) - { - return mpfr::bits2digits(precision); - } - - inline static int digits10(const mpfr::mpreal& x) - { - return mpfr::bits2digits(x.getPrecision()); - } - - inline static int max_digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec()) - { - return digits10(precision); - } -#else - // Digits and round_style are NOT constants when it comes to mpreal. - // If possible, please use functions digits() and round_style() defined above. - // - // These (default) values are preserved for compatibility with existing libraries, e.g. boost. - // Change them accordingly to your application. - // - // For example, if you use 256 bits of precision uniformly in your program, then: - // digits = 256 - // digits10 = 77 - // max_digits10 = 78 - // - // Approximate formula for decimal digits is: digits10 = floor(log10(2) * digits). See bits2digits() for more details. - - static const std::float_round_style round_style = round_to_nearest; - static const int digits = 53; - static const int digits10 = 15; - static const int max_digits10 = 16; -#endif - }; - -} - -#endif /* __MPREAL_H__ */ +/* + MPFR C++: Multi-precision floating point number class for C++. + Based on MPFR library: http://mpfr.org + + Project homepage: http://www.holoborodko.com/pavel/mpfr + Contact e-mail: pavel@holoborodko.com + + Copyright (c) 2008-2016 Pavel Holoborodko + + Contributors: + Dmitriy Gubanov, Konstantin Holoborodko, Brian Gladman, + Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen, + Pere Constans, Peter van Hoof, Gael Guennebaud, Tsai Chia Cheng, + Alexei Zubanov, Jauhien Piatlicki, Victor Berger, John Westwood, + Petr Aleksandrov, Orion Poplawski, Charles Karney, Arash Partow, + Rodney James, Jorge Leitao, Jerome Benoit. + + Licensing: + (A) MPFR C++ is under GNU General Public License ("GPL"). + + (B) Non-free licenses may also be purchased from the author, for users who + do not want their programs protected by the GPL. + + The non-free licenses are for users that wish to use MPFR C++ in + their products but are unwilling to release their software + under the GPL (which would require them to release source code + and allow free redistribution). + + Such users can purchase an unlimited-use license from the author. + Contact us for more details. + + GNU General Public License ("GPL") copyright permissions statement: + ************************************************************************** + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +#ifndef __MPREAL_H__ +#define __MPREAL_H__ + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +// Options +#define MPREAL_HAVE_MSVC_DEBUGVIEW // Enable Debugger Visualizer for "Debug" builds in MSVC. +#define MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS // Enable extended std::numeric_limits specialization. + // Meaning that "digits", "round_style" and similar members are defined as functions, not constants. + // See std::numeric_limits at the end of the file for more information. + +// Library version +#define MPREAL_VERSION_MAJOR 3 +#define MPREAL_VERSION_MINOR 6 +#define MPREAL_VERSION_PATCHLEVEL 5 +#define MPREAL_VERSION_STRING "3.6.5" + +// Detect compiler using signatures from http://predef.sourceforge.net/ +#if defined(__GNUC__) && defined(__INTEL_COMPILER) + #define IsInf(x) isinf EIGEN_NOT_A_MACRO (x) // Intel ICC compiler on Linux + +#elif defined(_MSC_VER) // Microsoft Visual C++ + #define IsInf(x) (!_finite(x)) + +#else + #define IsInf(x) std::isinf EIGEN_NOT_A_MACRO (x) // GNU C/C++ (and/or other compilers), just hope for C99 conformance +#endif + +// A Clang feature extension to determine compiler features. +#ifndef __has_feature + #define __has_feature(x) 0 +#endif + +// Detect support for r-value references (move semantic). +// Move semantic should be enabled with great care in multi-threading environments, +// especially if MPFR uses custom memory allocators. +// Everything should be thread-safe and support passing ownership over thread boundary. +#if (__has_feature(cxx_rvalue_references) || \ + defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L || \ + (defined(_MSC_VER) && _MSC_VER >= 1600) && !defined(MPREAL_DISABLE_MOVE_SEMANTIC)) + + #define MPREAL_HAVE_MOVE_SUPPORT + + // Use fields in mpfr_t structure to check if it was initialized / set dummy initialization + #define mpfr_is_initialized(x) (0 != (x)->_mpfr_d) + #define mpfr_set_uninitialized(x) ((x)->_mpfr_d = 0 ) +#endif + +// Detect support for explicit converters. +#if (__has_feature(cxx_explicit_conversions) || \ + (defined(__GXX_EXPERIMENTAL_CXX0X__) && __GNUC_MINOR__ >= 5) || __cplusplus >= 201103L || \ + (defined(_MSC_VER) && _MSC_VER >= 1800) || \ + (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 1300)) + + #define MPREAL_HAVE_EXPLICIT_CONVERTERS +#endif + +#define MPFR_USE_INTMAX_T // Enable 64-bit integer types - should be defined before mpfr.h + +#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG) + #define MPREAL_MSVC_DEBUGVIEW_CODE DebugView = toString(); + #define MPREAL_MSVC_DEBUGVIEW_DATA std::string DebugView; +#else + #define MPREAL_MSVC_DEBUGVIEW_CODE + #define MPREAL_MSVC_DEBUGVIEW_DATA +#endif + +#include + +#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0)) + #include // Needed for random() +#endif + +// Less important options +#define MPREAL_DOUBLE_BITS_OVERFLOW -1 // Triggers overflow exception during conversion to double if mpreal + // cannot fit in MPREAL_DOUBLE_BITS_OVERFLOW bits + // = -1 disables overflow checks (default) + +// Fast replacement for mpfr_set_zero(x, +1): +// (a) uses low-level data members, might not be forward compatible +// (b) sign is not set, add (x)->_mpfr_sign = 1; +#define mpfr_set_zero_fast(x) ((x)->_mpfr_exp = __MPFR_EXP_ZERO) + +#if defined(__GNUC__) + #define MPREAL_PERMISSIVE_EXPR __extension__ +#else + #define MPREAL_PERMISSIVE_EXPR +#endif + +namespace mpfr { + +class mpreal { +private: + mpfr_t mp; + +public: + + // Get default rounding mode & precision + inline static mp_rnd_t get_default_rnd() { return (mp_rnd_t)(mpfr_get_default_rounding_mode()); } + inline static mp_prec_t get_default_prec() { return (mpfr_get_default_prec)(); } + + // Constructors && type conversions + mpreal(); + mpreal(const mpreal& u); + mpreal(const mpf_t u); + mpreal(const mpz_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const mpq_t u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const long double u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const unsigned long long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const long long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const unsigned long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const unsigned int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd()); + + // Construct mpreal from mpfr_t structure. + // shared = true allows to avoid deep copy, so that mpreal and 'u' share the same data & pointers. + mpreal(const mpfr_t u, bool shared = false); + + mpreal(const char* s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd()); + mpreal(const std::string& s, mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd()); + + ~mpreal(); + +#ifdef MPREAL_HAVE_MOVE_SUPPORT + mpreal& operator=(mpreal&& v); + mpreal(mpreal&& u); +#endif + + // Operations + // = + // +, -, *, /, ++, --, <<, >> + // *=, +=, -=, /=, + // <, >, ==, <=, >= + + // = + mpreal& operator=(const mpreal& v); + mpreal& operator=(const mpf_t v); + mpreal& operator=(const mpz_t v); + mpreal& operator=(const mpq_t v); + mpreal& operator=(const long double v); + mpreal& operator=(const double v); + mpreal& operator=(const unsigned long int v); + mpreal& operator=(const unsigned long long int v); + mpreal& operator=(const long long int v); + mpreal& operator=(const unsigned int v); + mpreal& operator=(const long int v); + mpreal& operator=(const int v); + mpreal& operator=(const char* s); + mpreal& operator=(const std::string& s); + template mpreal& operator= (const std::complex& z); + + // + + mpreal& operator+=(const mpreal& v); + mpreal& operator+=(const mpf_t v); + mpreal& operator+=(const mpz_t v); + mpreal& operator+=(const mpq_t v); + mpreal& operator+=(const long double u); + mpreal& operator+=(const double u); + mpreal& operator+=(const unsigned long int u); + mpreal& operator+=(const unsigned int u); + mpreal& operator+=(const long int u); + mpreal& operator+=(const int u); + + mpreal& operator+=(const long long int u); + mpreal& operator+=(const unsigned long long int u); + mpreal& operator-=(const long long int u); + mpreal& operator-=(const unsigned long long int u); + mpreal& operator*=(const long long int u); + mpreal& operator*=(const unsigned long long int u); + mpreal& operator/=(const long long int u); + mpreal& operator/=(const unsigned long long int u); + + const mpreal operator+() const; + mpreal& operator++ (); + const mpreal operator++ (int); + + // - + mpreal& operator-=(const mpreal& v); + mpreal& operator-=(const mpz_t v); + mpreal& operator-=(const mpq_t v); + mpreal& operator-=(const long double u); + mpreal& operator-=(const double u); + mpreal& operator-=(const unsigned long int u); + mpreal& operator-=(const unsigned int u); + mpreal& operator-=(const long int u); + mpreal& operator-=(const int u); + const mpreal operator-() const; + friend const mpreal operator-(const unsigned long int b, const mpreal& a); + friend const mpreal operator-(const unsigned int b, const mpreal& a); + friend const mpreal operator-(const long int b, const mpreal& a); + friend const mpreal operator-(const int b, const mpreal& a); + friend const mpreal operator-(const double b, const mpreal& a); + mpreal& operator-- (); + const mpreal operator-- (int); + + // * + mpreal& operator*=(const mpreal& v); + mpreal& operator*=(const mpz_t v); + mpreal& operator*=(const mpq_t v); + mpreal& operator*=(const long double v); + mpreal& operator*=(const double v); + mpreal& operator*=(const unsigned long int v); + mpreal& operator*=(const unsigned int v); + mpreal& operator*=(const long int v); + mpreal& operator*=(const int v); + + // / + mpreal& operator/=(const mpreal& v); + mpreal& operator/=(const mpz_t v); + mpreal& operator/=(const mpq_t v); + mpreal& operator/=(const long double v); + mpreal& operator/=(const double v); + mpreal& operator/=(const unsigned long int v); + mpreal& operator/=(const unsigned int v); + mpreal& operator/=(const long int v); + mpreal& operator/=(const int v); + friend const mpreal operator/(const unsigned long int b, const mpreal& a); + friend const mpreal operator/(const unsigned int b, const mpreal& a); + friend const mpreal operator/(const long int b, const mpreal& a); + friend const mpreal operator/(const int b, const mpreal& a); + friend const mpreal operator/(const double b, const mpreal& a); + + //<<= Fast Multiplication by 2^u + mpreal& operator<<=(const unsigned long int u); + mpreal& operator<<=(const unsigned int u); + mpreal& operator<<=(const long int u); + mpreal& operator<<=(const int u); + + //>>= Fast Division by 2^u + mpreal& operator>>=(const unsigned long int u); + mpreal& operator>>=(const unsigned int u); + mpreal& operator>>=(const long int u); + mpreal& operator>>=(const int u); + + // Type Conversion operators + bool toBool ( ) const; + long toLong (mp_rnd_t mode = GMP_RNDZ) const; + unsigned long toULong (mp_rnd_t mode = GMP_RNDZ) const; + long long toLLong (mp_rnd_t mode = GMP_RNDZ) const; + unsigned long long toULLong (mp_rnd_t mode = GMP_RNDZ) const; + float toFloat (mp_rnd_t mode = GMP_RNDN) const; + double toDouble (mp_rnd_t mode = GMP_RNDN) const; + long double toLDouble (mp_rnd_t mode = GMP_RNDN) const; + +#if defined (MPREAL_HAVE_EXPLICIT_CONVERTERS) + explicit operator bool () const { return toBool(); } + explicit operator int () const { return int(toLong()); } + explicit operator long () const { return toLong(); } + explicit operator long long () const { return toLLong(); } + explicit operator unsigned () const { return unsigned(toULong()); } + explicit operator unsigned long () const { return toULong(); } + explicit operator unsigned long long () const { return toULLong(); } + explicit operator float () const { return toFloat(); } + explicit operator double () const { return toDouble(); } + explicit operator long double () const { return toLDouble(); } +#endif + + // Get raw pointers so that mpreal can be directly used in raw mpfr_* functions + ::mpfr_ptr mpfr_ptr(); + ::mpfr_srcptr mpfr_ptr() const; + ::mpfr_srcptr mpfr_srcptr() const; + + // Convert mpreal to string with n significant digits in base b + // n = -1 -> convert with the maximum available digits + std::string toString(int n = -1, int b = 10, mp_rnd_t mode = mpreal::get_default_rnd()) const; + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) + std::string toString(const std::string& format) const; +#endif + + std::ostream& output(std::ostream& os) const; + + // Math Functions + friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode); + friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); + friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode); + friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode); + friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode); + friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode); + friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode); + friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode); + friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode); + friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); + friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode); + friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode); + friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode); + friend int cmpabs(const mpreal& a,const mpreal& b); + + friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal logb (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal nextpow2(const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode); + friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode); + friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + + friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec, mp_rnd_t rnd_mode); + friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode); + + friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal tgamma (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode); + friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode); + friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode); + friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode); + friend const mpreal sum (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t rnd_mode); + friend int sgn (const mpreal& v); + +// MPFR 2.4.0 Specifics +#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) + friend int sinh_cosh (mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal li2 (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + friend const mpreal rec_sqrt (const mpreal& v, mp_rnd_t rnd_mode); + + // MATLAB's semantic equivalents + friend const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Remainder after division + friend const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Modulus after division +#endif + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) + friend const mpreal digamma (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal ai (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear +#endif + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0)) + friend const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode); // use gmp_randinit_default() to init state, gmp_randclear() to clear + friend const mpreal grandom (unsigned int seed); +#endif + + // Uniformly distributed random number generation in [0,1] using + // Mersenne-Twister algorithm by default. + // Use parameter to setup seed, e.g.: random((unsigned)time(NULL)) + // Check urandom() for more precise control. + friend const mpreal random(unsigned int seed); + + // Splits mpreal value into fractional and integer parts. + // Returns fractional part and stores integer part in n. + friend const mpreal modf(const mpreal& v, mpreal& n); + + // Constants + // don't forget to call mpfr_free_cache() for every thread where you are using const-functions + friend const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode); + friend const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode); + friend const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode); + friend const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode); + + // returns +inf iff sign>=0 otherwise -inf + friend const mpreal const_infinity(int sign, mp_prec_t prec); + + // Output/ Input + friend std::ostream& operator<<(std::ostream& os, const mpreal& v); + friend std::istream& operator>>(std::istream& is, mpreal& v); + + // Integer Related Functions + friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal ceil (const mpreal& v); + friend const mpreal floor(const mpreal& v); + friend const mpreal round(const mpreal& v); + friend const mpreal trunc(const mpreal& v); + friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal rint_floor (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal rint_round (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal rint_trunc (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode); + friend const mpreal remainder ( const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + + // Miscellaneous Functions + friend const mpreal nexttoward (const mpreal& x, const mpreal& y); + friend const mpreal nextabove (const mpreal& x); + friend const mpreal nextbelow (const mpreal& x); + + // use gmp_randinit_default() to init state, gmp_randclear() to clear + friend const mpreal urandomb (gmp_randstate_t& state); + +// MPFR < 2.4.2 Specifics +#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2)) + friend const mpreal random2 (mp_size_t size, mp_exp_t exp); +#endif + + // Instance Checkers + friend bool isnan EIGEN_NOT_A_MACRO (const mpreal& v); + friend bool (isinf) (const mpreal& v); + friend bool (isfinite) (const mpreal& v); + + friend bool isnum (const mpreal& v); + friend bool iszero (const mpreal& v); + friend bool isint (const mpreal& v); + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) + friend bool isregular(const mpreal& v); +#endif + + // Set/Get instance properties + inline mp_prec_t get_prec() const; + inline void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = get_default_rnd()); // Change precision with rounding mode + + // Aliases for get_prec(), set_prec() - needed for compatibility with std::complex interface + inline mpreal& setPrecision(int Precision, mp_rnd_t RoundingMode = get_default_rnd()); + inline int getPrecision() const; + + // Set mpreal to +/- inf, NaN, +/-0 + mpreal& setInf (int Sign = +1); + mpreal& setNan (); + mpreal& setZero (int Sign = +1); + mpreal& setSign (int Sign, mp_rnd_t RoundingMode = get_default_rnd()); + + //Exponent + mp_exp_t get_exp() const; + int set_exp(mp_exp_t e); + int check_range (int t, mp_rnd_t rnd_mode = get_default_rnd()); + int subnormalize (int t, mp_rnd_t rnd_mode = get_default_rnd()); + + // Inexact conversion from float + inline bool fits_in_bits(double x, int n); + + // Set/Get global properties + static void set_default_prec(mp_prec_t prec); + static void set_default_rnd(mp_rnd_t rnd_mode); + + static mp_exp_t get_emin (void); + static mp_exp_t get_emax (void); + static mp_exp_t get_emin_min (void); + static mp_exp_t get_emin_max (void); + static mp_exp_t get_emax_min (void); + static mp_exp_t get_emax_max (void); + static int set_emin (mp_exp_t exp); + static int set_emax (mp_exp_t exp); + + // Efficient swapping of two mpreal values - needed for std algorithms + friend void swap(mpreal& x, mpreal& y); + + friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); + +private: + // Human friendly Debug Preview in Visual Studio. + // Put one of these lines: + // + // mpfr::mpreal= ; Show value only + // mpfr::mpreal=, bits ; Show value & precision + // + // at the beginning of + // [Visual Studio Installation Folder]\Common7\Packages\Debugger\autoexp.dat + MPREAL_MSVC_DEBUGVIEW_DATA + + // "Smart" resources deallocation. Checks if instance initialized before deletion. + void clear(::mpfr_ptr); +}; + +////////////////////////////////////////////////////////////////////////// +// Exceptions +class conversion_overflow : public std::exception { +public: + std::string why() { return "inexact conversion from floating point"; } +}; + +////////////////////////////////////////////////////////////////////////// +// Constructors & converters +// Default constructor: creates mp number and initializes it to 0. +inline mpreal::mpreal() +{ + mpfr_init2(mpfr_ptr(), mpreal::get_default_prec()); + mpfr_set_zero_fast(mpfr_ptr()); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const mpreal& u) +{ + mpfr_init2(mpfr_ptr(),mpfr_get_prec(u.mpfr_srcptr())); + mpfr_set (mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +#ifdef MPREAL_HAVE_MOVE_SUPPORT +inline mpreal::mpreal(mpreal&& other) +{ + mpfr_set_uninitialized(mpfr_ptr()); // make sure "other" holds null-pointer (in uninitialized state) + mpfr_swap(mpfr_ptr(), other.mpfr_ptr()); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal& mpreal::operator=(mpreal&& other) +{ + if (this != &other) + { + mpfr_swap(mpfr_ptr(), other.mpfr_ptr()); // destructor for "other" will be called just afterwards + MPREAL_MSVC_DEBUGVIEW_CODE; + } + return *this; +} +#endif + +inline mpreal::mpreal(const mpfr_t u, bool shared) +{ + if(shared) + { + std::memcpy(mpfr_ptr(), u, sizeof(mpfr_t)); + } + else + { + mpfr_init2(mpfr_ptr(), mpfr_get_prec(u)); + mpfr_set (mpfr_ptr(), u, mpreal::get_default_rnd()); + } + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const mpf_t u) +{ + mpfr_init2(mpfr_ptr(),(mp_prec_t) mpf_get_prec(u)); // (gmp: mp_bitcnt_t) unsigned long -> long (mpfr: mp_prec_t) + mpfr_set_f(mpfr_ptr(),u,mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const mpz_t u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2(mpfr_ptr(), prec); + mpfr_set_z(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const mpq_t u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2(mpfr_ptr(), prec); + mpfr_set_q(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const double u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2(mpfr_ptr(), prec); + +#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1) + if(fits_in_bits(u, MPREAL_DOUBLE_BITS_OVERFLOW)) + { + mpfr_set_d(mpfr_ptr(), u, mode); + }else + throw conversion_overflow(); +#else + mpfr_set_d(mpfr_ptr(), u, mode); +#endif + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const long double u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_ld(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const unsigned long long int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_uj(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const long long int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_sj(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const unsigned long int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_ui(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const unsigned int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_ui(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const long int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_si(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const int u, mp_prec_t prec, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_si(mpfr_ptr(), u, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_str(mpfr_ptr(), s, base, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mpreal::mpreal(const std::string& s, mp_prec_t prec, int base, mp_rnd_t mode) +{ + mpfr_init2 (mpfr_ptr(), prec); + mpfr_set_str(mpfr_ptr(), s.c_str(), base, mode); + + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline void mpreal::clear(::mpfr_ptr x) +{ +#ifdef MPREAL_HAVE_MOVE_SUPPORT + if(mpfr_is_initialized(x)) +#endif + mpfr_clear(x); +} + +inline mpreal::~mpreal() +{ + clear(mpfr_ptr()); +} + +// internal namespace needed for template magic +namespace internal{ + + // Use SFINAE to restrict arithmetic operations instantiation only for numeric types + // This is needed for smooth integration with libraries based on expression templates, like Eigen. + // TODO: Do the same for boolean operators. + template struct result_type {}; + + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; + template <> struct result_type {typedef mpreal type;}; +} + +// + Addition +template +inline const typename internal::result_type::type + operator+(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) += rhs; } + +template +inline const typename internal::result_type::type + operator+(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) += lhs; } + +// - Subtraction +template +inline const typename internal::result_type::type + operator-(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) -= rhs; } + +template +inline const typename internal::result_type::type + operator-(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) -= rhs; } + +// * Multiplication +template +inline const typename internal::result_type::type + operator*(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) *= rhs; } + +template +inline const typename internal::result_type::type + operator*(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) *= lhs; } + +// / Division +template +inline const typename internal::result_type::type + operator/(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) /= rhs; } + +template +inline const typename internal::result_type::type + operator/(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) /= rhs; } + +////////////////////////////////////////////////////////////////////////// +// sqrt +const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +// abs +inline const mpreal abs(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()); + +////////////////////////////////////////////////////////////////////////// +// pow +const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); +inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd()); + +////////////////////////////////////////////////////////////////////////// +// Estimate machine epsilon for the given precision +// Returns smallest eps such that 1.0 + eps != 1.0 +inline mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec()); + +// Returns smallest eps such that x + eps != x (relative machine epsilon) +inline mpreal machine_epsilon(const mpreal& x); + +// Gives max & min values for the required precision, +// minval is 'safe' meaning 1 / minval does not overflow +// maxval is 'safe' meaning 1 / maxval does not underflow +inline mpreal minval(mp_prec_t prec = mpreal::get_default_prec()); +inline mpreal maxval(mp_prec_t prec = mpreal::get_default_prec()); + +// 'Dirty' equality check 1: |a-b| < min{|a|,|b|} * eps +inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps); + +// 'Dirty' equality check 2: |a-b| < min{|a|,|b|} * eps( min{|a|,|b|} ) +inline bool isEqualFuzzy(const mpreal& a, const mpreal& b); + +// 'Bitwise' equality check +// maxUlps - a and b can be apart by maxUlps binary numbers. +inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps); + +////////////////////////////////////////////////////////////////////////// +// Convert precision in 'bits' to decimal digits and vice versa. +// bits = ceil(digits*log[2](10)) +// digits = floor(bits*log[10](2)) + +inline mp_prec_t digits2bits(int d); +inline int bits2digits(mp_prec_t b); + +////////////////////////////////////////////////////////////////////////// +// min, max +const mpreal (max)(const mpreal& x, const mpreal& y); +const mpreal (min)(const mpreal& x, const mpreal& y); + +////////////////////////////////////////////////////////////////////////// +// Implementation +////////////////////////////////////////////////////////////////////////// + +////////////////////////////////////////////////////////////////////////// +// Operators - Assignment +inline mpreal& mpreal::operator=(const mpreal& v) +{ + if (this != &v) + { + mp_prec_t tp = mpfr_get_prec( mpfr_srcptr()); + mp_prec_t vp = mpfr_get_prec(v.mpfr_srcptr()); + + if(tp != vp){ + clear(mpfr_ptr()); + mpfr_init2(mpfr_ptr(), vp); + } + + mpfr_set(mpfr_ptr(), v.mpfr_srcptr(), mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + } + return *this; +} + +inline mpreal& mpreal::operator=(const mpf_t v) +{ + mpfr_set_f(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const mpz_t v) +{ + mpfr_set_z(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const mpq_t v) +{ + mpfr_set_q(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const long double v) +{ + mpfr_set_ld(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const double v) +{ +#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1) + if(fits_in_bits(v, MPREAL_DOUBLE_BITS_OVERFLOW)) + { + mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd()); + }else + throw conversion_overflow(); +#else + mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd()); +#endif + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const unsigned long int v) +{ + mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const unsigned int v) +{ + mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const unsigned long long int v) +{ + mpfr_set_uj(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const long long int v) +{ + mpfr_set_sj(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const long int v) +{ + mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const int v) +{ + mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd()); + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator=(const char* s) +{ + // Use other converters for more precise control on base & precision & rounding: + // + // mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) + // mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode) + // + // Here we assume base = 10 and we use precision of target variable. + + mpfr_t t; + + mpfr_init2(t, mpfr_get_prec(mpfr_srcptr())); + + if(0 == mpfr_set_str(t, s, 10, mpreal::get_default_rnd())) + { + mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + } + + clear(t); + return *this; +} + +inline mpreal& mpreal::operator=(const std::string& s) +{ + // Use other converters for more precise control on base & precision & rounding: + // + // mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode) + // mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode) + // + // Here we assume base = 10 and we use precision of target variable. + + mpfr_t t; + + mpfr_init2(t, mpfr_get_prec(mpfr_srcptr())); + + if(0 == mpfr_set_str(t, s.c_str(), 10, mpreal::get_default_rnd())) + { + mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + } + + clear(t); + return *this; +} + +template +inline mpreal& mpreal::operator= (const std::complex& z) +{ + return *this = z.real(); +} + +////////////////////////////////////////////////////////////////////////// +// + Addition +inline mpreal& mpreal::operator+=(const mpreal& v) +{ + mpfr_add(mpfr_ptr(), mpfr_srcptr(), v.mpfr_srcptr(), mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator+=(const mpq_t u) +{ + mpfr_add_q(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator+=(const unsigned int u) +{ + mpfr_add_ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator+=(const long int u) +{ + mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator+=(const int u) +{ + mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator+=(const long long int u) { *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator+=(const unsigned long long int u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator-=(const long long int u) { *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator-=(const unsigned long long int u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator*=(const long long int u) { *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator*=(const unsigned long long int u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator/=(const long long int u) { *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } +inline mpreal& mpreal::operator/=(const unsigned long long int u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; } + +inline const mpreal mpreal::operator+()const { return mpreal(*this); } + +inline const mpreal operator+(const mpreal& a, const mpreal& b) +{ + mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); + mpfr_add(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); + return c; +} + +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(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator-=(const mpz_t v) +{ + mpfr_sub_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator-=(const mpq_t v) +{ + mpfr_sub_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator-=(const unsigned int v) +{ + mpfr_sub_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator-=(const long int v) +{ + mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator-=(const int v) +{ + mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline const mpreal mpreal::operator-()const +{ + mpreal u(*this); + mpfr_neg(u.mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd()); + return u; +} + +inline const mpreal operator-(const mpreal& a, const mpreal& b) +{ + mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); + mpfr_sub(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); + return c; +} + +inline const mpreal operator-(const double b, const mpreal& a) +{ +#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + mpfr_d_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +#else + mpreal x(b, mpfr_get_prec(a.mpfr_ptr())); + x -= a; + return x; +#endif +} + +inline const mpreal operator-(const unsigned long int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator-(const unsigned int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator-(const long int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator-(const int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +////////////////////////////////////////////////////////////////////////// +// * Multiplication +inline mpreal& mpreal::operator*= (const mpreal& v) +{ + mpfr_mul(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator*=(const mpz_t v) +{ + mpfr_mul_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator*=(const mpq_t v) +{ + mpfr_mul_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator*=(const unsigned int v) +{ + mpfr_mul_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator*=(const long int v) +{ + mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator*=(const int v) +{ + mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline const mpreal operator*(const mpreal& a, const mpreal& b) +{ + mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr()))); + mpfr_mul(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); + return c; +} + +////////////////////////////////////////////////////////////////////////// +// / Division +inline mpreal& mpreal::operator/=(const mpreal& v) +{ + mpfr_div(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator/=(const mpz_t v) +{ + mpfr_div_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator/=(const mpq_t v) +{ + mpfr_div_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_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(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator/=(const unsigned int v) +{ + mpfr_div_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator/=(const long int v) +{ + mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator/=(const int v) +{ + mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline const mpreal operator/(const mpreal& a, const mpreal& b) +{ + mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_srcptr()), mpfr_get_prec(b.mpfr_srcptr()))); + mpfr_div(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd()); + return c; +} + +inline const mpreal operator/(const unsigned long int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator/(const unsigned int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator/(const long int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +} + +inline const mpreal operator/(const int b, const mpreal& a) +{ + mpreal x(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_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(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_d_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd()); + return x; +#else + mpreal x(0, mpfr_get_prec(a.mpfr_ptr())); + x /= a; + return x; +#endif +} + +////////////////////////////////////////////////////////////////////////// +// Shifts operators - Multiplication/Division by power of 2 +inline mpreal& mpreal::operator<<=(const unsigned long int u) +{ + mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator<<=(const unsigned int u) +{ + mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator<<=(const long int u) +{ + mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator<<=(const int u) +{ + mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator>>=(const unsigned long int u) +{ + mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator>>=(const unsigned int u) +{ + mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator>>=(const long int u) +{ + mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::operator>>=(const int u) +{ + mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),static_cast(u),mpreal::get_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(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(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(k)); +} + +inline const mpreal operator>>(const mpreal& v, const int k) +{ + return div_2si(v,static_cast(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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),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.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode); + return x; +} + +////////////////////////////////////////////////////////////////////////// +//Relational operators + +// WARNING: +// +// Please note that following checks for double-NaN are guaranteed to work only in IEEE math mode: +// +// isnan(b) = (b != b) +// isnan(b) = !(b == b) (we use in code below) +// +// Be cautions if you use compiler options which break strict IEEE compliance (e.g. -ffast-math in GCC). +// Use std::isnan instead (C++11). + +inline bool operator > (const mpreal& a, const mpreal& b ){ return (mpfr_greater_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } +inline bool operator > (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 ); } +inline bool operator > (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 ); } +inline bool operator > (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 ); } +inline bool operator > (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 ); } +inline bool operator > (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) > 0 ); } +inline bool operator > (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) > 0 ); } + +inline bool operator >= (const mpreal& a, const mpreal& b ){ return (mpfr_greaterequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } +inline bool operator >= (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 ); } +inline bool operator >= (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 ); } +inline bool operator >= (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 ); } +inline bool operator >= (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 ); } +inline bool operator >= (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) >= 0 ); } +inline bool operator >= (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) >= 0 ); } + +inline bool operator < (const mpreal& a, const mpreal& b ){ return (mpfr_less_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } +inline bool operator < (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 ); } +inline bool operator < (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 ); } +inline bool operator < (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 ); } +inline bool operator < (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 ); } +inline bool operator < (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) < 0 ); } +inline bool operator < (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) < 0 ); } + +inline bool operator <= (const mpreal& a, const mpreal& b ){ return (mpfr_lessequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } +inline bool operator <= (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 ); } +inline bool operator <= (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 ); } +inline bool operator <= (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 ); } +inline bool operator <= (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 ); } +inline bool operator <= (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) <= 0 ); } +inline bool operator <= (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) <= 0 ); } + +inline bool operator == (const mpreal& a, const mpreal& b ){ return (mpfr_equal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 ); } +inline bool operator == (const mpreal& a, const unsigned long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 ); } +inline bool operator == (const mpreal& a, const unsigned int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 ); } +inline bool operator == (const mpreal& a, const long int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 ); } +inline bool operator == (const mpreal& a, const int b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 ); } +inline bool operator == (const mpreal& a, const long double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) == 0 ); } +inline bool operator == (const mpreal& a, const double b ){ return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) == 0 ); } + +inline bool operator != (const mpreal& a, const mpreal& b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const unsigned long int b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const unsigned int b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const long int b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const int b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const long double b ){ return !(a == b); } +inline bool operator != (const mpreal& a, const double b ){ return !(a == b); } + +inline bool isnan EIGEN_NOT_A_MACRO (const mpreal& op){ return (mpfr_nan_p (op.mpfr_srcptr()) != 0 ); } +inline bool (isinf) (const mpreal& op){ return (mpfr_inf_p (op.mpfr_srcptr()) != 0 ); } +inline bool (isfinite) (const mpreal& op){ return (mpfr_number_p (op.mpfr_srcptr()) != 0 ); } +inline bool iszero (const mpreal& op){ return (mpfr_zero_p (op.mpfr_srcptr()) != 0 ); } +inline bool isint (const mpreal& op){ return (mpfr_integer_p(op.mpfr_srcptr()) != 0 ); } + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) +inline bool isregular(const mpreal& op){ return (mpfr_regular_p(op.mpfr_srcptr()));} +#endif + +////////////////////////////////////////////////////////////////////////// +// Type Converters +inline bool mpreal::toBool ( ) const { return mpfr_zero_p (mpfr_srcptr()) == 0; } +inline long mpreal::toLong (mp_rnd_t mode) const { return mpfr_get_si (mpfr_srcptr(), mode); } +inline unsigned long mpreal::toULong (mp_rnd_t mode) const { return mpfr_get_ui (mpfr_srcptr(), mode); } +inline float mpreal::toFloat (mp_rnd_t mode) const { return mpfr_get_flt(mpfr_srcptr(), mode); } +inline double mpreal::toDouble (mp_rnd_t mode) const { return mpfr_get_d (mpfr_srcptr(), mode); } +inline long double mpreal::toLDouble(mp_rnd_t mode) const { return mpfr_get_ld (mpfr_srcptr(), mode); } +inline long long mpreal::toLLong (mp_rnd_t mode) const { return mpfr_get_sj (mpfr_srcptr(), mode); } +inline unsigned long long mpreal::toULLong (mp_rnd_t mode) const { return mpfr_get_uj (mpfr_srcptr(), mode); } + +inline ::mpfr_ptr mpreal::mpfr_ptr() { return mp; } +inline ::mpfr_srcptr mpreal::mpfr_ptr() const { return mp; } +inline ::mpfr_srcptr mpreal::mpfr_srcptr() const { return mp; } + +template +inline std::string toString(T t, std::ios_base & (*f)(std::ios_base&)) +{ + std::ostringstream oss; + oss << f << t; + return oss.str(); +} + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) + +inline std::string mpreal::toString(const std::string& format) const +{ + char *s = NULL; + std::string out; + + if( !format.empty() ) + { + if(!(mpfr_asprintf(&s, format.c_str(), mpfr_srcptr()) < 0)) + { + out = std::string(s); + + mpfr_free_str(s); + } + } + + return out; +} + +#endif + +inline std::string mpreal::toString(int n, int b, mp_rnd_t mode) const +{ + // TODO: Add extended format specification (f, e, rounding mode) as it done in output operator + (void)b; + (void)mode; + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)) + + std::ostringstream format; + + int digits = (n >= 0) ? n : 2 + bits2digits(mpfr_get_prec(mpfr_srcptr())); + + format << "%." << digits << "RNg"; + + return toString(format.str()); + +#else + + char *s, *ns = NULL; + size_t slen, nslen; + mp_exp_t exp; + std::string out; + + if(mpfr_inf_p(mp)) + { + if(mpfr_sgn(mp)>0) return "+Inf"; + else return "-Inf"; + } + + if(mpfr_zero_p(mp)) return "0"; + if(mpfr_nan_p(mp)) return "NaN"; + + s = mpfr_get_str(NULL, &exp, b, 0, mp, mode); + ns = mpfr_get_str(NULL, &exp, b, (std::max)(0,n), mp, mode); + + if(s!=NULL && ns!=NULL) + { + slen = strlen(s); + nslen = strlen(ns); + if(nslen<=slen) + { + mpfr_free_str(s); + s = ns; + slen = nslen; + } + else { + mpfr_free_str(ns); + } + + // Make human eye-friendly formatting if possible + if (exp>0 && static_cast(exp)s+exp) ptr--; + + if(ptr==s+exp) out = std::string(s,exp+1); + else out = std::string(s,exp+1)+'.'+std::string(s+exp+1,ptr-(s+exp+1)+1); + + //out = string(s,exp+1)+'.'+string(s+exp+1); + } + else + { + // Remove zeros starting from right end + char* ptr = s+slen-1; + while (*ptr=='0' && ptr>s+exp-1) ptr--; + + if(ptr==s+exp-1) out = std::string(s,exp); + else out = std::string(s,exp)+'.'+std::string(s+exp,ptr-(s+exp)+1); + + //out = string(s,exp)+'.'+string(s+exp); + } + + }else{ // exp<0 || exp>slen + if(s[0]=='-') + { + // Remove zeros starting from right end + char* ptr = s+slen-1; + while (*ptr=='0' && ptr>s+1) ptr--; + + if(ptr==s+1) out = std::string(s,2); + else out = std::string(s,2)+'.'+std::string(s+2,ptr-(s+2)+1); + + //out = string(s,2)+'.'+string(s+2); + } + else + { + // Remove zeros starting from right end + char* ptr = s+slen-1; + while (*ptr=='0' && ptr>s) ptr--; + + if(ptr==s) out = std::string(s,1); + else out = std::string(s,1)+'.'+std::string(s+1,ptr-(s+1)+1); + + //out = string(s,1)+'.'+string(s+1); + } + + // Make final string + if(--exp) + { + if(exp>0) out += "e+"+mpfr::toString(exp,std::dec); + else out += "e"+mpfr::toString(exp,std::dec); + } + } + + mpfr_free_str(s); + return out; + }else{ + return "conversion error!"; + } +#endif +} + + +////////////////////////////////////////////////////////////////////////// +// I/O +inline std::ostream& mpreal::output(std::ostream& os) const +{ + std::ostringstream format; + const std::ios::fmtflags flags = os.flags(); + + format << ((flags & std::ios::showpos) ? "%+" : "%"); + if (os.precision() >= 0) + format << '.' << os.precision() << "R*" + << ((flags & std::ios::floatfield) == std::ios::fixed ? 'f' : + (flags & std::ios::floatfield) == std::ios::scientific ? 'e' : + 'g'); + else + format << "R*e"; + + char *s = NULL; + if(!(mpfr_asprintf(&s, format.str().c_str(), + mpfr::mpreal::get_default_rnd(), + mpfr_srcptr()) + < 0)) + { + os << std::string(s); + mpfr_free_str(s); + } + return os; +} + +inline std::ostream& operator<<(std::ostream& os, const mpreal& v) +{ + return v.output(os); +} + +inline std::istream& operator>>(std::istream &is, mpreal& v) +{ + // TODO: use cout::hexfloat and other flags to setup base + std::string tmp; + is >> tmp; + mpfr_set_str(v.mpfr_ptr(), tmp.c_str(), 10, mpreal::get_default_rnd()); + return is; +} + +////////////////////////////////////////////////////////////////////////// +// 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; + + return mp_prec_t(std::ceil( d * LOG2_10 )); +} + +inline int bits2digits(mp_prec_t b) +{ + const double LOG10_2 = 0.30102999566398119; + + return int(std::floor( b * LOG10_2 )); +} + +////////////////////////////////////////////////////////////////////////// +// Set/Get number properties +inline mpreal& mpreal::setSign(int sign, mp_rnd_t RoundingMode) +{ + mpfr_setsign(mpfr_ptr(), mpfr_srcptr(), sign < 0, RoundingMode); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline int mpreal::getPrecision() const +{ + return int(mpfr_get_prec(mpfr_srcptr())); +} + +inline mpreal& mpreal::setPrecision(int Precision, mp_rnd_t RoundingMode) +{ + mpfr_prec_round(mpfr_ptr(), Precision, RoundingMode); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::setInf(int sign) +{ + mpfr_set_inf(mpfr_ptr(), sign); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::setNan() +{ + mpfr_set_nan(mpfr_ptr()); + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mpreal& mpreal::setZero(int sign) +{ +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) + mpfr_set_zero(mpfr_ptr(), sign); +#else + mpfr_set_si(mpfr_ptr(), 0, (mpfr_get_default_rounding_mode)()); + setSign(sign); +#endif + + MPREAL_MSVC_DEBUGVIEW_CODE; + return *this; +} + +inline mp_prec_t mpreal::get_prec() const +{ + return mpfr_get_prec(mpfr_srcptr()); +} + +inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode) +{ + mpfr_prec_round(mpfr_ptr(),prec,rnd_mode); + MPREAL_MSVC_DEBUGVIEW_CODE; +} + +inline mp_exp_t mpreal::get_exp () const +{ + return mpfr_get_exp(mpfr_srcptr()); +} + +inline int mpreal::set_exp (mp_exp_t e) +{ + int x = mpfr_set_exp(mpfr_ptr(), e); + MPREAL_MSVC_DEBUGVIEW_CODE; + return x; +} + +inline const mpreal frexp(const mpreal& x, mp_exp_t* exp, mp_rnd_t mode = mpreal::get_default_rnd()) +{ + mpreal y(x); +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0)) + mpfr_frexp(exp,y.mpfr_ptr(),x.mpfr_srcptr(),mode); +#else + *exp = mpfr_get_exp(y.mpfr_srcptr()); + mpfr_set_exp(y.mpfr_ptr(),0); +#endif + return y; +} + +inline const mpreal ldexp(const mpreal& v, mp_exp_t exp) +{ + mpreal x(v); + + // rounding is not important since we are just increasing the exponent (= exact operation) + mpfr_mul_2si(x.mpfr_ptr(), x.mpfr_srcptr(), exp, mpreal::get_default_rnd()); + return x; +} + +inline const mpreal scalbn(const mpreal& v, mp_exp_t exp) +{ + return ldexp(v, exp); +} + +inline mpreal machine_epsilon(mp_prec_t prec) +{ + /* the smallest eps such that 1 + eps != 1 */ + return machine_epsilon(mpreal(1, prec)); +} + +inline mpreal machine_epsilon(const mpreal& x) +{ + /* the smallest eps such that x + eps != x */ + if( x < 0) + { + return nextabove(-x) + x; + }else{ + return nextabove( x) - x; + } +} + +// minval is 'safe' meaning 1 / minval does not overflow +inline mpreal minval(mp_prec_t prec) +{ + /* min = 1/2 * 2^emin = 2^(emin - 1) */ + return mpreal(1, prec) << mpreal::get_emin()-1; +} + +// maxval is 'safe' meaning 1 / maxval does not underflow +inline mpreal maxval(mp_prec_t prec) +{ + /* max = (1 - eps) * 2^emax, eps is machine epsilon */ + return (mpreal(1, prec) - machine_epsilon(prec)) << mpreal::get_emax(); +} + +inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps) +{ + 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) <= eps; +} + +inline bool isEqualFuzzy(const mpreal& a, const mpreal& b) +{ + return isEqualFuzzy(a, b, machine_epsilon((max)(1, (min)(abs(a), abs(b))))); +} + +////////////////////////////////////////////////////////////////////////// +// C++11 sign functions. +inline mpreal copysign(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal rop(0, mpfr_get_prec(x.mpfr_ptr())); + mpfr_setsign(rop.mpfr_ptr(), x.mpfr_srcptr(), mpfr_signbit(y.mpfr_srcptr()), rnd_mode); + return rop; +} + +inline bool signbit(const mpreal& x) +{ + return mpfr_signbit(x.mpfr_srcptr()); +} + +inline mpreal& setsignbit(mpreal& x, bool minus, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpfr_setsign(x.mpfr_ptr(), x.mpfr_srcptr(), minus, rnd_mode); + return x; +} + +inline const mpreal modf(const mpreal& v, mpreal& n) +{ + mpreal f(v); + + // rounding is not important since we are using the same number + mpfr_frac (f.mpfr_ptr(),f.mpfr_srcptr(),mpreal::get_default_rnd()); + mpfr_trunc(n.mpfr_ptr(),v.mpfr_srcptr()); + return f; +} + +inline int mpreal::check_range (int t, mp_rnd_t rnd_mode) +{ + return mpfr_check_range(mpfr_ptr(),t,rnd_mode); +} + +inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode) +{ + int r = mpfr_subnormalize(mpfr_ptr(),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 +////////////////////////////////////////////////////////////////////////// +#define MPREAL_UNARY_MATH_FUNCTION_BODY(f) \ + mpreal y(0, mpfr_get_prec(x.mpfr_srcptr())); \ + mpfr_##f(y.mpfr_ptr(), x.mpfr_srcptr(), r); \ + return y; + +inline const mpreal sqr (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ MPREAL_UNARY_MATH_FUNCTION_BODY(sqr ); } + +inline const mpreal sqrt (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ MPREAL_UNARY_MATH_FUNCTION_BODY(sqrt); } + +inline const mpreal sqrt(const unsigned long int x, mp_rnd_t r) +{ + mpreal y; + mpfr_sqrt_ui(y.mpfr_ptr(), x, r); + return y; +} + +inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode) +{ + return sqrt(static_cast(v),rnd_mode); +} + +inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode) +{ + if (v>=0) return sqrt(static_cast(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(v),rnd_mode); + else return mpreal().setNan(); // NaN +} + +inline const mpreal root(const mpreal& x, unsigned long int k, mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal y(0, mpfr_get_prec(x.mpfr_srcptr())); + #if (MPFR_VERSION >= MPFR_VERSION_NUM(4,0,0)) + mpfr_rootn_ui(y.mpfr_ptr(), x.mpfr_srcptr(), k, r); + #else + mpfr_root(y.mpfr_ptr(), x.mpfr_srcptr(), k, r); + #endif + return y; +} + +inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal y(0, mpfr_get_prec(a.mpfr_srcptr())); + mpfr_dim(y.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), r); + return y; +} + +inline int cmpabs(const mpreal& a,const mpreal& b) +{ + return mpfr_cmpabs(a.mpfr_ptr(), b.mpfr_srcptr()); +} + +inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + return mpfr_sin_cos(s.mpfr_ptr(), c.mpfr_ptr(), v.mpfr_srcptr(), rnd_mode); +} + +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& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cbrt ); } +inline const mpreal fabs (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(abs ); } +inline const mpreal abs (const mpreal& x, mp_rnd_t r) { MPREAL_UNARY_MATH_FUNCTION_BODY(abs ); } +inline const mpreal log (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log ); } +inline const mpreal log2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log2 ); } +inline const mpreal log10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log10); } +inline const mpreal exp (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp ); } +inline const mpreal exp2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp2 ); } +inline const mpreal exp10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(exp10); } +inline const mpreal cos (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cos ); } +inline const mpreal sin (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sin ); } +inline const mpreal tan (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(tan ); } +inline const mpreal sec (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sec ); } +inline const mpreal csc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(csc ); } +inline const mpreal cot (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cot ); } +inline const mpreal acos (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(acos ); } +inline const mpreal asin (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(asin ); } +inline const mpreal atan (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(atan ); } + +inline const mpreal logb (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { return log2 (abs(x),r); } + +inline const mpreal acot (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return atan (1/v, r); } +inline const mpreal asec (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return acos (1/v, r); } +inline const mpreal acsc (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return asin (1/v, r); } +inline const mpreal acoth (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return atanh(1/v, r); } +inline const mpreal asech (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return acosh(1/v, r); } +inline const mpreal acsch (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) { return asinh(1/v, r); } + +inline const mpreal cosh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(cosh ); } +inline const mpreal sinh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sinh ); } +inline const mpreal tanh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(tanh ); } +inline const mpreal sech (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(sech ); } +inline const mpreal csch (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(csch ); } +inline const mpreal coth (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(coth ); } +inline const mpreal acosh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(acosh); } +inline const mpreal asinh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(asinh); } +inline const mpreal atanh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(atanh); } + +inline const mpreal log1p (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(log1p ); } +inline const mpreal expm1 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(expm1 ); } +inline const mpreal eint (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(eint ); } +inline const mpreal gamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(gamma ); } +inline const mpreal tgamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(gamma ); } +inline const mpreal lngamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(lngamma); } +inline const mpreal zeta (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(zeta ); } +inline const mpreal erf (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(erf ); } +inline const mpreal erfc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(erfc ); } +inline const mpreal besselj0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(j0 ); } +inline const mpreal besselj1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(j1 ); } +inline const mpreal bessely0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(y0 ); } +inline const mpreal bessely1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(y1 ); } + +inline const mpreal nextpow2(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal y(0, x.getPrecision()); + + if(!iszero(x)) + y = ceil(log2(abs(x,r),r)); + + return y; +} + +inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); + mpfr_atan2(a.mpfr_ptr(), y.mpfr_srcptr(), x.mpfr_srcptr(), rnd_mode); + return a; +} + +inline const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); + mpfr_hypot(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); + return a; +} + +inline const mpreal hypot(const mpreal& a, const mpreal& b, const mpreal& c) +{ + if(isnan EIGEN_NOT_A_MACRO (a) || isnan EIGEN_NOT_A_MACRO (b) || isnan EIGEN_NOT_A_MACRO(c)) return mpreal().setNan(); + else + { + mpreal absa = abs(a), absb = abs(b), absc = abs(c); + mpreal w = (std::max)(absa, (std::max)(absb, absc)); + mpreal r; + + if (!iszero(w)) + { + mpreal iw = 1/w; + r = w * sqrt(sqr(absa*iw) + sqr(absb*iw) + sqr(absc*iw)); + } + + return r; + } +} + +inline const mpreal hypot(const mpreal& a, const mpreal& b, const mpreal& c, const mpreal& d) +{ + if(isnan EIGEN_NOT_A_MACRO (a) || isnan EIGEN_NOT_A_MACRO (b) || isnan EIGEN_NOT_A_MACRO (c) || isnan EIGEN_NOT_A_MACRO (d)) return mpreal().setNan(); + else + { + mpreal absa = abs(a), absb = abs(b), absc = abs(c), absd = abs(d); + mpreal w = (std::max)(absa, (std::max)(absb, (std::max)(absc, absd))); + mpreal r; + + if (!iszero(w)) + { + mpreal iw = 1/w; + r = w * sqrt(sqr(absa*iw) + sqr(absb*iw) + sqr(absc*iw) + sqr(absd*iw)); + } + + return r; + } +} + +inline const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); + mpfr_remainder(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); + return a; +} + +inline const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision())); + mpfr_remquo(a.mpfr_ptr(),q, x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode); + return a; +} + +inline const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::get_default_prec(), + mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal x(0, prec); + mpfr_fac_ui(x.mpfr_ptr(),v,rnd_mode); + return x; +} + + +inline const mpreal lgamma (const mpreal& v, int *signp = 0, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal x(v); + int tsignp; + + if(signp) mpfr_lgamma(x.mpfr_ptr(), signp,v.mpfr_srcptr(),rnd_mode); + else mpfr_lgamma(x.mpfr_ptr(),&tsignp,v.mpfr_srcptr(),rnd_mode); + + return x; +} + + +inline const mpreal besseljn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal y(0, x.getPrecision()); + mpfr_jn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r); + return y; +} + +inline const mpreal besselyn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal y(0, x.getPrecision()); + mpfr_yn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r); + return y; +} + +inline const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a; + mp_prec_t p1, p2, p3; + + p1 = v1.get_prec(); + p2 = v2.get_prec(); + p3 = v3.get_prec(); + + a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1)); + + mpfr_fma(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode); + return a; +} + +inline const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a; + mp_prec_t p1, p2, p3; + + p1 = v1.get_prec(); + p2 = v2.get_prec(); + p3 = v3.get_prec(); + + a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1)); + + mpfr_fms(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode); + return a; +} + +inline const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal a; + mp_prec_t p1, p2; + + p1 = v1.get_prec(); + p2 = v2.get_prec(); + + a.set_prec(p1>p2?p1:p2); + + mpfr_agm(a.mp, v1.mp, v2.mp, rnd_mode); + + return a; +} + +inline const mpreal sum (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t mode = mpreal::get_default_rnd()) +{ + mpfr_srcptr *p = new mpfr_srcptr[n]; + + for (unsigned long int i = 0; i < n; i++) + p[i] = tab[i].mpfr_srcptr(); + + mpreal x; + status = mpfr_sum(x.mpfr_ptr(), (mpfr_ptr*)p, n, mode); + + delete [] p; + 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 = mpreal::get_default_rnd()) +{ + return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode); +} + +inline const mpreal li2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) +{ + MPREAL_UNARY_MATH_FUNCTION_BODY(li2); +} + +inline const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + /* R = rem(X,Y) if Y != 0, returns X - n * Y where n = trunc(X/Y). */ + return fmod(x, y, rnd_mode); +} + +inline const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + (void)rnd_mode; + + /* + + m = mod(x,y) if y != 0, returns x - n*y where n = floor(x/y) + + The following are true by convention: + - mod(x,0) is x + - mod(x,x) is 0 + - mod(x,y) for x != y and y != 0 has the same sign as y. + + */ + + if(iszero(y)) return x; + if(x == y) return 0; + + mpreal m = x - floor(x / y) * y; + + return copysign(abs(m),y); // make sure result has the same sign as Y +} + +inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + 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::get_default_rnd()) +{ + 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& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(digamma); } +inline const mpreal ai (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(ai); } +#endif // MPFR 3.0.0 Specifics + +////////////////////////////////////////////////////////////////////////// +// Constants +inline const mpreal const_log2 (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal x(0, p); + mpfr_const_log2(x.mpfr_ptr(), r); + return x; +} + +inline const mpreal const_pi (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal x(0, p); + mpfr_const_pi(x.mpfr_ptr(), r); + return x; +} + +inline const mpreal const_euler (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal x(0, p); + mpfr_const_euler(x.mpfr_ptr(), r); + return x; +} + +inline const mpreal const_catalan (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd()) +{ + mpreal x(0, p); + mpfr_const_catalan(x.mpfr_ptr(), r); + return x; +} + +inline const mpreal const_infinity (int sign = 1, mp_prec_t p = mpreal::get_default_prec()) +{ + mpreal x(0, p); + mpfr_set_inf(x.mpfr_ptr(), sign); + return x; +} + +////////////////////////////////////////////////////////////////////////// +// Integer Related Functions +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 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint ); } +inline const mpreal rint_ceil (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_ceil ); } +inline const mpreal rint_floor (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_floor); } +inline const mpreal rint_round (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_round); } +inline const mpreal rint_trunc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(rint_trunc); } +inline const mpreal frac (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) { MPREAL_UNARY_MATH_FUNCTION_BODY(frac ); } + +////////////////////////////////////////////////////////////////////////// +// Miscellaneous Functions +inline int sgn(const mpreal& op) +{ + // Please note, this is classic signum function which ignores sign of zero. + // Use signbit if you need sign of zero. + return mpfr_sgn(op.mpfr_srcptr()); +} + +////////////////////////////////////////////////////////////////////////// +// Miscellaneous Functions +inline void swap (mpreal& a, mpreal& b) { mpfr_swap(a.mpfr_ptr(),b.mpfr_ptr()); } +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= MPFR_VERSION_NUM(3,0,0)) +inline const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal x; + mpfr_urandom(x.mpfr_ptr(), 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.mpfr_ptr(),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 = 0) +{ +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) + static gmp_randstate_t state; + static bool initialize = true; + + if(initialize) + { + gmp_randinit_default(state); + gmp_randseed_ui(state,0); + initialize = 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 + +} + +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0) && MPFR_VERSION < MPFR_VERSION_NUM(4,0,0)) + +// TODO: +// Use mpfr_nrandom since mpfr_grandom is deprecated +#if defined(_MSC_VER) +#pragma warning( push ) +#pragma warning( disable : 1478) +#endif +inline const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + mpreal x; + mpfr_grandom(x.mpfr_ptr(), NULL, state, rnd_mode); + return x; +} +#if defined(_MSC_VER) +#pragma warning( pop ) +#endif + +inline const mpreal grandom(unsigned int seed = 0) +{ + static gmp_randstate_t state; + static bool initialize = true; + + if(initialize) + { + gmp_randinit_default(state); + gmp_randseed_ui(state,0); + initialize = false; + } + + if(seed != 0) gmp_randseed_ui(state,seed); + + return mpfr::grandom(state); +} +#endif + +////////////////////////////////////////////////////////////////////////// +// Set/Get global properties +inline void mpreal::set_default_prec(mp_prec_t prec) +{ + mpfr_set_default_prec(prec); +} + +inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode) +{ + mpfr_set_default_rounding_mode(rnd_mode); +} + +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::get_default_rnd()) +{ + 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::get_default_rnd()) +{ + 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::get_default_rnd()) +{ + 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(b),rnd_mode); +} + +inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd()) +{ + 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(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::get_default_rnd()) +{ + 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(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(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(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(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(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(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(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(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(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(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(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(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(mpreal(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(a),mpreal(b),rnd_mode); //mpfr_ui_pow + }else{ + return pow(mpreal(a),static_cast(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(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(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(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(mpreal(a),static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(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(a),static_cast(b),rnd_mode); //mpfr_ui_pow_ui + else return pow(static_cast(a),mpreal(b),rnd_mode); //mpfr_ui_pow + }else{ + return pow(mpreal(a),static_cast(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(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(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(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(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(b),rnd_mode); // mpfr_pow_ui +} + +inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode) +{ + return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si +} + +inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode) +{ + return pow(mpreal(a),static_cast(b),rnd_mode); // mpfr_pow_si +} +} // End of mpfr namespace + +// Explicit specialization of std::swap for mpreal numbers +// Thus standard algorithms will use efficient version of swap (due to Koenig lookup) +// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap +namespace std +{ + // we are allowed to extend namespace std with specializations only + template <> + inline void swap(mpfr::mpreal& x, mpfr::mpreal& y) + { + return mpfr::swap(x, y); + } + + template<> + class numeric_limits + { + public: + static const bool is_specialized = true; + static const bool is_signed = true; + static const bool is_integer = false; + static const bool is_exact = false; + static const int radix = 2; + + static const bool has_infinity = true; + static const bool has_quiet_NaN = true; + static const bool has_signaling_NaN = true; + + static const bool is_iec559 = true; // = IEEE 754 + static const bool is_bounded = true; + static const bool is_modulo = false; + static const bool traps = true; + static const bool tinyness_before = true; + + static const float_denorm_style has_denorm = denorm_absent; + + inline static mpfr::mpreal (min) (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::minval(precision); } + inline static mpfr::mpreal (max) (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(precision); } + inline static mpfr::mpreal lowest (mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(precision); } + + // Returns smallest eps such that 1 + eps != 1 (classic machine epsilon) + inline static mpfr::mpreal epsilon(mp_prec_t precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(precision); } + + // Returns smallest eps such that x + eps != x (relative machine epsilon) + inline static mpfr::mpreal epsilon(const mpfr::mpreal& x) { return mpfr::machine_epsilon(x); } + + inline static mpfr::mpreal round_error(mp_prec_t precision = mpfr::mpreal::get_default_prec()) + { + mp_rnd_t r = mpfr::mpreal::get_default_rnd(); + + if(r == GMP_RNDN) return mpfr::mpreal(0.5, precision); + else return mpfr::mpreal(1.0, precision); + } + + inline static const mpfr::mpreal infinity() { return mpfr::const_infinity(); } + inline static const mpfr::mpreal quiet_NaN() { return mpfr::mpreal().setNan(); } + inline static const mpfr::mpreal signaling_NaN() { return mpfr::mpreal().setNan(); } + inline static const mpfr::mpreal denorm_min() { return (min)(); } + + // Please note, exponent range is not fixed in MPFR + static const int min_exponent = MPFR_EMIN_DEFAULT; + static const int max_exponent = MPFR_EMAX_DEFAULT; + MPREAL_PERMISSIVE_EXPR static const int min_exponent10 = (int) (MPFR_EMIN_DEFAULT * 0.3010299956639811); + MPREAL_PERMISSIVE_EXPR static const int max_exponent10 = (int) (MPFR_EMAX_DEFAULT * 0.3010299956639811); + +#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS + + // Following members should be constant according to standard, but they can be variable in MPFR + // So we define them as functions here. + // + // This is preferable way for std::numeric_limits specialization. + // But it is incompatible with standard std::numeric_limits and might not work with other libraries, e.g. boost. + // See below for compatible implementation. + inline static float_round_style round_style() + { + mp_rnd_t r = mpfr::mpreal::get_default_rnd(); + + switch (r) + { + case GMP_RNDN: return round_to_nearest; + case GMP_RNDZ: return round_toward_zero; + case GMP_RNDU: return round_toward_infinity; + case GMP_RNDD: return round_toward_neg_infinity; + default: return round_indeterminate; + } + } + + inline static int digits() { return int(mpfr::mpreal::get_default_prec()); } + inline static int digits(const mpfr::mpreal& x) { return x.getPrecision(); } + + inline static int digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec()) + { + return mpfr::bits2digits(precision); + } + + inline static int digits10(const mpfr::mpreal& x) + { + return mpfr::bits2digits(x.getPrecision()); + } + + inline static int max_digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec()) + { + return digits10(precision); + } +#else + // Digits and round_style are NOT constants when it comes to mpreal. + // If possible, please use functions digits() and round_style() defined above. + // + // These (default) values are preserved for compatibility with existing libraries, e.g. boost. + // Change them accordingly to your application. + // + // For example, if you use 256 bits of precision uniformly in your program, then: + // digits = 256 + // digits10 = 77 + // max_digits10 = 78 + // + // Approximate formula for decimal digits is: digits10 = floor(log10(2) * digits). See bits2digits() for more details. + + static const std::float_round_style round_style = round_to_nearest; + static const int digits = 53; + static const int digits10 = 15; + static const int max_digits10 = 16; +#endif + }; + +} + +#endif /* __MPREAL_H__ */ -- cgit v1.2.3