| // This file is part of a joint effort between Eigen, a lightweight C++ template library |
| // for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/) |
| // |
| // Copyright (C) 2010 Pavel Holoborodko <pavel@holoborodko.com> |
| // Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com> |
| // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| // |
| // Contributors: |
| // Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen, Pere Constans |
| |
| #ifndef EIGEN_MPREALSUPPORT_MODULE_H |
| #define EIGEN_MPREALSUPPORT_MODULE_H |
| |
| #include <ctime> |
| #include <mpreal.h> |
| #include <Eigen/Core> |
| |
| namespace Eigen { |
| |
| /** \ingroup Unsupported_modules |
| * \defgroup MPRealSupport_Module MPFRC++ Support module |
| * |
| * \code |
| * #include <Eigen/MPRealSupport> |
| * \endcode |
| * |
| * This module provides support for multi precision floating point numbers |
| * via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a> |
| * library which itself is built upon <a href="http://www.mpfr.org/">MPFR</a>/<a href="http://gmplib.org/">GMP</a>. |
| * |
| * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder. |
| * |
| * Here is an example: |
| * |
| \code |
| #include <iostream> |
| #include <Eigen/MPRealSupport> |
| #include <Eigen/LU> |
| using namespace mpfr; |
| using namespace Eigen; |
| int main() |
| { |
| // set precision to 256 bits (double has only 53 bits) |
| mpreal::set_default_prec(256); |
| // Declare matrix and vector types with multi-precision scalar type |
| typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp; |
| typedef Matrix<mpreal,Dynamic,1> VectorXmp; |
| |
| MatrixXmp A = MatrixXmp::Random(100,100); |
| VectorXmp b = VectorXmp::Random(100); |
| |
| // Solve Ax=b using LU |
| VectorXmp x = A.lu().solve(b); |
| std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl; |
| return 0; |
| } |
| \endcode |
| * |
| */ |
| |
| template<> struct NumTraits<mpfr::mpreal> |
| : GenericNumTraits<mpfr::mpreal> |
| { |
| enum { |
| IsInteger = 0, |
| IsSigned = 1, |
| IsComplex = 0, |
| RequireInitialization = 1, |
| ReadCost = 10, |
| AddCost = 10, |
| MulCost = 40 |
| }; |
| |
| typedef mpfr::mpreal Real; |
| typedef mpfr::mpreal NonInteger; |
| |
| inline static mpfr::mpreal highest() { return mpfr::mpreal_max(mpfr::mpreal::get_default_prec()); } |
| inline static mpfr::mpreal lowest() { return -mpfr::mpreal_max(mpfr::mpreal::get_default_prec()); } |
| |
| inline static Real epsilon() |
| { |
| return mpfr::machine_epsilon(mpfr::mpreal::get_default_prec()); |
| } |
| inline static Real dummy_precision() |
| { |
| unsigned int weak_prec = ((mpfr::mpreal::get_default_prec()-1)*90)/100; |
| return mpfr::machine_epsilon(weak_prec); |
| } |
| }; |
| |
| namespace internal { |
| |
| template<> mpfr::mpreal random<mpfr::mpreal>() |
| { |
| #if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) |
| static gmp_randstate_t state; |
| static bool isFirstTime = true; |
| |
| if(isFirstTime) |
| { |
| gmp_randinit_default(state); |
| gmp_randseed_ui(state,(unsigned)time(NULL)); |
| isFirstTime = false; |
| } |
| |
| return mpfr::urandom(state)*2-1; |
| #else |
| return mpfr::mpreal(random<double>()); |
| #endif |
| } |
| |
| template<> mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b) |
| { |
| return a + (b-a) * random<mpfr::mpreal>(); |
| } |
| |
| bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) |
| { |
| return mpfr::abs(a) <= mpfr::abs(b) * prec; |
| } |
| |
| inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) |
| { |
| return mpfr::abs(a - b) <= (mpfr::min)(mpfr::abs(a), mpfr::abs(b)) * prec; |
| } |
| |
| inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) |
| { |
| return a <= b || isApprox(a, b, prec); |
| } |
| |
| template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x) |
| { return x.toLDouble(); } |
| template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x) |
| { return x.toDouble(); } |
| template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x) |
| { return x.toLong(); } |
| template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x) |
| { return int(x.toLong()); } |
| |
| } // end namespace internal |
| } |
| |
| #endif // EIGEN_MPREALSUPPORT_MODULE_H |