154 lines
4.8 KiB
Plaintext
154 lines
4.8 KiB
Plaintext
// 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>
|
|
//
|
|
// Eigen is free software; you can redistribute it and/or
|
|
// modify it under the terms of the GNU Lesser General Public
|
|
// License as published by the Free Software Foundation; either
|
|
// version 3 of the License, or (at your option) any later version.
|
|
//
|
|
// Alternatively, 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 2 of
|
|
// the License, or (at your option) any later version.
|
|
//
|
|
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
|
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
|
// GNU General Public License for more details.
|
|
//
|
|
// You should have received a copy of the GNU Lesser General Public
|
|
// License and a copy of the GNU General Public License along with
|
|
// this library. If not, see <http://www.gnu.org/licenses/>.
|
|
//
|
|
// 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 <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/?page_id=12">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/Mpfrc++Support>
|
|
#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);
|
|
}
|
|
|
|
} // end namespace internal
|
|
}
|
|
|
|
#endif // EIGEN_MPREALSUPPORT_MODULE_H
|