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// 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 {
/** \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>.
*
* 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,
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>();
}
template<> struct conj_impl<mpfr::mpreal> { inline static const mpfr::mpreal& run(const mpfr::mpreal& x) { return x; } };
template<> struct real_impl<mpfr::mpreal> { inline static const mpfr::mpreal& run(const mpfr::mpreal& x) { return x; } };
template<> struct imag_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal&) { return mpfr::mpreal(0); } };
template<> struct abs_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::fabs(x); } };
template<> struct abs2_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return x*x; } };
template<> struct sqrt_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::sqrt(x); } };
template<> struct exp_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::exp(x); } };
template<> struct log_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::log(x); } };
template<> struct sin_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::sin(x); } };
template<> struct cos_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x) { return mpfr::cos(x); } };
template<> struct pow_impl<mpfr::mpreal> { inline static const mpfr::mpreal run(const mpfr::mpreal& x, const mpfr::mpreal& y) { return mpfr::pow(x, y); } };
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
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