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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) 2010-2012 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/.
#ifndef EIGEN_MPREALSUPPORT_MODULE_H
#define EIGEN_MPREALSUPPORT_MODULE_H
#include "../../Eigen/Core"
#include <mpreal.h>
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/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>.
*
* \warning MPFR C++ is licensed under the GPL.
*
* 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 = HugeCost,
AddCost = HugeCost,
MulCost = HugeCost
};
typedef mpfr::mpreal Real;
typedef mpfr::mpreal NonInteger;
static inline Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); }
static inline Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }
// Constants
static inline Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); }
static inline Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); }
static inline Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); }
static inline Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); }
static inline Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); }
static inline Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); }
#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS
static inline int digits10 (long Precision = mpfr::mpreal::get_default_prec()) { return std::numeric_limits<Real>::digits10(Precision); }
static inline int digits10 (const Real& x) { return std::numeric_limits<Real>::digits10(x); }
static inline int digits () { return std::numeric_limits<Real>::digits(); }
static inline int digits (const Real& x) { return std::numeric_limits<Real>::digits(x); }
#endif
static inline Real dummy_precision()
{
mpfr_prec_t weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100;
return mpfr::machine_epsilon(weak_prec);
}
};
namespace internal {
template<> inline mpfr::mpreal random<mpfr::mpreal>()
{
return mpfr::random();
}
template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b)
{
return a + (b-a) * random<mpfr::mpreal>();
}
inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
{
return mpfr::abs(a) <= mpfr::abs(b) * eps;
}
inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
{
return mpfr::isEqualFuzzy(a,b,eps);
}
inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
{
return a <= b || mpfr::isEqualFuzzy(a,b,eps);
}
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()); }
// Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff)
// This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal
template<>
class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false>
{
public:
typedef mpfr::mpreal ResScalar;
enum {
Vectorizable = false,
LhsPacketSize = 1,
RhsPacketSize = 1,
ResPacketSize = 1,
NumberOfRegisters = 1,
nr = 1,
mr = 1,
LhsProgress = 1,
RhsProgress = 1
};
typedef ResScalar LhsPacket;
typedef ResScalar RhsPacket;
typedef ResScalar ResPacket;
typedef LhsPacket LhsPacket4Packing;
};
template<typename Index, typename DataMapper, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,DataMapper,1,1,ConjugateLhs,ConjugateRhs>
{
typedef mpfr::mpreal mpreal;
EIGEN_DONT_INLINE
void operator()(const DataMapper& res, const mpreal* blockA, const mpreal* blockB,
Index rows, Index depth, Index cols, const mpreal& alpha,
Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0)
{
if(rows==0 || cols==0 || depth==0)
return;
mpreal acc1(0,mpfr_get_prec(blockA[0].mpfr_srcptr())),
tmp (0,mpfr_get_prec(blockA[0].mpfr_srcptr()));
if(strideA==-1) strideA = depth;
if(strideB==-1) strideB = depth;
for(Index i=0; i<rows; ++i)
{
for(Index j=0; j<cols; ++j)
{
const mpreal *A = blockA + i*strideA + offsetA;
const mpreal *B = blockB + j*strideB + offsetB;
acc1 = 0;
for(Index k=0; k<depth; k++)
{
mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_srcptr(), B[k].mpfr_srcptr(), mpreal::get_default_rnd());
mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
}
mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_srcptr(), alpha.mpfr_srcptr(), mpreal::get_default_rnd());
mpfr_add(res(i,j).mpfr_ptr(), res(i,j).mpfr_srcptr(), acc1.mpfr_srcptr(), mpreal::get_default_rnd());
}
}
}
};
} // end namespace internal
}
#endif // EIGEN_MPREALSUPPORT_MODULE_H
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