// 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>.
*
* 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 Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); }
inline static Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }
// Constants
inline static Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); }
inline static Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); }
inline static Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); }
inline static Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); }
inline static Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); }
inline static Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); }
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<> 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 {
nr = 2, // must be 2 for proper packing...
mr = 1,
WorkSpaceFactor = nr,
LhsProgress = 1,
RhsProgress = 1
};
};
template<typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,mr,nr,ConjugateLhs,ConjugateRhs>
{
typedef mpfr::mpreal mpreal;
EIGEN_DONT_INLINE
void operator()(mpreal* res, Index resStride, const mpreal* blockA, const mpreal* blockB, Index rows, Index depth, Index cols, mpreal alpha,
Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0, mpreal* /*unpackedB*/ = 0)
{
mpreal acc1, acc2, tmp;
if(strideA==-1) strideA = depth;
if(strideB==-1) strideB = depth;
for(Index j=0; j<cols; j+=nr)
{
Index actual_nr = (std::min<Index>)(nr,cols-j);
mpreal *C1 = res + j*resStride;
mpreal *C2 = res + (j+1)*resStride;
for(Index i=0; i<rows; i++)
{
mpreal *B = const_cast<mpreal*>(blockB) + j*strideB + offsetB*actual_nr;
mpreal *A = const_cast<mpreal*>(blockA) + i*strideA + offsetA;
acc1 = 0;
acc2 = 0;
for(Index k=0; k<depth; k++)
{
mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[0].mpfr_ptr(), mpreal::get_default_rnd());
mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
if(actual_nr==2) {
mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[1].mpfr_ptr(), mpreal::get_default_rnd());
mpfr_add(acc2.mpfr_ptr(), acc2.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
}
B+=actual_nr;
}
mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
mpfr_add(C1[i].mpfr_ptr(), C1[i].mpfr_ptr(), acc1.mpfr_ptr(), mpreal::get_default_rnd());
if(actual_nr==2) {
mpfr_mul(acc2.mpfr_ptr(), acc2.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
mpfr_add(C2[i].mpfr_ptr(), C2[i].mpfr_ptr(), acc2.mpfr_ptr(), mpreal::get_default_rnd());
}
}
}
}
};
} // end namespace internal
}
#endif // EIGEN_MPREALSUPPORT_MODULE_H