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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>. * * 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
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