204 lines
7.3 KiB
Plaintext
204 lines
7.3 KiB
Plaintext
// This file is part of a joint effort between Eigen, a lightweight C++ template library
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// for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/)
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//
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// Copyright (C) 2010-2012 Pavel Holoborodko <pavel@holoborodko.com>
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// Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com>
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// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_MPREALSUPPORT_MODULE_H
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#define EIGEN_MPREALSUPPORT_MODULE_H
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#include <Eigen/Core>
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#include <mpreal.h>
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namespace Eigen {
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/**
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* \defgroup MPRealSupport_Module MPFRC++ Support module
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* \code
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* #include <Eigen/MPRealSupport>
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* \endcode
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*
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* This module provides support for multi precision floating point numbers
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* via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a>
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* library which itself is built upon <a href="http://www.mpfr.org/">MPFR</a>/<a href="http://gmplib.org/">GMP</a>.
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*
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* You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder.
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*
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* Here is an example:
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*
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\code
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#include <iostream>
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#include <Eigen/MPRealSupport>
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#include <Eigen/LU>
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using namespace mpfr;
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using namespace Eigen;
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int main()
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{
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// set precision to 256 bits (double has only 53 bits)
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mpreal::set_default_prec(256);
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// Declare matrix and vector types with multi-precision scalar type
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typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp;
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typedef Matrix<mpreal,Dynamic,1> VectorXmp;
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MatrixXmp A = MatrixXmp::Random(100,100);
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VectorXmp b = VectorXmp::Random(100);
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// Solve Ax=b using LU
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VectorXmp x = A.lu().solve(b);
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std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl;
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return 0;
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}
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\endcode
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*
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*/
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template<> struct NumTraits<mpfr::mpreal>
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: GenericNumTraits<mpfr::mpreal>
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{
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enum {
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IsInteger = 0,
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IsSigned = 1,
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IsComplex = 0,
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RequireInitialization = 1,
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ReadCost = 10,
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AddCost = 10,
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MulCost = 40
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};
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typedef mpfr::mpreal Real;
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typedef mpfr::mpreal NonInteger;
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inline static Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); }
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inline static Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }
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// Constants
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inline static Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); }
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inline static Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); }
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inline static Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); }
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inline static Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); }
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inline static Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); }
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inline static Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); }
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inline static Real dummy_precision()
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{
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unsigned int weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100;
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return mpfr::machine_epsilon(weak_prec);
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}
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};
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namespace internal {
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template<> inline mpfr::mpreal random<mpfr::mpreal>()
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{
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return mpfr::random();
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}
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template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b)
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{
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return a + (b-a) * random<mpfr::mpreal>();
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}
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inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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{
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return mpfr::abs(a) <= mpfr::abs(b) * eps;
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}
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inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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{
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return mpfr::isEqualFuzzy(a,b,eps);
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}
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inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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{
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return a <= b || mpfr::isEqualFuzzy(a,b,eps);
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}
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template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x)
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{ return x.toLDouble(); }
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template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x)
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{ return x.toDouble(); }
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template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x)
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{ return x.toLong(); }
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template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x)
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{ return int(x.toLong()); }
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// Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff)
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// This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal
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template<>
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class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false>
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{
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public:
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typedef mpfr::mpreal ResScalar;
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enum {
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nr = 2, // must be 2 for proper packing...
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mr = 1,
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WorkSpaceFactor = nr,
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LhsProgress = 1,
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RhsProgress = 1
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};
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};
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template<typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
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struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,mr,nr,ConjugateLhs,ConjugateRhs>
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{
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typedef mpfr::mpreal mpreal;
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EIGEN_DONT_INLINE
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void operator()(mpreal* res, Index resStride, const mpreal* blockA, const mpreal* blockB, Index rows, Index depth, Index cols, mpreal alpha,
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Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0, mpreal* /*unpackedB*/ = 0)
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{
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mpreal acc1, acc2, tmp;
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if(strideA==-1) strideA = depth;
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if(strideB==-1) strideB = depth;
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for(Index j=0; j<cols; j+=nr)
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{
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Index actual_nr = (std::min<Index>)(nr,cols-j);
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mpreal *C1 = res + j*resStride;
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mpreal *C2 = res + (j+1)*resStride;
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for(Index i=0; i<rows; i++)
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{
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mpreal *B = const_cast<mpreal*>(blockB) + j*strideB + offsetB*actual_nr;
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mpreal *A = const_cast<mpreal*>(blockA) + i*strideA + offsetA;
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acc1 = 0;
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acc2 = 0;
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for(Index k=0; k<depth; k++)
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{
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mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[0].mpfr_ptr(), mpreal::get_default_rnd());
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mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
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if(actual_nr==2) {
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mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[1].mpfr_ptr(), mpreal::get_default_rnd());
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mpfr_add(acc2.mpfr_ptr(), acc2.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
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}
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B+=actual_nr;
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}
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mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
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mpfr_add(C1[i].mpfr_ptr(), C1[i].mpfr_ptr(), acc1.mpfr_ptr(), mpreal::get_default_rnd());
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if(actual_nr==2) {
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mpfr_mul(acc2.mpfr_ptr(), acc2.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
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mpfr_add(C2[i].mpfr_ptr(), C2[i].mpfr_ptr(), acc2.mpfr_ptr(), mpreal::get_default_rnd());
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}
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}
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}
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}
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};
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} // end namespace internal
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}
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#endif // EIGEN_MPREALSUPPORT_MODULE_H
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