[136] | 1 | // This file is part of a joint effort between Eigen, a lightweight C++ template library
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| 2 | // for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/)
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| 3 | //
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| 4 | // Copyright (C) 2010-2012 Pavel Holoborodko <pavel@holoborodko.com>
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| 5 | // Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com>
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| 6 | // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 7 | //
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| 8 | // This Source Code Form is subject to the terms of the Mozilla
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| 9 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 10 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 11 |
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| 12 | #ifndef EIGEN_MPREALSUPPORT_MODULE_H
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| 13 | #define EIGEN_MPREALSUPPORT_MODULE_H
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| 14 |
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| 15 | #include <Eigen/Core>
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| 16 | #include <mpreal.h>
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| 17 |
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| 18 | namespace Eigen {
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| 19 |
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| 20 | /**
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| 21 | * \defgroup MPRealSupport_Module MPFRC++ Support module
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| 22 | * \code
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| 23 | * #include <Eigen/MPRealSupport>
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| 24 | * \endcode
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| 25 | *
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| 26 | * This module provides support for multi precision floating point numbers
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| 27 | * via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a>
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| 28 | * 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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| 29 | *
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| 30 | * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder.
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| 31 | *
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| 32 | * Here is an example:
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| 33 | *
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| 34 | \code
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| 35 | #include <iostream>
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| 36 | #include <Eigen/MPRealSupport>
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| 37 | #include <Eigen/LU>
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| 38 | using namespace mpfr;
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| 39 | using namespace Eigen;
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| 40 | int main()
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| 41 | {
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| 42 | // set precision to 256 bits (double has only 53 bits)
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| 43 | mpreal::set_default_prec(256);
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| 44 | // Declare matrix and vector types with multi-precision scalar type
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| 45 | typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp;
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| 46 | typedef Matrix<mpreal,Dynamic,1> VectorXmp;
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| 47 |
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| 48 | MatrixXmp A = MatrixXmp::Random(100,100);
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| 49 | VectorXmp b = VectorXmp::Random(100);
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| 50 |
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| 51 | // Solve Ax=b using LU
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| 52 | VectorXmp x = A.lu().solve(b);
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| 53 | std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl;
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| 54 | return 0;
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| 55 | }
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| 56 | \endcode
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| 57 | *
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| 58 | */
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| 59 |
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| 60 | template<> struct NumTraits<mpfr::mpreal>
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| 61 | : GenericNumTraits<mpfr::mpreal>
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| 62 | {
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| 63 | enum {
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| 64 | IsInteger = 0,
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| 65 | IsSigned = 1,
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| 66 | IsComplex = 0,
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| 67 | RequireInitialization = 1,
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| 68 | ReadCost = 10,
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| 69 | AddCost = 10,
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| 70 | MulCost = 40
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| 71 | };
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| 72 |
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| 73 | typedef mpfr::mpreal Real;
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| 74 | typedef mpfr::mpreal NonInteger;
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| 75 |
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| 76 | inline static Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); }
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| 77 | inline static Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }
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| 78 |
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| 79 | // Constants
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| 80 | inline static Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); }
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| 81 | inline static Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); }
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| 82 | inline static Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); }
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| 83 | inline static Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); }
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| 84 |
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| 85 | inline static Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); }
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| 86 | inline static Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); }
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| 87 |
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| 88 | inline static Real dummy_precision()
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| 89 | {
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| 90 | unsigned int weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100;
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| 91 | return mpfr::machine_epsilon(weak_prec);
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| 92 | }
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| 93 | };
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| 94 |
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| 95 | namespace internal {
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| 96 |
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| 97 | template<> inline mpfr::mpreal random<mpfr::mpreal>()
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| 98 | {
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| 99 | return mpfr::random();
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| 100 | }
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| 101 |
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| 102 | template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b)
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| 103 | {
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| 104 | return a + (b-a) * random<mpfr::mpreal>();
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| 105 | }
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| 106 |
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| 107 | inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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| 108 | {
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| 109 | return mpfr::abs(a) <= mpfr::abs(b) * eps;
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| 110 | }
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| 111 |
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| 112 | inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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| 113 | {
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| 114 | return mpfr::isEqualFuzzy(a,b,eps);
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| 115 | }
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| 116 |
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| 117 | inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
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| 118 | {
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| 119 | return a <= b || mpfr::isEqualFuzzy(a,b,eps);
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| 120 | }
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| 121 |
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| 122 | template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x)
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| 123 | { return x.toLDouble(); }
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| 124 |
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| 125 | template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x)
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| 126 | { return x.toDouble(); }
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| 127 |
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| 128 | template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x)
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| 129 | { return x.toLong(); }
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| 130 |
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| 131 | template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x)
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| 132 | { return int(x.toLong()); }
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| 133 |
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| 134 | // Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff)
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| 135 | // This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal
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| 136 | template<>
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| 137 | class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false>
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| 138 | {
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| 139 | public:
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| 140 | typedef mpfr::mpreal ResScalar;
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| 141 | enum {
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| 142 | nr = 2, // must be 2 for proper packing...
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| 143 | mr = 1,
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| 144 | WorkSpaceFactor = nr,
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| 145 | LhsProgress = 1,
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| 146 | RhsProgress = 1
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| 147 | };
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| 148 | };
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| 149 |
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| 150 | template<typename Index, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
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| 151 | struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,mr,nr,ConjugateLhs,ConjugateRhs>
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| 152 | {
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| 153 | typedef mpfr::mpreal mpreal;
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| 154 |
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| 155 | EIGEN_DONT_INLINE
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| 156 | void operator()(mpreal* res, Index resStride, const mpreal* blockA, const mpreal* blockB, Index rows, Index depth, Index cols, mpreal alpha,
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| 157 | Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0, mpreal* /*unpackedB*/ = 0)
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| 158 | {
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| 159 | mpreal acc1, acc2, tmp;
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| 160 |
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| 161 | if(strideA==-1) strideA = depth;
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| 162 | if(strideB==-1) strideB = depth;
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| 163 |
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| 164 | for(Index j=0; j<cols; j+=nr)
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| 165 | {
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| 166 | Index actual_nr = (std::min<Index>)(nr,cols-j);
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| 167 | mpreal *C1 = res + j*resStride;
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| 168 | mpreal *C2 = res + (j+1)*resStride;
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| 169 | for(Index i=0; i<rows; i++)
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| 170 | {
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| 171 | mpreal *B = const_cast<mpreal*>(blockB) + j*strideB + offsetB*actual_nr;
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| 172 | mpreal *A = const_cast<mpreal*>(blockA) + i*strideA + offsetA;
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| 173 | acc1 = 0;
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| 174 | acc2 = 0;
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| 175 | for(Index k=0; k<depth; k++)
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| 176 | {
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| 177 | mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[0].mpfr_ptr(), mpreal::get_default_rnd());
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| 178 | mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
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| 179 |
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| 180 | if(actual_nr==2) {
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| 181 | mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_ptr(), B[1].mpfr_ptr(), mpreal::get_default_rnd());
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| 182 | mpfr_add(acc2.mpfr_ptr(), acc2.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
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| 183 | }
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| 184 |
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| 185 | B+=actual_nr;
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| 186 | }
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| 187 |
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| 188 | mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
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| 189 | mpfr_add(C1[i].mpfr_ptr(), C1[i].mpfr_ptr(), acc1.mpfr_ptr(), mpreal::get_default_rnd());
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| 190 |
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| 191 | if(actual_nr==2) {
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| 192 | mpfr_mul(acc2.mpfr_ptr(), acc2.mpfr_ptr(), alpha.mpfr_ptr(), mpreal::get_default_rnd());
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| 193 | mpfr_add(C2[i].mpfr_ptr(), C2[i].mpfr_ptr(), acc2.mpfr_ptr(), mpreal::get_default_rnd());
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| 194 | }
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| 195 | }
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| 196 | }
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| 197 | }
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| 198 | };
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| 199 |
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| 200 | } // end namespace internal
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| 201 | }
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| 202 |
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| 203 | #endif // EIGEN_MPREALSUPPORT_MODULE_H
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