1 // This file is part of a joint effort between Eigen, a lightweight C++ template library 2 // for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/) 3 // 4 // Copyright (C) 2010-2012 Pavel Holoborodko <pavel (a] holoborodko.com> 5 // Copyright (C) 2010 Konstantin Holoborodko <konstantin (a] holoborodko.com> 6 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud (a] inria.fr> 7 // 8 // This Source Code Form is subject to the terms of the Mozilla 9 // Public License v. 2.0. If a copy of the MPL was not distributed 10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 11 12 #ifndef EIGEN_MPREALSUPPORT_MODULE_H 13 #define EIGEN_MPREALSUPPORT_MODULE_H 14 15 #include <Eigen/Core> 16 #include <mpreal.h> 17 18 namespace Eigen { 19 20 /** 21 * \defgroup MPRealSupport_Module MPFRC++ Support module 22 * \code 23 * #include <Eigen/MPRealSupport> 24 * \endcode 25 * 26 * This module provides support for multi precision floating point numbers 27 * via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a> 28 * library which itself is built upon <a href="http://www.mpfr.org/">MPFR</a>/<a href="http://gmplib.org/">GMP</a>. 29 * 30 * \warning MPFR C++ is licensed under the GPL. 31 * 32 * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder. 33 * 34 * Here is an example: 35 * 36 \code 37 #include <iostream> 38 #include <Eigen/MPRealSupport> 39 #include <Eigen/LU> 40 using namespace mpfr; 41 using namespace Eigen; 42 int main() 43 { 44 // set precision to 256 bits (double has only 53 bits) 45 mpreal::set_default_prec(256); 46 // Declare matrix and vector types with multi-precision scalar type 47 typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp; 48 typedef Matrix<mpreal,Dynamic,1> VectorXmp; 49 50 MatrixXmp A = MatrixXmp::Random(100,100); 51 VectorXmp b = VectorXmp::Random(100); 52 53 // Solve Ax=b using LU 54 VectorXmp x = A.lu().solve(b); 55 std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl; 56 return 0; 57 } 58 \endcode 59 * 60 */ 61 62 template<> struct NumTraits<mpfr::mpreal> 63 : GenericNumTraits<mpfr::mpreal> 64 { 65 enum { 66 IsInteger = 0, 67 IsSigned = 1, 68 IsComplex = 0, 69 RequireInitialization = 1, 70 ReadCost = HugeCost, 71 AddCost = HugeCost, 72 MulCost = HugeCost 73 }; 74 75 typedef mpfr::mpreal Real; 76 typedef mpfr::mpreal NonInteger; 77 78 static inline Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); } 79 static inline Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); } 80 81 // Constants 82 static inline Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); } 83 static inline Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); } 84 static inline Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); } 85 static inline Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); } 86 87 static inline Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); } 88 static inline Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); } 89 90 #ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS 91 static inline int digits10 (long Precision = mpfr::mpreal::get_default_prec()) { return std::numeric_limits<Real>::digits10(Precision); } 92 static inline int digits10 (const Real& x) { return std::numeric_limits<Real>::digits10(x); } 93 #endif 94 95 static inline Real dummy_precision() 96 { 97 mpfr_prec_t weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100; 98 return mpfr::machine_epsilon(weak_prec); 99 } 100 }; 101 102 namespace internal { 103 104 template<> inline mpfr::mpreal random<mpfr::mpreal>() 105 { 106 return mpfr::random(); 107 } 108 109 template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b) 110 { 111 return a + (b-a) * random<mpfr::mpreal>(); 112 } 113 114 inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps) 115 { 116 return mpfr::abs(a) <= mpfr::abs(b) * eps; 117 } 118 119 inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps) 120 { 121 return mpfr::isEqualFuzzy(a,b,eps); 122 } 123 124 inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps) 125 { 126 return a <= b || mpfr::isEqualFuzzy(a,b,eps); 127 } 128 129 template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x) 130 { return x.toLDouble(); } 131 132 template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x) 133 { return x.toDouble(); } 134 135 template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x) 136 { return x.toLong(); } 137 138 template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x) 139 { return int(x.toLong()); } 140 141 // Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff) 142 // This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal 143 template<> 144 class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false> 145 { 146 public: 147 typedef mpfr::mpreal ResScalar; 148 enum { 149 Vectorizable = false, 150 LhsPacketSize = 1, 151 RhsPacketSize = 1, 152 ResPacketSize = 1, 153 NumberOfRegisters = 1, 154 nr = 1, 155 mr = 1, 156 LhsProgress = 1, 157 RhsProgress = 1 158 }; 159 typedef ResScalar LhsPacket; 160 typedef ResScalar RhsPacket; 161 typedef ResScalar ResPacket; 162 163 }; 164 165 166 167 template<typename Index, typename DataMapper, bool ConjugateLhs, bool ConjugateRhs> 168 struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,DataMapper,1,1,ConjugateLhs,ConjugateRhs> 169 { 170 typedef mpfr::mpreal mpreal; 171 172 EIGEN_DONT_INLINE 173 void operator()(const DataMapper& res, const mpreal* blockA, const mpreal* blockB, 174 Index rows, Index depth, Index cols, const mpreal& alpha, 175 Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0) 176 { 177 if(rows==0 || cols==0 || depth==0) 178 return; 179 180 mpreal acc1(0,mpfr_get_prec(blockA[0].mpfr_srcptr())), 181 tmp (0,mpfr_get_prec(blockA[0].mpfr_srcptr())); 182 183 if(strideA==-1) strideA = depth; 184 if(strideB==-1) strideB = depth; 185 186 for(Index i=0; i<rows; ++i) 187 { 188 for(Index j=0; j<cols; ++j) 189 { 190 const mpreal *A = blockA + i*strideA + offsetA; 191 const mpreal *B = blockB + j*strideB + offsetB; 192 193 acc1 = 0; 194 for(Index k=0; k<depth; k++) 195 { 196 mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_srcptr(), B[k].mpfr_srcptr(), mpreal::get_default_rnd()); 197 mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd()); 198 } 199 200 mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_srcptr(), alpha.mpfr_srcptr(), mpreal::get_default_rnd()); 201 mpfr_add(res(i,j).mpfr_ptr(), res(i,j).mpfr_srcptr(), acc1.mpfr_srcptr(), mpreal::get_default_rnd()); 202 } 203 } 204 } 205 }; 206 } // end namespace internal 207 } 208 209 #endif // EIGEN_MPREALSUPPORT_MODULE_H 210
