1 | // This file is part of Eigen, a lightweight C++ template library |
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2 | // for linear algebra. |
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3 | // |
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4 | // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
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5 | // |
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6 | // This Source Code Form is subject to the terms of the Mozilla |
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed |
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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9 | |
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10 | #ifndef EIGEN_GENERAL_MATRIX_MATRIX_H |
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11 | #define EIGEN_GENERAL_MATRIX_MATRIX_H |
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12 | |
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13 | namespace Eigen { |
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14 | |
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15 | namespace internal { |
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16 | |
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17 | template<typename _LhsScalar, typename _RhsScalar> class level3_blocking; |
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18 | |
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19 | /* Specialization for a row-major destination matrix => simple transposition of the product */ |
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20 | template< |
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21 | typename Index, |
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22 | typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
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23 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs> |
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24 | struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor> |
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25 | { |
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26 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
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27 | static EIGEN_STRONG_INLINE void run( |
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28 | Index rows, Index cols, Index depth, |
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29 | const LhsScalar* lhs, Index lhsStride, |
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30 | const RhsScalar* rhs, Index rhsStride, |
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31 | ResScalar* res, Index resStride, |
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32 | ResScalar alpha, |
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33 | level3_blocking<RhsScalar,LhsScalar>& blocking, |
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34 | GemmParallelInfo<Index>* info = 0) |
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35 | { |
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36 | // transpose the product such that the result is column major |
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37 | general_matrix_matrix_product<Index, |
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38 | RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, |
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39 | LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, |
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40 | ColMajor> |
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41 | ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info); |
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42 | } |
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43 | }; |
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44 | |
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45 | /* Specialization for a col-major destination matrix |
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46 | * => Blocking algorithm following Goto's paper */ |
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47 | template< |
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48 | typename Index, |
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49 | typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
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50 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs> |
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51 | struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor> |
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52 | { |
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53 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
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54 | static void run(Index rows, Index cols, Index depth, |
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55 | const LhsScalar* _lhs, Index lhsStride, |
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56 | const RhsScalar* _rhs, Index rhsStride, |
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57 | ResScalar* res, Index resStride, |
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58 | ResScalar alpha, |
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59 | level3_blocking<LhsScalar,RhsScalar>& blocking, |
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60 | GemmParallelInfo<Index>* info = 0) |
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61 | { |
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62 | const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride); |
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63 | const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride); |
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64 | |
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65 | typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
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66 | |
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67 | Index kc = blocking.kc(); // cache block size along the K direction |
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68 | Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction |
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69 | //Index nc = blocking.nc(); // cache block size along the N direction |
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70 | |
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71 | gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
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72 | gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs; |
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73 | gebp_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; |
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74 | |
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75 | #ifdef EIGEN_HAS_OPENMP |
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76 | if(info) |
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77 | { |
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78 | // this is the parallel version! |
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79 | Index tid = omp_get_thread_num(); |
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80 | Index threads = omp_get_num_threads(); |
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81 | |
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82 | std::size_t sizeA = kc*mc; |
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83 | std::size_t sizeW = kc*Traits::WorkSpaceFactor; |
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84 | ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, 0); |
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85 | ei_declare_aligned_stack_constructed_variable(RhsScalar, w, sizeW, 0); |
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86 | |
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87 | RhsScalar* blockB = blocking.blockB(); |
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88 | eigen_internal_assert(blockB!=0); |
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89 | |
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90 | // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs... |
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91 | for(Index k=0; k<depth; k+=kc) |
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92 | { |
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93 | const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A' |
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94 | |
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95 | // In order to reduce the chance that a thread has to wait for the other, |
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96 | // let's start by packing A'. |
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97 | pack_lhs(blockA, &lhs(0,k), lhsStride, actual_kc, mc); |
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98 | |
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99 | // Pack B_k to B' in a parallel fashion: |
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100 | // each thread packs the sub block B_k,j to B'_j where j is the thread id. |
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101 | |
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102 | // However, before copying to B'_j, we have to make sure that no other thread is still using it, |
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103 | // i.e., we test that info[tid].users equals 0. |
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104 | // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it. |
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105 | while(info[tid].users!=0) {} |
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106 | info[tid].users += threads; |
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107 | |
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108 | pack_rhs(blockB+info[tid].rhs_start*actual_kc, &rhs(k,info[tid].rhs_start), rhsStride, actual_kc, info[tid].rhs_length); |
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109 | |
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110 | // Notify the other threads that the part B'_j is ready to go. |
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111 | info[tid].sync = k; |
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112 | |
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113 | // Computes C_i += A' * B' per B'_j |
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114 | for(Index shift=0; shift<threads; ++shift) |
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115 | { |
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116 | Index j = (tid+shift)%threads; |
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117 | |
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118 | // At this point we have to make sure that B'_j has been updated by the thread j, |
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119 | // we use testAndSetOrdered to mimic a volatile access. |
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120 | // However, no need to wait for the B' part which has been updated by the current thread! |
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121 | if(shift>0) |
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122 | while(info[j].sync!=k) {} |
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123 | |
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124 | gebp(res+info[j].rhs_start*resStride, resStride, blockA, blockB+info[j].rhs_start*actual_kc, mc, actual_kc, info[j].rhs_length, alpha, -1,-1,0,0, w); |
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125 | } |
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126 | |
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127 | // Then keep going as usual with the remaining A' |
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128 | for(Index i=mc; i<rows; i+=mc) |
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129 | { |
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130 | const Index actual_mc = (std::min)(i+mc,rows)-i; |
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131 | |
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132 | // pack A_i,k to A' |
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133 | pack_lhs(blockA, &lhs(i,k), lhsStride, actual_kc, actual_mc); |
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134 | |
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135 | // C_i += A' * B' |
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136 | gebp(res+i, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1,-1,0,0, w); |
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137 | } |
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138 | |
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139 | // Release all the sub blocks B'_j of B' for the current thread, |
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140 | // i.e., we simply decrement the number of users by 1 |
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141 | for(Index j=0; j<threads; ++j) |
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142 | #pragma omp atomic |
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143 | --(info[j].users); |
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144 | } |
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145 | } |
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146 | else |
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147 | #endif // EIGEN_HAS_OPENMP |
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148 | { |
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149 | EIGEN_UNUSED_VARIABLE(info); |
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150 | |
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151 | // this is the sequential version! |
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152 | std::size_t sizeA = kc*mc; |
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153 | std::size_t sizeB = kc*cols; |
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154 | std::size_t sizeW = kc*Traits::WorkSpaceFactor; |
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155 | |
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156 | ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA()); |
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157 | ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB()); |
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158 | ei_declare_aligned_stack_constructed_variable(RhsScalar, blockW, sizeW, blocking.blockW()); |
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159 | |
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160 | // For each horizontal panel of the rhs, and corresponding panel of the lhs... |
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161 | // (==GEMM_VAR1) |
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162 | for(Index k2=0; k2<depth; k2+=kc) |
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163 | { |
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164 | const Index actual_kc = (std::min)(k2+kc,depth)-k2; |
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165 | |
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166 | // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs. |
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167 | // => Pack rhs's panel into a sequential chunk of memory (L2 caching) |
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168 | // Note that this panel will be read as many times as the number of blocks in the lhs's |
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169 | // vertical panel which is, in practice, a very low number. |
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170 | pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols); |
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171 | |
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172 | |
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173 | // For each mc x kc block of the lhs's vertical panel... |
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174 | // (==GEPP_VAR1) |
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175 | for(Index i2=0; i2<rows; i2+=mc) |
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176 | { |
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177 | const Index actual_mc = (std::min)(i2+mc,rows)-i2; |
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178 | |
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179 | // We pack the lhs's block into a sequential chunk of memory (L1 caching) |
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180 | // Note that this block will be read a very high number of times, which is equal to the number of |
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181 | // micro vertical panel of the large rhs's panel (e.g., cols/4 times). |
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182 | pack_lhs(blockA, &lhs(i2,k2), lhsStride, actual_kc, actual_mc); |
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183 | |
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184 | // Everything is packed, we can now call the block * panel kernel: |
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185 | gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW); |
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186 | |
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187 | } |
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188 | } |
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189 | } |
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190 | } |
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191 | |
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192 | }; |
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193 | |
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194 | /********************************************************************************* |
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195 | * Specialization of GeneralProduct<> for "large" GEMM, i.e., |
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196 | * implementation of the high level wrapper to general_matrix_matrix_product |
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197 | **********************************************************************************/ |
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198 | |
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199 | template<typename Lhs, typename Rhs> |
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200 | struct traits<GeneralProduct<Lhs,Rhs,GemmProduct> > |
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201 | : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> > |
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202 | {}; |
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203 | |
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204 | template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType> |
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205 | struct gemm_functor |
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206 | { |
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207 | gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, Scalar actualAlpha, |
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208 | BlockingType& blocking) |
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209 | : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking) |
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210 | {} |
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211 | |
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212 | void initParallelSession() const |
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213 | { |
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214 | m_blocking.allocateB(); |
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215 | } |
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216 | |
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217 | void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const |
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218 | { |
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219 | if(cols==-1) |
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220 | cols = m_rhs.cols(); |
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221 | |
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222 | Gemm::run(rows, cols, m_lhs.cols(), |
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223 | /*(const Scalar*)*/&m_lhs.coeffRef(row,0), m_lhs.outerStride(), |
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224 | /*(const Scalar*)*/&m_rhs.coeffRef(0,col), m_rhs.outerStride(), |
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225 | (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(), |
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226 | m_actualAlpha, m_blocking, info); |
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227 | } |
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228 | |
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229 | protected: |
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230 | const Lhs& m_lhs; |
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231 | const Rhs& m_rhs; |
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232 | Dest& m_dest; |
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233 | Scalar m_actualAlpha; |
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234 | BlockingType& m_blocking; |
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235 | }; |
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236 | |
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237 | template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1, |
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238 | bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space; |
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239 | |
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240 | template<typename _LhsScalar, typename _RhsScalar> |
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241 | class level3_blocking |
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242 | { |
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243 | typedef _LhsScalar LhsScalar; |
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244 | typedef _RhsScalar RhsScalar; |
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245 | |
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246 | protected: |
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247 | LhsScalar* m_blockA; |
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248 | RhsScalar* m_blockB; |
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249 | RhsScalar* m_blockW; |
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250 | |
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251 | DenseIndex m_mc; |
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252 | DenseIndex m_nc; |
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253 | DenseIndex m_kc; |
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254 | |
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255 | public: |
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256 | |
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257 | level3_blocking() |
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258 | : m_blockA(0), m_blockB(0), m_blockW(0), m_mc(0), m_nc(0), m_kc(0) |
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259 | {} |
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260 | |
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261 | inline DenseIndex mc() const { return m_mc; } |
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262 | inline DenseIndex nc() const { return m_nc; } |
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263 | inline DenseIndex kc() const { return m_kc; } |
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264 | |
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265 | inline LhsScalar* blockA() { return m_blockA; } |
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266 | inline RhsScalar* blockB() { return m_blockB; } |
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267 | inline RhsScalar* blockW() { return m_blockW; } |
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268 | }; |
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269 | |
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270 | template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor> |
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271 | class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true> |
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272 | : public level3_blocking< |
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273 | typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type, |
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274 | typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type> |
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275 | { |
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276 | enum { |
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277 | Transpose = StorageOrder==RowMajor, |
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278 | ActualRows = Transpose ? MaxCols : MaxRows, |
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279 | ActualCols = Transpose ? MaxRows : MaxCols |
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280 | }; |
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281 | typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar; |
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282 | typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar; |
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283 | typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
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284 | enum { |
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285 | SizeA = ActualRows * MaxDepth, |
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286 | SizeB = ActualCols * MaxDepth, |
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287 | SizeW = MaxDepth * Traits::WorkSpaceFactor |
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288 | }; |
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289 | |
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290 | EIGEN_ALIGN16 LhsScalar m_staticA[SizeA]; |
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291 | EIGEN_ALIGN16 RhsScalar m_staticB[SizeB]; |
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292 | EIGEN_ALIGN16 RhsScalar m_staticW[SizeW]; |
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293 | |
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294 | public: |
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295 | |
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296 | gemm_blocking_space(DenseIndex /*rows*/, DenseIndex /*cols*/, DenseIndex /*depth*/) |
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297 | { |
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298 | this->m_mc = ActualRows; |
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299 | this->m_nc = ActualCols; |
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300 | this->m_kc = MaxDepth; |
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301 | this->m_blockA = m_staticA; |
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302 | this->m_blockB = m_staticB; |
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303 | this->m_blockW = m_staticW; |
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304 | } |
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305 | |
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306 | inline void allocateA() {} |
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307 | inline void allocateB() {} |
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308 | inline void allocateW() {} |
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309 | inline void allocateAll() {} |
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310 | }; |
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311 | |
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312 | template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor> |
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313 | class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false> |
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314 | : public level3_blocking< |
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315 | typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type, |
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316 | typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type> |
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317 | { |
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318 | enum { |
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319 | Transpose = StorageOrder==RowMajor |
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320 | }; |
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321 | typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar; |
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322 | typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar; |
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323 | typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
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324 | |
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325 | DenseIndex m_sizeA; |
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326 | DenseIndex m_sizeB; |
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327 | DenseIndex m_sizeW; |
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328 | |
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329 | public: |
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330 | |
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331 | gemm_blocking_space(DenseIndex rows, DenseIndex cols, DenseIndex depth) |
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332 | { |
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333 | this->m_mc = Transpose ? cols : rows; |
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334 | this->m_nc = Transpose ? rows : cols; |
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335 | this->m_kc = depth; |
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336 | |
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337 | computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc); |
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338 | m_sizeA = this->m_mc * this->m_kc; |
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339 | m_sizeB = this->m_kc * this->m_nc; |
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340 | m_sizeW = this->m_kc*Traits::WorkSpaceFactor; |
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341 | } |
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342 | |
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343 | void allocateA() |
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344 | { |
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345 | if(this->m_blockA==0) |
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346 | this->m_blockA = aligned_new<LhsScalar>(m_sizeA); |
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347 | } |
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348 | |
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349 | void allocateB() |
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350 | { |
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351 | if(this->m_blockB==0) |
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352 | this->m_blockB = aligned_new<RhsScalar>(m_sizeB); |
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353 | } |
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354 | |
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355 | void allocateW() |
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356 | { |
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357 | if(this->m_blockW==0) |
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358 | this->m_blockW = aligned_new<RhsScalar>(m_sizeW); |
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359 | } |
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360 | |
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361 | void allocateAll() |
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362 | { |
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363 | allocateA(); |
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364 | allocateB(); |
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365 | allocateW(); |
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366 | } |
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367 | |
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368 | ~gemm_blocking_space() |
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369 | { |
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370 | aligned_delete(this->m_blockA, m_sizeA); |
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371 | aligned_delete(this->m_blockB, m_sizeB); |
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372 | aligned_delete(this->m_blockW, m_sizeW); |
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373 | } |
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374 | }; |
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375 | |
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376 | } // end namespace internal |
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377 | |
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378 | template<typename Lhs, typename Rhs> |
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379 | class GeneralProduct<Lhs, Rhs, GemmProduct> |
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380 | : public ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> |
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381 | { |
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382 | enum { |
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383 | MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime) |
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384 | }; |
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385 | public: |
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386 | EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct) |
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387 | |
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388 | typedef typename Lhs::Scalar LhsScalar; |
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389 | typedef typename Rhs::Scalar RhsScalar; |
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390 | typedef Scalar ResScalar; |
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391 | |
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392 | GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) |
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393 | { |
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394 | typedef internal::scalar_product_op<LhsScalar,RhsScalar> BinOp; |
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395 | EIGEN_CHECK_BINARY_COMPATIBILIY(BinOp,LhsScalar,RhsScalar); |
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396 | } |
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397 | |
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398 | template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const |
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399 | { |
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400 | eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols()); |
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401 | |
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402 | typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs); |
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403 | typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs); |
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404 | |
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405 | Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs) |
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406 | * RhsBlasTraits::extractScalarFactor(m_rhs); |
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407 | |
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408 | typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar, |
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409 | Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType; |
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410 | |
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411 | typedef internal::gemm_functor< |
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412 | Scalar, Index, |
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413 | internal::general_matrix_matrix_product< |
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414 | Index, |
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415 | LhsScalar, (_ActualLhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate), |
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416 | RhsScalar, (_ActualRhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate), |
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417 | (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>, |
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418 | _ActualLhsType, _ActualRhsType, Dest, BlockingType> GemmFunctor; |
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419 | |
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420 | BlockingType blocking(dst.rows(), dst.cols(), lhs.cols()); |
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421 | |
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422 | internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>(GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), this->rows(), this->cols(), Dest::Flags&RowMajorBit); |
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423 | } |
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424 | }; |
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425 | |
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426 | } // end namespace Eigen |
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427 | |
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428 | #endif // EIGEN_GENERAL_MATRIX_MATRIX_H |
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