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00001 // This file is part of Eigen, a lightweight C++ template library 00002 // for linear algebra. 00003 // 00004 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> 00005 // 00006 // This Source Code Form is subject to the terms of the Mozilla 00007 // Public License v. 2.0. If a copy of the MPL was not distributed 00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 00009 00010 #ifndef EIGEN_GENERAL_MATRIX_MATRIX_H 00011 #define EIGEN_GENERAL_MATRIX_MATRIX_H 00012 00013 namespace Eigen { 00014 00015 namespace internal { 00016 00017 template<typename _LhsScalar, typename _RhsScalar> class level3_blocking; 00018 00019 /* Specialization for a row-major destination matrix => simple transposition of the product */ 00020 template< 00021 typename Index, 00022 typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 00023 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs> 00024 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor> 00025 { 00026 typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; 00027 static EIGEN_STRONG_INLINE void run( 00028 Index rows, Index cols, Index depth, 00029 const LhsScalar* lhs, Index lhsStride, 00030 const RhsScalar* rhs, Index rhsStride, 00031 ResScalar* res, Index resStride, 00032 ResScalar alpha, 00033 level3_blocking<RhsScalar,LhsScalar>& blocking, 00034 GemmParallelInfo<Index>* info = 0) 00035 { 00036 // transpose the product such that the result is column major 00037 general_matrix_matrix_product<Index, 00038 RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, 00039 LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, 00040 ColMajor> 00041 ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info); 00042 } 00043 }; 00044 00045 /* Specialization for a col-major destination matrix 00046 * => Blocking algorithm following Goto's paper */ 00047 template< 00048 typename Index, 00049 typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 00050 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs> 00051 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor> 00052 { 00053 00054 typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; 00055 static void run(Index rows, Index cols, Index depth, 00056 const LhsScalar* _lhs, Index lhsStride, 00057 const RhsScalar* _rhs, Index rhsStride, 00058 ResScalar* res, Index resStride, 00059 ResScalar alpha, 00060 level3_blocking<LhsScalar,RhsScalar>& blocking, 00061 GemmParallelInfo<Index>* info = 0) 00062 { 00063 const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride); 00064 const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride); 00065 00066 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 00067 00068 Index kc = blocking.kc(); // cache block size along the K direction 00069 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction 00070 //Index nc = blocking.nc(); // cache block size along the N direction 00071 00072 gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; 00073 gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs; 00074 gebp_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; 00075 00076 #ifdef EIGEN_HAS_OPENMP 00077 if(info) 00078 { 00079 // this is the parallel version! 00080 Index tid = omp_get_thread_num(); 00081 Index threads = omp_get_num_threads(); 00082 00083 std::size_t sizeA = kc*mc; 00084 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 00085 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, 0); 00086 ei_declare_aligned_stack_constructed_variable(RhsScalar, w, sizeW, 0); 00087 00088 RhsScalar* blockB = blocking.blockB(); 00089 eigen_internal_assert(blockB!=0); 00090 00091 // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs... 00092 for(Index k=0; k<depth; k+=kc) 00093 { 00094 const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A' 00095 00096 // In order to reduce the chance that a thread has to wait for the other, 00097 // let's start by packing A'. 00098 pack_lhs(blockA, &lhs(0,k), lhsStride, actual_kc, mc); 00099 00100 // Pack B_k to B' in a parallel fashion: 00101 // each thread packs the sub block B_k,j to B'_j where j is the thread id. 00102 00103 // However, before copying to B'_j, we have to make sure that no other thread is still using it, 00104 // i.e., we test that info[tid].users equals 0. 00105 // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it. 00106 while(info[tid].users!=0) {} 00107 info[tid].users += threads; 00108 00109 pack_rhs(blockB+info[tid].rhs_start*actual_kc, &rhs(k,info[tid].rhs_start), rhsStride, actual_kc, info[tid].rhs_length); 00110 00111 // Notify the other threads that the part B'_j is ready to go. 00112 info[tid].sync = k; 00113 00114 // Computes C_i += A' * B' per B'_j 00115 for(Index shift=0; shift<threads; ++shift) 00116 { 00117 Index j = (tid+shift)%threads; 00118 00119 // At this point we have to make sure that B'_j has been updated by the thread j, 00120 // we use testAndSetOrdered to mimic a volatile access. 00121 // However, no need to wait for the B' part which has been updated by the current thread! 00122 if(shift>0) 00123 while(info[j].sync!=k) {} 00124 00125 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); 00126 } 00127 00128 // Then keep going as usual with the remaining A' 00129 for(Index i=mc; i<rows; i+=mc) 00130 { 00131 const Index actual_mc = (std::min)(i+mc,rows)-i; 00132 00133 // pack A_i,k to A' 00134 pack_lhs(blockA, &lhs(i,k), lhsStride, actual_kc, actual_mc); 00135 00136 // C_i += A' * B' 00137 gebp(res+i, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1,-1,0,0, w); 00138 } 00139 00140 // Release all the sub blocks B'_j of B' for the current thread, 00141 // i.e., we simply decrement the number of users by 1 00142 for(Index j=0; j<threads; ++j) 00143 #pragma omp atomic 00144 --(info[j].users); 00145 } 00146 } 00147 else 00148 #endif // EIGEN_HAS_OPENMP 00149 { 00150 EIGEN_UNUSED_VARIABLE(info); 00151 00152 // this is the sequential version! 00153 std::size_t sizeA = kc*mc; 00154 std::size_t sizeB = kc*cols; 00155 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 00156 00157 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA()); 00158 ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB()); 00159 ei_declare_aligned_stack_constructed_variable(RhsScalar, blockW, sizeW, blocking.blockW()); 00160 00161 // For each horizontal panel of the rhs, and corresponding panel of the lhs... 00162 // (==GEMM_VAR1) 00163 for(Index k2=0; k2<depth; k2+=kc) 00164 { 00165 const Index actual_kc = (std::min)(k2+kc,depth)-k2; 00166 00167 // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs. 00168 // => Pack rhs's panel into a sequential chunk of memory (L2 caching) 00169 // Note that this panel will be read as many times as the number of blocks in the lhs's 00170 // vertical panel which is, in practice, a very low number. 00171 pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols); 00172 00173 // For each mc x kc block of the lhs's vertical panel... 00174 // (==GEPP_VAR1) 00175 for(Index i2=0; i2<rows; i2+=mc) 00176 { 00177 const Index actual_mc = (std::min)(i2+mc,rows)-i2; 00178 00179 // We pack the lhs's block into a sequential chunk of memory (L1 caching) 00180 // Note that this block will be read a very high number of times, which is equal to the number of 00181 // micro vertical panel of the large rhs's panel (e.g., cols/4 times). 00182 pack_lhs(blockA, &lhs(i2,k2), lhsStride, actual_kc, actual_mc); 00183 00184 // Everything is packed, we can now call the block * panel kernel: 00185 gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW); 00186 } 00187 } 00188 } 00189 } 00190 00191 }; 00192 00193 /********************************************************************************* 00194 * Specialization of GeneralProduct<> for "large" GEMM, i.e., 00195 * implementation of the high level wrapper to general_matrix_matrix_product 00196 **********************************************************************************/ 00197 00198 template<typename Lhs, typename Rhs> 00199 struct traits<GeneralProduct<Lhs,Rhs,GemmProduct> > 00200 : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> > 00201 {}; 00202 00203 template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType> 00204 struct gemm_functor 00205 { 00206 gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha, 00207 BlockingType& blocking) 00208 : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking) 00209 {} 00210 00211 void initParallelSession() const 00212 { 00213 m_blocking.allocateB(); 00214 } 00215 00216 void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const 00217 { 00218 if(cols==-1) 00219 cols = m_rhs.cols(); 00220 00221 Gemm::run(rows, cols, m_lhs.cols(), 00222 /*(const Scalar*)*/&m_lhs.coeffRef(row,0), m_lhs.outerStride(), 00223 /*(const Scalar*)*/&m_rhs.coeffRef(0,col), m_rhs.outerStride(), 00224 (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(), 00225 m_actualAlpha, m_blocking, info); 00226 } 00227 00228 protected: 00229 const Lhs& m_lhs; 00230 const Rhs& m_rhs; 00231 Dest& m_dest; 00232 Scalar m_actualAlpha; 00233 BlockingType& m_blocking; 00234 }; 00235 00236 template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1, 00237 bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space; 00238 00239 template<typename _LhsScalar, typename _RhsScalar> 00240 class level3_blocking 00241 { 00242 typedef _LhsScalar LhsScalar; 00243 typedef _RhsScalar RhsScalar; 00244 00245 protected: 00246 LhsScalar* m_blockA; 00247 RhsScalar* m_blockB; 00248 RhsScalar* m_blockW; 00249 00250 DenseIndex m_mc; 00251 DenseIndex m_nc; 00252 DenseIndex m_kc; 00253 00254 public: 00255 00256 level3_blocking() 00257 : m_blockA(0), m_blockB(0), m_blockW(0), m_mc(0), m_nc(0), m_kc(0) 00258 {} 00259 00260 inline DenseIndex mc() const { return m_mc; } 00261 inline DenseIndex nc() const { return m_nc; } 00262 inline DenseIndex kc() const { return m_kc; } 00263 00264 inline LhsScalar* blockA() { return m_blockA; } 00265 inline RhsScalar* blockB() { return m_blockB; } 00266 inline RhsScalar* blockW() { return m_blockW; } 00267 }; 00268 00269 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor> 00270 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true> 00271 : public level3_blocking< 00272 typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type, 00273 typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type> 00274 { 00275 enum { 00276 Transpose = StorageOrder==RowMajor, 00277 ActualRows = Transpose ? MaxCols : MaxRows, 00278 ActualCols = Transpose ? MaxRows : MaxCols 00279 }; 00280 typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar; 00281 typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar; 00282 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 00283 enum { 00284 SizeA = ActualRows * MaxDepth, 00285 SizeB = ActualCols * MaxDepth, 00286 SizeW = MaxDepth * Traits::WorkSpaceFactor 00287 }; 00288 00289 EIGEN_ALIGN16 LhsScalar m_staticA[SizeA]; 00290 EIGEN_ALIGN16 RhsScalar m_staticB[SizeB]; 00291 EIGEN_ALIGN16 RhsScalar m_staticW[SizeW]; 00292 00293 public: 00294 00295 gemm_blocking_space(DenseIndex /*rows*/, DenseIndex /*cols*/, DenseIndex /*depth*/) 00296 { 00297 this->m_mc = ActualRows; 00298 this->m_nc = ActualCols; 00299 this->m_kc = MaxDepth; 00300 this->m_blockA = m_staticA; 00301 this->m_blockB = m_staticB; 00302 this->m_blockW = m_staticW; 00303 } 00304 00305 inline void allocateA() {} 00306 inline void allocateB() {} 00307 inline void allocateW() {} 00308 inline void allocateAll() {} 00309 }; 00310 00311 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor> 00312 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false> 00313 : public level3_blocking< 00314 typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type, 00315 typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type> 00316 { 00317 enum { 00318 Transpose = StorageOrder==RowMajor 00319 }; 00320 typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar; 00321 typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar; 00322 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 00323 00324 DenseIndex m_sizeA; 00325 DenseIndex m_sizeB; 00326 DenseIndex m_sizeW; 00327 00328 public: 00329 00330 gemm_blocking_space(DenseIndex rows, DenseIndex cols, DenseIndex depth) 00331 { 00332 this->m_mc = Transpose ? cols : rows; 00333 this->m_nc = Transpose ? rows : cols; 00334 this->m_kc = depth; 00335 00336 computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc); 00337 m_sizeA = this->m_mc * this->m_kc; 00338 m_sizeB = this->m_kc * this->m_nc; 00339 m_sizeW = this->m_kc*Traits::WorkSpaceFactor; 00340 } 00341 00342 void allocateA() 00343 { 00344 if(this->m_blockA==0) 00345 this->m_blockA = aligned_new<LhsScalar>(m_sizeA); 00346 } 00347 00348 void allocateB() 00349 { 00350 if(this->m_blockB==0) 00351 this->m_blockB = aligned_new<RhsScalar>(m_sizeB); 00352 } 00353 00354 void allocateW() 00355 { 00356 if(this->m_blockW==0) 00357 this->m_blockW = aligned_new<RhsScalar>(m_sizeW); 00358 } 00359 00360 void allocateAll() 00361 { 00362 allocateA(); 00363 allocateB(); 00364 allocateW(); 00365 } 00366 00367 ~gemm_blocking_space() 00368 { 00369 aligned_delete(this->m_blockA, m_sizeA); 00370 aligned_delete(this->m_blockB, m_sizeB); 00371 aligned_delete(this->m_blockW, m_sizeW); 00372 } 00373 }; 00374 00375 } // end namespace internal 00376 00377 template<typename Lhs, typename Rhs> 00378 class GeneralProduct<Lhs, Rhs, GemmProduct> 00379 : public ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> 00380 { 00381 enum { 00382 MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime) 00383 }; 00384 public: 00385 EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct) 00386 00387 typedef typename Lhs::Scalar LhsScalar; 00388 typedef typename Rhs::Scalar RhsScalar; 00389 typedef Scalar ResScalar; 00390 00391 GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) 00392 { 00393 typedef internal::scalar_product_op<LhsScalar,RhsScalar> BinOp; 00394 EIGEN_CHECK_BINARY_COMPATIBILIY(BinOp,LhsScalar,RhsScalar); 00395 } 00396 00397 template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const 00398 { 00399 eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols()); 00400 00401 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs); 00402 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs); 00403 00404 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs) 00405 * RhsBlasTraits::extractScalarFactor(m_rhs); 00406 00407 typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar, 00408 Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType; 00409 00410 typedef internal::gemm_functor< 00411 Scalar, Index, 00412 internal::general_matrix_matrix_product< 00413 Index, 00414 LhsScalar, (_ActualLhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate), 00415 RhsScalar, (_ActualRhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate), 00416 (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>, 00417 _ActualLhsType, _ActualRhsType, Dest, BlockingType> GemmFunctor; 00418 00419 BlockingType blocking(dst.rows(), dst.cols(), lhs.cols()); 00420 00421 internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>(GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), this->rows(), this->cols(), Dest::Flags&RowMajorBit); 00422 } 00423 }; 00424 00425 } // end namespace Eigen 00426 00427 #endif // EIGEN_GENERAL_MATRIX_MATRIX_H