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