GeneralMatrixMatrix.h
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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 typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
00054 static void run(Index rows, Index cols, Index depth,
00055   const LhsScalar* _lhs, Index lhsStride,
00056   const RhsScalar* _rhs, Index rhsStride,
00057   ResScalar* res, Index resStride,
00058   ResScalar alpha,
00059   level3_blocking<LhsScalar,RhsScalar>& blocking,
00060   GemmParallelInfo<Index>* info = 0)
00061 {
00062   const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00063   const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00064 
00065   typedef gebp_traits<LhsScalar,RhsScalar> Traits;
00066 
00067   Index kc = blocking.kc();                   // cache block size along the K direction
00068   Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00069   //Index nc = blocking.nc(); // cache block size along the N direction
00070 
00071   gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00072   gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
00073   gebp_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
00074 
00075 #ifdef EIGEN_HAS_OPENMP
00076   if(info)
00077   {
00078     // this is the parallel version!
00079     Index tid = omp_get_thread_num();
00080     Index threads = omp_get_num_threads();
00081     
00082     std::size_t sizeA = kc*mc;
00083     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00084     ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, 0);
00085     ei_declare_aligned_stack_constructed_variable(RhsScalar, w, sizeW, 0);
00086     
00087     RhsScalar* blockB = blocking.blockB();
00088     eigen_internal_assert(blockB!=0);
00089 
00090     // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
00091     for(Index k=0; k<depth; k+=kc)
00092     {
00093       const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
00094 
00095       // In order to reduce the chance that a thread has to wait for the other,
00096       // let's start by packing A'.
00097       pack_lhs(blockA, &lhs(0,k), lhsStride, actual_kc, mc);
00098 
00099       // Pack B_k to B' in a parallel fashion:
00100       // each thread packs the sub block B_k,j to B'_j where j is the thread id.
00101 
00102       // However, before copying to B'_j, we have to make sure that no other thread is still using it,
00103       // i.e., we test that info[tid].users equals 0.
00104       // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
00105       while(info[tid].users!=0) {}
00106       info[tid].users += threads;
00107 
00108       pack_rhs(blockB+info[tid].rhs_start*actual_kc, &rhs(k,info[tid].rhs_start), rhsStride, actual_kc, info[tid].rhs_length);
00109 
00110       // Notify the other threads that the part B'_j is ready to go.
00111       info[tid].sync = k;
00112 
00113       // Computes C_i += A' * B' per B'_j
00114       for(Index shift=0; shift<threads; ++shift)
00115       {
00116         Index j = (tid+shift)%threads;
00117 
00118         // At this point we have to make sure that B'_j has been updated by the thread j,
00119         // we use testAndSetOrdered to mimic a volatile access.
00120         // However, no need to wait for the B' part which has been updated by the current thread!
00121         if(shift>0)
00122           while(info[j].sync!=k) {}
00123 
00124         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);
00125       }
00126 
00127       // Then keep going as usual with the remaining A'
00128       for(Index i=mc; i<rows; i+=mc)
00129       {
00130         const Index actual_mc = (std::min)(i+mc,rows)-i;
00131 
00132         // pack A_i,k to A'
00133         pack_lhs(blockA, &lhs(i,k), lhsStride, actual_kc, actual_mc);
00134 
00135         // C_i += A' * B'
00136         gebp(res+i, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1,-1,0,0, w);
00137       }
00138 
00139       // Release all the sub blocks B'_j of B' for the current thread,
00140       // i.e., we simply decrement the number of users by 1
00141       for(Index j=0; j<threads; ++j)
00142         #pragma omp atomic
00143         --(info[j].users);
00144     }
00145   }
00146   else
00147 #endif // EIGEN_HAS_OPENMP
00148   {
00149     EIGEN_UNUSED_VARIABLE(info);
00150 
00151     // this is the sequential version!
00152     std::size_t sizeA = kc*mc;
00153     std::size_t sizeB = kc*cols;
00154     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00155 
00156     ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
00157     ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
00158     ei_declare_aligned_stack_constructed_variable(RhsScalar, blockW, sizeW, blocking.blockW());
00159 
00160     // For each horizontal panel of the rhs, and corresponding panel of the lhs...
00161     // (==GEMM_VAR1)
00162     for(Index k2=0; k2<depth; k2+=kc)
00163     {
00164       const Index actual_kc = (std::min)(k2+kc,depth)-k2;
00165 
00166       // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
00167       // => Pack rhs's panel into a sequential chunk of memory (L2 caching)
00168       // Note that this panel will be read as many times as the number of blocks in the lhs's
00169       // vertical panel which is, in practice, a very low number.
00170       pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
00171 
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 /*********************************************************************************
00195 *  Specialization of GeneralProduct<> for "large" GEMM, i.e.,
00196 *  implementation of the high level wrapper to general_matrix_matrix_product
00197 **********************************************************************************/
00198 
00199 template<typename Lhs, typename Rhs>
00200 struct traits<GeneralProduct<Lhs,Rhs,GemmProduct> >
00201  : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> >
00202 {};
00203 
00204 template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
00205 struct gemm_functor
00206 {
00207   gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, Scalar actualAlpha,
00208                   BlockingType& blocking)
00209     : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
00210   {}
00211 
00212   void initParallelSession() const
00213   {
00214     m_blocking.allocateB();
00215   }
00216 
00217   void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
00218   {
00219     if(cols==-1)
00220       cols = m_rhs.cols();
00221 
00222     Gemm::run(rows, cols, m_lhs.cols(),
00223               /*(const Scalar*)*/&m_lhs.coeffRef(row,0), m_lhs.outerStride(),
00224               /*(const Scalar*)*/&m_rhs.coeffRef(0,col), m_rhs.outerStride(),
00225               (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(),
00226               m_actualAlpha, m_blocking, info);
00227   }
00228 
00229   protected:
00230     const Lhs& m_lhs;
00231     const Rhs& m_rhs;
00232     Dest& m_dest;
00233     Scalar m_actualAlpha;
00234     BlockingType& m_blocking;
00235 };
00236 
00237 template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
00238 bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
00239 
00240 template<typename _LhsScalar, typename _RhsScalar>
00241 class level3_blocking
00242 {
00243     typedef _LhsScalar LhsScalar;
00244     typedef _RhsScalar RhsScalar;
00245 
00246   protected:
00247     LhsScalar* m_blockA;
00248     RhsScalar* m_blockB;
00249     RhsScalar* m_blockW;
00250 
00251     DenseIndex m_mc;
00252     DenseIndex m_nc;
00253     DenseIndex m_kc;
00254 
00255   public:
00256 
00257     level3_blocking()
00258       : m_blockA(0), m_blockB(0), m_blockW(0), m_mc(0), m_nc(0), m_kc(0)
00259     {}
00260 
00261     inline DenseIndex mc() const { return m_mc; }
00262     inline DenseIndex nc() const { return m_nc; }
00263     inline DenseIndex kc() const { return m_kc; }
00264 
00265     inline LhsScalar* blockA() { return m_blockA; }
00266     inline RhsScalar* blockB() { return m_blockB; }
00267     inline RhsScalar* blockW() { return m_blockW; }
00268 };
00269 
00270 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
00271 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true>
00272   : public level3_blocking<
00273       typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
00274       typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
00275 {
00276     enum {
00277       Transpose = StorageOrder==RowMajor,
00278       ActualRows = Transpose ? MaxCols : MaxRows,
00279       ActualCols = Transpose ? MaxRows : MaxCols
00280     };
00281     typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
00282     typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
00283     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
00284     enum {
00285       SizeA = ActualRows * MaxDepth,
00286       SizeB = ActualCols * MaxDepth,
00287       SizeW = MaxDepth * Traits::WorkSpaceFactor
00288     };
00289 
00290     EIGEN_ALIGN16 LhsScalar m_staticA[SizeA];
00291     EIGEN_ALIGN16 RhsScalar m_staticB[SizeB];
00292     EIGEN_ALIGN16 RhsScalar m_staticW[SizeW];
00293 
00294   public:
00295 
00296     gemm_blocking_space(DenseIndex /*rows*/, DenseIndex /*cols*/, DenseIndex /*depth*/)
00297     {
00298       this->m_mc = ActualRows;
00299       this->m_nc = ActualCols;
00300       this->m_kc = MaxDepth;
00301       this->m_blockA = m_staticA;
00302       this->m_blockB = m_staticB;
00303       this->m_blockW = m_staticW;
00304     }
00305 
00306     inline void allocateA() {}
00307     inline void allocateB() {}
00308     inline void allocateW() {}
00309     inline void allocateAll() {}
00310 };
00311 
00312 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
00313 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>
00314   : public level3_blocking<
00315       typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
00316       typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
00317 {
00318     enum {
00319       Transpose = StorageOrder==RowMajor
00320     };
00321     typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
00322     typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
00323     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
00324 
00325     DenseIndex m_sizeA;
00326     DenseIndex m_sizeB;
00327     DenseIndex m_sizeW;
00328 
00329   public:
00330 
00331     gemm_blocking_space(DenseIndex rows, DenseIndex cols, DenseIndex depth)
00332     {
00333       this->m_mc = Transpose ? cols : rows;
00334       this->m_nc = Transpose ? rows : cols;
00335       this->m_kc = depth;
00336 
00337       computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc);
00338       m_sizeA = this->m_mc * this->m_kc;
00339       m_sizeB = this->m_kc * this->m_nc;
00340       m_sizeW = this->m_kc*Traits::WorkSpaceFactor;
00341     }
00342 
00343     void allocateA()
00344     {
00345       if(this->m_blockA==0)
00346         this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
00347     }
00348 
00349     void allocateB()
00350     {
00351       if(this->m_blockB==0)
00352         this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
00353     }
00354 
00355     void allocateW()
00356     {
00357       if(this->m_blockW==0)
00358         this->m_blockW = aligned_new<RhsScalar>(m_sizeW);
00359     }
00360 
00361     void allocateAll()
00362     {
00363       allocateA();
00364       allocateB();
00365       allocateW();
00366     }
00367 
00368     ~gemm_blocking_space()
00369     {
00370       aligned_delete(this->m_blockA, m_sizeA);
00371       aligned_delete(this->m_blockB, m_sizeB);
00372       aligned_delete(this->m_blockW, m_sizeW);
00373     }
00374 };
00375 
00376 } // end namespace internal
00377 
00378 template<typename Lhs, typename Rhs>
00379 class GeneralProduct<Lhs, Rhs, GemmProduct>
00380   : public ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs>
00381 {
00382     enum {
00383       MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)
00384     };
00385   public:
00386     EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
00387     
00388     typedef typename  Lhs::Scalar LhsScalar;
00389     typedef typename  Rhs::Scalar RhsScalar;
00390     typedef           Scalar      ResScalar;
00391 
00392     GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
00393     {
00394       typedef internal::scalar_product_op<LhsScalar,RhsScalar> BinOp;
00395       EIGEN_CHECK_BINARY_COMPATIBILIY(BinOp,LhsScalar,RhsScalar);
00396     }
00397 
00398     template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
00399     {
00400       eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
00401 
00402       typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
00403       typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
00404 
00405       Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
00406                                  * RhsBlasTraits::extractScalarFactor(m_rhs);
00407 
00408       typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
00409               Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
00410 
00411       typedef internal::gemm_functor<
00412         Scalar, Index,
00413         internal::general_matrix_matrix_product<
00414           Index,
00415           LhsScalar, (_ActualLhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
00416           RhsScalar, (_ActualRhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
00417           (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>,
00418         _ActualLhsType, _ActualRhsType, Dest, BlockingType> GemmFunctor;
00419 
00420       BlockingType blocking(dst.rows(), dst.cols(), lhs.cols());
00421 
00422       internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>(GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), this->rows(), this->cols(), Dest::Flags&RowMajorBit);
00423     }
00424 };
00425 
00426 } // end namespace Eigen
00427 
00428 #endif // EIGEN_GENERAL_MATRIX_MATRIX_H


win_eigen
Author(s): Daniel Stonier
autogenerated on Mon Oct 6 2014 12:24:34