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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename _LhsScalar, typename _RhsScalar> class level3_blocking;
+
+/* Specialization for a row-major destination matrix => simple transposition of the product */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor>
+{
+ typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols, Index depth,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsStride,
+ ResScalar* res, Index resStride,
+ ResScalar alpha,
+ level3_blocking<RhsScalar,LhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+ {
+ // transpose the product such that the result is column major
+ general_matrix_matrix_product<Index,
+ RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
+ LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
+ ColMajor>
+ ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info);
+ }
+};
+
+/* Specialization for a col-major destination matrix
+ * => Blocking algorithm following Goto's paper */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor>
+{
+typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+static void run(Index rows, Index cols, Index depth,
+ const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsStride,
+ ResScalar* res, Index resStride,
+ ResScalar alpha,
+ level3_blocking<LhsScalar,RhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+{
+ const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
+ const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ //Index nc = blocking.nc(); // cache block size along the N direction
+
+ gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
+ gebp_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
+
+#ifdef EIGEN_HAS_OPENMP
+ if(info)
+ {
+ // this is the parallel version!
+ Index tid = omp_get_thread_num();
+ Index threads = omp_get_num_threads();
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, 0);
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, w, sizeW, 0);
+
+ RhsScalar* blockB = blocking.blockB();
+ eigen_internal_assert(blockB!=0);
+
+ // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
+ for(Index k=0; k<depth; k+=kc)
+ {
+ const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
+
+ // In order to reduce the chance that a thread has to wait for the other,
+ // let's start by packing A'.
+ pack_lhs(blockA, &lhs(0,k), lhsStride, actual_kc, mc);
+
+ // Pack B_k to B' in a parallel fashion:
+ // each thread packs the sub block B_k,j to B'_j where j is the thread id.
+
+ // However, before copying to B'_j, we have to make sure that no other thread is still using it,
+ // i.e., we test that info[tid].users equals 0.
+ // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
+ while(info[tid].users!=0) {}
+ info[tid].users += threads;
+
+ pack_rhs(blockB+info[tid].rhs_start*actual_kc, &rhs(k,info[tid].rhs_start), rhsStride, actual_kc, info[tid].rhs_length);
+
+ // Notify the other threads that the part B'_j is ready to go.
+ info[tid].sync = k;
+
+ // Computes C_i += A' * B' per B'_j
+ for(Index shift=0; shift<threads; ++shift)
+ {
+ Index j = (tid+shift)%threads;
+
+ // At this point we have to make sure that B'_j has been updated by the thread j,
+ // we use testAndSetOrdered to mimic a volatile access.
+ // However, no need to wait for the B' part which has been updated by the current thread!
+ if(shift>0)
+ while(info[j].sync!=k) {}
+
+ 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);
+ }
+
+ // Then keep going as usual with the remaining A'
+ for(Index i=mc; i<rows; i+=mc)
+ {
+ const Index actual_mc = (std::min)(i+mc,rows)-i;
+
+ // pack A_i,k to A'
+ pack_lhs(blockA, &lhs(i,k), lhsStride, actual_kc, actual_mc);
+
+ // C_i += A' * B'
+ gebp(res+i, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1,-1,0,0, w);
+ }
+
+ // Release all the sub blocks B'_j of B' for the current thread,
+ // i.e., we simply decrement the number of users by 1
+ for(Index j=0; j<threads; ++j)
+ #pragma omp atomic
+ --(info[j].users);
+ }
+ }
+ else
+#endif // EIGEN_HAS_OPENMP
+ {
+ EIGEN_UNUSED_VARIABLE(info);
+
+ // this is the sequential version!
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ std::size_t sizeW = kc*Traits::WorkSpaceFactor;
+
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockW, sizeW, blocking.blockW());
+
+ // For each horizontal panel of the rhs, and corresponding panel of the lhs...
+ // (==GEMM_VAR1)
+ for(Index k2=0; k2<depth; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,depth)-k2;
+
+ // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
+ // => Pack rhs's panel into a sequential chunk of memory (L2 caching)
+ // Note that this panel will be read as many times as the number of blocks in the lhs's
+ // vertical panel which is, in practice, a very low number.
+ pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
+
+
+ // For each mc x kc block of the lhs's vertical panel...
+ // (==GEPP_VAR1)
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,rows)-i2;
+
+ // We pack the lhs's block into a sequential chunk of memory (L1 caching)
+ // Note that this block will be read a very high number of times, which is equal to the number of
+ // micro vertical panel of the large rhs's panel (e.g., cols/4 times).
+ pack_lhs(blockA, &lhs(i2,k2), lhsStride, actual_kc, actual_mc);
+
+ // Everything is packed, we can now call the block * panel kernel:
+ gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
+
+ }
+ }
+ }
+}
+
+};
+
+/*********************************************************************************
+* Specialization of GeneralProduct<> for "large" GEMM, i.e.,
+* implementation of the high level wrapper to general_matrix_matrix_product
+**********************************************************************************/
+
+template<typename Lhs, typename Rhs>
+struct traits<GeneralProduct<Lhs,Rhs,GemmProduct> >
+ : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs> >
+{};
+
+template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
+struct gemm_functor
+{
+ gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, Scalar actualAlpha,
+ BlockingType& blocking)
+ : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
+ {}
+
+ void initParallelSession() const
+ {
+ m_blocking.allocateB();
+ }
+
+ void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
+ {
+ if(cols==-1)
+ cols = m_rhs.cols();
+
+ Gemm::run(rows, cols, m_lhs.cols(),
+ /*(const Scalar*)*/&m_lhs.coeffRef(row,0), m_lhs.outerStride(),
+ /*(const Scalar*)*/&m_rhs.coeffRef(0,col), m_rhs.outerStride(),
+ (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(),
+ m_actualAlpha, m_blocking, info);
+ }
+
+ protected:
+ const Lhs& m_lhs;
+ const Rhs& m_rhs;
+ Dest& m_dest;
+ Scalar m_actualAlpha;
+ BlockingType& m_blocking;
+};
+
+template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
+bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
+
+template<typename _LhsScalar, typename _RhsScalar>
+class level3_blocking
+{
+ typedef _LhsScalar LhsScalar;
+ typedef _RhsScalar RhsScalar;
+
+ protected:
+ LhsScalar* m_blockA;
+ RhsScalar* m_blockB;
+ RhsScalar* m_blockW;
+
+ DenseIndex m_mc;
+ DenseIndex m_nc;
+ DenseIndex m_kc;
+
+ public:
+
+ level3_blocking()
+ : m_blockA(0), m_blockB(0), m_blockW(0), m_mc(0), m_nc(0), m_kc(0)
+ {}
+
+ inline DenseIndex mc() const { return m_mc; }
+ inline DenseIndex nc() const { return m_nc; }
+ inline DenseIndex kc() const { return m_kc; }
+
+ inline LhsScalar* blockA() { return m_blockA; }
+ inline RhsScalar* blockB() { return m_blockB; }
+ inline RhsScalar* blockW() { return m_blockW; }
+};
+
+template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true>
+ : public level3_blocking<
+ typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
+ typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor,
+ ActualRows = Transpose ? MaxCols : MaxRows,
+ ActualCols = Transpose ? MaxRows : MaxCols
+ };
+ typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
+ typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+ enum {
+ SizeA = ActualRows * MaxDepth,
+ SizeB = ActualCols * MaxDepth,
+ SizeW = MaxDepth * Traits::WorkSpaceFactor
+ };
+
+ EIGEN_ALIGN16 LhsScalar m_staticA[SizeA];
+ EIGEN_ALIGN16 RhsScalar m_staticB[SizeB];
+ EIGEN_ALIGN16 RhsScalar m_staticW[SizeW];
+
+ public:
+
+ gemm_blocking_space(DenseIndex /*rows*/, DenseIndex /*cols*/, DenseIndex /*depth*/)
+ {
+ this->m_mc = ActualRows;
+ this->m_nc = ActualCols;
+ this->m_kc = MaxDepth;
+ this->m_blockA = m_staticA;
+ this->m_blockB = m_staticB;
+ this->m_blockW = m_staticW;
+ }
+
+ inline void allocateA() {}
+ inline void allocateB() {}
+ inline void allocateW() {}
+ inline void allocateAll() {}
+};
+
+template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>
+ : public level3_blocking<
+ typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
+ typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor
+ };
+ typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
+ typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ DenseIndex m_sizeA;
+ DenseIndex m_sizeB;
+ DenseIndex m_sizeW;
+
+ public:
+
+ gemm_blocking_space(DenseIndex rows, DenseIndex cols, DenseIndex depth)
+ {
+ this->m_mc = Transpose ? cols : rows;
+ this->m_nc = Transpose ? rows : cols;
+ this->m_kc = depth;
+
+ computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc);
+ m_sizeA = this->m_mc * this->m_kc;
+ m_sizeB = this->m_kc * this->m_nc;
+ m_sizeW = this->m_kc*Traits::WorkSpaceFactor;
+ }
+
+ void allocateA()
+ {
+ if(this->m_blockA==0)
+ this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
+ }
+
+ void allocateB()
+ {
+ if(this->m_blockB==0)
+ this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
+ }
+
+ void allocateW()
+ {
+ if(this->m_blockW==0)
+ this->m_blockW = aligned_new<RhsScalar>(m_sizeW);
+ }
+
+ void allocateAll()
+ {
+ allocateA();
+ allocateB();
+ allocateW();
+ }
+
+ ~gemm_blocking_space()
+ {
+ aligned_delete(this->m_blockA, m_sizeA);
+ aligned_delete(this->m_blockB, m_sizeB);
+ aligned_delete(this->m_blockW, m_sizeW);
+ }
+};
+
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class GeneralProduct<Lhs, Rhs, GemmProduct>
+ : public ProductBase<GeneralProduct<Lhs,Rhs,GemmProduct>, Lhs, Rhs>
+{
+ enum {
+ MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)
+ };
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
+
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef Scalar ResScalar;
+
+ GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {
+ typedef internal::scalar_product_op<LhsScalar,RhsScalar> BinOp;
+ EIGEN_CHECK_BINARY_COMPATIBILIY(BinOp,LhsScalar,RhsScalar);
+ }
+
+ template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
+ {
+ eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
+
+ typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
+ typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+ * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
+ Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
+
+ typedef internal::gemm_functor<
+ Scalar, Index,
+ internal::general_matrix_matrix_product<
+ Index,
+ LhsScalar, (_ActualLhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
+ RhsScalar, (_ActualRhsType::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
+ (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>,
+ _ActualLhsType, _ActualRhsType, Dest, BlockingType> GemmFunctor;
+
+ BlockingType blocking(dst.rows(), dst.cols(), lhs.cols());
+
+ internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>(GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), this->rows(), this->cols(), Dest::Flags&RowMajorBit);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_H
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