Eigen/src/Core/products/GeneralMatrixMatrix.h - platform/external/eigen - Git at Google

 // 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
	// 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_startresStride, resStride, blockA, blockB+info[j].rhs_startactual_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