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   int ResInnerStride>
25 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,ResInnerStride>
26 {
27   typedef gebp_traits<RhsScalar,LhsScalar> Traits;
28 
29   typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
30   static EIGEN_STRONG_INLINE void run(
31     Index rows, Index cols, Index depth,
32     const LhsScalar* lhs, Index lhsStride,
33     const RhsScalar* rhs, Index rhsStride,
34     ResScalar* res, Index resIncr, Index resStride,
35     ResScalar alpha,
36     level3_blocking<RhsScalar,LhsScalar>& blocking,
37     GemmParallelInfo<Index>* info = 0)
38   {
39     // transpose the product such that the result is column major
40     general_matrix_matrix_product<Index,
41       RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
42       LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
43       ColMajor,ResInnerStride>
44     ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resIncr,resStride,alpha,blocking,info);
45   }
46 };
47 
48 /*  Specialization for a col-major destination matrix
49  *    => Blocking algorithm following Goto's paper */
50 template<
51   typename Index,
52   typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
53   typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
54   int ResInnerStride>
55 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride>
56 {
57 
58 typedef gebp_traits<LhsScalar,RhsScalar> Traits;
59 
60 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
61 static void run(Index rows, Index cols, Index depth,
62   const LhsScalar* _lhs, Index lhsStride,
63   const RhsScalar* _rhs, Index rhsStride,
64   ResScalar* _res, Index resIncr, Index resStride,
65   ResScalar alpha,
66   level3_blocking<LhsScalar,RhsScalar>& blocking,
67   GemmParallelInfo<Index>* info = 0)
68 {
69   typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
70   typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
71   typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor,Unaligned,ResInnerStride> ResMapper;
72   LhsMapper lhs(_lhs, lhsStride);
73   RhsMapper rhs(_rhs, rhsStride);
74   ResMapper res(_res, resStride, resIncr);
75 
76   Index kc = blocking.kc();                   // cache block size along the K direction
77   Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
78   Index nc = (std::min)(cols,blocking.nc());  // cache block size along the N direction
79 
80   gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
81   gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
82   gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
83 
84 #ifdef EIGEN_HAS_OPENMP
85   if(info)
86   {
87     // this is the parallel version!
88     int tid = omp_get_thread_num();
89     int threads = omp_get_num_threads();
90 
91     LhsScalar* blockA = blocking.blockA();
92     eigen_internal_assert(blockA!=0);
93 
94     std::size_t sizeB = kc*nc;
95     ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, 0);
96 
97     // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
98     for(Index k=0; k<depth; k+=kc)
99     {
100       const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
101 
102       // In order to reduce the chance that a thread has to wait for the other,
103       // let's start by packing B'.
104       pack_rhs(blockB, rhs.getSubMapper(k,0), actual_kc, nc);
105 
106       // Pack A_k to A' in a parallel fashion:
107       // each thread packs the sub block A_k,i to A'_i where i is the thread id.
108 
109       // However, before copying to A'_i, we have to make sure that no other thread is still using it,
110       // i.e., we test that info[tid].users equals 0.
111       // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
112       while(info[tid].users!=0) {}
113       info[tid].users = threads;
114 
115       pack_lhs(blockA+info[tid].lhs_start*actual_kc, lhs.getSubMapper(info[tid].lhs_start,k), actual_kc, info[tid].lhs_length);
116 
117       // Notify the other threads that the part A'_i is ready to go.
118       info[tid].sync = k;
119 
120       // Computes C_i += A' * B' per A'_i
121       for(int shift=0; shift<threads; ++shift)
122       {
123         int i = (tid+shift)%threads;
124 
125         // At this point we have to make sure that A'_i has been updated by the thread i,
126         // we use testAndSetOrdered to mimic a volatile access.
127         // However, no need to wait for the B' part which has been updated by the current thread!
128         if (shift>0) {
129           while(info[i].sync!=k) {
130           }
131         }
132 
133         gebp(res.getSubMapper(info[i].lhs_start, 0), blockA+info[i].lhs_start*actual_kc, blockB, info[i].lhs_length, actual_kc, nc, alpha);
134       }
135 
136       // Then keep going as usual with the remaining B'
137       for(Index j=nc; j<cols; j+=nc)
138       {
139         const Index actual_nc = (std::min)(j+nc,cols)-j;
140 
141         // pack B_k,j to B'
142         pack_rhs(blockB, rhs.getSubMapper(k,j), actual_kc, actual_nc);
143 
144         // C_j += A' * B'
145         gebp(res.getSubMapper(0, j), blockA, blockB, rows, actual_kc, actual_nc, alpha);
146       }
147 
148       // Release all the sub blocks A'_i of A' for the current thread,
149       // i.e., we simply decrement the number of users by 1
150       for(Index i=0; i<threads; ++i)
151 #if !EIGEN_HAS_CXX11_ATOMIC
152         #pragma omp atomic
153 #endif
154         info[i].users -= 1;
155     }
156   }
157   else
158 #endif // EIGEN_HAS_OPENMP
159   {
160     EIGEN_UNUSED_VARIABLE(info);
161 
162     // this is the sequential version!
163     std::size_t sizeA = kc*mc;
164     std::size_t sizeB = kc*nc;
165 
166     ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
167     ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
168 
169     const bool pack_rhs_once = mc!=rows && kc==depth && nc==cols;
170 
171     // For each horizontal panel of the rhs, and corresponding panel of the lhs...
172     for(Index i2=0; i2<rows; i2+=mc)
173     {
174       const Index actual_mc = (std::min)(i2+mc,rows)-i2;
175 
176       for(Index k2=0; k2<depth; k2+=kc)
177       {
178         const Index actual_kc = (std::min)(k2+kc,depth)-k2;
179 
180         // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
181         // => Pack lhs's panel into a sequential chunk of memory (L2/L3 caching)
182         // Note that this panel will be read as many times as the number of blocks in the rhs's
183         // horizontal panel which is, in practice, a very low number.
184         pack_lhs(blockA, lhs.getSubMapper(i2,k2), actual_kc, actual_mc);
185 
186         // For each kc x nc block of the rhs's horizontal panel...
187         for(Index j2=0; j2<cols; j2+=nc)
188         {
189           const Index actual_nc = (std::min)(j2+nc,cols)-j2;
190 
191           // We pack the rhs's block into a sequential chunk of memory (L2 caching)
192           // Note that this block will be read a very high number of times, which is equal to the number of
193           // micro horizontal panel of the large rhs's panel (e.g., rows/12 times).
194           if((!pack_rhs_once) || i2==0)
195             pack_rhs(blockB, rhs.getSubMapper(k2,j2), actual_kc, actual_nc);
196 
197           // Everything is packed, we can now call the panel * block kernel:
198           gebp(res.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, alpha);
199         }
200       }
201     }
202   }
203 }
204 
205 };
206 
207 /*********************************************************************************
208 *  Specialization of generic_product_impl for "large" GEMM, i.e.,
209 *  implementation of the high level wrapper to general_matrix_matrix_product
210 **********************************************************************************/
211 
212 template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
213 struct gemm_functor
214 {
215   gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha, BlockingType& blocking)
216     : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
217   {}
218 
219   void initParallelSession(Index num_threads) const
220   {
221     m_blocking.initParallel(m_lhs.rows(), m_rhs.cols(), m_lhs.cols(), num_threads);
222     m_blocking.allocateA();
223   }
224 
225   void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
226   {
227     if(cols==-1)
228       cols = m_rhs.cols();
229 
230     Gemm::run(rows, cols, m_lhs.cols(),
231               &m_lhs.coeffRef(row,0), m_lhs.outerStride(),
232               &m_rhs.coeffRef(0,col), m_rhs.outerStride(),
233               (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.innerStride(), m_dest.outerStride(),
234               m_actualAlpha, m_blocking, info);
235   }
236 
237   typedef typename Gemm::Traits Traits;
238 
239   protected:
240     const Lhs& m_lhs;
241     const Rhs& m_rhs;
242     Dest& m_dest;
243     Scalar m_actualAlpha;
244     BlockingType& m_blocking;
245 };
246 
247 template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
248 bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
249 
250 template<typename _LhsScalar, typename _RhsScalar>
251 class level3_blocking
252 {
253     typedef _LhsScalar LhsScalar;
254     typedef _RhsScalar RhsScalar;
255 
256   protected:
257     LhsScalar* m_blockA;
258     RhsScalar* m_blockB;
259 
260     Index m_mc;
261     Index m_nc;
262     Index m_kc;
263 
264   public:
265 
266     level3_blocking()
267       : m_blockA(0), m_blockB(0), m_mc(0), m_nc(0), m_kc(0)
268     {}
269 
270     inline Index mc() const { return m_mc; }
271     inline Index nc() const { return m_nc; }
272     inline Index kc() const { return m_kc; }
273 
274     inline LhsScalar* blockA() { return m_blockA; }
275     inline RhsScalar* blockB() { return m_blockB; }
276 };
277 
278 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
279 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true /* == FiniteAtCompileTime */>
280   : public level3_blocking<
281       typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
282       typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
283 {
284     enum {
285       Transpose = StorageOrder==RowMajor,
286       ActualRows = Transpose ? MaxCols : MaxRows,
287       ActualCols = Transpose ? MaxRows : MaxCols
288     };
289     typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
290     typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
291     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
292     enum {
293       SizeA = ActualRows * MaxDepth,
294       SizeB = ActualCols * MaxDepth
295     };
296 
297 #if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
298     EIGEN_ALIGN_MAX LhsScalar m_staticA[SizeA];
299     EIGEN_ALIGN_MAX RhsScalar m_staticB[SizeB];
300 #else
301     EIGEN_ALIGN_MAX char m_staticA[SizeA * sizeof(LhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
302     EIGEN_ALIGN_MAX char m_staticB[SizeB * sizeof(RhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
303 #endif
304 
305   public:
306 
307     gemm_blocking_space(Index /*rows*/, Index /*cols*/, Index /*depth*/, Index /*num_threads*/, bool /*full_rows = false*/)
308     {
309       this->m_mc = ActualRows;
310       this->m_nc = ActualCols;
311       this->m_kc = MaxDepth;
312 #if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
313       this->m_blockA = m_staticA;
314       this->m_blockB = m_staticB;
315 #else
316       this->m_blockA = reinterpret_cast<LhsScalar*>((internal::UIntPtr(m_staticA) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
317       this->m_blockB = reinterpret_cast<RhsScalar*>((internal::UIntPtr(m_staticB) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
318 #endif
319     }
320 
321     void initParallel(Index, Index, Index, Index)
322     {}
323 
324     inline void allocateA() {}
325     inline void allocateB() {}
326     inline void allocateAll() {}
327 };
328 
329 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
330 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>
331   : public level3_blocking<
332       typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
333       typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
334 {
335     enum {
336       Transpose = StorageOrder==RowMajor
337     };
338     typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
339     typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
340     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
341 
342     Index m_sizeA;
343     Index m_sizeB;
344 
345   public:
346 
347     gemm_blocking_space(Index rows, Index cols, Index depth, Index num_threads, bool l3_blocking)
348     {
349       this->m_mc = Transpose ? cols : rows;
350       this->m_nc = Transpose ? rows : cols;
351       this->m_kc = depth;
352 
353       if(l3_blocking)
354       {
355         computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc, num_threads);
356       }
357       else  // no l3 blocking
358       {
359         Index n = this->m_nc;
360         computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, n, num_threads);
361       }
362 
363       m_sizeA = this->m_mc * this->m_kc;
364       m_sizeB = this->m_kc * this->m_nc;
365     }
366 
367     void initParallel(Index rows, Index cols, Index depth, Index num_threads)
368     {
369       this->m_mc = Transpose ? cols : rows;
370       this->m_nc = Transpose ? rows : cols;
371       this->m_kc = depth;
372 
373       eigen_internal_assert(this->m_blockA==0 && this->m_blockB==0);
374       Index m = this->m_mc;
375       computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, m, this->m_nc, num_threads);
376       m_sizeA = this->m_mc * this->m_kc;
377       m_sizeB = this->m_kc * this->m_nc;
378     }
379 
380     void allocateA()
381     {
382       if(this->m_blockA==0)
383         this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
384     }
385 
386     void allocateB()
387     {
388       if(this->m_blockB==0)
389         this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
390     }
391 
392     void allocateAll()
393     {
394       allocateA();
395       allocateB();
396     }
397 
398     ~gemm_blocking_space()
399     {
400       aligned_delete(this->m_blockA, m_sizeA);
401       aligned_delete(this->m_blockB, m_sizeB);
402     }
403 };
404 
405 } // end namespace internal
406 
407 namespace internal {
408 
409 template<typename Lhs, typename Rhs>
410 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
411   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct> >
412 {
413   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
414   typedef typename Lhs::Scalar LhsScalar;
415   typedef typename Rhs::Scalar RhsScalar;
416 
417   typedef internal::blas_traits<Lhs> LhsBlasTraits;
418   typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
419   typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;
420 
421   typedef internal::blas_traits<Rhs> RhsBlasTraits;
422   typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
423   typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
424 
425   enum {
426     MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)
427   };
428 
429   typedef generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> lazyproduct;
430 
431   template<typename Dst>
432   static void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
433   {
434     // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=404 for a discussion and helper program
435     // to determine the following heuristic.
436     // EIGEN_GEMM_TO_COEFFBASED_THRESHOLD is typically defined to 20 in GeneralProduct.h,
437     // unless it has been specialized by the user or for a given architecture.
438     // Note that the condition rhs.rows()>0 was required because lazy product is (was?) not happy with empty inputs.
439     // I'm not sure it is still required.
440     if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
441       lazyproduct::eval_dynamic(dst, lhs, rhs, internal::assign_op<typename Dst::Scalar,Scalar>());
442     else
443     {
444       dst.setZero();
445       scaleAndAddTo(dst, lhs, rhs, Scalar(1));
446     }
447   }
448 
449   template<typename Dst>
450   static void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
451   {
452     if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
453       lazyproduct::eval_dynamic(dst, lhs, rhs, internal::add_assign_op<typename Dst::Scalar,Scalar>());
454     else
455       scaleAndAddTo(dst,lhs, rhs, Scalar(1));
456   }
457 
458   template<typename Dst>
459   static void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
460   {
461     if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
462       lazyproduct::eval_dynamic(dst, lhs, rhs, internal::sub_assign_op<typename Dst::Scalar,Scalar>());
463     else
464       scaleAndAddTo(dst, lhs, rhs, Scalar(-1));
465   }
466 
467   template<typename Dest>
468   static void scaleAndAddTo(Dest& dst, const Lhs& a_lhs, const Rhs& a_rhs, const Scalar& alpha)
469   {
470     eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());
471     if(a_lhs.cols()==0 || a_lhs.rows()==0 || a_rhs.cols()==0)
472       return;
473 
474     if (dst.cols() == 1)
475     {
476       // Fallback to GEMV if either the lhs or rhs is a runtime vector
477       typename Dest::ColXpr dst_vec(dst.col(0));
478       return internal::generic_product_impl<Lhs,typename Rhs::ConstColXpr,DenseShape,DenseShape,GemvProduct>
479         ::scaleAndAddTo(dst_vec, a_lhs, a_rhs.col(0), alpha);
480     }
481     else if (dst.rows() == 1)
482     {
483       // Fallback to GEMV if either the lhs or rhs is a runtime vector
484       typename Dest::RowXpr dst_vec(dst.row(0));
485       return internal::generic_product_impl<typename Lhs::ConstRowXpr,Rhs,DenseShape,DenseShape,GemvProduct>
486         ::scaleAndAddTo(dst_vec, a_lhs.row(0), a_rhs, alpha);
487     }
488 
489     typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
490     typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
491 
492     Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
493                                * RhsBlasTraits::extractScalarFactor(a_rhs);
494 
495     typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
496             Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
497 
498     typedef internal::gemm_functor<
499       Scalar, Index,
500       internal::general_matrix_matrix_product<
501         Index,
502         LhsScalar, (ActualLhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
503         RhsScalar, (ActualRhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
504         (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,
505         Dest::InnerStrideAtCompileTime>,
506       ActualLhsTypeCleaned, ActualRhsTypeCleaned, Dest, BlockingType> GemmFunctor;
507 
508     BlockingType blocking(dst.rows(), dst.cols(), lhs.cols(), 1, true);
509     internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>
510         (GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), a_lhs.rows(), a_rhs.cols(), a_lhs.cols(), Dest::Flags&RowMajorBit);
511   }
512 };
513 
514 } // end namespace internal
515 
516 } // end namespace Eigen
517 
518 #endif // EIGEN_GENERAL_MATRIX_MATRIX_H
519