xref: /aosp_15_r20/external/eigen/Eigen/src/Core/util/BlasUtil.h (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4) 
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009-2010 Gael Guennebaud <[email protected]>
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_BLASUTIL_H
11 #define EIGEN_BLASUTIL_H
12 
13 // This file contains many lightweight helper classes used to
14 // implement and control fast level 2 and level 3 BLAS-like routines.
15 
16 namespace Eigen {
17 
18 namespace internal {
19 
20 // forward declarations
21 template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>
22 struct gebp_kernel;
23 
24 template<typename Scalar, typename Index, typename DataMapper, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>
25 struct gemm_pack_rhs;
26 
27 template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, int StorageOrder, bool Conjugate = false, bool PanelMode = false>
28 struct gemm_pack_lhs;
29 
30 template<
31   typename Index,
32   typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
33   typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
34   int ResStorageOrder, int ResInnerStride>
35 struct general_matrix_matrix_product;
36 
37 template<typename Index,
38          typename LhsScalar, typename LhsMapper, int LhsStorageOrder, bool ConjugateLhs,
39          typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version=Specialized>
40 struct general_matrix_vector_product;
41 
42 template<typename From,typename To> struct get_factor {
runget_factor43   EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); }
44 };
45 
46 template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
47   EIGEN_DEVICE_FUNC
48   static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
49 };
50 
51 
52 template<typename Scalar, typename Index>
53 class BlasVectorMapper {
54   public:
55   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}
56 
57   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
58     return m_data[i];
59   }
60   template <typename Packet, int AlignmentType>
61   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const {
62     return ploadt<Packet, AlignmentType>(m_data + i);
63   }
64 
65   template <typename Packet>
66   EIGEN_DEVICE_FUNC bool aligned(Index i) const {
67     return (UIntPtr(m_data+i)%sizeof(Packet))==0;
68   }
69 
70   protected:
71   Scalar* m_data;
72 };
73 
74 template<typename Scalar, typename Index, int AlignmentType, int Incr=1>
75 class BlasLinearMapper;
76 
77 template<typename Scalar, typename Index, int AlignmentType>
78 class BlasLinearMapper<Scalar,Index,AlignmentType>
79 {
80 public:
81   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data, Index incr=1)
82     : m_data(data)
83   {
84     EIGEN_ONLY_USED_FOR_DEBUG(incr);
85     eigen_assert(incr==1);
86   }
87 
88   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {
89     internal::prefetch(&operator()(i));
90   }
91 
92   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
93     return m_data[i];
94   }
95 
96   template<typename PacketType>
97   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const {
98     return ploadt<PacketType, AlignmentType>(m_data + i);
99   }
100 
101   template<typename PacketType>
102   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType &p) const {
103     pstoret<Scalar, PacketType, AlignmentType>(m_data + i, p);
104   }
105 
106 protected:
107   Scalar *m_data;
108 };
109 
110 // Lightweight helper class to access matrix coefficients.
111 template<typename Scalar, typename Index, int StorageOrder, int AlignmentType = Unaligned, int Incr = 1>
112 class blas_data_mapper;
113 
114 // TMP to help PacketBlock store implementation.
115 // There's currently no known use case for PacketBlock load.
116 // The default implementation assumes ColMajor order.
117 // It always store each packet sequentially one `stride` apart.
118 template<typename Index, typename Scalar, typename Packet, int n, int idx, int StorageOrder>
119 struct PacketBlockManagement
120 {
121   PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, StorageOrder> pbm;
122   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
123     pbm.store(to, stride, i, j, block);
124     pstoreu<Scalar>(to + i + (j + idx)*stride, block.packet[idx]);
125   }
126 };
127 
128 // PacketBlockManagement specialization to take care of RowMajor order without ifs.
129 template<typename Index, typename Scalar, typename Packet, int n, int idx>
130 struct PacketBlockManagement<Index, Scalar, Packet, n, idx, RowMajor>
131 {
132   PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, RowMajor> pbm;
133   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
134     pbm.store(to, stride, i, j, block);
135     pstoreu<Scalar>(to + j + (i + idx)*stride, block.packet[idx]);
136   }
137 };
138 
139 template<typename Index, typename Scalar, typename Packet, int n, int StorageOrder>
140 struct PacketBlockManagement<Index, Scalar, Packet, n, -1, StorageOrder>
141 {
142   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
143     EIGEN_UNUSED_VARIABLE(to);
144     EIGEN_UNUSED_VARIABLE(stride);
145     EIGEN_UNUSED_VARIABLE(i);
146     EIGEN_UNUSED_VARIABLE(j);
147     EIGEN_UNUSED_VARIABLE(block);
148   }
149 };
150 
151 template<typename Index, typename Scalar, typename Packet, int n>
152 struct PacketBlockManagement<Index, Scalar, Packet, n, -1, RowMajor>
153 {
154   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
155     EIGEN_UNUSED_VARIABLE(to);
156     EIGEN_UNUSED_VARIABLE(stride);
157     EIGEN_UNUSED_VARIABLE(i);
158     EIGEN_UNUSED_VARIABLE(j);
159     EIGEN_UNUSED_VARIABLE(block);
160   }
161 };
162 
163 template<typename Scalar, typename Index, int StorageOrder, int AlignmentType>
164 class blas_data_mapper<Scalar,Index,StorageOrder,AlignmentType,1>
165 {
166 public:
167   typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;
168   typedef BlasVectorMapper<Scalar, Index> VectorMapper;
169 
170   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr=1)
171    : m_data(data), m_stride(stride)
172   {
173     EIGEN_ONLY_USED_FOR_DEBUG(incr);
174     eigen_assert(incr==1);
175   }
176 
177   EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>
178   getSubMapper(Index i, Index j) const {
179     return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);
180   }
181 
182   EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
183     return LinearMapper(&operator()(i, j));
184   }
185 
186   EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
187     return VectorMapper(&operator()(i, j));
188   }
189 
190 
191   EIGEN_DEVICE_FUNC
192   EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {
193     return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride];
194   }
195 
196   template<typename PacketType>
197   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const {
198     return ploadt<PacketType, AlignmentType>(&operator()(i, j));
199   }
200 
201   template <typename PacketT, int AlignmentT>
202   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const {
203     return ploadt<PacketT, AlignmentT>(&operator()(i, j));
204   }
205 
206   template<typename SubPacket>
207   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
208     pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
209   }
210 
211   template<typename SubPacket>
212   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
213     return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
214   }
215 
216   EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
217   EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }
218 
219   EIGEN_DEVICE_FUNC Index firstAligned(Index size) const {
220     if (UIntPtr(m_data)%sizeof(Scalar)) {
221       return -1;
222     }
223     return internal::first_default_aligned(m_data, size);
224   }
225 
226   template<typename SubPacket, int n>
227   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i, Index j, const PacketBlock<SubPacket, n> &block) const {
228     PacketBlockManagement<Index, Scalar, SubPacket, n, n-1, StorageOrder> pbm;
229     pbm.store(m_data, m_stride, i, j, block);
230   }
231 protected:
232   Scalar* EIGEN_RESTRICT m_data;
233   const Index m_stride;
234 };
235 
236 // Implementation of non-natural increment (i.e. inner-stride != 1)
237 // The exposed API is not complete yet compared to the Incr==1 case
238 // because some features makes less sense in this case.
239 template<typename Scalar, typename Index, int AlignmentType, int Incr>
240 class BlasLinearMapper
241 {
242 public:
243   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data,Index incr) : m_data(data), m_incr(incr) {}
244 
245   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {
246     internal::prefetch(&operator()(i));
247   }
248 
249   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
250     return m_data[i*m_incr.value()];
251   }
252 
253   template<typename PacketType>
254   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const {
255     return pgather<Scalar,PacketType>(m_data + i*m_incr.value(), m_incr.value());
256   }
257 
258   template<typename PacketType>
259   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType &p) const {
260     pscatter<Scalar, PacketType>(m_data + i*m_incr.value(), p, m_incr.value());
261   }
262 
263 protected:
264   Scalar *m_data;
265   const internal::variable_if_dynamic<Index,Incr> m_incr;
266 };
267 
268 template<typename Scalar, typename Index, int StorageOrder, int AlignmentType,int Incr>
269 class blas_data_mapper
270 {
271 public:
272   typedef BlasLinearMapper<Scalar, Index, AlignmentType,Incr> LinearMapper;
273 
274   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr) : m_data(data), m_stride(stride), m_incr(incr) {}
275 
276   EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE blas_data_mapper
277   getSubMapper(Index i, Index j) const {
278     return blas_data_mapper(&operator()(i, j), m_stride, m_incr.value());
279   }
280 
281   EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
282     return LinearMapper(&operator()(i, j), m_incr.value());
283   }
284 
285   EIGEN_DEVICE_FUNC
286   EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {
287     return m_data[StorageOrder==RowMajor ? j*m_incr.value() + i*m_stride : i*m_incr.value() + j*m_stride];
288   }
289 
290   template<typename PacketType>
291   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const {
292     return pgather<Scalar,PacketType>(&operator()(i, j),m_incr.value());
293   }
294 
295   template <typename PacketT, int AlignmentT>
296   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const {
297     return pgather<Scalar,PacketT>(&operator()(i, j),m_incr.value());
298   }
299 
300   template<typename SubPacket>
301   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
302     pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
303   }
304 
305   template<typename SubPacket>
306   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
307     return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
308   }
309 
310   // storePacketBlock_helper defines a way to access values inside the PacketBlock, this is essentially required by the Complex types.
311   template<typename SubPacket, typename ScalarT, int n, int idx>
312   struct storePacketBlock_helper
313   {
314     storePacketBlock_helper<SubPacket, ScalarT, n, idx-1> spbh;
315     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
316       spbh.store(sup, i,j,block);
317       for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
318       {
319         ScalarT *v = &sup->operator()(i+l, j+idx);
320         *v = block.packet[idx][l];
321       }
322     }
323   };
324 
325   template<typename SubPacket, int n, int idx>
326   struct storePacketBlock_helper<SubPacket, std::complex<float>, n, idx>
327   {
328     storePacketBlock_helper<SubPacket, std::complex<float>, n, idx-1> spbh;
329     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
330       spbh.store(sup,i,j,block);
331       for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
332       {
333         std::complex<float> *v = &sup->operator()(i+l, j+idx);
334         v->real(block.packet[idx].v[2*l+0]);
335         v->imag(block.packet[idx].v[2*l+1]);
336       }
337     }
338   };
339 
340   template<typename SubPacket, int n, int idx>
341   struct storePacketBlock_helper<SubPacket, std::complex<double>, n, idx>
342   {
343     storePacketBlock_helper<SubPacket, std::complex<double>, n, idx-1> spbh;
344     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
345       spbh.store(sup,i,j,block);
346       for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
347       {
348         std::complex<double> *v = &sup->operator()(i+l, j+idx);
349         v->real(block.packet[idx].v[2*l+0]);
350         v->imag(block.packet[idx].v[2*l+1]);
351       }
352     }
353   };
354 
355   template<typename SubPacket, typename ScalarT, int n>
356   struct storePacketBlock_helper<SubPacket, ScalarT, n, -1>
357   {
358     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
359     }
360   };
361 
362   template<typename SubPacket, int n>
363   struct storePacketBlock_helper<SubPacket, std::complex<float>, n, -1>
364   {
365     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
366     }
367   };
368 
369   template<typename SubPacket, int n>
370   struct storePacketBlock_helper<SubPacket, std::complex<double>, n, -1>
371   {
372     EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
373     }
374   };
375   // This function stores a PacketBlock on m_data, this approach is really quite slow compare to Incr=1 and should be avoided when possible.
376   template<typename SubPacket, int n>
377   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i, Index j, const PacketBlock<SubPacket, n>&block) const {
378     storePacketBlock_helper<SubPacket, Scalar, n, n-1> spb;
379     spb.store(this, i,j,block);
380   }
381 protected:
382   Scalar* EIGEN_RESTRICT m_data;
383   const Index m_stride;
384   const internal::variable_if_dynamic<Index,Incr> m_incr;
385 };
386 
387 // lightweight helper class to access matrix coefficients (const version)
388 template<typename Scalar, typename Index, int StorageOrder>
389 class const_blas_data_mapper : public blas_data_mapper<const Scalar, Index, StorageOrder> {
390   public:
391   EIGEN_ALWAYS_INLINE const_blas_data_mapper(const Scalar *data, Index stride) : blas_data_mapper<const Scalar, Index, StorageOrder>(data, stride) {}
392 
393   EIGEN_ALWAYS_INLINE const_blas_data_mapper<Scalar, Index, StorageOrder> getSubMapper(Index i, Index j) const {
394     return const_blas_data_mapper<Scalar, Index, StorageOrder>(&(this->operator()(i, j)), this->m_stride);
395   }
396 };
397 
398 
399 /* Helper class to analyze the factors of a Product expression.
400  * In particular it allows to pop out operator-, scalar multiples,
401  * and conjugate */
402 template<typename XprType> struct blas_traits
403 {
404   typedef typename traits<XprType>::Scalar Scalar;
405   typedef const XprType& ExtractType;
406   typedef XprType _ExtractType;
407   enum {
408     IsComplex = NumTraits<Scalar>::IsComplex,
409     IsTransposed = false,
410     NeedToConjugate = false,
411     HasUsableDirectAccess = (    (int(XprType::Flags)&DirectAccessBit)
412                               && (   bool(XprType::IsVectorAtCompileTime)
413                                   || int(inner_stride_at_compile_time<XprType>::ret) == 1)
414                              ) ?  1 : 0,
415     HasScalarFactor = false
416   };
417   typedef typename conditional<bool(HasUsableDirectAccess),
418     ExtractType,
419     typename _ExtractType::PlainObject
420     >::type DirectLinearAccessType;
421   static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return x; }
422   static inline EIGEN_DEVICE_FUNC const Scalar extractScalarFactor(const XprType&) { return Scalar(1); }
423 };
424 
425 // pop conjugate
426 template<typename Scalar, typename NestedXpr>
427 struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >
428  : blas_traits<NestedXpr>
429 {
430   typedef blas_traits<NestedXpr> Base;
431   typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;
432   typedef typename Base::ExtractType ExtractType;
433 
434   enum {
435     IsComplex = NumTraits<Scalar>::IsComplex,
436     NeedToConjugate = Base::NeedToConjugate ? 0 : IsComplex
437   };
438   static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
439   static inline Scalar extractScalarFactor(const XprType& x) { return conj(Base::extractScalarFactor(x.nestedExpression())); }
440 };
441 
442 // pop scalar multiple
443 template<typename Scalar, typename NestedXpr, typename Plain>
444 struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >
445  : blas_traits<NestedXpr>
446 {
447   enum {
448     HasScalarFactor = true
449   };
450   typedef blas_traits<NestedXpr> Base;
451   typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;
452   typedef typename Base::ExtractType ExtractType;
453   static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }
454   static inline EIGEN_DEVICE_FUNC Scalar extractScalarFactor(const XprType& x)
455   { return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs()); }
456 };
457 template<typename Scalar, typename NestedXpr, typename Plain>
458 struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >
459  : blas_traits<NestedXpr>
460 {
461   enum {
462     HasScalarFactor = true
463   };
464   typedef blas_traits<NestedXpr> Base;
465   typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;
466   typedef typename Base::ExtractType ExtractType;
467   static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }
468   static inline Scalar extractScalarFactor(const XprType& x)
469   { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }
470 };
471 template<typename Scalar, typename Plain1, typename Plain2>
472 struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1>,
473                                                             const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain2> > >
474  : blas_traits<CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1> >
475 {};
476 
477 // pop opposite
478 template<typename Scalar, typename NestedXpr>
479 struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >
480  : blas_traits<NestedXpr>
481 {
482   enum {
483     HasScalarFactor = true
484   };
485   typedef blas_traits<NestedXpr> Base;
486   typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
487   typedef typename Base::ExtractType ExtractType;
488   static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
489   static inline Scalar extractScalarFactor(const XprType& x)
490   { return - Base::extractScalarFactor(x.nestedExpression()); }
491 };
492 
493 // pop/push transpose
494 template<typename NestedXpr>
495 struct blas_traits<Transpose<NestedXpr> >
496  : blas_traits<NestedXpr>
497 {
498   typedef typename NestedXpr::Scalar Scalar;
499   typedef blas_traits<NestedXpr> Base;
500   typedef Transpose<NestedXpr> XprType;
501   typedef Transpose<const typename Base::_ExtractType>  ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS
502   typedef Transpose<const typename Base::_ExtractType> _ExtractType;
503   typedef typename conditional<bool(Base::HasUsableDirectAccess),
504     ExtractType,
505     typename ExtractType::PlainObject
506     >::type DirectLinearAccessType;
507   enum {
508     IsTransposed = Base::IsTransposed ? 0 : 1
509   };
510   static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }
511   static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }
512 };
513 
514 template<typename T>
515 struct blas_traits<const T>
516      : blas_traits<T>
517 {};
518 
519 template<typename T, bool HasUsableDirectAccess=blas_traits<T>::HasUsableDirectAccess>
520 struct extract_data_selector {
521   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static const typename T::Scalar* run(const T& m)
522   {
523     return blas_traits<T>::extract(m).data();
524   }
525 };
526 
527 template<typename T>
528 struct extract_data_selector<T,false> {
529   static typename T::Scalar* run(const T&) { return 0; }
530 };
531 
532 template<typename T>
533 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const typename T::Scalar* extract_data(const T& m)
534 {
535   return extract_data_selector<T>::run(m);
536 }
537 
538 /**
539  * \c combine_scalar_factors extracts and multiplies factors from GEMM and GEMV products.
540  * There is a specialization for booleans
541  */
542 template<typename ResScalar, typename Lhs, typename Rhs>
543 struct combine_scalar_factors_impl
544 {
545   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const Lhs& lhs, const Rhs& rhs)
546   {
547     return blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
548   }
549   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
550   {
551     return alpha * blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
552   }
553 };
554 template<typename Lhs, typename Rhs>
555 struct combine_scalar_factors_impl<bool, Lhs, Rhs>
556 {
557   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const Lhs& lhs, const Rhs& rhs)
558   {
559     return blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
560   }
561   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const bool& alpha, const Lhs& lhs, const Rhs& rhs)
562   {
563     return alpha && blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
564   }
565 };
566 
567 template<typename ResScalar, typename Lhs, typename Rhs>
568 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar combine_scalar_factors(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
569 {
570   return combine_scalar_factors_impl<ResScalar,Lhs,Rhs>::run(alpha, lhs, rhs);
571 }
572 template<typename ResScalar, typename Lhs, typename Rhs>
573 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar combine_scalar_factors(const Lhs& lhs, const Rhs& rhs)
574 {
575   return combine_scalar_factors_impl<ResScalar,Lhs,Rhs>::run(lhs, rhs);
576 }
577 
578 
579 } // end namespace internal
580 
581 } // end namespace Eigen
582 
583 #endif // EIGEN_BLASUTIL_H
584