aboutsummaryrefslogtreecommitdiffhomepage
path: root/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
blob: e72ddb4a9b905339110bf9c8f2c3e2b12f035f46 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// 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_CXX11_TENSOR_TENSOR_CONTRACTION_H
#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H

namespace Eigen {

/** \class TensorContraction
  * \ingroup CXX11_Tensor_Module
  *
  * \brief Tensor contraction class.
  *
  *
  */
namespace internal {
#if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM)
template<typename Scalar, typename Index>
void pack_simple(Scalar * dst, const Scalar * src, Index cols, Index rows, Index lddst, Index ldsrc) {
  size_t psize = packet_traits<Scalar>::size;           // Packet size
  typedef typename packet_traits<Scalar>::type Packet;  // Packet type
  size_t alignment = psize*sizeof(Scalar);              // Needed alignment
  if (rows % psize == 0 && (lddst*sizeof(Scalar)) % alignment == 0 &&
     (ldsrc*sizeof(Scalar)) % alignment == 0 &&
     reinterpret_cast<uintptr_t>(src) % alignment == 0 &&
     reinterpret_cast<uintptr_t>(dst) % alignment == 0) {
    // Optimized version using packets
    size_t num_packets = rows / psize;
    for (Index col = 0; col < cols; ++col) {
      EIGEN_ASM_COMMENT("begin pack_simple inner copy");
      // Unrolled manually 4 times.
      for (size_t i=0; i < num_packets/4; ++i) {
        internal::pstore(dst, internal::pload<Packet>(src));
        dst += psize; src += psize;
        internal::pstore(dst, internal::pload<Packet>(src));
        dst += psize; src += psize;
        internal::pstore(dst, internal::pload<Packet>(src));
        dst += psize; src += psize;
        internal::pstore(dst, internal::pload<Packet>(src));
        dst += psize; src += psize;
      }
      for (size_t i=0; i < num_packets%4; ++i) {
        internal::pstore(dst, internal::pload<Packet>(src));
        dst += psize; src += psize;
      }
      dst += lddst - num_packets*psize;
      src += ldsrc - num_packets*psize;
      EIGEN_ASM_COMMENT("end pack_simple inner copy");
    }
  } else {
    // Naive memcpy calls
    for (Index col = 0; col < cols; ++col) {
      memcpy(dst + col*lddst, src + col*ldsrc, rows*sizeof(Scalar));
    }
  }
}

template<typename LhsScalar, typename RhsScalar, typename Scalar>
  struct libxsmm_wrapper {
    libxsmm_wrapper() {}
    libxsmm_wrapper(int, int, int, int, int, int, int, float, float, int) {}
    void operator()(const LhsScalar*, const RhsScalar*, Scalar*) {}
    void operator()(const LhsScalar*, const RhsScalar*, Scalar*, const LhsScalar*, const RhsScalar*, const Scalar*) {}
  };

  template<>
  struct libxsmm_wrapper<float, float, float>: public libxsmm_mmfunction<float> {
    libxsmm_wrapper(): libxsmm_mmfunction() {}
    libxsmm_wrapper(int flags, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta, int prefetch) :
        libxsmm_mmfunction(flags, m, n, k, lda, ldb, ldc, alpha, beta, prefetch) {}
  };

  template<>
  struct libxsmm_wrapper<double, double, double>: public libxsmm_mmfunction<double> {
    libxsmm_wrapper(): libxsmm_mmfunction() {}
    libxsmm_wrapper(int flags, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta, int prefetch) :
        libxsmm_mmfunction(flags, m, n, k, lda, ldb, ldc, alpha, beta, prefetch) {}
  };
#endif


template<typename Dimensions, typename LhsXprType, typename RhsXprType>
struct traits<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> >
{
  // Type promotion to handle the case where the types of the lhs and the rhs are different.
  typedef typename gebp_traits<typename remove_const<typename LhsXprType::Scalar>::type,
                               typename remove_const<typename RhsXprType::Scalar>::type>::ResScalar Scalar;

  typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,
                                        typename traits<RhsXprType>::StorageKind>::ret StorageKind;
  typedef typename promote_index_type<typename traits<LhsXprType>::Index,
                                      typename traits<RhsXprType>::Index>::type Index;
  typedef typename LhsXprType::Nested LhsNested;
  typedef typename RhsXprType::Nested RhsNested;
  typedef typename remove_reference<LhsNested>::type _LhsNested;
  typedef typename remove_reference<RhsNested>::type _RhsNested;

  // From NumDims below.
  static const int NumDimensions = traits<RhsXprType>::NumDimensions + traits<RhsXprType>::NumDimensions - 2 * array_size<Dimensions>::value;
  static const int Layout = traits<LhsXprType>::Layout;
  typedef typename conditional<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
  typename traits<LhsXprType>::PointerType, typename traits<RhsXprType>::PointerType>::type PointerType;

  enum {
    Flags = 0
  };
};

template<typename Dimensions, typename LhsXprType, typename RhsXprType>
struct eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, Eigen::Dense>
{
  typedef const TensorContractionOp<Dimensions, LhsXprType, RhsXprType>& type;
};

template<typename Dimensions, typename LhsXprType, typename RhsXprType>
struct nested<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, 1, typename eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> >::type>
{
  typedef TensorContractionOp<Dimensions, LhsXprType, RhsXprType> type;
};

template<typename Indices_, typename LeftArgType_, typename RightArgType_, typename Device_>
struct traits<TensorEvaluator<const TensorContractionOp<Indices_, LeftArgType_, RightArgType_>, Device_> > {
  typedef Indices_ Indices;
  typedef LeftArgType_ LeftArgType;
  typedef RightArgType_ RightArgType;
  typedef Device_ Device;

  // From NumDims below.
  static const int NumDimensions = traits<LeftArgType_>::NumDimensions + traits<RightArgType_>::NumDimensions - 2 * array_size<Indices_>::value;
};

}  // end namespace internal

template<typename Indices, typename LhsXprType, typename RhsXprType>
class TensorContractionOp : public TensorBase<TensorContractionOp<Indices, LhsXprType, RhsXprType>, ReadOnlyAccessors>
{
  public:
  typedef typename Eigen::internal::traits<TensorContractionOp>::Scalar Scalar;
  typedef typename internal::gebp_traits<typename LhsXprType::CoeffReturnType,
                                                   typename RhsXprType::CoeffReturnType>::ResScalar CoeffReturnType;
  typedef typename Eigen::internal::nested<TensorContractionOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorContractionOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorContractionOp>::Index Index;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionOp(
      const LhsXprType& lhs, const RhsXprType& rhs, const Indices& dims)
      : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_indices(dims) {}

  EIGEN_DEVICE_FUNC
  const Indices& indices() const { return m_indices; }

  /** \returns the nested expressions */
  EIGEN_DEVICE_FUNC
  const typename internal::remove_all<typename LhsXprType::Nested>::type&
  lhsExpression() const { return m_lhs_xpr; }

  EIGEN_DEVICE_FUNC
  const typename internal::remove_all<typename RhsXprType::Nested>::type&
  rhsExpression() const { return m_rhs_xpr; }

  protected:
    typename LhsXprType::Nested m_lhs_xpr;
    typename RhsXprType::Nested m_rhs_xpr;
    const Indices m_indices;
};


template<typename Derived>
struct TensorContractionEvaluatorBase
{
  typedef typename internal::traits<Derived>::Indices Indices;
  typedef typename internal::traits<Derived>::LeftArgType LeftArgType;
  typedef typename internal::traits<Derived>::RightArgType RightArgType;
  typedef typename internal::traits<Derived>::Device Device;

  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;
  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;
  typedef typename XprType::Index Index;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;

  enum {
    IsAligned = true,
    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),
    Layout = TensorEvaluator<LeftArgType, Device>::Layout,
    CoordAccess = false,  // to be implemented
    RawAccess = true
  };

  // Most of the code is assuming that both input tensors are ColMajor. If the
  // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
  // If we want to compute A * B = C, where A is LHS and B is RHS, the code
  // will pretend B is LHS and A is RHS.
  typedef typename internal::conditional<
    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;
  typedef typename internal::conditional<
    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;

  static const int LDims =
      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
  static const int RDims =
      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
  static const int ContractDims = internal::array_size<Indices>::value;
  static const int NumDims = LDims + RDims - 2 * ContractDims;

  typedef array<Index, ContractDims> contract_t;
  typedef array<Index, LDims - ContractDims> left_nocontract_t;
  typedef array<Index, RDims - ContractDims> right_nocontract_t;

  typedef DSizes<Index, NumDims> Dimensions;

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  TensorContractionEvaluatorBase(const XprType& op, const Device& device)
    : m_leftImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
                          op.lhsExpression(), op.rhsExpression()), device),
    m_rightImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
                          op.rhsExpression(), op.lhsExpression()), device),
        m_device(device),
        m_result(NULL) {
    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) ==
         static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)),
                        YOU_MADE_A_PROGRAMMING_MISTAKE);


    DSizes<Index, LDims> eval_left_dims;
    DSizes<Index, RDims> eval_right_dims;
    array<IndexPair<Index>, ContractDims> eval_op_indices;
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      // For ColMajor, we keep using the existing dimensions
      for (int i = 0; i < LDims; i++) {
        eval_left_dims[i] = m_leftImpl.dimensions()[i];
      }
      for (int i = 0; i < RDims; i++) {
        eval_right_dims[i] = m_rightImpl.dimensions()[i];
      }
      // We keep the pairs of contracting indices.
      for (int i = 0; i < ContractDims; i++) {
        eval_op_indices[i].first = op.indices()[i].first;
        eval_op_indices[i].second = op.indices()[i].second;
      }
    } else {
      // For RowMajor, we need to reverse the existing dimensions
      for (int i = 0; i < LDims; i++) {
        eval_left_dims[i] = m_leftImpl.dimensions()[LDims - i - 1];
      }
      for (int i = 0; i < RDims; i++) {
        eval_right_dims[i] = m_rightImpl.dimensions()[RDims - i - 1];
      }
      // We need to flip all the pairs of contracting indices as well as
      // reversing the dimensions.
      for (int i = 0; i < ContractDims; i++) {
        eval_op_indices[i].first = LDims - 1 - op.indices()[ContractDims - 1 - i].second;
        eval_op_indices[i].second = RDims - 1 - op.indices()[ContractDims - 1 - i].first;
      }
    }

    // Check for duplicate axes and make sure the first index in eval_op_indices
    // is increasing. Using O(n^2) sorting is OK since ContractDims is small
    for (int i = 0; i < ContractDims; i++) {
      for (int j = i + 1; j < ContractDims; j++) {
        eigen_assert(eval_op_indices[j].first != eval_op_indices[i].first &&
                     eval_op_indices[j].second != eval_op_indices[i].second &&
                     "contraction axes should be unique");
        if (eval_op_indices[j].first < eval_op_indices[i].first) {
          numext::swap(eval_op_indices[j], eval_op_indices[i]);
        }
      }
    }

    array<Index, LDims> lhs_strides;
    lhs_strides[0] = 1;
    for (int i = 0; i < LDims-1; ++i) {
      lhs_strides[i+1] = lhs_strides[i] * eval_left_dims[i];
    }

    array<Index, RDims> rhs_strides;
    rhs_strides[0] = 1;
    for (int i = 0; i < RDims-1; ++i) {
      rhs_strides[i+1] = rhs_strides[i] * eval_right_dims[i];
    }

    if (m_i_strides.size() > 0) m_i_strides[0] = 1;
    if (m_j_strides.size() > 0) m_j_strides[0] = 1;
    if (m_k_strides.size() > 0) m_k_strides[0] = 1;

    m_i_size = 1;
    m_j_size = 1;
    m_k_size = 1;

    // To compute the dimension, we simply concatenate the non-contracting
    // dimensions of the left and then the right tensor. Additionally, we also
    // compute the strides corresponding to the left non-contracting
    // dimensions and right non-contracting dimensions.
    m_lhs_inner_dim_contiguous = true;
    int dim_idx = 0;
    unsigned int nocontract_idx = 0;

    for (int i = 0; i < LDims; i++) {
      // find if we are contracting on index i of left tensor
      bool contracting = false;
      for (int j = 0; j < ContractDims; j++) {
        if (eval_op_indices[j].first == i) {
          contracting = true;
          break;
        }
      }
      if (!contracting) {
        // add dimension size to output dimensions
        m_dimensions[dim_idx] = eval_left_dims[i];
        m_left_nocontract_strides[nocontract_idx] = lhs_strides[i];
        if (dim_idx != i) {
          m_lhs_inner_dim_contiguous = false;
        }
        if (nocontract_idx+1 < internal::array_size<left_nocontract_t>::value) {
          m_i_strides[nocontract_idx+1] =
              m_i_strides[nocontract_idx] * eval_left_dims[i];
        } else {
          m_i_size = m_i_strides[nocontract_idx] * eval_left_dims[i];
        }
        dim_idx++;
        nocontract_idx++;
      }
    }

    nocontract_idx = 0;
    for (int i = 0; i < RDims; i++) {
      bool contracting = false;
      // find if we are contracting on index i of right tensor
      for (int j = 0; j < ContractDims; j++) {
        if (eval_op_indices[j].second == i) {
          contracting = true;
          break;
        }
      }
      if (!contracting) {
        m_dimensions[dim_idx] = eval_right_dims[i];
        if (nocontract_idx+1 < internal::array_size<right_nocontract_t>::value) {
          m_j_strides[nocontract_idx+1] =
              m_j_strides[nocontract_idx] * eval_right_dims[i];
        } else {
          m_j_size = m_j_strides[nocontract_idx] * eval_right_dims[i];
        }
        m_right_nocontract_strides[nocontract_idx] = rhs_strides[i];
        dim_idx++;
        nocontract_idx++;
      }
    }

    // Now compute the strides corresponding to the contracting dimensions. We
    // assumed above that non-contracting axes are represented in the same order
    // in the matrix as they are in the tensor. This is not the case for
    // contracting axes. As the contracting axes must be of the same size in
    // each tensor, we'll only look at the first tensor here.
    m_rhs_inner_dim_contiguous = true;
    m_rhs_inner_dim_reordered = false;
    for (int i = 0; i < ContractDims; i++) {
      Index left = eval_op_indices[i].first;
      Index right = eval_op_indices[i].second;

      Index size = eval_left_dims[left];
      eigen_assert(size == eval_right_dims[right] &&
                   "Contraction axes must be same size");

      if (i+1 < static_cast<int>(internal::array_size<contract_t>::value)) {
        m_k_strides[i+1] = m_k_strides[i] * size;
      } else {
        m_k_size = m_k_strides[i] * size;
      }
      m_left_contracting_strides[i] = lhs_strides[left];
      m_right_contracting_strides[i] = rhs_strides[right];

      if (i > 0 && right < eval_op_indices[i-1].second) {
        m_rhs_inner_dim_reordered = true;
      }
      if (right != i) {
        m_rhs_inner_dim_contiguous = false;
      }
    }

    EnableXSMMIfPossible(eval_op_indices);

    // If the layout is RowMajor, we need to reverse the m_dimensions
    if (static_cast<int>(Layout) == static_cast<int>(RowMajor)) {
      for (int i = 0, j = NumDims - 1; i < j; i++, j--) {
        numext::swap(m_dimensions[i], m_dimensions[j]);
      }
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar * data) {
    m_leftImpl.evalSubExprsIfNeeded(NULL);
    m_rightImpl.evalSubExprsIfNeeded(NULL);
    if (data) {
      evalTo(data);
      return false;
    } else {
      m_result = static_cast<Scalar *>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
      evalTo(m_result);
      return true;
    }
  }

  EIGEN_DEVICE_FUNC void evalTo(Scalar* buffer) const {
    if (this->m_lhs_inner_dim_contiguous) {
      if (this->m_rhs_inner_dim_contiguous) {
        if (this->m_rhs_inner_dim_reordered) {
          static_cast<const Derived*>(this)->template evalProduct<true, true, true, Unaligned>(buffer);
        }
        else {
          static_cast<const Derived*>(this)->template evalProduct<true, true, false, Unaligned>(buffer);
        }
      }
      else {
       if (this->m_rhs_inner_dim_reordered) {
          static_cast<const Derived*>(this)->template evalProduct<true, false, true, Unaligned>(buffer);
        }
        else {
          static_cast<const Derived*>(this)->template evalProduct<true, false, false, Unaligned>(buffer);
        }
      }
    }
    else {
      if (this->m_rhs_inner_dim_contiguous) {
        if (this->m_rhs_inner_dim_reordered) {
          static_cast<const Derived*>(this)->template evalProduct<false, true, true, Unaligned>(buffer);
        }
        else {
          static_cast<const Derived*>(this)->template evalProduct<false, true, false, Unaligned>(buffer);
        }
      }
      else {
       if (this->m_rhs_inner_dim_reordered) {
          static_cast<const Derived*>(this)->template evalProduct<false, false, true, Unaligned>(buffer);
        }
        else {
          static_cast<const Derived*>(this)->template evalProduct<false, false, false, Unaligned>(buffer);
        }
      }
    }
  }

  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
  EIGEN_DEVICE_FUNC void evalGemv(Scalar* buffer) const {
    const Index rows = m_i_size;
    const Index cols = m_k_size;

    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;
    typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
    typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
    const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
    const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;
    const int lhs_alignment = LeftEvaluator::IsAligned ? Aligned : Unaligned;
    const int rhs_alignment = RightEvaluator::IsAligned ? Aligned : Unaligned;
    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
                                                   LeftEvaluator, left_nocontract_t,
                                                   contract_t, lhs_packet_size,
                                                   lhs_inner_dim_contiguous,
                                                   false, lhs_alignment> LhsMapper;

    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
                                                   RightEvaluator, right_nocontract_t,
                                                   contract_t, rhs_packet_size,
                                                   rhs_inner_dim_contiguous,
                                                   rhs_inner_dim_reordered, rhs_alignment> RhsMapper;

    LhsMapper lhs(m_leftImpl, m_left_nocontract_strides, m_i_strides,
                  m_left_contracting_strides, m_k_strides);
    RhsMapper rhs(m_rightImpl, m_right_nocontract_strides, m_j_strides,
                  m_right_contracting_strides, m_k_strides);

    const Scalar alpha(1);
    const Index resIncr(1);

    // zero out the result buffer (which must be of size at least rows * sizeof(Scalar)
    m_device.memset(buffer, 0, rows * sizeof(Scalar));

    internal::general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,false,RhsScalar,RhsMapper,false>::run(
        rows, cols, lhs, rhs,
        buffer, resIncr, alpha);
  }

  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
  EIGEN_DEVICE_FUNC void evalGemm(Scalar* buffer) const {
    #if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM)
    if (m_can_use_xsmm) {
      evalGemmXSMM(buffer);
      return;
    }
    #endif

    // columns in left side, rows in right side
    const Index k = this->m_k_size;

    // rows in left side
    const Index m = this->m_i_size;

    // columns in right side
    const Index n = this->m_j_size;

    // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar)
    this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));

    // define mr, nr, and all of my data mapper types
    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;
    typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;

    const Index nr = Traits::nr;
    const Index mr = Traits::mr;

    typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
    typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;

    const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
    const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;

    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
                                                   LeftEvaluator, left_nocontract_t,
                                                   contract_t, lhs_packet_size,
                                                   lhs_inner_dim_contiguous,
                                                   false, Unaligned> LhsMapper;

    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
                                                   RightEvaluator, right_nocontract_t,
                                                   contract_t, rhs_packet_size,
                                                   rhs_inner_dim_contiguous,
                                                   rhs_inner_dim_reordered, Unaligned> RhsMapper;

    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;

    // Declare GEBP packing and kernel structs
    internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, mr, Traits::LhsProgress, ColMajor> pack_lhs;
    internal::gemm_pack_rhs<RhsScalar, Index, typename RhsMapper::SubMapper, nr, ColMajor> pack_rhs;

    internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper, mr, nr, false, false> gebp;

    // initialize data mappers
    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
                  this->m_left_contracting_strides, this->m_k_strides);

    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
                  this->m_right_contracting_strides, this->m_k_strides);

    OutputMapper output(buffer, m);

    // Sizes of the blocks to load in cache. See the Goto paper for details.
    internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index, internal::ShardByCol> blocking(k, m, n, 1);
    const Index kc = blocking.kc();
    const Index mc = numext::mini(m, blocking.mc());
    const Index nc = numext::mini(n, blocking.nc());
    const Index sizeA = mc * kc;
    const Index sizeB = kc * nc;

    LhsScalar* blockA = static_cast<LhsScalar *>(this->m_device.allocate(sizeA * sizeof(LhsScalar)));
    RhsScalar* blockB = static_cast<RhsScalar *>(this->m_device.allocate(sizeB * sizeof(RhsScalar)));

    for(Index i2=0; i2<m; i2+=mc)
    {
      const Index actual_mc = numext::mini(i2+mc,m)-i2;
      for (Index k2 = 0; k2 < k; k2 += kc) {
        // make sure we don't overshoot right edge of left matrix, then pack vertical panel
        const Index actual_kc = numext::mini(k2 + kc, k) - k2;
        pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc, 0, 0);

        // series of horizontal blocks
        for (Index j2 = 0; j2 < n; j2 += nc) {
          // make sure we don't overshoot right edge of right matrix, then pack block
          const Index actual_nc = numext::mini(j2 + nc, n) - j2;
          pack_rhs(blockB, rhs.getSubMapper(k2, j2), actual_kc, actual_nc, 0, 0);

          // call gebp (matrix kernel)
          // The parameters here are copied from Eigen's GEMM implementation
          gebp(output.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, Scalar(1), -1, -1, 0, 0);
        }
      }
    }

    this->m_device.deallocate(blockA);
    this->m_device.deallocate(blockB);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
    m_leftImpl.cleanup();
    m_rightImpl.cleanup();

    if (m_result != NULL) {
      m_device.deallocate(m_result);
      m_result = NULL;
    }
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_result[index];
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {
    return TensorOpCost(sizeof(CoeffReturnType), 0, 0);
  }

  template<int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
    return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Eigen::internal::traits<XprType>::PointerType data() const { return m_result; }

protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void EnableXSMMIfPossible(const array<IndexPair<Index>, ContractDims>& eval_op_indices) {
    m_can_use_xsmm = false;

#if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM)
    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;
    if (!std::is_same<Scalar, LhsScalar>::value ||
        !std::is_same<Scalar, RhsScalar>::value ||
        !(std::is_same<Scalar, float>::value ||
          std::is_same<Scalar, double>::value) ||
        m_leftImpl.data() == NULL ||
        m_rightImpl.data() == NULL) {
      return;
    }

    // Check if we can use faster matmul algorithms. For contraction to be
    // equivalent to matmul, we need both lhs and rhs contracting dims sequences
    // to be either a prefix or suffix of all dims. Also, the order of both
    // must be the same, so we don't have to do reordering.
    // For example:
    // * OK: lhs 4D, rhs 4D, contraction: [(0, 2), (1, 3)]
    // * BAD: lhs 3D, rhs 3D, contraction: [(1,1)]
    // * BAD: lhs 3D, rhs 3D, contraction: [(0, 0), (2, 2)]
    // * BAD: lhs 3D, rhs 3D, contraction: [(0, 2), (1, 1)]
    // Depending if contraction dims are prefix or suffix of all dims we need to
    // pre-transpose matrices in matmul algorithm:
    // lhs: prefix -> transpose, suffix -> no transpose
    // rhs: prefix -> no transpose, suffix -> transpose
    // For example, for lhs 2D, rhs 2D, contraction [(1, 0)] is regular,
    // non-transposed matmul.
    if (ContractDims == 0) {
      // This case is totally uninteresting, filter it out to avoid problems
      // with iterations in further tests.
      return;
    }

    // Check if RHS dims list is increasing. LHS already is, so if not, the
    // order is different and we cannot do matmul.
    for (int i = 1; i < ContractDims; i++) {
      if (eval_op_indices[i].second < eval_op_indices[i-1].second) {
        return;
      }
    }

    // Check if no holes.
    int diff;
    for (int i = 1; i < ContractDims; i++) {
      // LHS contract dims are sorted to form an increasing seq.
      diff = eval_op_indices[i].first - eval_op_indices[i-1].first;
      if (diff != 1) {
        return;
      }
      // Now we may already assume RHS contract dims seq is increasing too.
      diff = eval_op_indices[i].second - eval_op_indices[i-1].second;
      if (diff != 1) {
        return;
      }
    }

    // Check if suffix or prefix.
    if (eval_op_indices[0].first != 0 &&
        eval_op_indices[ContractDims-1].first != LDims-1) {
      return;
    }
    if (eval_op_indices[0].second != 0 &&
        eval_op_indices[ContractDims-1].second != RDims-1) {
      return;
    }

    m_can_use_xsmm = true;
#else
    EIGEN_UNUSED_VARIABLE(eval_op_indices);
#endif
  }

#if defined(EIGEN_VECTORIZE_AVX) && defined(EIGEN_USE_LIBXSMM)
  EIGEN_DEVICE_FUNC void evalGemmXSMM(Scalar* buffer) const {
    // columns in left side, rows in right side
    const Index k = this->m_k_size;

    // rows in left side
    const Index m = this->m_i_size;

    // columns in right side
    const Index n = this->m_j_size;

    const bool transposeA = !m_lhs_inner_dim_contiguous;
    const bool transposeB = !m_rhs_inner_dim_contiguous;

    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;

    internal::TensorXsmmContractionBlocking<LhsScalar, RhsScalar, Index> blocking(
        k, m, n, 1, transposeA, transposeB);

    // Outer blocks sizes
    const Index mc_outer = blocking.outer_m();
    const Index nc_outer = blocking.outer_n();
    const Index kc_outer = blocking.outer_k();
    // Inner blocks sizes
    const Index mc = blocking.mc();
    const Index nc = blocking.nc();
    const Index kc = blocking.kc();
    // Decisions whether we should copy parts of matrices
    const bool copyA = blocking.copyA();
    const bool copyB = blocking.copyB();

    const LhsScalar* leftData = m_leftImpl.data();
    const RhsScalar* rightData = m_rightImpl.data();

    const libxsmm_blasint stride_A = static_cast<libxsmm_blasint>(transposeA ? k : m);
    const libxsmm_blasint stride_B = static_cast<libxsmm_blasint>(transposeB ? n : k);
    const libxsmm_blasint stride_C = static_cast<libxsmm_blasint>(m);

    const libxsmm_blasint stride_blockA = static_cast<libxsmm_blasint>(mc);
    // Use bigger stride to avoid hitting same cache line too often.
    // This consistently gives +~0.5 Gflops.
    const libxsmm_blasint stride_panelB = static_cast<libxsmm_blasint>(
        kc % 32 == 0 ? kc + 16 : kc
    );

    // Kernel for the general case (not edges)
    internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar> kernel;

    LhsScalar* blockA = NULL;
    RhsScalar* panelB = NULL;

    if (copyA) {
      blockA = static_cast<LhsScalar*>(this->m_device.allocate(mc * kc * sizeof(LhsScalar)));
    }
    if (copyB) {
      panelB = static_cast<RhsScalar*>(this->m_device.allocate(nc_outer * stride_panelB * sizeof(RhsScalar)));
    }

    const Index kernel_stride_A = copyA ? stride_blockA : stride_A;
    const Index kernel_stride_B = copyB ? stride_panelB : stride_B;
    kernel = internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar>(0, mc, nc, kc, kernel_stride_A, kernel_stride_B, stride_C, 1, 1, blocking.prefetch());

    // Outer blocking
    for (Index ki_outer = 0; ki_outer < k; ki_outer += kc_outer) {
      for (Index mi_outer = 0; mi_outer < m; mi_outer += mc_outer) {
        for (Index ni_outer = 0; ni_outer < n; ni_outer += nc_outer) {
          using numext::mini;

          Index actual_nc_outer = mini(ni_outer+nc_outer, n) - ni_outer;

          // Inner blocking
          for (Index ki = ki_outer; ki < mini(ki_outer+kc_outer, k); ki += kc) {
            const Index actual_kc = mini(ki_outer+kc_outer, mini(ki+kc, k)) - ki;
            const float beta = ki == 0 ? 0 : 1;

            if (copyB) {
              if (transposeB) {
                libxsmm_otrans(panelB, rightData + ki*stride_B + ni_outer, sizeof(RhsScalar), actual_nc_outer, actual_kc, stride_B, stride_panelB);
              } else {
                internal::pack_simple<RhsScalar, Index>(panelB, rightData + ni_outer*stride_B + ki, actual_nc_outer, actual_kc, stride_panelB, stride_B);
              }
            }

            for (Index mi = mi_outer; mi < mini(mi_outer+mc_outer, m); mi += mc) {
              const Index actual_mc = mini(mi_outer+mc_outer, mini(mi+mc, m)) - mi;

              const LhsScalar* a = transposeA ? leftData + mi*stride_A + ki :
                                                leftData + ki*stride_A + mi;

              if (copyA) {
                if (transposeA) {
                  libxsmm_otrans(blockA, a, sizeof(LhsScalar), actual_kc, actual_mc, stride_A, stride_blockA);
                } else {
                  internal::pack_simple<LhsScalar, Index>(blockA, a, actual_kc, actual_mc, stride_blockA, stride_A);
                }
              }
              const LhsScalar* actual_a = copyA ? blockA : a;

              for (Index ni = ni_outer; ni < mini(ni_outer+nc_outer, n); ni += nc) {
                const Index actual_nc = mini(ni_outer+nc_outer, mini(ni+nc, n)) - ni;

                const RhsScalar* b = rightData + ni*stride_B + ki;
                Scalar* c = buffer + ni*stride_C + mi;
                const Scalar* cp = c + nc*stride_C;

                const RhsScalar* actual_b = copyB ? panelB + (ni-ni_outer)*stride_panelB : b;
                const RhsScalar* bp = copyB ? panelB + nc*stride_panelB : b + nc*stride_B;

                if (actual_mc == mc && actual_kc == kc && actual_nc == nc && beta == 1) {
                  // Most used, cached kernel.
                  kernel(actual_a, actual_b, c, actual_a, bp, cp);
                } else {
                  // Edges - use libxsmm kernel cache.
                  internal::libxsmm_wrapper<LhsScalar, RhsScalar, Scalar>(0, actual_mc, actual_nc, actual_kc, kernel_stride_A, kernel_stride_B, stride_C, 1, beta, blocking.prefetch())(actual_a, actual_b, c, actual_a, bp, cp);
                }
              }
            }
          }
        }
      }
    }

    if (copyA) {
      this->m_device.deallocate(blockA);
    }
    if (copyB) {
      this->m_device.deallocate(panelB);
    }
  }
#endif

  // Prevent assignment
  TensorContractionEvaluatorBase& operator = (const TensorContractionEvaluatorBase&);
  Dimensions m_dimensions;

  contract_t m_k_strides;
  contract_t m_left_contracting_strides;
  contract_t m_right_contracting_strides;

  bool m_lhs_inner_dim_contiguous;
  bool m_rhs_inner_dim_contiguous;
  bool m_rhs_inner_dim_reordered;

  left_nocontract_t m_i_strides;
  right_nocontract_t m_j_strides;
  left_nocontract_t m_left_nocontract_strides;
  right_nocontract_t m_right_nocontract_strides;

  Index m_i_size;
  Index m_j_size;
  Index m_k_size;

  TensorEvaluator<EvalLeftArgType, Device> m_leftImpl;
  TensorEvaluator<EvalRightArgType, Device> m_rightImpl;
  const Device& m_device;
  Scalar* m_result;
  bool m_can_use_xsmm;
};


// evaluator for default device
template<typename Indices, typename LeftArgType, typename RightArgType, typename Device>
struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> :
    public TensorContractionEvaluatorBase<
      TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> > {
  typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> Self;
  typedef TensorContractionEvaluatorBase<Self> Base;

  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;
  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;
  typedef typename XprType::Index Index;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;

  enum {
    Layout = TensorEvaluator<LeftArgType, Device>::Layout
  };

  // Most of the code is assuming that both input tensors are ColMajor. If the
  // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
  // If we want to compute A * B = C, where A is LHS and B is RHS, the code
  // will pretend B is LHS and A is RHS.
  typedef typename internal::conditional<
    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;
  typedef typename internal::conditional<
    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;

  static const int LDims =
      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
  static const int RDims =
      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
  static const int ContractDims = internal::array_size<Indices>::value;

  typedef array<Index, ContractDims> contract_t;
  typedef array<Index, LDims - ContractDims> left_nocontract_t;
  typedef array<Index, RDims - ContractDims> right_nocontract_t;

  static const int NumDims = LDims + RDims - 2 * ContractDims;

  // Could we use NumDimensions here?
  typedef DSizes<Index, NumDims> Dimensions;

  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device) :
      Base(op, device) { }

  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
  EIGEN_DEVICE_FUNC void evalProduct(Scalar* buffer) const {
    if (this->m_j_size == 1) {
      this->template evalGemv<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);
      return;
    }

    this->template evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);
  }
};

} // end namespace Eigen

#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H