Blame view

tools/cub-1.8.0/experimental/defunct/example_coo_spmv.cu 36.3 KB
8dcb6dfcb   Yannick Estève   first commit
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
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
  /******************************************************************************
   * Copyright (c) 2011, Duane Merrill.  All rights reserved.
   * Copyright (c) 2011-2018, NVIDIA CORPORATION.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions are met:
   *     * Redistributions of source code must retain the above copyright
   *       notice, this list of conditions and the following disclaimer.
   *     * Redistributions in binary form must reproduce the above copyright
   *       notice, this list of conditions and the following disclaimer in the
   *       documentation and/or other materials provided with the distribution.
   *     * Neither the name of the NVIDIA CORPORATION nor the
   *       names of its contributors may be used to endorse or promote products
   *       derived from this software without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
   * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE FOR ANY
   * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
   * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
   * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   *
   ******************************************************************************/
  
  /******************************************************************************
   * An implementation of COO SpMV using prefix scan to implement a
   * reduce-value-by-row strategy
   ******************************************************************************/
  
  // Ensure printing of CUDA runtime errors to console
  #define CUB_STDERR
  
  #include <iterator>
  #include <vector>
  #include <string>
  #include <algorithm>
  #include <stdio.h>
  
  #include <cub/cub.cuh>
  
  #include "coo_graph.cuh"
  #include "../test/test_util.h"
  
  using namespace cub;
  using namespace std;
  
  
  /******************************************************************************
   * Globals, constants, and typedefs
   ******************************************************************************/
  
  typedef int         VertexId;   // uint32s as vertex ids
  typedef double      Value;      // double-precision floating point values
  
  bool                    g_verbose       = false;
  int                     g_timing_iterations    = 1;
  CachingDeviceAllocator  g_allocator;
  
  
  /******************************************************************************
   * Texture referencing
   ******************************************************************************/
  
  /**
   * Templated texture reference type for multiplicand vector
   */
  template <typename Value>
  struct TexVector
  {
      // Texture type to actually use (e.g., because CUDA doesn't load doubles as texture items)
      typedef typename If<(Equals<Value, double>::VALUE), uint2, Value>::Type CastType;
  
      // Texture reference type
      typedef texture<CastType, cudaTextureType1D, cudaReadModeElementType> TexRef;
  
      static TexRef ref;
  
      /**
       * Bind textures
       */
      static void BindTexture(void *d_in, int elements)
      {
          cudaChannelFormatDesc tex_desc = cudaCreateChannelDesc<CastType>();
          if (d_in)
          {
              size_t offset;
              size_t bytes = sizeof(CastType) * elements;
              CubDebugExit(cudaBindTexture(&offset, ref, d_in, tex_desc, bytes));
          }
      }
  
      /**
       * Unbind textures
       */
      static void UnbindTexture()
      {
          CubDebugExit(cudaUnbindTexture(ref));
      }
  
      /**
       * Load
       */
      static __device__ __forceinline__ Value Load(int offset)
      {
          Value output;
          reinterpret_cast<typename TexVector<Value>::CastType &>(output) = tex1Dfetch(TexVector<Value>::ref, offset);
          return output;
      }
  };
  
  // Texture reference definitions
  template <typename Value>
  typename TexVector<Value>::TexRef TexVector<Value>::ref = 0;
  
  
  /******************************************************************************
   * Utility types
   ******************************************************************************/
  
  
  /**
   * A partial dot-product sum paired with a corresponding row-id
   */
  template <typename VertexId, typename Value>
  struct PartialProduct
  {
      VertexId    row;            /// Row-id
      Value       partial;        /// PartialProduct sum
  };
  
  
  /**
   * A partial dot-product sum paired with a corresponding row-id (specialized for double-int pairings)
   */
  template <>
  struct PartialProduct<int, double>
  {
      long long   row;            /// Row-id
      double      partial;        /// PartialProduct sum
  };
  
  
  /**
   * Reduce-value-by-row scan operator
   */
  struct ReduceByKeyOp
  {
      template <typename PartialProduct>
      __device__ __forceinline__ PartialProduct operator()(
          const PartialProduct &first,
          const PartialProduct &second)
      {
          PartialProduct retval;
  
          retval.partial = (second.row != first.row) ?
                  second.partial :
                  first.partial + second.partial;
  
          retval.row = second.row;
          return retval;
      }
  };
  
  
  /**
   * Stateful block-wide prefix operator for BlockScan
   */
  template <typename PartialProduct>
  struct BlockPrefixCallbackOp
  {
      // Running block-wide prefix
      PartialProduct running_prefix;
  
      /**
       * Returns the block-wide running_prefix in thread-0
       */
      __device__ __forceinline__ PartialProduct operator()(
          const PartialProduct &block_aggregate)              ///< The aggregate sum of the BlockScan inputs
      {
          ReduceByKeyOp scan_op;
  
          PartialProduct retval = running_prefix;
          running_prefix = scan_op(running_prefix, block_aggregate);
          return retval;
      }
  };
  
  
  /**
   * Operator for detecting discontinuities in a list of row identifiers.
   */
  struct NewRowOp
  {
      /// Returns true if row_b is the start of a new row
      template <typename VertexId>
      __device__ __forceinline__ bool operator()(
          const VertexId& row_a,
          const VertexId& row_b)
      {
          return (row_a != row_b);
      }
  };
  
  
  
  /******************************************************************************
   * Persistent thread block types
   ******************************************************************************/
  
  /**
   * SpMV thread block abstraction for processing a contiguous segment of
   * sparse COO tiles.
   */
  template <
      int             BLOCK_THREADS,
      int             ITEMS_PER_THREAD,
      typename        VertexId,
      typename        Value>
  struct PersistentBlockSpmv
  {
      //---------------------------------------------------------------------
      // Types and constants
      //---------------------------------------------------------------------
  
      // Constants
      enum
      {
          TILE_ITEMS = BLOCK_THREADS * ITEMS_PER_THREAD,
      };
  
      // Head flag type
      typedef int HeadFlag;
  
      // Partial dot product type
      typedef PartialProduct<VertexId, Value> PartialProduct;
  
      // Parameterized BlockScan type for reduce-value-by-row scan
      typedef BlockScan<PartialProduct, BLOCK_THREADS, BLOCK_SCAN_RAKING_MEMOIZE> BlockScan;
  
      // Parameterized BlockExchange type for exchanging rows between warp-striped -> blocked arrangements
      typedef BlockExchange<VertexId, BLOCK_THREADS, ITEMS_PER_THREAD, true> BlockExchangeRows;
  
      // Parameterized BlockExchange type for exchanging values between warp-striped -> blocked arrangements
      typedef BlockExchange<Value, BLOCK_THREADS, ITEMS_PER_THREAD, true> BlockExchangeValues;
  
      // Parameterized BlockDiscontinuity type for setting head-flags for each new row segment
      typedef BlockDiscontinuity<HeadFlag, BLOCK_THREADS> BlockDiscontinuity;
  
      // Shared memory type for this thread block
      struct TempStorage
      {
          union
          {
              typename BlockExchangeRows::TempStorage         exchange_rows;      // Smem needed for BlockExchangeRows
              typename BlockExchangeValues::TempStorage       exchange_values;    // Smem needed for BlockExchangeValues
              struct
              {
                  typename BlockScan::TempStorage             scan;               // Smem needed for BlockScan
                  typename BlockDiscontinuity::TempStorage    discontinuity;      // Smem needed for BlockDiscontinuity
              };
          };
  
          VertexId        first_block_row;    ///< The first row-ID seen by this thread block
          VertexId        last_block_row;     ///< The last row-ID seen by this thread block
          Value           first_product;      ///< The first dot-product written by this thread block
      };
  
      //---------------------------------------------------------------------
      // Thread fields
      //---------------------------------------------------------------------
  
      TempStorage                     &temp_storage;
      BlockPrefixCallbackOp<PartialProduct>   prefix_op;
      VertexId                        *d_rows;
      VertexId                        *d_columns;
      Value                           *d_values;
      Value                           *d_vector;
      Value                           *d_result;
      PartialProduct                  *d_block_partials;
      int                             block_offset;
      int                             block_end;
  
  
      //---------------------------------------------------------------------
      // Operations
      //---------------------------------------------------------------------
  
      /**
       * Constructor
       */
      __device__ __forceinline__
      PersistentBlockSpmv(
          TempStorage                 &temp_storage,
          VertexId                    *d_rows,
          VertexId                    *d_columns,
          Value                       *d_values,
          Value                       *d_vector,
          Value                       *d_result,
          PartialProduct              *d_block_partials,
          int                         block_offset,
          int                         block_end)
      :
          temp_storage(temp_storage),
          d_rows(d_rows),
          d_columns(d_columns),
          d_values(d_values),
          d_vector(d_vector),
          d_result(d_result),
          d_block_partials(d_block_partials),
          block_offset(block_offset),
          block_end(block_end)
      {
          // Initialize scalar shared memory values
          if (threadIdx.x == 0)
          {
              VertexId first_block_row            = d_rows[block_offset];
              VertexId last_block_row             = d_rows[block_end - 1];
  
              temp_storage.first_block_row        = first_block_row;
              temp_storage.last_block_row         = last_block_row;
              temp_storage.first_product          = Value(0);
  
              // Initialize prefix_op to identity
              prefix_op.running_prefix.row        = first_block_row;
              prefix_op.running_prefix.partial    = Value(0);
          }
  
          __syncthreads();
      }
  
  
      /**
       * Processes a COO input tile of edges, outputting dot products for each row
       */
      template <bool FULL_TILE>
      __device__ __forceinline__ void ProcessTile(
          int block_offset,
          int guarded_items = 0)
      {
          VertexId        columns[ITEMS_PER_THREAD];
          VertexId        rows[ITEMS_PER_THREAD];
          Value           values[ITEMS_PER_THREAD];
          PartialProduct  partial_sums[ITEMS_PER_THREAD];
          HeadFlag        head_flags[ITEMS_PER_THREAD];
  
          // Load a thread block-striped tile of A (sparse row-ids, column-ids, and values)
          if (FULL_TILE)
          {
              // Unguarded loads
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_columns + block_offset, columns);
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_values + block_offset, values);
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_rows + block_offset, rows);
          }
          else
          {
              // This is a partial-tile (e.g., the last tile of input).  Extend the coordinates of the last
              // vertex for out-of-bound items, but zero-valued
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_columns + block_offset, columns, guarded_items, VertexId(0));
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_values + block_offset, values, guarded_items, Value(0));
              LoadDirectWarpStriped<LOAD_DEFAULT>(threadIdx.x, d_rows + block_offset, rows, guarded_items, temp_storage.last_block_row);
          }
  
          // Load the referenced values from x and compute the dot product partials sums
          #pragma unroll
          for (int ITEM = 0; ITEM < ITEMS_PER_THREAD; ITEM++)
          {
  #if CUB_PTX_ARCH >= 350
              values[ITEM] *= ThreadLoad<LOAD_LDG>(d_vector + columns[ITEM]);
  #else
              values[ITEM] *= TexVector<Value>::Load(columns[ITEM]);
  #endif
          }
  
          // Transpose from warp-striped to blocked arrangement
          BlockExchangeValues(temp_storage.exchange_values).WarpStripedToBlocked(values);
  
          __syncthreads();
  
          // Transpose from warp-striped to blocked arrangement
          BlockExchangeRows(temp_storage.exchange_rows).WarpStripedToBlocked(rows);
  
          // Barrier for smem reuse and coherence
          __syncthreads();
  
          // FlagT row heads by looking for discontinuities
          BlockDiscontinuity(temp_storage.discontinuity).FlagHeads(
              head_flags,                     // (Out) Head flags
              rows,                           // Original row ids
              NewRowOp(),                     // Functor for detecting start of new rows
              prefix_op.running_prefix.row);  // Last row ID from previous tile to compare with first row ID in this tile
  
          // Assemble partial product structures
          #pragma unroll
          for (int ITEM = 0; ITEM < ITEMS_PER_THREAD; ITEM++)
          {
              partial_sums[ITEM].partial = values[ITEM];
              partial_sums[ITEM].row = rows[ITEM];
          }
  
          // Reduce reduce-value-by-row across partial_sums using exclusive prefix scan
          PartialProduct block_aggregate;
          BlockScan(temp_storage.scan).ExclusiveScan(
              partial_sums,                   // Scan input
              partial_sums,                   // Scan output
              ReduceByKeyOp(),                // Scan operator
              block_aggregate,                // Block-wide total (unused)
              prefix_op);                     // Prefix operator for seeding the block-wide scan with the running total
  
          // Barrier for smem reuse and coherence
          __syncthreads();
  
          // Scatter an accumulated dot product if it is the head of a valid row
          #pragma unroll
          for (int ITEM = 0; ITEM < ITEMS_PER_THREAD; ITEM++)
          {
              if (head_flags[ITEM])
              {
                  d_result[partial_sums[ITEM].row] = partial_sums[ITEM].partial;
  
                  // Save off the first partial product that this thread block will scatter
                  if (partial_sums[ITEM].row == temp_storage.first_block_row)
                  {
                      temp_storage.first_product = partial_sums[ITEM].partial;
                  }
              }
          }
      }
  
  
      /**
       * Iterate over input tiles belonging to this thread block
       */
      __device__ __forceinline__
      void ProcessTiles()
      {
          // Process full tiles
          while (block_offset <= block_end - TILE_ITEMS)
          {
              ProcessTile<true>(block_offset);
              block_offset += TILE_ITEMS;
          }
  
          // Process the last, partially-full tile (if present)
          int guarded_items = block_end - block_offset;
          if (guarded_items)
          {
              ProcessTile<false>(block_offset, guarded_items);
          }
  
          if (threadIdx.x == 0)
          {
              if (gridDim.x == 1)
              {
                  // Scatter the final aggregate (this kernel contains only 1 thread block)
                  d_result[prefix_op.running_prefix.row] = prefix_op.running_prefix.partial;
              }
              else
              {
                  // Write the first and last partial products from this thread block so
                  // that they can be subsequently "fixed up" in the next kernel.
  
                  PartialProduct first_product;
                  first_product.row       = temp_storage.first_block_row;
                  first_product.partial   = temp_storage.first_product;
  
                  d_block_partials[blockIdx.x * 2]          = first_product;
                  d_block_partials[(blockIdx.x * 2) + 1]    = prefix_op.running_prefix;
              }
          }
      }
  };
  
  
  /**
   * Threadblock abstraction for "fixing up" an array of interblock SpMV partial products.
   */
  template <
      int             BLOCK_THREADS,
      int             ITEMS_PER_THREAD,
      typename        VertexId,
      typename        Value>
  struct FinalizeSpmvBlock
  {
      //---------------------------------------------------------------------
      // Types and constants
      //---------------------------------------------------------------------
  
      // Constants
      enum
      {
          TILE_ITEMS = BLOCK_THREADS * ITEMS_PER_THREAD,
      };
  
      // Head flag type
      typedef int HeadFlag;
  
      // Partial dot product type
      typedef PartialProduct<VertexId, Value> PartialProduct;
  
      // Parameterized BlockScan type for reduce-value-by-row scan
      typedef BlockScan<PartialProduct, BLOCK_THREADS, BLOCK_SCAN_RAKING_MEMOIZE> BlockScan;
  
      // Parameterized BlockDiscontinuity type for setting head-flags for each new row segment
      typedef BlockDiscontinuity<HeadFlag, BLOCK_THREADS> BlockDiscontinuity;
  
      // Shared memory type for this thread block
      struct TempStorage
      {
          typename BlockScan::TempStorage           scan;               // Smem needed for reduce-value-by-row scan
          typename BlockDiscontinuity::TempStorage  discontinuity;      // Smem needed for head-flagging
  
          VertexId last_block_row;
      };
  
  
      //---------------------------------------------------------------------
      // Thread fields
      //---------------------------------------------------------------------
  
      TempStorage                     &temp_storage;
      BlockPrefixCallbackOp<PartialProduct>   prefix_op;
      Value                           *d_result;
      PartialProduct                  *d_block_partials;
      int                             num_partials;
  
  
      //---------------------------------------------------------------------
      // Operations
      //---------------------------------------------------------------------
  
      /**
       * Constructor
       */
      __device__ __forceinline__
      FinalizeSpmvBlock(
          TempStorage                 &temp_storage,
          Value                       *d_result,
          PartialProduct              *d_block_partials,
          int                         num_partials)
      :
          temp_storage(temp_storage),
          d_result(d_result),
          d_block_partials(d_block_partials),
          num_partials(num_partials)
      {
          // Initialize scalar shared memory values
          if (threadIdx.x == 0)
          {
              VertexId first_block_row            = d_block_partials[0].row;
              VertexId last_block_row             = d_block_partials[num_partials - 1].row;
              temp_storage.last_block_row         = last_block_row;
  
              // Initialize prefix_op to identity
              prefix_op.running_prefix.row        = first_block_row;
              prefix_op.running_prefix.partial    = Value(0);
          }
  
          __syncthreads();
      }
  
  
      /**
       * Processes a COO input tile of edges, outputting dot products for each row
       */
      template <bool FULL_TILE>
      __device__ __forceinline__
      void ProcessTile(
          int block_offset,
          int guarded_items = 0)
      {
          VertexId        rows[ITEMS_PER_THREAD];
          PartialProduct  partial_sums[ITEMS_PER_THREAD];
          HeadFlag        head_flags[ITEMS_PER_THREAD];
  
          // Load a tile of block partials from previous kernel
          if (FULL_TILE)
          {
              // Full tile
  #if CUB_PTX_ARCH >= 350
              LoadDirectBlocked<LOAD_LDG>(threadIdx.x, d_block_partials + block_offset, partial_sums);
  #else
              LoadDirectBlocked(threadIdx.x, d_block_partials + block_offset, partial_sums);
  #endif
          }
          else
          {
              // Partial tile (extend zero-valued coordinates of the last partial-product for out-of-bounds items)
              PartialProduct default_sum;
              default_sum.row = temp_storage.last_block_row;
              default_sum.partial = Value(0);
  
  #if CUB_PTX_ARCH >= 350
              LoadDirectBlocked<LOAD_LDG>(threadIdx.x, d_block_partials + block_offset, partial_sums, guarded_items, default_sum);
  #else
              LoadDirectBlocked(threadIdx.x, d_block_partials + block_offset, partial_sums, guarded_items, default_sum);
  #endif
          }
  
          // Copy out row IDs for row-head flagging
          #pragma unroll
          for (int ITEM = 0; ITEM < ITEMS_PER_THREAD; ITEM++)
          {
              rows[ITEM] = partial_sums[ITEM].row;
          }
  
          // FlagT row heads by looking for discontinuities
          BlockDiscontinuity(temp_storage.discontinuity).FlagHeads(
              rows,                           // Original row ids
              head_flags,                     // (Out) Head flags
              NewRowOp(),                     // Functor for detecting start of new rows
              prefix_op.running_prefix.row);   // Last row ID from previous tile to compare with first row ID in this tile
  
          // Reduce reduce-value-by-row across partial_sums using exclusive prefix scan
          PartialProduct block_aggregate;
          BlockScan(temp_storage.scan).ExclusiveScan(
              partial_sums,                   // Scan input
              partial_sums,                   // Scan output
              ReduceByKeyOp(),                // Scan operator
              block_aggregate,                // Block-wide total (unused)
              prefix_op);                     // Prefix operator for seeding the block-wide scan with the running total
  
          // Scatter an accumulated dot product if it is the head of a valid row
          #pragma unroll
          for (int ITEM = 0; ITEM < ITEMS_PER_THREAD; ITEM++)
          {
              if (head_flags[ITEM])
              {
                  d_result[partial_sums[ITEM].row] = partial_sums[ITEM].partial;
              }
          }
      }
  
  
      /**
       * Iterate over input tiles belonging to this thread block
       */
      __device__ __forceinline__
      void ProcessTiles()
      {
          // Process full tiles
          int block_offset = 0;
          while (block_offset <= num_partials - TILE_ITEMS)
          {
              ProcessTile<true>(block_offset);
              block_offset += TILE_ITEMS;
          }
  
          // Process final partial tile (if present)
          int guarded_items = num_partials - block_offset;
          if (guarded_items)
          {
              ProcessTile<false>(block_offset, guarded_items);
          }
  
          // Scatter the final aggregate (this kernel contains only 1 thread block)
          if (threadIdx.x == 0)
          {
              d_result[prefix_op.running_prefix.row] = prefix_op.running_prefix.partial;
          }
      }
  };
  
  
  /******************************************************************************
   * Kernel entrypoints
   ******************************************************************************/
  
  
  
  /**
   * SpMV kernel whose thread blocks each process a contiguous segment of sparse COO tiles.
   */
  template <
      int                             BLOCK_THREADS,
      int                             ITEMS_PER_THREAD,
      typename                        VertexId,
      typename                        Value>
  __launch_bounds__ (BLOCK_THREADS)
  __global__ void CooKernel(
      GridEvenShare<int>              even_share,
      PartialProduct<VertexId, Value> *d_block_partials,
      VertexId                        *d_rows,
      VertexId                        *d_columns,
      Value                           *d_values,
      Value                           *d_vector,
      Value                           *d_result)
  {
      // Specialize SpMV thread block abstraction type
      typedef PersistentBlockSpmv<BLOCK_THREADS, ITEMS_PER_THREAD, VertexId, Value> PersistentBlockSpmv;
  
      // Shared memory allocation
      __shared__ typename PersistentBlockSpmv::TempStorage temp_storage;
  
      // Initialize thread block even-share to tell us where to start and stop our tile-processing
      even_share.BlockInit();
  
      // Construct persistent thread block
      PersistentBlockSpmv persistent_block(
          temp_storage,
          d_rows,
          d_columns,
          d_values,
          d_vector,
          d_result,
          d_block_partials,
          even_share.block_offset,
          even_share.block_end);
  
      // Process input tiles
      persistent_block.ProcessTiles();
  }
  
  
  /**
   * Kernel for "fixing up" an array of interblock SpMV partial products.
   */
  template <
      int                             BLOCK_THREADS,
      int                             ITEMS_PER_THREAD,
      typename                        VertexId,
      typename                        Value>
  __launch_bounds__ (BLOCK_THREADS,  1)
  __global__ void CooFinalizeKernel(
      PartialProduct<VertexId, Value> *d_block_partials,
      int                             num_partials,
      Value                           *d_result)
  {
      // Specialize "fix-up" thread block abstraction type
      typedef FinalizeSpmvBlock<BLOCK_THREADS, ITEMS_PER_THREAD, VertexId, Value> FinalizeSpmvBlock;
  
      // Shared memory allocation
      __shared__ typename FinalizeSpmvBlock::TempStorage temp_storage;
  
      // Construct persistent thread block
      FinalizeSpmvBlock persistent_block(temp_storage, d_result, d_block_partials, num_partials);
  
      // Process input tiles
      persistent_block.ProcessTiles();
  }
  
  
  
  //---------------------------------------------------------------------
  // Host subroutines
  //---------------------------------------------------------------------
  
  
  /**
   * Simple test of device
   */
  template <
      int                         COO_BLOCK_THREADS,
      int                         COO_ITEMS_PER_THREAD,
      int                         COO_SUBSCRIPTION_FACTOR,
      int                         FINALIZE_BLOCK_THREADS,
      int                         FINALIZE_ITEMS_PER_THREAD,
      typename                    VertexId,
      typename                    Value>
  void TestDevice(
      CooGraph<VertexId, Value>&  coo_graph,
      Value*                      h_vector,
      Value*                      h_reference)
  {
      typedef PartialProduct<VertexId, Value> PartialProduct;
  
      const int COO_TILE_SIZE = COO_BLOCK_THREADS * COO_ITEMS_PER_THREAD;
  
      // SOA device storage
      VertexId        *d_rows;             // SOA graph row coordinates
      VertexId        *d_columns;          // SOA graph col coordinates
      Value           *d_values;           // SOA graph values
      Value           *d_vector;           // Vector multiplicand
      Value           *d_result;           // Output row
      PartialProduct  *d_block_partials;   // Temporary storage for communicating dot product partials between thread blocks
  
      // Create SOA version of coo_graph on host
      int             num_edges   = coo_graph.coo_tuples.size();
      VertexId        *h_rows     = new VertexId[num_edges];
      VertexId        *h_columns  = new VertexId[num_edges];
      Value           *h_values   = new Value[num_edges];
      for (int i = 0; i < num_edges; i++)
      {
          h_rows[i]       = coo_graph.coo_tuples[i].row;
          h_columns[i]    = coo_graph.coo_tuples[i].col;
          h_values[i]     = coo_graph.coo_tuples[i].val;
      }
  
      // Get CUDA properties
      Device device_props;
      CubDebugExit(device_props.Init());
  
      // Determine launch configuration from kernel properties
      int coo_sm_occupancy;
      CubDebugExit(device_props.MaxSmOccupancy(
          coo_sm_occupancy,
          CooKernel<COO_BLOCK_THREADS, COO_ITEMS_PER_THREAD, VertexId, Value>,
          COO_BLOCK_THREADS));
      int max_coo_grid_size   = device_props.sm_count * coo_sm_occupancy * COO_SUBSCRIPTION_FACTOR;
  
      // Construct an even-share work distribution
      GridEvenShare<int> even_share(num_edges, max_coo_grid_size, COO_TILE_SIZE);
      int coo_grid_size  = even_share.grid_size;
      int num_partials   = coo_grid_size * 2;
  
      // Allocate COO device arrays
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_rows,            sizeof(VertexId) * num_edges));
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_columns,         sizeof(VertexId) * num_edges));
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_values,          sizeof(Value) * num_edges));
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_vector,          sizeof(Value) * coo_graph.col_dim));
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_result,          sizeof(Value) * coo_graph.row_dim));
      CubDebugExit(g_allocator.DeviceAllocate((void**)&d_block_partials,  sizeof(PartialProduct) * num_partials));
  
      // Copy host arrays to device
      CubDebugExit(cudaMemcpy(d_rows,     h_rows,     sizeof(VertexId) * num_edges,       cudaMemcpyHostToDevice));
      CubDebugExit(cudaMemcpy(d_columns,  h_columns,  sizeof(VertexId) * num_edges,       cudaMemcpyHostToDevice));
      CubDebugExit(cudaMemcpy(d_values,   h_values,   sizeof(Value) * num_edges,          cudaMemcpyHostToDevice));
      CubDebugExit(cudaMemcpy(d_vector,   h_vector,   sizeof(Value) * coo_graph.col_dim,  cudaMemcpyHostToDevice));
  
      // Bind textures
      TexVector<Value>::BindTexture(d_vector, coo_graph.col_dim);
  
      // Print debug info
      printf("CooKernel<%d, %d><<<%d, %d>>>(...), Max SM occupancy: %d
  ",
          COO_BLOCK_THREADS, COO_ITEMS_PER_THREAD, coo_grid_size, COO_BLOCK_THREADS, coo_sm_occupancy);
      if (coo_grid_size > 1)
      {
          printf("CooFinalizeKernel<<<1, %d>>>(...)
  ", FINALIZE_BLOCK_THREADS);
      }
      fflush(stdout);
  
      CubDebugExit(cudaDeviceSetSharedMemConfig(cudaSharedMemBankSizeEightByte));
  
      // Run kernel (always run one iteration without timing)
      GpuTimer gpu_timer;
      float elapsed_millis = 0.0;
      for (int i = 0; i <= g_timing_iterations; i++)
      {
          gpu_timer.Start();
  
          // Initialize output
          CubDebugExit(cudaMemset(d_result, 0, coo_graph.row_dim * sizeof(Value)));
  
          // Run the COO kernel
          CooKernel<COO_BLOCK_THREADS, COO_ITEMS_PER_THREAD><<<coo_grid_size, COO_BLOCK_THREADS>>>(
              even_share,
              d_block_partials,
              d_rows,
              d_columns,
              d_values,
              d_vector,
              d_result);
  
          if (coo_grid_size > 1)
          {
              // Run the COO finalize kernel
              CooFinalizeKernel<FINALIZE_BLOCK_THREADS, FINALIZE_ITEMS_PER_THREAD><<<1, FINALIZE_BLOCK_THREADS>>>(
                  d_block_partials,
                  num_partials,
                  d_result);
          }
  
          gpu_timer.Stop();
  
          if (i > 0)
              elapsed_millis += gpu_timer.ElapsedMillis();
      }
  
      // Force any kernel stdio to screen
      CubDebugExit(cudaThreadSynchronize());
      fflush(stdout);
  
      // Display timing
      if (g_timing_iterations > 0)
      {
          float avg_elapsed = elapsed_millis / g_timing_iterations;
          int total_bytes = ((sizeof(VertexId) + sizeof(VertexId)) * 2 * num_edges) + (sizeof(Value) * coo_graph.row_dim);
          printf("%d iterations, average elapsed (%.3f ms), utilized bandwidth (%.3f GB/s), GFLOPS(%.3f)
  ",
              g_timing_iterations,
              avg_elapsed,
              total_bytes / avg_elapsed / 1000.0 / 1000.0,
              num_edges * 2 / avg_elapsed / 1000.0 / 1000.0);
      }
  
      // Check results
      int compare = CompareDeviceResults(h_reference, d_result, coo_graph.row_dim, true, g_verbose);
      printf("%s
  ", compare ? "FAIL" : "PASS");
      AssertEquals(0, compare);
  
      // Cleanup
      TexVector<Value>::UnbindTexture();
      CubDebugExit(g_allocator.DeviceFree(d_block_partials));
      CubDebugExit(g_allocator.DeviceFree(d_rows));
      CubDebugExit(g_allocator.DeviceFree(d_columns));
      CubDebugExit(g_allocator.DeviceFree(d_values));
      CubDebugExit(g_allocator.DeviceFree(d_vector));
      CubDebugExit(g_allocator.DeviceFree(d_result));
      delete[] h_rows;
      delete[] h_columns;
      delete[] h_values;
  }
  
  
  /**
   * Compute reference answer on CPU
   */
  template <typename VertexId, typename Value>
  void ComputeReference(
      CooGraph<VertexId, Value>&  coo_graph,
      Value*                      h_vector,
      Value*                      h_reference)
  {
      for (VertexId i = 0; i < coo_graph.row_dim; i++)
      {
          h_reference[i] = 0.0;
      }
  
      for (VertexId i = 0; i < coo_graph.coo_tuples.size(); i++)
      {
          h_reference[coo_graph.coo_tuples[i].row] +=
              coo_graph.coo_tuples[i].val *
              h_vector[coo_graph.coo_tuples[i].col];
      }
  }
  
  
  /**
   * Assign arbitrary values to vector items
   */
  template <typename Value>
  void AssignVectorValues(Value *vector, int col_dim)
  {
      for (int i = 0; i < col_dim; i++)
      {
          vector[i] = 1.0;
      }
  }
  
  
  /**
   * Main
   */
  int main(int argc, char** argv)
  {
      // Initialize command line
      CommandLineArgs args(argc, argv);
      g_verbose = args.CheckCmdLineFlag("v");
      args.GetCmdLineArgument("i", g_timing_iterations);
  
      // Print usage
      if (args.CheckCmdLineFlag("help"))
      {
          printf("%s
   [--device=<device-id>] [--v] [--iterations=<test iterations>] [--grid-size=<grid-size>]
  "
              "\t--type=wheel --spokes=<spokes>
  "
              "\t--type=grid2d --width=<width> [--no-self-loops]
  "
              "\t--type=grid3d --width=<width> [--no-self-loops]
  "
              "\t--type=market --file=<file>
  "
              "
  ", argv[0]);
          exit(0);
      }
  
      // Initialize device
      CubDebugExit(args.DeviceInit());
  
      // Get graph type
      string type;
      args.GetCmdLineArgument("type", type);
  
      // Generate graph structure
  
      CpuTimer timer;
      timer.Start();
      CooGraph<VertexId, Value> coo_graph;
      if (type == string("grid2d"))
      {
          VertexId width;
          args.GetCmdLineArgument("width", width);
          bool self_loops = !args.CheckCmdLineFlag("no-self-loops");
          printf("Generating %s grid2d width(%d)... ", (self_loops) ? "5-pt" : "4-pt", width); fflush(stdout);
          if (coo_graph.InitGrid2d(width, self_loops)) exit(1);
      } else if (type == string("grid3d"))
      {
          VertexId width;
          args.GetCmdLineArgument("width", width);
          bool self_loops = !args.CheckCmdLineFlag("no-self-loops");
          printf("Generating %s grid3d width(%d)... ", (self_loops) ? "7-pt" : "6-pt", width); fflush(stdout);
          if (coo_graph.InitGrid3d(width, self_loops)) exit(1);
      }
      else if (type == string("wheel"))
      {
          VertexId spokes;
          args.GetCmdLineArgument("spokes", spokes);
          printf("Generating wheel spokes(%d)... ", spokes); fflush(stdout);
          if (coo_graph.InitWheel(spokes)) exit(1);
      }
      else if (type == string("market"))
      {
          string filename;
          args.GetCmdLineArgument("file", filename);
          printf("Generating MARKET for %s... ", filename.c_str()); fflush(stdout);
          if (coo_graph.InitMarket(filename)) exit(1);
      }
      else
      {
          printf("Unsupported graph type
  ");
          exit(1);
      }
      timer.Stop();
      printf("Done (%.3fs). %d non-zeros, %d rows, %d columns
  ",
          timer.ElapsedMillis() / 1000.0,
          coo_graph.coo_tuples.size(),
          coo_graph.row_dim,
          coo_graph.col_dim);
      fflush(stdout);
  
      if (g_verbose)
      {
          cout << coo_graph << "
  ";
      }
  
      // Create vector
      Value *h_vector = new Value[coo_graph.col_dim];
      AssignVectorValues(h_vector, coo_graph.col_dim);
      if (g_verbose)
      {
          printf("Vector[%d]: ", coo_graph.col_dim);
          DisplayResults(h_vector, coo_graph.col_dim);
          printf("
  
  ");
      }
  
      // Compute reference answer
      Value *h_reference = new Value[coo_graph.row_dim];
      ComputeReference(coo_graph, h_vector, h_reference);
      if (g_verbose)
      {
          printf("Results[%d]: ", coo_graph.row_dim);
          DisplayResults(h_reference, coo_graph.row_dim);
          printf("
  
  ");
      }
  
      // Parameterization for SM35
      enum
      {
          COO_BLOCK_THREADS           = 64,
          COO_ITEMS_PER_THREAD        = 10,
          COO_SUBSCRIPTION_FACTOR     = 4,
          FINALIZE_BLOCK_THREADS      = 256,
          FINALIZE_ITEMS_PER_THREAD   = 4,
      };
  
      // Run GPU version
      TestDevice<
          COO_BLOCK_THREADS,
          COO_ITEMS_PER_THREAD,
          COO_SUBSCRIPTION_FACTOR,
          FINALIZE_BLOCK_THREADS,
          FINALIZE_ITEMS_PER_THREAD>(coo_graph, h_vector, h_reference);
  
      // Cleanup
      delete[] h_vector;
      delete[] h_reference;
  
      return 0;
  }