Blame view

tools/cub-1.8.0/cub/block/block_discontinuity.cuh 53.3 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
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
  /******************************************************************************
   * 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.
   *
   ******************************************************************************/
  
  /**
   * \file
   * The cub::BlockDiscontinuity class provides [<em>collective</em>](index.html#sec0) methods for flagging discontinuities within an ordered set of items partitioned across a CUDA thread block.
   */
  
  #pragma once
  
  #include "../util_type.cuh"
  #include "../util_ptx.cuh"
  #include "../util_namespace.cuh"
  
  /// Optional outer namespace(s)
  CUB_NS_PREFIX
  
  /// CUB namespace
  namespace cub {
  
  /**
   * \brief The BlockDiscontinuity class provides [<em>collective</em>](index.html#sec0) methods for flagging discontinuities within an ordered set of items partitioned across a CUDA thread block. ![](discont_logo.png)
   * \ingroup BlockModule
   *
   * \tparam T                The data type to be flagged.
   * \tparam BLOCK_DIM_X      The thread block length in threads along the X dimension
   * \tparam BLOCK_DIM_Y      <b>[optional]</b> The thread block length in threads along the Y dimension (default: 1)
   * \tparam BLOCK_DIM_Z      <b>[optional]</b> The thread block length in threads along the Z dimension (default: 1)
   * \tparam PTX_ARCH         <b>[optional]</b> \ptxversion
   *
   * \par Overview
   * - A set of "head flags" (or "tail flags") is often used to indicate corresponding items
   *   that differ from their predecessors (or successors).  For example, head flags are convenient
   *   for demarcating disjoint data segments as part of a segmented scan or reduction.
   * - \blocked
   *
   * \par Performance Considerations
   * - \granularity
   *
   * \par A Simple Example
   * \blockcollective{BlockDiscontinuity}
   * \par
   * The code snippet below illustrates the head flagging of 512 integer items that
   * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
   * where each thread owns 4 consecutive items.
   * \par
   * \code
   * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
   *
   * __global__ void ExampleKernel(...)
   * {
   *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
   *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
   *
   *     // Allocate shared memory for BlockDiscontinuity
   *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
   *
   *     // Obtain a segment of consecutive items that are blocked across threads
   *     int thread_data[4];
   *     ...
   *
   *     // Collectively compute head flags for discontinuities in the segment
   *     int head_flags[4];
   *     BlockDiscontinuity(temp_storage).FlagHeads(head_flags, thread_data, cub::Inequality());
   *
   * \endcode
   * \par
   * Suppose the set of input \p thread_data across the block of threads is
   * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], [3,4,4,4], ... }</tt>.
   * The corresponding output \p head_flags in those threads will be
   * <tt>{ [1,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
   *
   * \par Performance Considerations
   * - Incurs zero bank conflicts for most types
   *
   */
  template <
      typename    T,
      int         BLOCK_DIM_X,
      int         BLOCK_DIM_Y     = 1,
      int         BLOCK_DIM_Z     = 1,
      int         PTX_ARCH        = CUB_PTX_ARCH>
  class BlockDiscontinuity
  {
  private:
  
      /******************************************************************************
       * Constants and type definitions
       ******************************************************************************/
  
      /// Constants
      enum
      {
          /// The thread block size in threads
          BLOCK_THREADS = BLOCK_DIM_X * BLOCK_DIM_Y * BLOCK_DIM_Z,
      };
  
  
      /// Shared memory storage layout type (last element from each thread's input)
      struct _TempStorage
      {
          T first_items[BLOCK_THREADS];
          T last_items[BLOCK_THREADS];
      };
  
  
      /******************************************************************************
       * Utility methods
       ******************************************************************************/
  
      /// Internal storage allocator
      __device__ __forceinline__ _TempStorage& PrivateStorage()
      {
          __shared__ _TempStorage private_storage;
          return private_storage;
      }
  
  
      /// Specialization for when FlagOp has third index param
      template <typename FlagOp, bool HAS_PARAM = BinaryOpHasIdxParam<T, FlagOp>::HAS_PARAM>
      struct ApplyOp
      {
          // Apply flag operator
          static __device__ __forceinline__ bool FlagT(FlagOp flag_op, const T &a, const T &b, int idx)
          {
              return flag_op(a, b, idx);
          }
      };
  
      /// Specialization for when FlagOp does not have a third index param
      template <typename FlagOp>
      struct ApplyOp<FlagOp, false>
      {
          // Apply flag operator
          static __device__ __forceinline__ bool FlagT(FlagOp flag_op, const T &a, const T &b, int /*idx*/)
          {
              return flag_op(a, b);
          }
      };
  
      /// Templated unrolling of item comparison (inductive case)
      template <int ITERATION, int MAX_ITERATIONS>
      struct Iterate
      {
          // Head flags
          template <
              int             ITEMS_PER_THREAD,
              typename        FlagT,
              typename        FlagOp>
          static __device__ __forceinline__ void FlagHeads(
              int                     linear_tid,
              FlagT                   (&flags)[ITEMS_PER_THREAD],         ///< [out] Calling thread's discontinuity head_flags
              T                       (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
              T                       (&preds)[ITEMS_PER_THREAD],         ///< [out] Calling thread's predecessor items
              FlagOp                  flag_op)                            ///< [in] Binary boolean flag predicate
          {
              preds[ITERATION] = input[ITERATION - 1];
  
              flags[ITERATION] = ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  preds[ITERATION],
                  input[ITERATION],
                  (linear_tid * ITEMS_PER_THREAD) + ITERATION);
  
              Iterate<ITERATION + 1, MAX_ITERATIONS>::FlagHeads(linear_tid, flags, input, preds, flag_op);
          }
  
          // Tail flags
          template <
              int             ITEMS_PER_THREAD,
              typename        FlagT,
              typename        FlagOp>
          static __device__ __forceinline__ void FlagTails(
              int                     linear_tid,
              FlagT                   (&flags)[ITEMS_PER_THREAD],         ///< [out] Calling thread's discontinuity head_flags
              T                       (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
              FlagOp                  flag_op)                            ///< [in] Binary boolean flag predicate
          {
              flags[ITERATION] = ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  input[ITERATION],
                  input[ITERATION + 1],
                  (linear_tid * ITEMS_PER_THREAD) + ITERATION + 1);
  
              Iterate<ITERATION + 1, MAX_ITERATIONS>::FlagTails(linear_tid, flags, input, flag_op);
          }
  
      };
  
      /// Templated unrolling of item comparison (termination case)
      template <int MAX_ITERATIONS>
      struct Iterate<MAX_ITERATIONS, MAX_ITERATIONS>
      {
          // Head flags
          template <
              int             ITEMS_PER_THREAD,
              typename        FlagT,
              typename        FlagOp>
          static __device__ __forceinline__ void FlagHeads(
              int                     /*linear_tid*/,
              FlagT                   (&/*flags*/)[ITEMS_PER_THREAD],         ///< [out] Calling thread's discontinuity head_flags
              T                       (&/*input*/)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
              T                       (&/*preds*/)[ITEMS_PER_THREAD],         ///< [out] Calling thread's predecessor items
              FlagOp                  /*flag_op*/)                            ///< [in] Binary boolean flag predicate
          {}
  
          // Tail flags
          template <
              int             ITEMS_PER_THREAD,
              typename        FlagT,
              typename        FlagOp>
          static __device__ __forceinline__ void FlagTails(
              int                     /*linear_tid*/,
              FlagT                   (&/*flags*/)[ITEMS_PER_THREAD],         ///< [out] Calling thread's discontinuity head_flags
              T                       (&/*input*/)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
              FlagOp                  /*flag_op*/)                            ///< [in] Binary boolean flag predicate
          {}
      };
  
  
      /******************************************************************************
       * Thread fields
       ******************************************************************************/
  
      /// Shared storage reference
      _TempStorage &temp_storage;
  
      /// Linear thread-id
      unsigned int linear_tid;
  
  
  public:
  
      /// \smemstorage{BlockDiscontinuity}
      struct TempStorage : Uninitialized<_TempStorage> {};
  
  
      /******************************************************************//**
       * 
  ame Collective constructors
       *********************************************************************/
      //@{
  
      /**
       * \brief Collective constructor using a private static allocation of shared memory as temporary storage.
       */
      __device__ __forceinline__ BlockDiscontinuity()
      :
          temp_storage(PrivateStorage()),
          linear_tid(RowMajorTid(BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z))
      {}
  
  
      /**
       * \brief Collective constructor using the specified memory allocation as temporary storage.
       */
      __device__ __forceinline__ BlockDiscontinuity(
          TempStorage &temp_storage)  ///< [in] Reference to memory allocation having layout type TempStorage
      :
          temp_storage(temp_storage.Alias()),
          linear_tid(RowMajorTid(BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z))
      {}
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Head flag operations
       *********************************************************************/
      //@{
  
  
  #ifndef DOXYGEN_SHOULD_SKIP_THIS    // Do not document
  
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeads(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          T               (&preds)[ITEMS_PER_THREAD],         ///< [out] Calling thread's predecessor items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share last item
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          if (linear_tid == 0)
          {
              // Set flag for first thread-item (preds[0] is undefined)
              head_flags[0] = 1;
          }
          else
          {
              preds[0] = temp_storage.last_items[linear_tid - 1];
              head_flags[0] = ApplyOp<FlagOp>::FlagT(flag_op, preds[0], input[0], linear_tid * ITEMS_PER_THREAD);
          }
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
      }
  
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeads(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          T               (&preds)[ITEMS_PER_THREAD],         ///< [out] Calling thread's predecessor items
          FlagOp          flag_op,                            ///< [in] Binary boolean flag predicate
          T               tile_predecessor_item)              ///< [in] <b>[<em>thread</em><sub>0</sub> only]</b> Item with which to compare the first tile item (<tt>input<sub>0</sub></tt> from <em>thread</em><sub>0</sub>).
      {
          // Share last item
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          // Set flag for first thread-item
          preds[0] = (linear_tid == 0) ?
              tile_predecessor_item :              // First thread
              temp_storage.last_items[linear_tid - 1];
  
          head_flags[0] = ApplyOp<FlagOp>::FlagT(flag_op, preds[0], input[0], linear_tid * ITEMS_PER_THREAD);
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
      }
  
  #endif // DOXYGEN_SHOULD_SKIP_THIS
  
  
      /**
       * \brief Sets head flags indicating discontinuities between items partitioned across the thread block, for which the first item has no reference and is always flagged.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is always flagged.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute head flags for discontinuities in the segment
       *     int head_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagHeads(head_flags, thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], [3,4,4,4], ... }</tt>.
       * The corresponding output \p head_flags in those threads will be
       * <tt>{ [1,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeads(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          T preds[ITEMS_PER_THREAD];
          FlagHeads(head_flags, input, preds, flag_op);
      }
  
  
      /**
       * \brief Sets head flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is compared
       *   against \p tile_predecessor_item.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Have thread0 obtain the predecessor item for the entire tile
       *     int tile_predecessor_item;
       *     if (threadIdx.x == 0) tile_predecessor_item == ...
       *
       *     // Collectively compute head flags for discontinuities in the segment
       *     int head_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagHeads(
       *         head_flags, thread_data, cub::Inequality(), tile_predecessor_item);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], [3,4,4,4], ... }</tt>,
       * and that \p tile_predecessor_item is \p 0.  The corresponding output \p head_flags in those threads will be
       * <tt>{ [0,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeads(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op,                            ///< [in] Binary boolean flag predicate
          T               tile_predecessor_item)              ///< [in] <b>[<em>thread</em><sub>0</sub> only]</b> Item with which to compare the first tile item (<tt>input<sub>0</sub></tt> from <em>thread</em><sub>0</sub>).
      {
          T preds[ITEMS_PER_THREAD];
          FlagHeads(head_flags, input, preds, flag_op, tile_predecessor_item);
      }
  
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Tail flag operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Sets tail flags indicating discontinuities between items partitioned across the thread block, for which the last item has no reference and is always flagged.
       *
       * \par
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is always flagged.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute tail flags for discontinuities in the segment
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(tail_flags, thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>.
       * The corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,1] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagTails(
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share first item
          temp_storage.first_items[linear_tid] = input[0];
  
          CTA_SYNC();
  
          // Set flag for last thread-item
          tail_flags[ITEMS_PER_THREAD - 1] = (linear_tid == BLOCK_THREADS - 1) ?
              1 :                             // Last thread
              ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  input[ITEMS_PER_THREAD - 1],
                  temp_storage.first_items[linear_tid + 1],
                  (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
      /**
       * \brief Sets tail flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is compared
       *   against \p tile_successor_item.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Have thread127 obtain the successor item for the entire tile
       *     int tile_successor_item;
       *     if (threadIdx.x == 127) tile_successor_item == ...
       *
       *     // Collectively compute tail flags for discontinuities in the segment
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(
       *         tail_flags, thread_data, cub::Inequality(), tile_successor_item);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>
       * and that \p tile_successor_item is \p 125.  The corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,0] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagTails(
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op,                            ///< [in] Binary boolean flag predicate
          T               tile_successor_item)                ///< [in] <b>[<em>thread</em><sub><tt>BLOCK_THREADS</tt>-1</sub> only]</b> Item with which to compare the last tile item (<tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> from <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>).
      {
          // Share first item
          temp_storage.first_items[linear_tid] = input[0];
  
          CTA_SYNC();
  
          // Set flag for last thread-item
          T successor_item = (linear_tid == BLOCK_THREADS - 1) ?
              tile_successor_item :              // Last thread
              temp_storage.first_items[linear_tid + 1];
  
          tail_flags[ITEMS_PER_THREAD - 1] = ApplyOp<FlagOp>::FlagT(
              flag_op,
              input[ITEMS_PER_THREAD - 1],
              successor_item,
              (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Head & tail flag operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Sets both head and tail flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is always flagged.
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is always flagged.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head- and tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute head and flags for discontinuities in the segment
       *     int head_flags[4];
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(
       *         head_flags, tail_flags, thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>
       * and that the tile_successor_item is \p 125.  The corresponding output \p head_flags
       * in those threads will be <tt>{ [1,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       * and the corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,1] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeadsAndTails(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share first and last items
          temp_storage.first_items[linear_tid] = input[0];
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          T preds[ITEMS_PER_THREAD];
  
          // Set flag for first thread-item
          preds[0] = temp_storage.last_items[linear_tid - 1];
          if (linear_tid == 0)
          {
              head_flags[0] = 1;
          }
          else
          {
              head_flags[0] = ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  preds[0],
                  input[0],
                  linear_tid * ITEMS_PER_THREAD);
          }
  
  
          // Set flag for last thread-item
          tail_flags[ITEMS_PER_THREAD - 1] = (linear_tid == BLOCK_THREADS - 1) ?
              1 :                             // Last thread
              ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  input[ITEMS_PER_THREAD - 1],
                  temp_storage.first_items[linear_tid + 1],
                  (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
      /**
       * \brief Sets both head and tail flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is always flagged.
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is compared
       *   against \p tile_predecessor_item.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head- and tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Have thread127 obtain the successor item for the entire tile
       *     int tile_successor_item;
       *     if (threadIdx.x == 127) tile_successor_item == ...
       *
       *     // Collectively compute head and flags for discontinuities in the segment
       *     int head_flags[4];
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(
       *         head_flags, tail_flags, tile_successor_item, thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>
       * and that the tile_successor_item is \p 125.  The corresponding output \p head_flags
       * in those threads will be <tt>{ [1,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       * and the corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,0] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeadsAndTails(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               tile_successor_item,                ///< [in] <b>[<em>thread</em><sub><tt>BLOCK_THREADS</tt>-1</sub> only]</b> Item with which to compare the last tile item (<tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> from <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>).
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share first and last items
          temp_storage.first_items[linear_tid] = input[0];
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          T preds[ITEMS_PER_THREAD];
  
          // Set flag for first thread-item
          if (linear_tid == 0)
          {
              head_flags[0] = 1;
          }
          else
          {
              preds[0] = temp_storage.last_items[linear_tid - 1];
              head_flags[0] = ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  preds[0],
                  input[0],
                  linear_tid * ITEMS_PER_THREAD);
          }
  
          // Set flag for last thread-item
          T successor_item = (linear_tid == BLOCK_THREADS - 1) ?
              tile_successor_item :              // Last thread
              temp_storage.first_items[linear_tid + 1];
  
          tail_flags[ITEMS_PER_THREAD - 1] = ApplyOp<FlagOp>::FlagT(
              flag_op,
              input[ITEMS_PER_THREAD - 1],
              successor_item,
              (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
      /**
       * \brief Sets both head and tail flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is compared
       *   against \p tile_predecessor_item.
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is always flagged.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head- and tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Have thread0 obtain the predecessor item for the entire tile
       *     int tile_predecessor_item;
       *     if (threadIdx.x == 0) tile_predecessor_item == ...
       *
       *     // Have thread127 obtain the successor item for the entire tile
       *     int tile_successor_item;
       *     if (threadIdx.x == 127) tile_successor_item == ...
       *
       *     // Collectively compute head and flags for discontinuities in the segment
       *     int head_flags[4];
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(
       *         head_flags, tile_predecessor_item, tail_flags, tile_successor_item,
       *         thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>,
       * that the \p tile_predecessor_item is \p 0, and that the
       * \p tile_successor_item is \p 125.  The corresponding output \p head_flags
       * in those threads will be <tt>{ [0,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       * and the corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,1] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeadsAndTails(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               tile_predecessor_item,              ///< [in] <b>[<em>thread</em><sub>0</sub> only]</b> Item with which to compare the first tile item (<tt>input<sub>0</sub></tt> from <em>thread</em><sub>0</sub>).
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share first and last items
          temp_storage.first_items[linear_tid] = input[0];
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          T preds[ITEMS_PER_THREAD];
  
          // Set flag for first thread-item
          preds[0] = (linear_tid == 0) ?
              tile_predecessor_item :              // First thread
              temp_storage.last_items[linear_tid - 1];
  
          head_flags[0] = ApplyOp<FlagOp>::FlagT(
              flag_op,
              preds[0],
              input[0],
              linear_tid * ITEMS_PER_THREAD);
  
          // Set flag for last thread-item
          tail_flags[ITEMS_PER_THREAD - 1] = (linear_tid == BLOCK_THREADS - 1) ?
              1 :                             // Last thread
              ApplyOp<FlagOp>::FlagT(
                  flag_op,
                  input[ITEMS_PER_THREAD - 1],
                  temp_storage.first_items[linear_tid + 1],
                  (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
      /**
       * \brief Sets both head and tail flags indicating discontinuities between items partitioned across the thread block.
       *
       * \par
       * - The flag <tt>head_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(</tt><em>previous-item</em><tt>, input<sub><em>i</em></sub>)</tt>
       *   returns \p true (where <em>previous-item</em> is either the preceding item
       *   in the same thread or the last item in the previous thread).
       * - For <em>thread</em><sub>0</sub>, item <tt>input<sub>0</sub></tt> is compared
       *   against \p tile_predecessor_item.
       * - The flag <tt>tail_flags<sub><em>i</em></sub></tt> is set for item
       *   <tt>input<sub><em>i</em></sub></tt> when
       *   <tt>flag_op(input<sub><em>i</em></sub>, </tt><em>next-item</em><tt>)</tt>
       *   returns \p true (where <em>next-item</em> is either the next item
       *   in the same thread or the first item in the next thread).
       * - For <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>, item
       *   <tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> is compared
       *   against \p tile_successor_item.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates the head- and tail-flagging of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_discontinuity.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockDiscontinuity for a 1D block of 128 threads on type int
       *     typedef cub::BlockDiscontinuity<int, 128> BlockDiscontinuity;
       *
       *     // Allocate shared memory for BlockDiscontinuity
       *     __shared__ typename BlockDiscontinuity::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Have thread0 obtain the predecessor item for the entire tile
       *     int tile_predecessor_item;
       *     if (threadIdx.x == 0) tile_predecessor_item == ...
       *
       *     // Have thread127 obtain the successor item for the entire tile
       *     int tile_successor_item;
       *     if (threadIdx.x == 127) tile_successor_item == ...
       *
       *     // Collectively compute head and flags for discontinuities in the segment
       *     int head_flags[4];
       *     int tail_flags[4];
       *     BlockDiscontinuity(temp_storage).FlagTails(
       *         head_flags, tile_predecessor_item, tail_flags, tile_successor_item,
       *         thread_data, cub::Inequality());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,0,1,1], [1,1,1,1], [2,3,3,3], ..., [124,125,125,125] }</tt>,
       * that the \p tile_predecessor_item is \p 0, and that the
       * \p tile_successor_item is \p 125.  The corresponding output \p head_flags
       * in those threads will be <tt>{ [0,0,1,0], [0,0,0,0], [1,1,0,0], [0,1,0,0], ... }</tt>.
       * and the corresponding output \p tail_flags in those threads will be
       * <tt>{ [0,1,0,0], [0,0,0,1], [1,0,0,...], ..., [1,0,0,0] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam FlagT                <b>[inferred]</b> The flag type (must be an integer type)
       * \tparam FlagOp               <b>[inferred]</b> Binary predicate functor type having member <tt>T operator()(const T &a, const T &b)</tt> or member <tt>T operator()(const T &a, const T &b, unsigned int b_index)</tt>, and returning \p true if a discontinuity exists between \p a and \p b, otherwise \p false.  \p b_index is the rank of b in the aggregate tile of data.
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        FlagT,
          typename        FlagOp>
      __device__ __forceinline__ void FlagHeadsAndTails(
          FlagT           (&head_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity head_flags
          T               tile_predecessor_item,              ///< [in] <b>[<em>thread</em><sub>0</sub> only]</b> Item with which to compare the first tile item (<tt>input<sub>0</sub></tt> from <em>thread</em><sub>0</sub>).
          FlagT           (&tail_flags)[ITEMS_PER_THREAD],    ///< [out] Calling thread's discontinuity tail_flags
          T               tile_successor_item,                ///< [in] <b>[<em>thread</em><sub><tt>BLOCK_THREADS</tt>-1</sub> only]</b> Item with which to compare the last tile item (<tt>input</tt><sub><em>ITEMS_PER_THREAD</em>-1</sub> from <em>thread</em><sub><em>BLOCK_THREADS</em>-1</sub>).
          T               (&input)[ITEMS_PER_THREAD],         ///< [in] Calling thread's input items
          FlagOp          flag_op)                            ///< [in] Binary boolean flag predicate
      {
          // Share first and last items
          temp_storage.first_items[linear_tid] = input[0];
          temp_storage.last_items[linear_tid] = input[ITEMS_PER_THREAD - 1];
  
          CTA_SYNC();
  
          T preds[ITEMS_PER_THREAD];
  
          // Set flag for first thread-item
          preds[0] = (linear_tid == 0) ?
              tile_predecessor_item :              // First thread
              temp_storage.last_items[linear_tid - 1];
  
          head_flags[0] = ApplyOp<FlagOp>::FlagT(
              flag_op,
              preds[0],
              input[0],
              linear_tid * ITEMS_PER_THREAD);
  
          // Set flag for last thread-item
          T successor_item = (linear_tid == BLOCK_THREADS - 1) ?
              tile_successor_item :              // Last thread
              temp_storage.first_items[linear_tid + 1];
  
          tail_flags[ITEMS_PER_THREAD - 1] = ApplyOp<FlagOp>::FlagT(
              flag_op,
              input[ITEMS_PER_THREAD - 1],
              successor_item,
              (linear_tid * ITEMS_PER_THREAD) + ITEMS_PER_THREAD);
  
          // Set head_flags for remaining items
          Iterate<1, ITEMS_PER_THREAD>::FlagHeads(linear_tid, head_flags, input, preds, flag_op);
  
          // Set tail_flags for remaining items
          Iterate<0, ITEMS_PER_THREAD - 1>::FlagTails(linear_tid, tail_flags, input, flag_op);
      }
  
  
  
  
      //@}  end member group
  
  };
  
  
  }               // CUB namespace
  CUB_NS_POSTFIX  // Optional outer namespace(s)