Blame view

tools/cub-1.8.0/cub/block/block_radix_sort.cuh 37.4 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
  /******************************************************************************
   * 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::BlockRadixSort class provides [<em>collective</em>](index.html#sec0) methods for radix sorting of items partitioned across a CUDA thread block.
   */
  
  
  #pragma once
  
  #include "block_exchange.cuh"
  #include "block_radix_rank.cuh"
  #include "../util_ptx.cuh"
  #include "../util_arch.cuh"
  #include "../util_type.cuh"
  #include "../util_namespace.cuh"
  
  /// Optional outer namespace(s)
  CUB_NS_PREFIX
  
  /// CUB namespace
  namespace cub {
  
  /**
   * \brief The BlockRadixSort class provides [<em>collective</em>](index.html#sec0) methods for sorting items partitioned across a CUDA thread block using a radix sorting method.  ![](sorting_logo.png)
   * \ingroup BlockModule
   *
   * \tparam KeyT                 KeyT type
   * \tparam BLOCK_DIM_X          The thread block length in threads along the X dimension
   * \tparam ITEMS_PER_THREAD     The number of items per thread
   * \tparam ValueT               <b>[optional]</b> ValueT type (default: cub::NullType, which indicates a keys-only sort)
   * \tparam RADIX_BITS           <b>[optional]</b> The number of radix bits per digit place (default: 4 bits)
   * \tparam MEMOIZE_OUTER_SCAN   <b>[optional]</b> Whether or not to buffer outer raking scan partials to incur fewer shared memory reads at the expense of higher register pressure (default: true for architectures SM35 and newer, false otherwise).
   * \tparam INNER_SCAN_ALGORITHM <b>[optional]</b> The cub::BlockScanAlgorithm algorithm to use (default: cub::BLOCK_SCAN_WARP_SCANS)
   * \tparam SMEM_CONFIG          <b>[optional]</b> Shared memory bank mode (default: \p cudaSharedMemBankSizeFourByte)
   * \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
   * - The [<em>radix sorting method</em>](http://en.wikipedia.org/wiki/Radix_sort) arranges
   *   items into ascending order.  It relies upon a positional representation for
   *   keys, i.e., each key is comprised of an ordered sequence of symbols (e.g., digits,
   *   characters, etc.) specified from least-significant to most-significant.  For a
   *   given input sequence of keys and a set of rules specifying a total ordering
   *   of the symbolic alphabet, the radix sorting method produces a lexicographic
   *   ordering of those keys.
   * - BlockRadixSort can sort all of the built-in C++ numeric primitive types
   *   (<tt>unsigned char</tt>, \p int, \p double, etc.) as well as CUDA's \p __half
   *   half-precision floating-point type. Within each key, the implementation treats fixed-length
   *   bit-sequences of \p RADIX_BITS as radix digit places.  Although the direct radix sorting
   *   method can only be applied to unsigned integral types, BlockRadixSort
   *   is able to sort signed and floating-point types via simple bit-wise transformations
   *   that ensure lexicographic key ordering.
   * - \rowmajor
   *
   * \par Performance Considerations
   * - \granularity
   *
   * \par A Simple Example
   * \blockcollective{BlockRadixSort}
   * \par
   * The code snippet below illustrates a sort of 512 integer keys 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_radix_sort.cuh>
   *
   * __global__ void ExampleKernel(...)
   * {
   *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer items each
   *     typedef cub::BlockRadixSort<int, 128, 4> BlockRadixSort;
   *
   *     // Allocate shared memory for BlockRadixSort
   *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
   *
   *     // Obtain a segment of consecutive items that are blocked across threads
   *     int thread_keys[4];
   *     ...
   *
   *     // Collectively sort the keys
   *     BlockRadixSort(temp_storage).Sort(thread_keys);
   *
   *     ...
   * \endcode
   * \par
   * Suppose the set of input \p thread_keys across the block of threads is
   * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
   * corresponding output \p thread_keys in those threads will be
   * <tt>{ [0,1,2,3], [4,5,6,7], [8,9,10,11], ..., [508,509,510,511] }</tt>.
   *
   */
  template <
      typename                KeyT,
      int                     BLOCK_DIM_X,
      int                     ITEMS_PER_THREAD,
      typename                ValueT                   = NullType,
      int                     RADIX_BITS              = 4,
      bool                    MEMOIZE_OUTER_SCAN      = (CUB_PTX_ARCH >= 350) ? true : false,
      BlockScanAlgorithm      INNER_SCAN_ALGORITHM    = BLOCK_SCAN_WARP_SCANS,
      cudaSharedMemConfig     SMEM_CONFIG             = cudaSharedMemBankSizeFourByte,
      int                     BLOCK_DIM_Y             = 1,
      int                     BLOCK_DIM_Z             = 1,
      int                     PTX_ARCH                = CUB_PTX_ARCH>
  class BlockRadixSort
  {
  private:
  
      /******************************************************************************
       * Constants and type definitions
       ******************************************************************************/
  
      enum
      {
          // The thread block size in threads
          BLOCK_THREADS               = BLOCK_DIM_X * BLOCK_DIM_Y * BLOCK_DIM_Z,
  
          // Whether or not there are values to be trucked along with keys
          KEYS_ONLY                   = Equals<ValueT, NullType>::VALUE,
      };
  
      // KeyT traits and unsigned bits type
      typedef Traits<KeyT>                        KeyTraits;
      typedef typename KeyTraits::UnsignedBits    UnsignedBits;
  
      /// Ascending BlockRadixRank utility type
      typedef BlockRadixRank<
              BLOCK_DIM_X,
              RADIX_BITS,
              false,
              MEMOIZE_OUTER_SCAN,
              INNER_SCAN_ALGORITHM,
              SMEM_CONFIG,
              BLOCK_DIM_Y,
              BLOCK_DIM_Z,
              PTX_ARCH>
          AscendingBlockRadixRank;
  
      /// Descending BlockRadixRank utility type
      typedef BlockRadixRank<
              BLOCK_DIM_X,
              RADIX_BITS,
              true,
              MEMOIZE_OUTER_SCAN,
              INNER_SCAN_ALGORITHM,
              SMEM_CONFIG,
              BLOCK_DIM_Y,
              BLOCK_DIM_Z,
              PTX_ARCH>
          DescendingBlockRadixRank;
  
      /// BlockExchange utility type for keys
      typedef BlockExchange<KeyT, BLOCK_DIM_X, ITEMS_PER_THREAD, false, BLOCK_DIM_Y, BLOCK_DIM_Z, PTX_ARCH> BlockExchangeKeys;
  
      /// BlockExchange utility type for values
      typedef BlockExchange<ValueT, BLOCK_DIM_X, ITEMS_PER_THREAD, false, BLOCK_DIM_Y, BLOCK_DIM_Z, PTX_ARCH> BlockExchangeValues;
  
      /// Shared memory storage layout type
      union _TempStorage
      {
          typename AscendingBlockRadixRank::TempStorage  asending_ranking_storage;
          typename DescendingBlockRadixRank::TempStorage descending_ranking_storage;
          typename BlockExchangeKeys::TempStorage        exchange_keys;
          typename BlockExchangeValues::TempStorage      exchange_values;
      };
  
  
      /******************************************************************************
       * Thread fields
       ******************************************************************************/
  
      /// Shared storage reference
      _TempStorage &temp_storage;
  
      /// Linear thread-id
      unsigned int linear_tid;
  
      /******************************************************************************
       * Utility methods
       ******************************************************************************/
  
      /// Internal storage allocator
      __device__ __forceinline__ _TempStorage& PrivateStorage()
      {
          __shared__ _TempStorage private_storage;
          return private_storage;
      }
  
      /// Rank keys (specialized for ascending sort)
      __device__ __forceinline__ void RankKeys(
          UnsignedBits    (&unsigned_keys)[ITEMS_PER_THREAD],
          int             (&ranks)[ITEMS_PER_THREAD],
          int             begin_bit,
          int             pass_bits,
          Int2Type<false> /*is_descending*/)
      {
          AscendingBlockRadixRank(temp_storage.asending_ranking_storage).RankKeys(
              unsigned_keys,
              ranks,
              begin_bit,
              pass_bits);
      }
  
      /// Rank keys (specialized for descending sort)
      __device__ __forceinline__ void RankKeys(
          UnsignedBits    (&unsigned_keys)[ITEMS_PER_THREAD],
          int             (&ranks)[ITEMS_PER_THREAD],
          int             begin_bit,
          int             pass_bits,
          Int2Type<true>  /*is_descending*/)
      {
          DescendingBlockRadixRank(temp_storage.descending_ranking_storage).RankKeys(
              unsigned_keys,
              ranks,
              begin_bit,
              pass_bits);
      }
  
      /// ExchangeValues (specialized for key-value sort, to-blocked arrangement)
      __device__ __forceinline__ void ExchangeValues(
          ValueT          (&values)[ITEMS_PER_THREAD],
          int             (&ranks)[ITEMS_PER_THREAD],
          Int2Type<false> /*is_keys_only*/,
          Int2Type<true>  /*is_blocked*/)
      {
          CTA_SYNC();
  
          // Exchange values through shared memory in blocked arrangement
          BlockExchangeValues(temp_storage.exchange_values).ScatterToBlocked(values, ranks);
      }
  
      /// ExchangeValues (specialized for key-value sort, to-striped arrangement)
      __device__ __forceinline__ void ExchangeValues(
          ValueT          (&values)[ITEMS_PER_THREAD],
          int             (&ranks)[ITEMS_PER_THREAD],
          Int2Type<false> /*is_keys_only*/,
          Int2Type<false> /*is_blocked*/)
      {
          CTA_SYNC();
  
          // Exchange values through shared memory in blocked arrangement
          BlockExchangeValues(temp_storage.exchange_values).ScatterToStriped(values, ranks);
      }
  
      /// ExchangeValues (specialized for keys-only sort)
      template <int IS_BLOCKED>
      __device__ __forceinline__ void ExchangeValues(
          ValueT                  (&/*values*/)[ITEMS_PER_THREAD],
          int                     (&/*ranks*/)[ITEMS_PER_THREAD],
          Int2Type<true>          /*is_keys_only*/,
          Int2Type<IS_BLOCKED>    /*is_blocked*/)
      {}
  
      /// Sort blocked arrangement
      template <int DESCENDING, int KEYS_ONLY>
      __device__ __forceinline__ void SortBlocked(
          KeyT                    (&keys)[ITEMS_PER_THREAD],          ///< Keys to sort
          ValueT                  (&values)[ITEMS_PER_THREAD],        ///< Values to sort
          int                     begin_bit,                          ///< The beginning (least-significant) bit index needed for key comparison
          int                     end_bit,                            ///< The past-the-end (most-significant) bit index needed for key comparison
          Int2Type<DESCENDING>    is_descending,                      ///< Tag whether is a descending-order sort
          Int2Type<KEYS_ONLY>     is_keys_only)                       ///< Tag whether is keys-only sort
      {
          UnsignedBits (&unsigned_keys)[ITEMS_PER_THREAD] =
              reinterpret_cast<UnsignedBits (&)[ITEMS_PER_THREAD]>(keys);
  
          // Twiddle bits if necessary
          #pragma unroll
          for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
          {
              unsigned_keys[KEY] = KeyTraits::TwiddleIn(unsigned_keys[KEY]);
          }
  
          // Radix sorting passes
          while (true)
          {
              int pass_bits = CUB_MIN(RADIX_BITS, end_bit - begin_bit);
  
              // Rank the blocked keys
              int ranks[ITEMS_PER_THREAD];
              RankKeys(unsigned_keys, ranks, begin_bit, pass_bits, is_descending);
              begin_bit += RADIX_BITS;
  
              CTA_SYNC();
  
              // Exchange keys through shared memory in blocked arrangement
              BlockExchangeKeys(temp_storage.exchange_keys).ScatterToBlocked(keys, ranks);
  
              // Exchange values through shared memory in blocked arrangement
              ExchangeValues(values, ranks, is_keys_only, Int2Type<true>());
  
              // Quit if done
              if (begin_bit >= end_bit) break;
  
              CTA_SYNC();
          }
  
          // Untwiddle bits if necessary
          #pragma unroll
          for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
          {
              unsigned_keys[KEY] = KeyTraits::TwiddleOut(unsigned_keys[KEY]);
          }
      }
  
  public:
  
  #ifndef DOXYGEN_SHOULD_SKIP_THIS    // Do not document
  
      /// Sort blocked -> striped arrangement
      template <int DESCENDING, int KEYS_ONLY>
      __device__ __forceinline__ void SortBlockedToStriped(
          KeyT                    (&keys)[ITEMS_PER_THREAD],          ///< Keys to sort
          ValueT                  (&values)[ITEMS_PER_THREAD],        ///< Values to sort
          int                     begin_bit,                          ///< The beginning (least-significant) bit index needed for key comparison
          int                     end_bit,                            ///< The past-the-end (most-significant) bit index needed for key comparison
          Int2Type<DESCENDING>    is_descending,                      ///< Tag whether is a descending-order sort
          Int2Type<KEYS_ONLY>     is_keys_only)                       ///< Tag whether is keys-only sort
      {
          UnsignedBits (&unsigned_keys)[ITEMS_PER_THREAD] =
              reinterpret_cast<UnsignedBits (&)[ITEMS_PER_THREAD]>(keys);
  
          // Twiddle bits if necessary
          #pragma unroll
          for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
          {
              unsigned_keys[KEY] = KeyTraits::TwiddleIn(unsigned_keys[KEY]);
          }
  
          // Radix sorting passes
          while (true)
          {
              int pass_bits = CUB_MIN(RADIX_BITS, end_bit - begin_bit);
  
              // Rank the blocked keys
              int ranks[ITEMS_PER_THREAD];
              RankKeys(unsigned_keys, ranks, begin_bit, pass_bits, is_descending);
              begin_bit += RADIX_BITS;
  
              CTA_SYNC();
  
              // Check if this is the last pass
              if (begin_bit >= end_bit)
              {
                  // Last pass exchanges keys through shared memory in striped arrangement
                  BlockExchangeKeys(temp_storage.exchange_keys).ScatterToStriped(keys, ranks);
  
                  // Last pass exchanges through shared memory in striped arrangement
                  ExchangeValues(values, ranks, is_keys_only, Int2Type<false>());
  
                  // Quit
                  break;
              }
  
              // Exchange keys through shared memory in blocked arrangement
              BlockExchangeKeys(temp_storage.exchange_keys).ScatterToBlocked(keys, ranks);
  
              // Exchange values through shared memory in blocked arrangement
              ExchangeValues(values, ranks, is_keys_only, Int2Type<true>());
  
              CTA_SYNC();
          }
  
          // Untwiddle bits if necessary
          #pragma unroll
          for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
          {
              unsigned_keys[KEY] = KeyTraits::TwiddleOut(unsigned_keys[KEY]);
          }
      }
  
  #endif // DOXYGEN_SHOULD_SKIP_THIS
  
      /// \smemstorage{BlockRadixSort}
      struct TempStorage : Uninitialized<_TempStorage> {};
  
  
      /******************************************************************//**
       * 
  ame Collective constructors
       *********************************************************************/
      //@{
  
      /**
       * \brief Collective constructor using a private static allocation of shared memory as temporary storage.
       */
      __device__ __forceinline__ BlockRadixSort()
      :
          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__ BlockRadixSort(
          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 Sorting (blocked arrangements)
       *********************************************************************/
      //@{
  
      /**
       * \brief Performs an ascending block-wide radix sort over a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys.
       *
       * \par
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys each
       *     typedef cub::BlockRadixSort<int, 128, 4> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     ...
       *
       *     // Collectively sort the keys
       *     BlockRadixSort(temp_storage).Sort(thread_keys);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.
       * The corresponding output \p thread_keys in those threads will be
       * <tt>{ [0,1,2,3], [4,5,6,7], [8,9,10,11], ..., [508,509,510,511] }</tt>.
       */
      __device__ __forceinline__ void Sort(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          NullType values[ITEMS_PER_THREAD];
  
          SortBlocked(keys, values, begin_bit, end_bit, Int2Type<false>(), Int2Type<KEYS_ONLY>());
      }
  
  
      /**
       * \brief Performs an ascending block-wide radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys and values.
       *
       * \par
       * - BlockRadixSort can only accommodate one associated tile of values. To "truck along"
       *   more than one tile of values, simply perform a key-value sort of the keys paired
       *   with a temporary value array that enumerates the key indices.  The reordered indices
       *   can then be used as a gather-vector for exchanging other associated tile data through
       *   shared memory.
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys and values that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive pairs.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys and values each
       *     typedef cub::BlockRadixSort<int, 128, 4, int> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     int thread_values[4];
       *     ...
       *
       *     // Collectively sort the keys and values among block threads
       *     BlockRadixSort(temp_storage).Sort(thread_keys, thread_values);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [0,1,2,3], [4,5,6,7], [8,9,10,11], ..., [508,509,510,511] }</tt>.
       *
       */
      __device__ __forceinline__ void Sort(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          ValueT  (&values)[ITEMS_PER_THREAD],        ///< [in-out] Values to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          SortBlocked(keys, values, begin_bit, end_bit, Int2Type<false>(), Int2Type<KEYS_ONLY>());
      }
  
      /**
       * \brief Performs a descending block-wide radix sort over a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys.
       *
       * \par
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys each
       *     typedef cub::BlockRadixSort<int, 128, 4> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     ...
       *
       *     // Collectively sort the keys
       *     BlockRadixSort(temp_storage).Sort(thread_keys);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.
       * The corresponding output \p thread_keys in those threads will be
       * <tt>{ [511,510,509,508], [11,10,9,8], [7,6,5,4], ..., [3,2,1,0] }</tt>.
       */
      __device__ __forceinline__ void SortDescending(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          NullType values[ITEMS_PER_THREAD];
  
          SortBlocked(keys, values, begin_bit, end_bit, Int2Type<true>(), Int2Type<KEYS_ONLY>());
      }
  
  
      /**
       * \brief Performs a descending block-wide radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys and values.
       *
       * \par
       * - BlockRadixSort can only accommodate one associated tile of values. To "truck along"
       *   more than one tile of values, simply perform a key-value sort of the keys paired
       *   with a temporary value array that enumerates the key indices.  The reordered indices
       *   can then be used as a gather-vector for exchanging other associated tile data through
       *   shared memory.
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys and values that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive pairs.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys and values each
       *     typedef cub::BlockRadixSort<int, 128, 4, int> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     int thread_values[4];
       *     ...
       *
       *     // Collectively sort the keys and values among block threads
       *     BlockRadixSort(temp_storage).Sort(thread_keys, thread_values);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [511,510,509,508], [11,10,9,8], [7,6,5,4], ..., [3,2,1,0] }</tt>.
       *
       */
      __device__ __forceinline__ void SortDescending(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          ValueT  (&values)[ITEMS_PER_THREAD],        ///< [in-out] Values to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          SortBlocked(keys, values, begin_bit, end_bit, Int2Type<true>(), Int2Type<KEYS_ONLY>());
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Sorting (blocked arrangement -> striped arrangement)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Performs an ascending radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys, leaving them in a [<em>striped arrangement</em>](index.html#sec5sec3).
       *
       * \par
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys that
       * are initially partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive keys.  The final partitioning is striped.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys each
       *     typedef cub::BlockRadixSort<int, 128, 4> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     ...
       *
       *     // Collectively sort the keys
       *     BlockRadixSort(temp_storage).SortBlockedToStriped(thread_keys);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [0,128,256,384], [1,129,257,385], [2,130,258,386], ..., [127,255,383,511] }</tt>.
       *
       */
      __device__ __forceinline__ void SortBlockedToStriped(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          NullType values[ITEMS_PER_THREAD];
  
          SortBlockedToStriped(keys, values, begin_bit, end_bit, Int2Type<false>(), Int2Type<KEYS_ONLY>());
      }
  
  
      /**
       * \brief Performs an ascending radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys and values, leaving them in a [<em>striped arrangement</em>](index.html#sec5sec3).
       *
       * \par
       * - BlockRadixSort can only accommodate one associated tile of values. To "truck along"
       *   more than one tile of values, simply perform a key-value sort of the keys paired
       *   with a temporary value array that enumerates the key indices.  The reordered indices
       *   can then be used as a gather-vector for exchanging other associated tile data through
       *   shared memory.
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys and values that
       * are initially partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive pairs.  The final partitioning is striped.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys and values each
       *     typedef cub::BlockRadixSort<int, 128, 4, int> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     int thread_values[4];
       *     ...
       *
       *     // Collectively sort the keys and values among block threads
       *     BlockRadixSort(temp_storage).SortBlockedToStriped(thread_keys, thread_values);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [0,128,256,384], [1,129,257,385], [2,130,258,386], ..., [127,255,383,511] }</tt>.
       *
       */
      __device__ __forceinline__ void SortBlockedToStriped(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          ValueT  (&values)[ITEMS_PER_THREAD],        ///< [in-out] Values to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          SortBlockedToStriped(keys, values, begin_bit, end_bit, Int2Type<false>(), Int2Type<KEYS_ONLY>());
      }
  
  
      /**
       * \brief Performs a descending radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys, leaving them in a [<em>striped arrangement</em>](index.html#sec5sec3).
       *
       * \par
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys that
       * are initially partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive keys.  The final partitioning is striped.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys each
       *     typedef cub::BlockRadixSort<int, 128, 4> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     ...
       *
       *     // Collectively sort the keys
       *     BlockRadixSort(temp_storage).SortBlockedToStriped(thread_keys);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [511,383,255,127], [386,258,130,2], [385,257,128,1], ..., [384,256,128,0] }</tt>.
       *
       */
      __device__ __forceinline__ void SortDescendingBlockedToStriped(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          NullType values[ITEMS_PER_THREAD];
  
          SortBlockedToStriped(keys, values, begin_bit, end_bit, Int2Type<true>(), Int2Type<KEYS_ONLY>());
      }
  
  
      /**
       * \brief Performs a descending radix sort across a [<em>blocked arrangement</em>](index.html#sec5sec3) of keys and values, leaving them in a [<em>striped arrangement</em>](index.html#sec5sec3).
       *
       * \par
       * - BlockRadixSort can only accommodate one associated tile of values. To "truck along"
       *   more than one tile of values, simply perform a key-value sort of the keys paired
       *   with a temporary value array that enumerates the key indices.  The reordered indices
       *   can then be used as a gather-vector for exchanging other associated tile data through
       *   shared memory.
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a sort of 512 integer keys and values that
       * are initially partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive pairs.  The final partitioning is striped.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer keys and values each
       *     typedef cub::BlockRadixSort<int, 128, 4, int> BlockRadixSort;
       *
       *     // Allocate shared memory for BlockRadixSort
       *     __shared__ typename BlockRadixSort::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_keys[4];
       *     int thread_values[4];
       *     ...
       *
       *     // Collectively sort the keys and values among block threads
       *     BlockRadixSort(temp_storage).SortBlockedToStriped(thread_keys, thread_values);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_keys across the block of threads is
       * <tt>{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }</tt>.  The
       * corresponding output \p thread_keys in those threads will be
       * <tt>{ [511,383,255,127], [386,258,130,2], [385,257,128,1], ..., [384,256,128,0] }</tt>.
       *
       */
      __device__ __forceinline__ void SortDescendingBlockedToStriped(
          KeyT    (&keys)[ITEMS_PER_THREAD],          ///< [in-out] Keys to sort
          ValueT  (&values)[ITEMS_PER_THREAD],        ///< [in-out] Values to sort
          int     begin_bit   = 0,                    ///< [in] <b>[optional]</b> The beginning (least-significant) bit index needed for key comparison
          int     end_bit     = sizeof(KeyT) * 8)      ///< [in] <b>[optional]</b> The past-the-end (most-significant) bit index needed for key comparison
      {
          SortBlockedToStriped(keys, values, begin_bit, end_bit, Int2Type<true>(), Int2Type<KEYS_ONLY>());
      }
  
  
      //@}  end member group
  
  };
  
  /**
   * \example example_block_radix_sort.cu
   */
  
  }               // CUB namespace
  CUB_NS_POSTFIX  // Optional outer namespace(s)