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tools/cub-1.8.0/cub/device/device_radix_sort.cuh 41.4 KB
8dcb6dfcb   Yannick Estève   first commit
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  /******************************************************************************
   * 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
   * cub::DeviceRadixSort provides device-wide, parallel operations for computing a radix sort across a sequence of data items residing within device-accessible memory.
   */
  
  #pragma once
  
  #include <stdio.h>
  #include <iterator>
  
  #include "dispatch/dispatch_radix_sort.cuh"
  #include "../util_arch.cuh"
  #include "../util_namespace.cuh"
  
  /// Optional outer namespace(s)
  CUB_NS_PREFIX
  
  /// CUB namespace
  namespace cub {
  
  
  /**
   * \brief DeviceRadixSort provides device-wide, parallel operations for computing a radix sort across a sequence of data items residing within device-accessible memory. ![](sorting_logo.png)
   * \ingroup SingleModule
   *
   * \par Overview
   * The [<em>radix sorting method</em>](http://en.wikipedia.org/wiki/Radix_sort) arranges
   * items into ascending (or descending) order.  The algorithm 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.
   *
   * \par
   * DeviceRadixSort 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.  Although the direct radix sorting
   * method can only be applied to unsigned integral types, DeviceRadixSort
   * is able to sort signed and floating-point types via simple bit-wise transformations
   * that ensure lexicographic key ordering.
   *
   * \par Usage Considerations
   * \cdp_class{DeviceRadixSort}
   *
   * \par Performance
   * \linear_performance{radix sort} The following chart illustrates DeviceRadixSort::SortKeys
   * performance across different CUDA architectures for uniform-random \p uint32 keys.
   * \plots_below
   *
   * \image html lsb_radix_sort_int32_keys.png
   *
   */
  struct DeviceRadixSort
  {
  
      /******************************************************************//**
       * 
  ame KeyT-value pairs
       *********************************************************************/
      //@{
  
      /**
       * \brief Sorts key-value pairs into ascending order. (~<em>2N </em>auxiliary storage required)
       *
       * \par
       * - The contents of the input data are not altered by the sorting operation
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageNP  For sorting using only <em>O</em>(<tt>P</tt>) temporary storage, see the sorting interface using DoubleBuffer wrappers below.
       * - \devicestorage
       *
       * \par Performance
       * The following charts illustrate saturated sorting performance across different
       * CUDA architectures for uniform-random <tt>uint32,uint32</tt> and
       * <tt>uint64,uint64</tt> pairs, respectively.
       *
       * \image html lsb_radix_sort_int32_pairs.png
       * \image html lsb_radix_sort_int64_pairs.png
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys
       * with associated vector of \p int values.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_keys_out;        // e.g., [        ...        ]
       * int  *d_values_in;       // e.g., [0, 1, 2, 3, 4, 5, 6]
       * int  *d_values_out;      // e.g., [        ...        ]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes,
       *     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes,
       *     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
       *
       * // d_keys_out            <-- [0, 3, 5, 6, 7, 8, 9]
       * // d_values_out          <-- [5, 4, 3, 1, 2, 0, 6]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       * \tparam ValueT    <b>[inferred]</b> ValueT type
       */
      template <
          typename            KeyT,
          typename            ValueT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortPairs(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          const KeyT          *d_keys_in,                             ///< [in] Pointer to the input data of key data to sort
          KeyT                *d_keys_out,                            ///< [out] Pointer to the sorted output sequence of key data
          const ValueT        *d_values_in,                           ///< [in] Pointer to the corresponding input sequence of associated value items
          ValueT              *d_values_out,                          ///< [out] Pointer to the correspondingly-reordered output sequence of associated value items
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          DoubleBuffer<KeyT>       d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
          DoubleBuffer<ValueT>     d_values(const_cast<ValueT*>(d_values_in), d_values_out);
  
          return DispatchRadixSort<false, KeyT, ValueT, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              false,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Sorts key-value pairs into ascending order. (~<em>N </em>auxiliary storage required)
       *
       * \par
       * - The sorting operation is given a pair of key buffers and a corresponding
       *   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
       *   structure that indicates which of the two buffers is "current" (and thus
       *   contains the input data to be sorted).
       * - The contents of both buffers within each pair may be altered by the sorting
       *   operation.
       * - Upon completion, the sorting operation will update the "current" indicator
       *   within each DoubleBuffer wrapper to reference which of the two buffers
       *   now contains the sorted output sequence (a function of the number of key bits
       *   specified and the targeted device architecture).
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageP
       * - \devicestorage
       *
       * \par Performance
       * The following charts illustrate saturated sorting performance across different
       * CUDA architectures for uniform-random <tt>uint32,uint32</tt> and
       * <tt>uint64,uint64</tt> pairs, respectively.
       *
       * \image html lsb_radix_sort_int32_pairs.png
       * \image html lsb_radix_sort_int64_pairs.png
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys
       * with associated vector of \p int values.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_key_alt_buf;     // e.g., [        ...        ]
       * int  *d_value_buf;       // e.g., [0, 1, 2, 3, 4, 5, 6]
       * int  *d_value_alt_buf;   // e.g., [        ...        ]
       * ...
       *
       * // Create a set of DoubleBuffers to wrap pairs of device pointers
       * cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
       * cub::DoubleBuffer<int> d_values(d_value_buf, d_value_alt_buf);
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
       *
       * // d_keys.Current()      <-- [0, 3, 5, 6, 7, 8, 9]
       * // d_values.Current()    <-- [5, 4, 3, 1, 2, 0, 6]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       * \tparam ValueT    <b>[inferred]</b> ValueT type
       */
      template <
          typename            KeyT,
          typename            ValueT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortPairs(
          void                    *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t                  &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          DoubleBuffer<KeyT>      &d_keys,                                ///< [in,out] Reference to the double-buffer of keys whose "current" device-accessible buffer contains the unsorted input keys and, upon return, is updated to point to the sorted output keys
          DoubleBuffer<ValueT>    &d_values,                              ///< [in,out] Double-buffer of values whose "current" device-accessible buffer contains the unsorted input values and, upon return, is updated to point to the sorted output values
          int                     num_items,                              ///< [in] Number of items to sort
          int                     begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                     end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t            stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                    debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          return DispatchRadixSort<false, KeyT, ValueT, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              true,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Sorts key-value pairs into descending order. (~<em>2N</em> auxiliary storage required).
       *
       * \par
       * - The contents of the input data are not altered by the sorting operation
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageNP  For sorting using only <em>O</em>(<tt>P</tt>) temporary storage, see the sorting interface using DoubleBuffer wrappers below.
       * - \devicestorage
       *
       * \par Performance
       * Performance is similar to DeviceRadixSort::SortPairs.
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys
       * with associated vector of \p int values.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_keys_out;        // e.g., [        ...        ]
       * int  *d_values_in;       // e.g., [0, 1, 2, 3, 4, 5, 6]
       * int  *d_values_out;      // e.g., [        ...        ]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortPairsDescending(d_temp_storage, temp_storage_bytes,
       *     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortPairsDescending(d_temp_storage, temp_storage_bytes,
       *     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
       *
       * // d_keys_out            <-- [9, 8, 7, 6, 5, 3, 0]
       * // d_values_out          <-- [6, 0, 2, 1, 3, 4, 5]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       * \tparam ValueT    <b>[inferred]</b> ValueT type
       */
      template <
          typename            KeyT,
          typename            ValueT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortPairsDescending(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          const KeyT          *d_keys_in,                             ///< [in] Pointer to the input data of key data to sort
          KeyT                *d_keys_out,                            ///< [out] Pointer to the sorted output sequence of key data
          const ValueT        *d_values_in,                           ///< [in] Pointer to the corresponding input sequence of associated value items
          ValueT              *d_values_out,                          ///< [out] Pointer to the correspondingly-reordered output sequence of associated value items
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          DoubleBuffer<KeyT>       d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
          DoubleBuffer<ValueT>     d_values(const_cast<ValueT*>(d_values_in), d_values_out);
  
          return DispatchRadixSort<true, KeyT, ValueT, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              false,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Sorts key-value pairs into descending order. (~<em>N </em>auxiliary storage required).
       *
       * \par
       * - The sorting operation is given a pair of key buffers and a corresponding
       *   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
       *   structure that indicates which of the two buffers is "current" (and thus
       *   contains the input data to be sorted).
       * - The contents of both buffers within each pair may be altered by the sorting
       *   operation.
       * - Upon completion, the sorting operation will update the "current" indicator
       *   within each DoubleBuffer wrapper to reference which of the two buffers
       *   now contains the sorted output sequence (a function of the number of key bits
       *   specified and the targeted device architecture).
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageP
       * - \devicestorage
       *
       * \par Performance
       * Performance is similar to DeviceRadixSort::SortPairs.
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys
       * with associated vector of \p int values.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_key_alt_buf;     // e.g., [        ...        ]
       * int  *d_value_buf;       // e.g., [0, 1, 2, 3, 4, 5, 6]
       * int  *d_value_alt_buf;   // e.g., [        ...        ]
       * ...
       *
       * // Create a set of DoubleBuffers to wrap pairs of device pointers
       * cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
       * cub::DoubleBuffer<int> d_values(d_value_buf, d_value_alt_buf);
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortPairsDescending(d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortPairsDescending(d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
       *
       * // d_keys.Current()      <-- [9, 8, 7, 6, 5, 3, 0]
       * // d_values.Current()    <-- [6, 0, 2, 1, 3, 4, 5]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       * \tparam ValueT    <b>[inferred]</b> ValueT type
       */
      template <
          typename            KeyT,
          typename            ValueT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortPairsDescending(
          void                    *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t                  &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          DoubleBuffer<KeyT>      &d_keys,                                ///< [in,out] Reference to the double-buffer of keys whose "current" device-accessible buffer contains the unsorted input keys and, upon return, is updated to point to the sorted output keys
          DoubleBuffer<ValueT>    &d_values,                              ///< [in,out] Double-buffer of values whose "current" device-accessible buffer contains the unsorted input values and, upon return, is updated to point to the sorted output values
          int                     num_items,                              ///< [in] Number of items to sort
          int                     begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                     end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t            stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                    debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          return DispatchRadixSort<true, KeyT, ValueT, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              true,
              stream,
              debug_synchronous);
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Keys-only
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Sorts keys into ascending order. (~<em>2N </em>auxiliary storage required)
       *
       * \par
       * - The contents of the input data are not altered by the sorting operation
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageNP  For sorting using only <em>O</em>(<tt>P</tt>) temporary storage, see the sorting interface using DoubleBuffer wrappers below.
       * - \devicestorage
       *
       * \par Performance
       * The following charts illustrate saturated sorting performance across different
       * CUDA architectures for uniform-random \p uint32 and \p uint64 keys, respectively.
       *
       * \image html lsb_radix_sort_int32_keys.png
       * \image html lsb_radix_sort_int64_keys.png
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_keys_out;        // e.g., [        ...        ]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortKeys(d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortKeys(d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
       *
       * // d_keys_out            <-- [0, 3, 5, 6, 7, 8, 9]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       */
      template <typename KeyT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortKeys(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          const KeyT          *d_keys_in,                             ///< [in] Pointer to the input data of key data to sort
          KeyT                *d_keys_out,                            ///< [out] Pointer to the sorted output sequence of key data
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // Null value type
          DoubleBuffer<KeyT>      d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
          DoubleBuffer<NullType>  d_values;
  
          return DispatchRadixSort<false, KeyT, NullType, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              false,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Sorts keys into ascending order. (~<em>N </em>auxiliary storage required).
       *
       * \par
       * - The sorting operation is given a pair of key buffers managed by a
       *   DoubleBuffer structure that indicates which of the two buffers is
       *   "current" (and thus contains the input data to be sorted).
       * - The contents of both buffers may be altered by the sorting operation.
       * - Upon completion, the sorting operation will update the "current" indicator
       *   within the DoubleBuffer wrapper to reference which of the two buffers
       *   now contains the sorted output sequence (a function of the number of key bits
       *   specified and the targeted device architecture).
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageP
       * - \devicestorage
       *
       * \par Performance
       * The following charts illustrate saturated sorting performance across different
       * CUDA architectures for uniform-random \p uint32 and \p uint64 keys, respectively.
       *
       * \image html lsb_radix_sort_int32_keys.png
       * \image html lsb_radix_sort_int64_keys.png
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_key_alt_buf;     // e.g., [        ...        ]
       * ...
       *
       * // Create a DoubleBuffer to wrap the pair of device pointers
       * cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortKeys(d_temp_storage, temp_storage_bytes, d_keys, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortKeys(d_temp_storage, temp_storage_bytes, d_keys, num_items);
       *
       * // d_keys.Current()      <-- [0, 3, 5, 6, 7, 8, 9]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       */
      template <typename KeyT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortKeys(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          DoubleBuffer<KeyT>  &d_keys,                                ///< [in,out] Reference to the double-buffer of keys whose "current" device-accessible buffer contains the unsorted input keys and, upon return, is updated to point to the sorted output keys
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // Null value type
          DoubleBuffer<NullType> d_values;
  
          return DispatchRadixSort<false, KeyT, NullType, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              true,
              stream,
              debug_synchronous);
      }
  
      /**
       * \brief Sorts keys into descending order. (~<em>2N</em> auxiliary storage required).
       *
       * \par
       * - The contents of the input data are not altered by the sorting operation
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageNP  For sorting using only <em>O</em>(<tt>P</tt>) temporary storage, see the sorting interface using DoubleBuffer wrappers below.
       * - \devicestorage
       *
       * \par Performance
       * Performance is similar to DeviceRadixSort::SortKeys.
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_keys_out;        // e.g., [        ...        ]
       * ...
       *
       * // Create a DoubleBuffer to wrap the pair of device pointers
       * cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortKeysDescending(d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortKeysDescending(d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
       *
       * // d_keys_out            <-- [9, 8, 7, 6, 5, 3, 0]s
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       */
      template <typename KeyT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortKeysDescending(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          const KeyT          *d_keys_in,                             ///< [in] Pointer to the input data of key data to sort
          KeyT                *d_keys_out,                            ///< [out] Pointer to the sorted output sequence of key data
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          DoubleBuffer<KeyT>      d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
          DoubleBuffer<NullType>  d_values;
  
          return DispatchRadixSort<true, KeyT, NullType, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              false,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Sorts keys into descending order. (~<em>N </em>auxiliary storage required).
       *
       * \par
       * - The sorting operation is given a pair of key buffers managed by a
       *   DoubleBuffer structure that indicates which of the two buffers is
       *   "current" (and thus contains the input data to be sorted).
       * - The contents of both buffers may be altered by the sorting operation.
       * - Upon completion, the sorting operation will update the "current" indicator
       *   within the DoubleBuffer wrapper to reference which of the two buffers
       *   now contains the sorted output sequence (a function of the number of key bits
       *   specified and the targeted device architecture).
       * - An optional bit subrange <tt>[begin_bit, end_bit)</tt> of differentiating key bits can be specified.  This can reduce overall sorting overhead and yield a corresponding performance improvement.
       * - \devicestorageP
       * - \devicestorage
       *
       * \par Performance
       * Performance is similar to DeviceRadixSort::SortKeys.
       *
       * \par Snippet
       * The code snippet below illustrates the sorting of a device vector of \p int keys.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for sorting data
       * int  num_items;          // e.g., 7
       * int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int  *d_key_alt_buf;     // e.g., [        ...        ]
       * ...
       *
       * // Create a DoubleBuffer to wrap the pair of device pointers
       * cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceRadixSort::SortKeysDescending(d_temp_storage, temp_storage_bytes, d_keys, num_items);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sorting operation
       * cub::DeviceRadixSort::SortKeysDescending(d_temp_storage, temp_storage_bytes, d_keys, num_items);
       *
       * // d_keys.Current()      <-- [9, 8, 7, 6, 5, 3, 0]
       *
       * \endcode
       *
       * \tparam KeyT      <b>[inferred]</b> KeyT type
       */
      template <typename KeyT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t SortKeysDescending(
          void                *d_temp_storage,                        ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                    ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          DoubleBuffer<KeyT>  &d_keys,                                ///< [in,out] Reference to the double-buffer of keys whose "current" device-accessible buffer contains the unsorted input keys and, upon return, is updated to point to the sorted output keys
          int                 num_items,                              ///< [in] Number of items to sort
          int                 begin_bit           = 0,                ///< [in] <b>[optional]</b> The least-significant bit index (inclusive)  needed for key comparison
          int                 end_bit             = sizeof(KeyT) * 8, ///< [in] <b>[optional]</b> The most-significant bit index (exclusive) needed for key comparison (e.g., sizeof(unsigned int) * 8)
          cudaStream_t        stream              = 0,                ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)            ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // Null value type
          DoubleBuffer<NullType> d_values;
  
          return DispatchRadixSort<true, KeyT, NullType, OffsetT>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_keys,
              d_values,
              num_items,
              begin_bit,
              end_bit,
              true,
              stream,
              debug_synchronous);
      }
  
  
      //@}  end member group
  
  
  };
  
  /**
   * \example example_device_radix_sort.cu
   */
  
  }               // CUB namespace
  CUB_NS_POSTFIX  // Optional outer namespace(s)