install/include/cub/block/block_radix_sort.cuh

/******************************************************************************
 * Copyright (c) 2011, Duane Merrill.  All rights reserved.
 * Copyright (c) 2011-2018, NVIDIA CORPORATION.  All rights reserved.
 * 
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 * modification, are permitted provided that the following conditions are met:
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 *       names of its contributors may be used to endorse or promote products
 *       derived from this software without specific prior written permission.
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/**
 * \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 "radix_rank_sort_operations.cuh"
#include "../config.cuh"
#include "../util_ptx.cuh"
#include "../util_type.cuh"

CUB_NAMESPACE_BEGIN

//! @rst
//! BlockRadixSort class provides :ref:`collective <collective-primitives>` methods for sorting 
//! items partitioned across a CUDA thread block using a radix sorting method.  
//!
//! .. image:: ../img/sorting_logo.png
//!     :align: center
//!
//! Overview
//! --------------------------------------------------
//!
//! The `radix sorting method <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.
//!
//! @rowmajor
//!
//! Supported Types
//! --------------------------------------------------
//!
//! BlockRadixSort can sort all of the built-in C++ numeric primitive types
//! (``unsigned char``, ``int``, ``double``, etc.) as well as CUDA's ``__half``
//! half-precision floating-point type. User-defined types are supported as long
//! as decomposer object is provided.
//!
//! Floating-Point Special Cases
//! --------------------------------------------------
//!
//! - Positive and negative zeros are considered equivalent, and will be treated
//!   as such in the output.
//! - No special handling is implemented for NaN values; these are sorted
//!   according to their bit representations after any transformations.
//!
//! Bitwise Key Transformations
//! --------------------------------------------------
//!
//! 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.
//!
//! These transformations must be considered when restricting the
//! ``[begin_bit, end_bit)`` range, as the bitwise transformations will occur
//! before the bit-range truncation.
//!
//! Any transformations applied to the keys prior to sorting are reversed
//! while writing to the final output buffer.
//!
//! Type Specific Bitwise Transformations
//! --------------------------------------------------
//!
//! To convert the input values into a radix-sortable bitwise representation,
//! the following transformations take place prior to sorting:
//!
//! * For unsigned integral values, the keys are used directly.
//! * For signed integral values, the sign bit is inverted.
//! * For positive floating point values, the sign bit is inverted.
//! * For negative floating point values, the full key is inverted.
//!
//! No Descending Sort Transformations
//! --------------------------------------------------
//!
//! Unlike ``DeviceRadixSort``, ``BlockRadixSort`` does not invert the input key bits
//! when performing a descending sort. Instead, it has special logic to reverse
//! the order of the keys while sorting.
//!
//! Stability
//! --------------------------------------------------
//!
//! BlockRadixSort is stable. For floating-point types -0.0 and +0.0
//! are considered equal and appear in the result in the same order as they
//! appear in the input.
//!
//!
//! Performance Considerations
//! --------------------------------------------------
//!
//! * @granularity
//!
//! A Simple Example
//! --------------------------------------------------
//!
//! @blockcollective{BlockRadixSort}
//!
//! 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.
//!
//! .. code-block:: c++
//!
//!     #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);
//!
//!         ...
//!
//! Suppose the set of input ``thread_keys`` across the block of threads is
//! ``{ [0,511,1,510], [2,509,3,508], [4,507,5,506], ..., [254,257,255,256] }``.  
//! The corresponding output ``thread_keys`` in those threads will be
//! ``{ [0,1,2,3], [4,5,6,7], [8,9,10,11], ..., [508,509,510,511] }``.
//!
//! Re-using dynamically allocating shared memory
//! --------------------------------------------------
//!
//! The following example under the examples/block folder illustrates usage of
//! dynamically shared memory with BlockReduce and how to re-purpose
//! the same memory region:
//! <a href="../../examples/block/example_block_reduce_dyn_smem.cu">example_block_reduce_dyn_smem.cu</a>
//!
//! This example can be easily adapted to the storage required by BlockRadixSort.
//! @endrst
//!
//! @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               
//!   **[optional]** ValueT type (default: cub::NullType, which indicates a keys-only sort)
//!
//! @tparam RADIX_BITS           
//!   **[optional]** The number of radix bits per digit place (default: 4 bits)
//!
//! @tparam MEMOIZE_OUTER_SCAN   
//!  **[optional]** 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 
//!   **[optional]** The cub::BlockScanAlgorithm algorithm to use 
//!   (default: cub::BLOCK_SCAN_WARP_SCANS)
//!
//! @tparam SMEM_CONFIG          
//!   **[optional]*8 Shared memory bank mode (default: `cudaSharedMemBankSizeFourByte`)
//!
//! @tparam BLOCK_DIM_Y          
//!   **[optional]** The thread block length in threads along the Y dimension (default: 1)
//!
//! @tparam BLOCK_DIM_Z          
//!   **[optional]** The thread block length in threads along the Z dimension (default: 1)
//!
//! @tparam LEGACY_PTX_ARCH      
//!   **[optional]** Unused
template <
    typename                KeyT,
    int                     BLOCK_DIM_X,
    int                     ITEMS_PER_THREAD,
    typename                ValueT                   = NullType,
    int                     RADIX_BITS              = 4,
    bool                    MEMOIZE_OUTER_SCAN      = true,
    BlockScanAlgorithm      INNER_SCAN_ALGORITHM    = BLOCK_SCAN_WARP_SCANS,
    cudaSharedMemConfig     SMEM_CONFIG             = cudaSharedMemBankSizeFourByte,
    int                     BLOCK_DIM_Y             = 1,
    int                     BLOCK_DIM_Z             = 1,
    int                     LEGACY_PTX_ARCH         = 0>
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                   = std::is_same<ValueT, NullType>::value,
    };

    // KeyT traits and unsigned bits type
    using traits = detail::radix::traits_t<KeyT>;
    using bit_ordered_type = typename traits::bit_ordered_type;
    using bit_ordered_conversion = typename traits::bit_ordered_conversion_policy;

    /// 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>
        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>
        DescendingBlockRadixRank;

    /// Digit extractor type
    using fundamental_digit_extractor_t = BFEDigitExtractor<KeyT>;

    /// BlockExchange utility type for keys
    typedef BlockExchange<KeyT, BLOCK_DIM_X, ITEMS_PER_THREAD, false, BLOCK_DIM_Y, BLOCK_DIM_Z> BlockExchangeKeys;

    /// BlockExchange utility type for values
    typedef BlockExchange<ValueT, BLOCK_DIM_X, ITEMS_PER_THREAD, false, BLOCK_DIM_Y, BLOCK_DIM_Z> 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)
    template <class DigitExtractorT>
    __device__ __forceinline__ void RankKeys(
        bit_ordered_type  (&unsigned_keys)[ITEMS_PER_THREAD],
        int               (&ranks)[ITEMS_PER_THREAD],
        DigitExtractorT   digit_extractor,
        Int2Type<false>   /*is_descending*/)
    {
        AscendingBlockRadixRank(temp_storage.asending_ranking_storage).RankKeys(
                unsigned_keys,
                ranks,
                digit_extractor);
    }

    /// Rank keys (specialized for descending sort)
    template <class DigitExtractorT>
    __device__ __forceinline__ void RankKeys(
        bit_ordered_type  (&unsigned_keys)[ITEMS_PER_THREAD],
        int               (&ranks)[ITEMS_PER_THREAD],
        DigitExtractorT   digit_extractor,
        Int2Type<true>    /*is_descending*/)
    {
        DescendingBlockRadixRank(temp_storage.descending_ranking_storage).RankKeys(
                unsigned_keys,
                ranks,
                digit_extractor);
    }

    /// 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, class DecomposerT = detail::identity_decomposer_t>
    __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
        DecomposerT             decomposer = {})
    {
        bit_ordered_type (&unsigned_keys)[ITEMS_PER_THREAD] =
            reinterpret_cast<bit_ordered_type(&)[ITEMS_PER_THREAD]>(keys);

        #pragma unroll
        for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
        {
            unsigned_keys[KEY] = bit_ordered_conversion::to_bit_ordered(decomposer, unsigned_keys[KEY]);
        }

        // Radix sorting passes
        while (true)
        {
            int pass_bits = CUB_MIN(RADIX_BITS, end_bit - begin_bit);
            auto digit_extractor = traits::template digit_extractor<fundamental_digit_extractor_t>(begin_bit, pass_bits, decomposer);

            // Rank the blocked keys
            int ranks[ITEMS_PER_THREAD];
            RankKeys(unsigned_keys, ranks, digit_extractor, 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] = bit_ordered_conversion::from_bit_ordered(decomposer, unsigned_keys[KEY]);
        }
    }

public:

#ifndef DOXYGEN_SHOULD_SKIP_THIS    // Do not document

    /// Sort blocked -> striped arrangement
    template <int DESCENDING, int KEYS_ONLY, class DecomposerT = detail::identity_decomposer_t>
    __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
        DecomposerT             decomposer = {})
    {
        bit_ordered_type (&unsigned_keys)[ITEMS_PER_THREAD] =
            reinterpret_cast<bit_ordered_type (&)[ITEMS_PER_THREAD]>(keys);

        #pragma unroll
        for (int KEY = 0; KEY < ITEMS_PER_THREAD; KEY++)
        {
            unsigned_keys[KEY] = bit_ordered_conversion::to_bit_ordered(decomposer, unsigned_keys[KEY]);
        }

        // Radix sorting passes
        while (true)
        {
            int pass_bits = CUB_MIN(RADIX_BITS, end_bit - begin_bit);
            auto digit_extractor = traits::template digit_extractor<fundamental_digit_extractor_t>(begin_bit, pass_bits, decomposer);

            // Rank the blocked keys
            int ranks[ITEMS_PER_THREAD];
            RankKeys(unsigned_keys, ranks, digit_extractor, 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] = bit_ordered_conversion::from_bit_ordered(decomposer, unsigned_keys[KEY]);
        }
    }

#endif // DOXYGEN_SHOULD_SKIP_THIS

    /// \smemstorage{BlockRadixSort}
    struct TempStorage : Uninitialized<_TempStorage> {};


    /******************************************************************//**
     * \name 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
    /******************************************************************//**
     * \name 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>());
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 2 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 1 key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-bits
    //!     :end-before: example-end keys-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      Sort(KeyT (&keys)[ITEMS_PER_THREAD], DecomposerT decomposer, int begin_bit, int end_bit)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlocked(keys,
                    values,
                    begin_bit,
                    end_bit,
                    Int2Type<false>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive keys.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys
    //!     :end-before: example-end keys
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      Sort(KeyT (&keys)[ITEMS_PER_THREAD], DecomposerT decomposer)
    {
        Sort(keys, decomposer, 0, detail::radix::traits_t<KeyT>::default_end_bit(decomposer));
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values.
    //!
    //! * 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
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 2 keys and values that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 1 pair.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-bits
    //!     :end-before: example-end pairs-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      Sort(KeyT (&keys)[ITEMS_PER_THREAD],
           ValueT (&values)[ITEMS_PER_THREAD],
           DecomposerT decomposer,
           int begin_bit,
           int end_bit)
    {
        SortBlocked(keys,
                    values,
                    begin_bit,
                    end_bit,
                    Int2Type<false>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values.
    //!
    //! * 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
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys and values that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive pairs.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs
    //!     :end-before: example-end pairs
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      Sort(KeyT (&keys)[ITEMS_PER_THREAD],
           ValueT (&values)[ITEMS_PER_THREAD],
           DecomposerT decomposer)
    {
        Sort(keys,
             values,
             decomposer,
             0,
             detail::radix::traits_t<KeyT>::default_end_bit(decomposer));
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 2 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 1 key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-descending-bits
    //!     :end-before: example-end keys-descending-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescending(KeyT (&keys)[ITEMS_PER_THREAD],
                     DecomposerT decomposer,
                     int begin_bit,
                     int end_bit)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlocked(keys,
                    values,
                    begin_bit,
                    end_bit,
                    Int2Type<true>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive keys.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-descending
    //!     :end-before: example-end keys-descending
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescending(KeyT (&keys)[ITEMS_PER_THREAD], DecomposerT decomposer)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlocked(keys,
                    values,
                    0,
                    detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                    Int2Type<true>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values.
    //!
    //! * 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
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 2 pairs that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 1 pair.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-descending-bits
    //!     :end-before: example-end pairs-descending-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescending(KeyT (&keys)[ITEMS_PER_THREAD],
                     ValueT (&values)[ITEMS_PER_THREAD],
                     DecomposerT decomposer,
                     int begin_bit,
                     int end_bit)
    {
        SortBlocked(keys,
                    values,
                    begin_bit,
                    end_bit,
                    Int2Type<true>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values.
    //!
    //! * 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
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys and values that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive pairs.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-descending
    //!     :end-before: example-end pairs-descending
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescending(KeyT (&keys)[ITEMS_PER_THREAD],
                     ValueT (&values)[ITEMS_PER_THREAD],
                     DecomposerT decomposer)
    {
        SortBlocked(keys,
                    values,
                    0,
                    detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                    Int2Type<true>(),
                    Int2Type<KEYS_ONLY>(),
                    decomposer);
    }

    //@}  end member group
    /******************************************************************//**
     * \name 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>());
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 4 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 2 consecutive keys. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-striped-bits
    //!     :end-before: example-end keys-striped-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                           DecomposerT decomposer,
                           int begin_bit,
                           int end_bit)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlockedToStriped(keys,
                             values,
                             begin_bit,
                             end_bit,
                             Int2Type<false>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive keys. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-striped
    //!     :end-before: example-end keys-striped
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD], DecomposerT decomposer)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlockedToStriped(keys,
                             values,
                             0,
                             detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                             Int2Type<false>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 4 pairs that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 2 consecutive pairs. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-striped-bits
    //!     :end-before: example-end pairs-striped-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                           ValueT (&values)[ITEMS_PER_THREAD],
                           DecomposerT decomposer,
                           int begin_bit,
                           int end_bit)
    {
        SortBlockedToStriped(keys,
                             values,
                             begin_bit,
                             end_bit,
                             Int2Type<false>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    //! @rst
    //! Performs an ascending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 pairs that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive pairs. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-striped
    //!     :end-before: example-end pairs-striped
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                           ValueT (&values)[ITEMS_PER_THREAD],
                           DecomposerT decomposer)
    {
        SortBlockedToStriped(keys,
                             values,
                             0,
                             detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                             Int2Type<false>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 4 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 2 consecutive keys. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-striped-descending-bits
    //!     :end-before: example-end keys-striped-descending-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescendingBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                                     DecomposerT decomposer,
                                     int begin_bit,
                                     int end_bit)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlockedToStriped(keys,
                             values,
                             begin_bit,
                             end_bit,
                             Int2Type<true>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive keys. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin keys-striped-descending
    //!     :end-before: example-end keys-striped-descending
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescendingBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD], DecomposerT decomposer)
    {
        NullType values[ITEMS_PER_THREAD];

        SortBlockedToStriped(keys,
                             values,
                             0,
                             detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                             Int2Type<true>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    /**
     * \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>());
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 4 keys and values that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 2 consecutive pairs. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-striped-descending-bits
    //!     :end-before: example-end pairs-striped-descending-bits
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    //!
    //! @param[in] begin_bit 
    //!   The least-significant bit index (inclusive) needed for 
    //!   key comparison
    //!
    //! @param[in] end_bit 
    //!   The most-significant bit index (exclusive) needed for key 
    //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescendingBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                                     ValueT (&values)[ITEMS_PER_THREAD],
                                     DecomposerT decomposer,
                                     int begin_bit,
                                     int end_bit)
    {
        SortBlockedToStriped(keys,
                             values,
                             begin_bit,
                             end_bit,
                             Int2Type<true>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    //! @rst
    //! Performs a descending block-wide radix sort over a 
    //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys and values, leaving them in a 
    //! :ref:`striped arrangement <flexible-data-arrangement>`.
    //!
    //! * @granularity
    //! * @smemreuse
    //!
    //! Snippet
    //! ==========================================================================
    //!
    //! Let's consider a user-defined ``custom_t`` type below. To sort an array of
    //! ``custom_t`` objects, we have to tell CUB about relevant members of the
    //! ``custom_t`` type. We do this by providing a decomposer that returns a
    //! tuple of references to relevant members of the key. 
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin custom-type
    //!     :end-before: example-end custom-type
    //!
    //! The code snippet below illustrates a sort of 6 keys and values that
    //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 2 threads
    //! where each thread owns 3 consecutive pairs. The final partitioning is striped.
    //!
    //! .. literalinclude:: ../../test/catch2_test_block_radix_sort_custom.cu
    //!     :language: c++
    //!     :dedent:
    //!     :start-after: example-begin pairs-striped-descending
    //!     :end-before: example-end pairs-striped-descending
    //!
    //! @endrst
    //!
    //! @tparam DecomposerT
    //!   **[inferred]** Type of a callable object responsible for decomposing a 
    //!   ``KeyT`` into a tuple of references to its constituent arithmetic types:
    //!   ``::cuda::std::tuple<ArithmeticTs&...> operator()(KeyT &key)``. 
    //!   The leftmost element of the tuple is considered the most significant. 
    //!   The call operator must not modify members of the key.
    //!
    //! @param[in,out] keys 
    //!   Keys to sort
    //!
    //! @param[in,out] values
    //!   Values to sort
    //!
    //! @param decomposer
    //!   Callable object responsible for decomposing a ``KeyT`` into a tuple of
    //!   references to its constituent arithmetic types. The leftmost element of 
    //!   the tuple is considered the most significant. The call operator must not 
    //!   modify members of the key.
    template <class DecomposerT>
    __device__ __forceinline__         //
      typename ::cuda::std::enable_if< //
        !::cuda::std::is_convertible<DecomposerT, int>::value>::type
      SortDescendingBlockedToStriped(KeyT (&keys)[ITEMS_PER_THREAD],
                                     ValueT (&values)[ITEMS_PER_THREAD],
                                     DecomposerT decomposer)
    {
        SortBlockedToStriped(keys,
                             values,
                             0,
                             detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
                             Int2Type<true>(),
                             Int2Type<KEYS_ONLY>(),
                             decomposer);
    }

    //@}  end member group

};

/**
 * \example example_block_radix_sort.cu
 */

CUB_NAMESPACE_END