// SPDX-FileCopyrightText: Copyright (c) 2011, Duane Merrill. All rights reserved.
// SPDX-FileCopyrightText: Copyright (c) 2011-2018, NVIDIA CORPORATION. All rights reserved.
// SPDX-License-Identifier: BSD-3

/**
 * @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 <cub/config.cuh>

#if defined(_CCCL_IMPLICIT_SYSTEM_HEADER_GCC)
#  pragma GCC system_header
#elif defined(_CCCL_IMPLICIT_SYSTEM_HEADER_CLANG)
#  pragma clang system_header
#elif defined(_CCCL_IMPLICIT_SYSTEM_HEADER_MSVC)
#  pragma system_header
#endif // no system header

#include <cub/block/block_exchange.cuh>
#include <cub/block/block_radix_rank.cuh>
#include <cub/block/radix_rank_sort_operations.cuh>
#include <cub/util_ptx.cuh>
#include <cub/util_type.cuh>

#include <cuda/std/__algorithm/min.h>
#include <cuda/std/__type_traits/enable_if.h>
#include <cuda/std/__type_traits/integral_constant.h>
#include <cuda/std/__type_traits/is_convertible.h>
#include <cuda/std/__type_traits/is_same.h>

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.
//!
//! .. tab-set-code::
//!
//!    .. code-block:: c++
//!
//!        #include <cub/cub.cuh>   // or equivalently <cub/block/block_radix_sort.cuh>
//!
//!        __global__ void kernel(...)
//!        {
//!            // Specialize BlockRadixSort for a 1D block of 128 threads owning 4 integer items each
//!            using BlockRadixSort = cub::BlockRadixSort<int, 128, 4>;
//!
//!            // 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);
//!
//!            ...
//!
//!    .. code-block:: python
//!
//!        from cuda import coop
//!        from pynvjitlink import patch
//!        patch.patch_numba_linker(lto=True)
//!
//!        # Specialize radix sort for a 1D block of 128 threads owning 4 integer items each
//!        block_radix_sort = coop.block.radix_sort_keys(numba.int32, 128, 4)
//!        temp_storage_bytes = block_radix_sort.temp_storage_bytes
//!
//!        @cuda.jit(link=block_radix_sort.files)
//!        def kernel():
//!            Allocate shared memory for radix sort
//!            temp_storage = cuda.shared.array(shape=temp_storage_bytes, dtype='uint8')
//!
//!            # Obtain a segment of consecutive items that are blocked across threads
//!            thread_keys = cuda.local.array(shape=items_per_thread, dtype=numba.int32)
//!            # ...
//!
//!            // Collectively sort the keys
//!            block_radix_sort(temp_storage, 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 ``block/example_block_reduce_dyn_smem.cu`` example illustrates usage of dynamically shared memory with
//! BlockReduce and how to re-purpose the same memory region.
//!
//! This example can be easily adapted to the storage required by BlockRadixSort.
//! @endrst
//!
//! @tparam KeyT
//!   KeyT type
//!
//! @tparam BlockDimX
//!   The thread block length in threads along the X dimension
//!
//! @tparam ItemsPerThread
//!   The number of items per thread
//!
//! @tparam ValueT
//!   **[optional]** ValueT type (default: cub::NullType, which indicates a keys-only sort)
//!
//! @tparam RadixBits
//!   **[optional]** The number of radix bits per digit place (default: 4 bits)
//!
//! @tparam MemoizeOuterScan
//!  **[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 InnerScanAlgorithm
//!   **[optional]** The cub::BlockScanAlgorithm algorithm to use
//!   (default: cub::BLOCK_SCAN_WARP_SCANS)
//!
//! @tparam SMemConfig
//!   **[optional]*8 Shared memory bank mode (default: `cudaSharedMemBankSizeFourByte`)
//!
//! @tparam BlockDimY
//!   **[optional]** The thread block length in threads along the Y dimension (default: 1)
//!
//! @tparam BlockDimZ
//!   **[optional]** The thread block length in threads along the Z dimension (default: 1)
//!
template <typename KeyT,
          int BlockDimX,
          int ItemsPerThread,
          typename ValueT                       = NullType,
          int RadixBits                         = 4,
          bool MemoizeOuterScan                 = true,
          BlockScanAlgorithm InnerScanAlgorithm = BLOCK_SCAN_WARP_SCANS,
          cudaSharedMemConfig SMemConfig        = cudaSharedMemBankSizeFourByte,
          int BlockDimY                         = 1,
          int BlockDimZ                         = 1>
class BlockRadixSort
{
private:
  /******************************************************************************
   * Constants and type definitions
   ******************************************************************************/

  // The thread block size in threads
  static constexpr int BLOCK_THREADS = BlockDimX * BlockDimY * BlockDimZ;

  // Whether or not there are values to be trucked along with keys
  static constexpr bool KEYS_ONLY = ::cuda::std::is_same_v<ValueT, NullType>;

  // 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
  using AscendingBlockRadixRank =
    BlockRadixRank<BlockDimX, RadixBits, false, MemoizeOuterScan, InnerScanAlgorithm, SMemConfig, BlockDimY, BlockDimZ>;

  /// Descending BlockRadixRank utility type
  using DescendingBlockRadixRank =
    BlockRadixRank<BlockDimX, RadixBits, true, MemoizeOuterScan, InnerScanAlgorithm, SMemConfig, BlockDimY, BlockDimZ>;

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

  /// BlockExchange utility type for keys
  using BlockExchangeKeys = BlockExchange<KeyT, BlockDimX, ItemsPerThread, false, BlockDimY, BlockDimZ>;

  /// BlockExchange utility type for values
  using BlockExchangeValues = BlockExchange<ValueT, BlockDimX, ItemsPerThread, false, BlockDimY, BlockDimZ>;

#ifndef _CCCL_DOXYGEN_INVOKED // Do not document
  /// 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;
  };
#endif // _CCCL_DOXYGEN_INVOKED

  /******************************************************************************
   * Thread fields
   ******************************************************************************/

  /// Shared storage reference
  _TempStorage& temp_storage;

  /// Linear thread-id
  unsigned int linear_tid;

  /******************************************************************************
   * Utility methods
   ******************************************************************************/

  /// Internal storage allocator
  _CCCL_DEVICE _CCCL_FORCEINLINE _TempStorage& PrivateStorage()
  {
    __shared__ _TempStorage private_storage;
    return private_storage;
  }

  /// Rank keys (specialized for ascending sort)
  template <class DigitExtractorT>
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  RankKeys(bit_ordered_type (&unsigned_keys)[ItemsPerThread],
           int (&ranks)[ItemsPerThread],
           DigitExtractorT digit_extractor,
           ::cuda::std::false_type /*is_descending*/)
  {
    AscendingBlockRadixRank(temp_storage.asending_ranking_storage).RankKeys(unsigned_keys, ranks, digit_extractor);
  }

  /// Rank keys (specialized for descending sort)
  template <class DigitExtractorT>
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  RankKeys(bit_ordered_type (&unsigned_keys)[ItemsPerThread],
           int (&ranks)[ItemsPerThread],
           DigitExtractorT digit_extractor,
           ::cuda::std::true_type /*is_descending*/)
  {
    DescendingBlockRadixRank(temp_storage.descending_ranking_storage).RankKeys(unsigned_keys, ranks, digit_extractor);
  }

  /// ExchangeValues (specialized for key-value sort, to-blocked arrangement)
  _CCCL_DEVICE _CCCL_FORCEINLINE void ExchangeValues(
    ValueT (&values)[ItemsPerThread],
    int (&ranks)[ItemsPerThread],
    ::cuda::std::false_type /*is_keys_only*/,
    ::cuda::std::true_type /*is_blocked*/)
  {
    __syncthreads();

    // 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)
  _CCCL_DEVICE _CCCL_FORCEINLINE void ExchangeValues(
    ValueT (&values)[ItemsPerThread],
    int (&ranks)[ItemsPerThread],
    ::cuda::std::false_type /*is_keys_only*/,
    ::cuda::std::false_type /*is_blocked*/)
  {
    __syncthreads();

    // Exchange values through shared memory in blocked arrangement
    BlockExchangeValues(temp_storage.exchange_values).ScatterToStriped(values, ranks);
  }

  /// ExchangeValues (specialized for keys-only sort)
  template <bool IS_BLOCKED>
  _CCCL_DEVICE _CCCL_FORCEINLINE void ExchangeValues(
    ValueT (& /*values*/)[ItemsPerThread],
    int (& /*ranks*/)[ItemsPerThread],
    ::cuda::std::true_type /*is_keys_only*/,
    ::cuda::std::bool_constant<IS_BLOCKED> /*is_blocked*/)
  {}

  /**
   * @brief Sort blocked arrangement
   *
   * @param keys
   *   Keys to sort
   *
   * @param values
   *   Values to sort
   *
   * @param begin_bit
   *   The beginning (least-significant) bit index needed for key comparison
   *
   * @param end_bit
   *   The past-the-end (most-significant) bit index needed for key comparison
   *
   * @param is_descending
   *   Tag whether is a descending-order sort
   *
   * @param is_keys_only
   *   Tag whether is keys-only sort
   */
  template <bool DESCENDING, bool KEYS_ONLY, class DecomposerT = detail::identity_decomposer_t>
  _CCCL_DEVICE _CCCL_FORCEINLINE void SortBlocked(
    KeyT (&keys)[ItemsPerThread],
    ValueT (&values)[ItemsPerThread],
    int begin_bit,
    int end_bit,
    ::cuda::std::bool_constant<DESCENDING> is_descending,
    ::cuda::std::bool_constant<KEYS_ONLY> is_keys_only,
    DecomposerT decomposer = {})
  {
    bit_ordered_type(&unsigned_keys)[ItemsPerThread] = reinterpret_cast<bit_ordered_type(&)[ItemsPerThread]>(keys);

    _CCCL_PRAGMA_UNROLL_FULL()
    for (int KEY = 0; KEY < ItemsPerThread; KEY++)
    {
      unsigned_keys[KEY] = bit_ordered_conversion::to_bit_ordered(decomposer, unsigned_keys[KEY]);
    }

    // Radix sorting passes
    while (true)
    {
      int pass_bits = ::cuda::std::min(RadixBits, 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[ItemsPerThread];
      RankKeys(unsigned_keys, ranks, digit_extractor, is_descending);
      begin_bit += RadixBits;

      __syncthreads();

      // 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, ::cuda::std::true_type());

      // Quit if done
      if (begin_bit >= end_bit)
      {
        break;
      }

      __syncthreads();
    }

    // Untwiddle bits if necessary
    _CCCL_PRAGMA_UNROLL_FULL()
    for (int KEY = 0; KEY < ItemsPerThread; KEY++)
    {
      unsigned_keys[KEY] = bit_ordered_conversion::from_bit_ordered(decomposer, unsigned_keys[KEY]);
    }
  }

public:
#ifndef _CCCL_DOXYGEN_INVOKED // Do not document

  /**
   * @brief Sort blocked -> striped arrangement
   *
   * @param keys
   *   Keys to sort
   *
   * @param values
   *   Values to sort
   *
   * @param begin_bit
   *   The beginning (least-significant) bit index needed for key comparison
   *
   * @param end_bit
   *   The past-the-end (most-significant) bit index needed for key comparison
   *
   * @param is_descending
   *   Tag whether is a descending-order sort
   *
   * @param is_keys_only
   *   Tag whether is keys-only sort
   */
  template <bool DESCENDING, bool KEYS_ONLY, class DecomposerT = detail::identity_decomposer_t>
  _CCCL_DEVICE _CCCL_FORCEINLINE void SortBlockedToStriped(
    KeyT (&keys)[ItemsPerThread],
    ValueT (&values)[ItemsPerThread],
    int begin_bit,
    int end_bit,
    ::cuda::std::bool_constant<DESCENDING> is_descending,
    ::cuda::std::bool_constant<KEYS_ONLY> is_keys_only,
    DecomposerT decomposer = {})
  {
    bit_ordered_type(&unsigned_keys)[ItemsPerThread] = reinterpret_cast<bit_ordered_type(&)[ItemsPerThread]>(keys);

    _CCCL_PRAGMA_UNROLL_FULL()
    for (int KEY = 0; KEY < ItemsPerThread; KEY++)
    {
      unsigned_keys[KEY] = bit_ordered_conversion::to_bit_ordered(decomposer, unsigned_keys[KEY]);
    }

    // Radix sorting passes
    while (true)
    {
      int pass_bits = ::cuda::std::min(RadixBits, 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[ItemsPerThread];
      RankKeys(unsigned_keys, ranks, digit_extractor, is_descending);
      begin_bit += RadixBits;

      __syncthreads();

      // 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, ::cuda::std::false_type());

        // 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, ::cuda::std::true_type());

      __syncthreads();
    }

    // Untwiddle bits if necessary
    _CCCL_PRAGMA_UNROLL_FULL()
    for (int KEY = 0; KEY < ItemsPerThread; KEY++)
    {
      unsigned_keys[KEY] = bit_ordered_conversion::from_bit_ordered(decomposer, unsigned_keys[KEY]);
    }
  }

#endif // _CCCL_DOXYGEN_INVOKED

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

  //! @name Collective constructors
  //! @{

  //! @brief Collective constructor using a private static allocation of shared memory as temporary storage.
  _CCCL_DEVICE _CCCL_FORCEINLINE BlockRadixSort()
      : temp_storage(PrivateStorage())
      , linear_tid(RowMajorTid(BlockDimX, BlockDimY, BlockDimZ))
  {}

  /**
   * @brief Collective constructor using the specified memory allocation as temporary storage.
   *
   * @param[in] temp_storage
   *   Reference to memory allocation having layout type TempStorage
   */
  _CCCL_DEVICE _CCCL_FORCEINLINE BlockRadixSort(TempStorage& temp_storage)
      : temp_storage(temp_storage.Alias())
      , linear_tid(RowMajorTid(BlockDimX, BlockDimY, BlockDimZ))
  {}

  //! @} end member group
  //! @name Sorting (blocked arrangements)
  //! @{

  //! @rst
  //! Performs an ascending block-wide radix sort over a
  //! :ref:`blocked arrangement <flexible-data-arrangement>` of keys.
  //!
  //! - @granularity
  //! - @smemreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys that
  //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128 threads
  //! where each thread owns 4 consecutive keys.
  //!
  //! .. 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 keys each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4>;
  //!
  //!        // 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] }``.
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  Sort(KeyT (&keys)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    NullType values[ItemsPerThread];

    SortBlocked(keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  Sort(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    NullType values[ItemsPerThread];

    SortBlocked(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  Sort(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer)
  {
    Sort(keys, decomposer, 0, detail::radix::traits_t<KeyT>::default_end_bit(decomposer));
  }

  //! @rst
  //! Performs an ascending block-wide radix sort across 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
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys and values that
  //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128 threads
  //! where each thread owns 4 consecutive pairs.
  //!
  //! .. 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 keys and values each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4, int>;
  //!
  //!        // 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 ``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] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in,out] values
  //!   Values to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void Sort(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    SortBlocked(keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  Sort(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    SortBlocked(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  Sort(KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer)
  {
    Sort(keys, values, decomposer, 0, detail::radix::traits_t<KeyT>::default_end_bit(decomposer));
  }

  //! @rst
  //! Performs a descending block-wide radix sort over a :ref:`blocked arrangement <flexible-data-arrangement>`
  //! of keys.
  //!
  //! - @granularity
  //! - @smemreuse
  //!
  //! 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.
  //!
  //! .. 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 keys each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4>;
  //!
  //!        // 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
  //! ``{ [511,510,509,508], [11,10,9,8], [7,6,5,4], ..., [3,2,1,0] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  SortDescending(KeyT (&keys)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    NullType values[ItemsPerThread];

    SortBlocked(keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescending(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    NullType values[ItemsPerThread];

    SortBlocked(
      keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescending(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer)
  {
    NullType values[ItemsPerThread];

    SortBlocked(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::true_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //! @rst
  //! Performs a descending block-wide radix sort across 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
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys and values that
  //! are partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128 threads
  //! where each thread owns 4 consecutive pairs.
  //!
  //! .. 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 keys and values each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4, int>;
  //!
  //!        // 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);
  //!
  //! 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
  //! ``{ [511,510,509,508], [11,10,9,8], [7,6,5,4], ..., [3,2,1,0] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in,out] values
  //!   Values to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void SortDescending(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    SortBlocked(keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescending(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    SortBlocked(
      keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescending(KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer)
  {
    SortBlocked(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::true_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //! @}  end member group
  //! @name Sorting (blocked arrangement -> striped arrangement)
  //! @{

  //! @rst
  //! Performs an ascending radix sort across a :ref:`blocked arrangement <flexible-data-arrangement>` of keys,
  //! leaving them in a :ref:`striped arrangement <flexible-data-arrangement>`.
  //!
  //! - @granularity
  //! - @smemreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys that
  //! are initially partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128
  //! threads where each thread owns 4 consecutive keys. The final partitioning is striped.
  //!
  //! .. 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 keys each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4>;
  //!
  //!        // 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);
  //!
  //! 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
  //! ``{ [0,128,256,384], [1,129,257,385], [2,130,258,386], ..., [127,255,383,511] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  SortBlockedToStriped(KeyT (&keys)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortBlockedToStriped(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortBlockedToStriped(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::false_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //! @rst
  //! Performs an ascending radix sort across a :ref:`blocked arrangement <flexible-data-arrangement>` of keys and
  //! values, leaving them in a :ref:`striped arrangement <flexible-data-arrangement>`.
  //!
  //! - 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
  //! +++++++
  //!
  //! 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.
  //!
  //! .. 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 keys and values each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4, int>;
  //!
  //!        // 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);
  //!
  //! 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
  //! ``{ [0,128,256,384], [1,129,257,385], [2,130,258,386], ..., [127,255,383,511] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in,out] values
  //!   Values to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void SortBlockedToStriped(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortBlockedToStriped(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::false_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortBlockedToStriped(KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer)
  {
    SortBlockedToStriped(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::false_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //! @rst
  //! Performs a descending radix sort across a :ref:`blocked arrangement <flexible-data-arrangement>`
  //! of keys, leaving them in a :ref:`striped arrangement <flexible-data-arrangement>`.
  //!
  //! - @granularity
  //! - @smemreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys that
  //! are initially partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128
  //! threads where each thread owns 4 consecutive keys. The final partitioning is striped.
  //!
  //! .. 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 keys each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4>;
  //!
  //!        // 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);
  //!
  //! 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
  //! ``{ [511,383,255,127], [386,258,130,2], [385,257,128,1], ..., [384,256,128,0] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void
  SortDescendingBlockedToStriped(KeyT (&keys)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescendingBlockedToStriped(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescendingBlockedToStriped(KeyT (&keys)[ItemsPerThread], DecomposerT decomposer)
  {
    NullType values[ItemsPerThread];

    SortBlockedToStriped(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::true_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //! @rst
  //! Performs a descending radix sort across a :ref:`blocked arrangement <flexible-data-arrangement>`
  //! of keys and values, leaving them in a :ref:`striped arrangement <flexible-data-arrangement>`
  //!
  //! - 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
  //! +++++++
  //!
  //! The code snippet below illustrates a sort of 512 integer keys and values that
  //! are initially partitioned in a :ref:`blocked arrangement <flexible-data-arrangement>` across 128
  //! threads where each thread owns 4 consecutive pairs. The final partitioning is striped.
  //!
  //! .. 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 keys and values each
  //!        using BlockRadixSort = cub::BlockRadixSort<int, 128, 4, int>;
  //!
  //!        // 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);
  //!
  //! 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
  //! ``{ [511,383,255,127], [386,258,130,2], [385,257,128,1], ..., [384,256,128,0] }``.
  //!
  //! @endrst
  //!
  //! @param[in,out] keys
  //!   Keys to sort
  //!
  //! @param[in,out] values
  //!   Values to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The beginning (least-significant) bit index needed for key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The past-the-end (most-significant) bit index needed for key comparison
  _CCCL_DEVICE _CCCL_FORCEINLINE void SortDescendingBlockedToStriped(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], int begin_bit = 0, int end_bit = sizeof(KeyT) * 8)
  {
    SortBlockedToStriped(keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescendingBlockedToStriped(
    KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer, int begin_bit, int end_bit)
  {
    SortBlockedToStriped(
      keys, values, begin_bit, end_bit, ::cuda::std::true_type(), detail::bool_constant_v<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:: ../../../cub/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:: ../../../cub/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>
  _CCCL_DEVICE _CCCL_FORCEINLINE //
  ::cuda::std::enable_if_t< //
    !::cuda::std::is_convertible_v<DecomposerT, int>>
  SortDescendingBlockedToStriped(KeyT (&keys)[ItemsPerThread], ValueT (&values)[ItemsPerThread], DecomposerT decomposer)
  {
    SortBlockedToStriped(
      keys,
      values,
      0,
      detail::radix::traits_t<KeyT>::default_end_bit(decomposer),
      ::cuda::std::true_type(),
      detail::bool_constant_v<KEYS_ONLY>,
      decomposer);
  }

  //@}  end member group
};

CUB_NAMESPACE_END
