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//! @file
//! cub::DeviceRadixSort provides device-wide, parallel operations for computing a radix sort across a sequence of data
//! items residing within device-accessible memory.

#pragma once

#include <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/detail/choose_offset.cuh>
#include <cub/detail/nvtx.cuh>
#include <cub/device/dispatch/dispatch_radix_sort.cuh>

#include <cuda/std/type_traits>

CUB_NAMESPACE_BEGIN

//! @brief DeviceRadixSort provides device-wide, parallel operations for
//!        computing a radix sort across a sequence of data items residing
//!        within device-accessible memory. ![](sorting_logo.png)
//!
//! @par Overview
//! The [*radix sorting method*](http://en.wikipedia.org/wiki/Radix_sort)
//! arranges items into ascending (or descending) order. The algorithm relies
//! upon a positional representation for keys, i.e., each key is comprised of an
//! ordered sequence of symbols (e.g., digits, characters, etc.) specified from
//! least-significant to most-significant. For a given input sequence of keys
//! and a set of rules specifying a total ordering of the symbolic alphabet, the
//! radix sorting method produces a lexicographic ordering of those keys.
//!
//! @par Supported Types
//! DeviceRadixSort can sort all of the built-in C++ numeric primitive types
//! (`unsigned char`, `int`, `double`, etc.) as well as CUDA's `__half`
//! and `__nv_bfloat16` 16-bit floating-point types. User-defined types are
//! supported as long as decomposer object is provided.
//!
//! @par 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.
//!
//! @par Transformations
//! Although the direct radix sorting method can only be applied to unsigned
//! integral types, DeviceRadixSort is able to sort signed and floating-point
//! types via simple bit-wise transformations that ensure lexicographic key
//! ordering. Additional transformations occur for descending sorts. 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.
//!
//! @par 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.
//!
//! For floating point types, positive and negative zero are a special case and
//! will be considered equivalent during sorting.
//!
//! @par Descending Sort Bitwise Transformations
//! If descending sort is used, the keys are inverted after performing any
//! type-specific transformations, and the resulting keys are sorted in ascending
//! order.
//!
//! @par Stability
//! DeviceRadixSort 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.
//!
//! @par Usage Considerations
//! @cdp_class{DeviceRadixSort}
//!
//! @par Performance
//! @linear_performance{radix sort} The following chart illustrates
//! DeviceRadixSort::SortKeys performance across different CUDA architectures
//! for uniform-random `uint32` keys.
//! @plots_below
//!
//! @image html lsb_radix_sort_int32_keys.png
struct DeviceRadixSort
{
private:
  template <SortOrder Order, typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static cudaError_t custom_radix_sort(
    ::cuda::std::false_type,
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    bool is_overwrite_okay,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    NumItemsT num_items,
    DecomposerT decomposer,
    int begin_bit,
    int end_bit,
    cudaStream_t stream);

  template <SortOrder Order, typename KeyT, typename ValueT, typename OffsetT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static cudaError_t custom_radix_sort(
    ::cuda::std::true_type,
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    bool is_overwrite_okay,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    OffsetT num_items,
    DecomposerT decomposer,
    int begin_bit,
    int end_bit,
    cudaStream_t stream)
  {
    return DispatchRadixSort<Order, KeyT, ValueT, OffsetT, DecomposerT>::Dispatch(
      d_temp_storage,
      temp_storage_bytes,
      d_keys,
      d_values,
      static_cast<OffsetT>(num_items),
      begin_bit,
      end_bit,
      is_overwrite_okay,
      stream,
      decomposer);
  }

  template <SortOrder Order, typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static cudaError_t custom_radix_sort(
    ::cuda::std::false_type,
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    bool is_overwrite_okay,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    NumItemsT num_items,
    DecomposerT decomposer,
    cudaStream_t stream);

  template <SortOrder Order, typename KeyT, typename ValueT, typename OffsetT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static cudaError_t custom_radix_sort(
    ::cuda::std::true_type,
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    bool is_overwrite_okay,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    OffsetT num_items,
    DecomposerT decomposer,
    cudaStream_t stream)
  {
    constexpr int begin_bit = 0;
    const int end_bit       = detail::radix::traits_t<KeyT>::default_end_bit(decomposer);

    return DeviceRadixSort::custom_radix_sort<Order>(
      ::cuda::std::true_type{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      num_items,
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  // Name reported for NVTX ranges
  _CCCL_HOST_DEVICE static constexpr auto GetName() -> const char*
  {
    return "cub::DeviceRadixSort";
  }

public:
  //! @name KeyT-value pairs
  //@{

  //! @brief Sorts key-value pairs into ascending order.
  //!        (`~2N` auxiliary storage required)
  //!
  //! @par
  //! - The contents of the input data are not altered by the sorting operation.
  //! - Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys_in,    d_keys_in    + num_items)`
  //!   - `[d_keys_out,   d_keys_out   + num_items)`
  //!   - `[d_values_in,  d_values_in  + num_items)`
  //!   - `[d_values_out, d_values_out + num_items)`
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageNP For sorting using only `O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! - @devicestorage
  //!
  //! @par Performance
  //! The following charts illustrate saturated sorting performance across
  //! different CUDA architectures for uniform-random `uint32, uint32` and
  //! `uint64, uint64` pairs, respectively.
  //!
  //! @image html lsb_radix_sort_int32_pairs.png
  //! @image html lsb_radix_sort_int64_pairs.png
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of `int`
  //! keys with associated vector of `int` values.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_keys_out;        // e.g., [        ...        ]
  //! int  *d_values_in;       // e.g., [0, 1, 2, 3, 4, 5, 6]
  //! int  *d_values_out;      // e.g., [        ...        ]
  //! ...
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes,
  //!     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortPairs(d_temp_storage, temp_storage_bytes,
  //!     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
  //!
  //! // d_keys_out            <-- [0, 3, 5, 6, 7, 8, 9]
  //! // d_values_out          <-- [5, 4, 3, 1, 2, 0, 6]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., sizeof(unsigned int) * 8)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortPairs(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    const KeyT* d_keys_in,
    KeyT* d_keys_out,
    const ValueT* d_values_in,
    ValueT* d_values_out,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());
    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    // TODO API that doesn't accept decomposer should also contain a static
    //      assert that the key type is fundamental.

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DispatchRadixSort<SortOrder::Ascending, KeyT, ValueT, OffsetT>::Dispatch(
      d_temp_storage,
      temp_storage_bytes,
      d_keys,
      d_values,
      static_cast<OffsetT>(num_items),
      begin_bit,
      end_bit,
      is_overwrite_okay,
      stream);
  }

  //! @rst
  //! Sorts key-value pairs into ascending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,    d_keys_in    + num_items)``
  //!   * ``[d_keys_out,   d_keys_out   + num_items)``
  //!   * ``[d_values_in,  d_values_in  + num_items)``
  //!   * ``[d_values_out, d_values_out + num_items)``
  //!
  //! * A bit subrange ``[begin_bit, end_bit)`` is provided to specify
  //!   differentiating key bits. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairs``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-bits
  //!     :end-before: example-end pairs-bits
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairs(void* d_temp_storage,
              size_t& temp_storage_bytes,
              const KeyT* d_keys_in,
              KeyT* d_keys_out,
              const ValueT* d_values_in,
              ValueT* d_values_out,
              NumItemsT num_items,
              DecomposerT decomposer,
              int begin_bit,
              int end_bit,
              cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());
    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @rst
  //! Sorts key-value pairs into ascending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,    d_keys_in    + num_items)``
  //!   * ``[d_keys_out,   d_keys_out   + num_items)``
  //!   * ``[d_values_in,  d_values_in  + num_items)``
  //!   * ``[d_values_out, d_values_out + num_items)``
  //!
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairs``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs
  //!     :end-before: example-end pairs
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairs(void* d_temp_storage,
              size_t& temp_storage_bytes,
              const KeyT* d_keys_in,
              KeyT* d_keys_out,
              const ValueT* d_values_in,
              ValueT* d_values_out,
              NumItemsT num_items,
              DecomposerT decomposer,
              cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());
    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @brief Sorts key-value pairs into ascending order.
  //!        (`~N` auxiliary storage required)
  //!
  //! @par
  //! - The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! - The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys.Current(),     d_keys.Current()     + num_items)`
  //!   - `[d_keys.Alternate(),   d_keys.Alternate()   + num_items)`
  //!   - `[d_values.Current(),   d_values.Current()   + num_items)`
  //!   - `[d_values.Alternate(), d_values.Alternate() + num_items)`
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! @par Performance
  //! The following charts illustrate saturated sorting performance across
  //! different CUDA architectures for uniform-random `uint32, uint32` and
  //! `uint64, uint64` pairs, respectively.
  //!
  //! @image html lsb_radix_sort_int32_pairs.png
  //! @image html lsb_radix_sort_int64_pairs.png
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of `int`
  //! keys with associated vector of `int` values.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers for
  //! // sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_key_alt_buf;     // e.g., [        ...        ]
  //! int  *d_value_buf;       // e.g., [0, 1, 2, 3, 4, 5, 6]
  //! int  *d_value_alt_buf;   // e.g., [        ...        ]
  //! ...
  //!
  //! // Create a set of DoubleBuffers to wrap pairs of device pointers
  //! cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
  //! cub::DoubleBuffer<int> d_values(d_value_buf, d_value_alt_buf);
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortPairs(
  //!   d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortPairs(
  //!   d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
  //!
  //! // d_keys.Current()      <-- [0, 3, 5, 6, 7, 8, 9]
  //! // d_values.Current()    <-- [5, 4, 3, 1, 2, 0, 6]
  //!
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortPairs(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    constexpr bool is_overwrite_okay = true;

    return DispatchRadixSort<SortOrder::Ascending, KeyT, ValueT, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts key-value pairs into ascending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! * The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   - ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   - ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!   - ``[d_values.Current(),   d_values.Current()   + num_items)``
  //!   - ``[d_values.Alternate(), d_values.Alternate() + num_items)``
  //!
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairs``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-db
  //!     :end-before: example-end pairs-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairs(void* d_temp_storage,
              size_t& temp_storage_bytes,
              DoubleBuffer<KeyT>& d_keys,
              DoubleBuffer<ValueT>& d_values,
              NumItemsT num_items,
              DecomposerT decomposer,
              cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @rst
  //! Sorts key-value pairs into ascending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! * The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   - ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   - ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!   - ``[d_values.Current(),   d_values.Current()   + num_items)``
  //!   - ``[d_values.Alternate(), d_values.Alternate() + num_items)``
  //!
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - An optional bit subrange ``[begin_bit, end_bit)`` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairs``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-bits-db
  //!     :end-before: example-end pairs-bits-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairs(void* d_temp_storage,
              size_t& temp_storage_bytes,
              DoubleBuffer<KeyT>& d_keys,
              DoubleBuffer<ValueT>& d_values,
              NumItemsT num_items,
              DecomposerT decomposer,
              int begin_bit,
              int end_bit,
              cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @brief Sorts key-value pairs into descending order.
  //!        (`~2N` auxiliary storage required).
  //!
  //! @par
  //! - The contents of the input data are not altered by the sorting operation.
  //! - Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys_in,    d_keys_in    + num_items)`
  //!   - `[d_keys_out,   d_keys_out   + num_items)`
  //!   - `[d_values_in,  d_values_in  + num_items)`
  //!   - `[d_values_out, d_values_out + num_items)`
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageNP  For sorting using only `O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! - @devicestorage
  //!
  //! @par Performance
  //! Performance is similar to DeviceRadixSort::SortPairs.
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of `int`
  //! keys with associated vector of `int` values.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_keys_out;        // e.g., [        ...        ]
  //! int  *d_values_in;       // e.g., [0, 1, 2, 3, 4, 5, 6]
  //! int  *d_values_out;      // e.g., [        ...        ]
  //! ...
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortPairsDescending(
  //!     d_temp_storage, temp_storage_bytes,
  //!     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortPairsDescending(
  //!     d_temp_storage, temp_storage_bytes,
  //!     d_keys_in, d_keys_out, d_values_in, d_values_out, num_items);
  //!
  //! // d_keys_out            <-- [9, 8, 7, 6, 5, 3, 0]
  //! // d_values_out          <-- [6, 0, 2, 1, 3, 4, 5]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortPairsDescending(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    const KeyT* d_keys_in,
    KeyT* d_keys_out,
    const ValueT* d_values_in,
    ValueT* d_values_out,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DispatchRadixSort<SortOrder::Descending, KeyT, ValueT, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts key-value pairs into descending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,    d_keys_in    + num_items)``
  //!   * ``[d_keys_out,   d_keys_out   + num_items)``
  //!   * ``[d_values_in,  d_values_in  + num_items)``
  //!   * ``[d_values_out, d_values_out + num_items)``
  //!
  //! * A bit subrange ``[begin_bit, end_bit)`` is provided to specify
  //!   differentiating key bits. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairsDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-descending-bits
  //!     :end-before: example-end pairs-descending-bits
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairsDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      const KeyT* d_keys_in,
      KeyT* d_keys_out,
      const ValueT* d_values_in,
      ValueT* d_values_out,
      NumItemsT num_items,
      DecomposerT decomposer,
      int begin_bit,
      int end_bit,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @rst
  //! Sorts key-value pairs into descending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,    d_keys_in    + num_items)``
  //!   * ``[d_keys_out,   d_keys_out   + num_items)``
  //!   * ``[d_values_in,  d_values_in  + num_items)``
  //!   * ``[d_values_out, d_values_out + num_items)``
  //!
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairsDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-descending
  //!     :end-before: example-end pairs-descending
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] d_values_in
  //!   Pointer to the corresponding input sequence of associated value items
  //!
  //! @param[out] d_values_out
  //!   Pointer to the correspondingly-reordered output sequence of associated
  //!   value items
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairsDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      const KeyT* d_keys_in,
      KeyT* d_keys_out,
      const ValueT* d_values_in,
      ValueT* d_values_out,
      NumItemsT num_items,
      DecomposerT decomposer,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<ValueT> d_values(const_cast<ValueT*>(d_values_in), d_values_out);

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @brief Sorts key-value pairs into descending order.
  //!        (`~N` auxiliary storage required).
  //!
  //! @par
  //! - The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! - The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys.Current(),     d_keys.Current()     + num_items)`
  //!   - `[d_keys.Alternate(),   d_keys.Alternate()   + num_items)`
  //!   - `[d_values.Current(),   d_values.Current()   + num_items)`
  //!   - `[d_values.Alternate(), d_values.Alternate() + num_items)`
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the number
  //!   of key bits specified and the targeted device architecture).
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! @par Performance
  //! Performance is similar to DeviceRadixSort::SortPairs.
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of `int`
  //! keys with associated vector of `int` values.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_key_alt_buf;     // e.g., [        ...        ]
  //! int  *d_value_buf;       // e.g., [0, 1, 2, 3, 4, 5, 6]
  //! int  *d_value_alt_buf;   // e.g., [        ...        ]
  //! ...
  //!
  //! // Create a set of DoubleBuffers to wrap pairs of device pointers
  //! cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
  //! cub::DoubleBuffer<int> d_values(d_value_buf, d_value_alt_buf);
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortPairsDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortPairsDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items);
  //!
  //! // d_keys.Current()      <-- [9, 8, 7, 6, 5, 3, 0]
  //! // d_values.Current()    <-- [6, 0, 2, 1, 3, 4, 5]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortPairsDescending(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    DoubleBuffer<KeyT>& d_keys,
    DoubleBuffer<ValueT>& d_values,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    constexpr bool is_overwrite_okay = true;

    return DispatchRadixSort<SortOrder::Descending, KeyT, ValueT, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts key-value pairs into descending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! * The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   - ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   - ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!   - ``[d_values.Current(),   d_values.Current()   + num_items)``
  //!   - ``[d_values.Alternate(), d_values.Alternate() + num_items)``
  //!
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairsDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-descending-db
  //!     :end-before: example-end pairs-descending-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairsDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      DoubleBuffer<KeyT>& d_keys,
      DoubleBuffer<ValueT>& d_values,
      NumItemsT num_items,
      DecomposerT decomposer,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @rst
  //! Sorts key-value pairs into descending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers and a corresponding
  //!   pair of associated value buffers.  Each pair is managed by a DoubleBuffer
  //!   structure that indicates which of the two buffers is "current" (and thus
  //!   contains the input data to be sorted).
  //! * The contents of both buffers within each pair may be altered by the
  //!   sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   - ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   - ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!   - ``[d_values.Current(),   d_values.Current()   + num_items)``
  //!   - ``[d_values.Alternate(), d_values.Alternate() + num_items)``
  //!
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within each DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - An optional bit subrange ``[begin_bit, end_bit)`` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortPairsDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin pairs-descending-bits-db
  //!     :end-before: example-end pairs-descending-bits-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam ValueT
  //!   **[inferred]** ValueT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in,out] d_values
  //!   Double-buffer of values whose "current" device-accessible buffer
  //!   contains the unsorted input values and, upon return, is updated to point
  //!   to the sorted output values
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename ValueT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortPairsDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      DoubleBuffer<KeyT>& d_keys,
      DoubleBuffer<ValueT>& d_values,
      NumItemsT num_items,
      DecomposerT decomposer,
      int begin_bit,
      int end_bit,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //@}  end member group
  /******************************************************************/ /**
                                                                        * @name Keys-only
                                                                        *********************************************************************/
  //@{

  //! @brief Sorts keys into ascending order.
  //!        (`~2N` auxiliary storage required)
  //!
  //! @par
  //! - The contents of the input data are not altered by the sorting operation.
  //! - Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys_in,    d_keys_in    + num_items)`
  //!   - `[d_keys_out,   d_keys_out   + num_items)`
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageNP  For sorting using only `O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! - @devicestorage
  //!
  //! @par Performance
  //! The following charts illustrate saturated sorting performance across
  //! different CUDA architectures for uniform-random `uint32` and `uint64`
  //! keys, respectively.
  //!
  //! @image html lsb_radix_sort_int32_keys.png
  //! @image html lsb_radix_sort_int64_keys.png
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of
  //! `int` keys.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_keys_out;        // e.g., [        ...        ]
  //! ...
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortKeys(
  //!   d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortKeys(
  //!   d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
  //!
  //! // d_keys_out            <-- [0, 3, 5, 6, 7, 8, 9]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortKeys(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    const KeyT* d_keys_in,
    KeyT* d_keys_out,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    // Null value type
    DoubleBuffer<NullType> d_values;

    return DispatchRadixSort<SortOrder::Ascending, KeyT, NullType, OffsetT>::Dispatch(
      d_temp_storage,
      temp_storage_bytes,
      d_keys,
      d_values,
      static_cast<OffsetT>(num_items),
      begin_bit,
      end_bit,
      is_overwrite_okay,
      stream);
  }

  //! @rst
  //! Sorts keys into ascending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,  d_keys_in  + num_items)``
  //!   * ``[d_keys_out, d_keys_out + num_items)``
  //!
  //! * A bit subrange ``[begin_bit, end_bit)`` is provided to specify
  //!   differentiating key bits. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeys``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-bits
  //!     :end-before: example-end keys-bits
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeys(void* d_temp_storage,
             size_t& temp_storage_bytes,
             const KeyT* d_keys_in,
             KeyT* d_keys_out,
             NumItemsT num_items,
             DecomposerT decomposer,
             int begin_bit,
             int end_bit,
             cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @rst
  //! Sorts keys into ascending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,  d_keys_in  + num_items)``
  //!   * ``[d_keys_out, d_keys_out + num_items)``
  //!
  //! * An optional bit subrange ``[begin_bit, end_bit)`` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeys``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys
  //!     :end-before: example-end keys
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeys(void* d_temp_storage,
             size_t& temp_storage_bytes,
             const KeyT* d_keys_in,
             KeyT* d_keys_out,
             NumItemsT num_items,
             DecomposerT decomposer,
             cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @brief Sorts keys into ascending order. (`~N` auxiliary storage required).
  //!
  //! @par
  //! - The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! - The contents of both buffers may be altered by the sorting operation.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys.Current(),     d_keys.Current()     + num_items)`
  //!   - `[d_keys.Alternate(),   d_keys.Alternate()   + num_items)`
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! @par Performance
  //! The following charts illustrate saturated sorting performance across
  //! different CUDA architectures for uniform-random `uint32` and `uint64`
  //! keys, respectively.
  //!
  //! @image html lsb_radix_sort_int32_keys.png
  //! @image html lsb_radix_sort_int64_keys.png
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of
  //! `int` keys.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_key_alt_buf;     // e.g., [        ...        ]
  //! ...
  //!
  //! // Create a DoubleBuffer to wrap the pair of device pointers
  //! cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortKeys(
  //!   d_temp_storage, temp_storage_bytes, d_keys, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortKeys(
  //!   d_temp_storage, temp_storage_bytes, d_keys, num_items);
  //!
  //! // d_keys.Current()      <-- [0, 3, 5, 6, 7, 8, 9]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortKeys(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    DoubleBuffer<KeyT>& d_keys,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    constexpr bool is_overwrite_okay = true;

    // Null value type
    DoubleBuffer<NullType> d_values;

    return DispatchRadixSort<SortOrder::Ascending, KeyT, NullType, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts keys into ascending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! * The contents of both buffers may be altered by the sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   * ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!
  //! * Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! * @devicestorageP
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeys``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-db
  //!     :end-before: example-end keys-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeys(void* d_temp_storage,
             size_t& temp_storage_bytes,
             DoubleBuffer<KeyT>& d_keys,
             NumItemsT num_items,
             DecomposerT decomposer,
             cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @rst
  //! Sorts keys into ascending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! * The contents of both buffers may be altered by the sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   * ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!
  //! * A bit subrange ``[begin_bit, end_bit)`` is provided to specify
  //!   differentiating key bits. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! * @devicestorageP
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeys``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-bits-db
  //!     :end-before: example-end keys-bits-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeys(void* d_temp_storage,
             size_t& temp_storage_bytes,
             DoubleBuffer<KeyT>& d_keys,
             NumItemsT num_items,
             DecomposerT decomposer,
             int begin_bit,
             int end_bit,
             cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Ascending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @brief Sorts keys into descending order.
  //!        (`~2N` auxiliary storage required).
  //!
  //! @par
  //! - The contents of the input data are not altered by the sorting operation.
  //! - Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys_in,    d_keys_in    + num_items)`
  //!   - `[d_keys_out,   d_keys_out   + num_items)`
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageNP For sorting using only `O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! - @devicestorage
  //!
  //! @par Performance
  //! Performance is similar to DeviceRadixSort::SortKeys.
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of
  //! `int` keys.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_keys_in;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_keys_out;        // e.g., [        ...        ]
  //! ...
  //!
  //! // Create a DoubleBuffer to wrap the pair of device pointers
  //! cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortKeysDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortKeysDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys_in, d_keys_out, num_items);
  //!
  //! // d_keys_out            <-- [9, 8, 7, 6, 5, 3, 0]s
  //!
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortKeysDescending(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    const KeyT* d_keys_in,
    KeyT* d_keys_out,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<NullType> d_values;

    return DispatchRadixSort<SortOrder::Descending, KeyT, NullType, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts keys into descending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,  d_keys_in  + num_items)``
  //!   * ``[d_keys_out, d_keys_out + num_items)``
  //!
  //! * An optional bit subrange ``[begin_bit, end_bit)`` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeysDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-descending-bits
  //!     :end-before: example-end keys-descending-bits
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeysDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      const KeyT* d_keys_in,
      KeyT* d_keys_out,
      NumItemsT num_items,
      DecomposerT decomposer,
      int begin_bit,
      int end_bit,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @rst
  //! Sorts keys into descending order using :math:`\approx 2N` auxiliary storage.
  //!
  //! * The contents of the input data are not altered by the sorting operation.
  //! * Pointers to contiguous memory must be used; iterators are not currently
  //!   supported.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys_in,  d_keys_in  + num_items)``
  //!   * ``[d_keys_out, d_keys_out + num_items)``
  //!
  //! * @devicestorageNP For sorting using only :math:`O(P)` temporary storage, see
  //!   the sorting interface using DoubleBuffer wrappers below.
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeysDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-descending
  //!     :end-before: example-end keys-descending
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in] d_keys_in
  //!   Pointer to the input data of key data to sort
  //!
  //! @param[out] d_keys_out
  //!   Pointer to the sorted output sequence of key data
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeysDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      const KeyT* d_keys_in,
      KeyT* d_keys_out,
      NumItemsT num_items,
      DecomposerT decomposer,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    // We cast away const-ness, but will *not* write to these arrays.
    // `DispatchRadixSort::Dispatch` will allocate temporary storage and
    // create a new double-buffer internally when the `is_overwrite_ok` flag
    // is not set.
    constexpr bool is_overwrite_okay = false;
    DoubleBuffer<KeyT> d_keys(const_cast<KeyT*>(d_keys_in), d_keys_out);
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @brief Sorts keys into descending order.
  //!        (`~N` auxiliary storage required).
  //!
  //! @par
  //! - The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! - The contents of both buffers may be altered by the sorting operation.
  //! - In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!   - `[d_keys.Current(),     d_keys.Current()     + num_items)`
  //!   - `[d_keys.Alternate(),   d_keys.Alternate()   + num_items)`
  //! - Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! - An optional bit subrange `[begin_bit, end_bit)` of differentiating key
  //!   bits can be specified. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! - @devicestorageP
  //! - @devicestorage
  //!
  //! @par Performance
  //! Performance is similar to DeviceRadixSort::SortKeys.
  //!
  //! @par Snippet
  //! The code snippet below illustrates the sorting of a device vector of `i`nt keys.
  //! @par
  //! @code
  //! #include <cub/cub.cuh>
  //! // or equivalently <cub/device/device_radix_sort.cuh>
  //!
  //! // Declare, allocate, and initialize device-accessible pointers
  //! // for sorting data
  //! int  num_items;          // e.g., 7
  //! int  *d_key_buf;         // e.g., [8, 6, 7, 5, 3, 0, 9]
  //! int  *d_key_alt_buf;     // e.g., [        ...        ]
  //! ...
  //!
  //! // Create a DoubleBuffer to wrap the pair of device pointers
  //! cub::DoubleBuffer<int> d_keys(d_key_buf, d_key_alt_buf);
  //!
  //! // Determine temporary device storage requirements
  //! void     *d_temp_storage = nullptr;
  //! size_t   temp_storage_bytes = 0;
  //! cub::DeviceRadixSort::SortKeysDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys, num_items);
  //!
  //! // Allocate temporary storage
  //! cudaMalloc(&d_temp_storage, temp_storage_bytes);
  //!
  //! // Run sorting operation
  //! cub::DeviceRadixSort::SortKeysDescending(
  //!   d_temp_storage, temp_storage_bytes, d_keys, num_items);
  //!
  //! // d_keys.Current()      <-- [9, 8, 7, 6, 5, 3, 0]
  //! @endcode
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @param[in] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items to sort
  //!
  //! @param[in] begin_bit
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `sizeof(unsigned int) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT>
  CUB_RUNTIME_FUNCTION static cudaError_t SortKeysDescending(
    void* d_temp_storage,
    size_t& temp_storage_bytes,
    DoubleBuffer<KeyT>& d_keys,
    NumItemsT num_items,
    int begin_bit       = 0,
    int end_bit         = sizeof(KeyT) * 8,
    cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // Unsigned integer type for global offsets.
    using OffsetT = detail::choose_offset_t<NumItemsT>;

    constexpr bool is_overwrite_okay = true;

    // Null value type
    DoubleBuffer<NullType> d_values;

    return DispatchRadixSort<SortOrder::Descending, KeyT, NullType, OffsetT>::Dispatch(
      d_temp_storage, temp_storage_bytes, d_keys, d_values, num_items, begin_bit, end_bit, is_overwrite_okay, stream);
  }

  //! @rst
  //! Sorts keys into descending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! * The contents of both buffers may be altered by the sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   * ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!
  //! * Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! * @devicestorageP
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeysDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-descending-db
  //!     :end-before: example-end keys-descending-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items 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] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeysDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      DoubleBuffer<KeyT>& d_keys,
      NumItemsT num_items,
      DecomposerT decomposer,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      stream);
  }

  //! @rst
  //! Sorts keys into descending order using :math:`\approx N` auxiliary storage.
  //!
  //! * The sorting operation is given a pair of key buffers managed by a
  //!   DoubleBuffer structure that indicates which of the two buffers is
  //!   "current" (and thus contains the input data to be sorted).
  //! * The contents of both buffers may be altered by the sorting operation.
  //! * In-place operations are not supported. There must be no overlap between
  //!   any of the provided ranges:
  //!
  //!   * ``[d_keys.Current(),     d_keys.Current()     + num_items)``
  //!   * ``[d_keys.Alternate(),   d_keys.Alternate()   + num_items)``
  //!
  //! * A bit subrange ``[begin_bit, end_bit)`` is provided to specify
  //!   differentiating key bits. This can reduce overall sorting overhead and
  //!   yield a corresponding performance improvement.
  //! * Upon completion, the sorting operation will update the "current"
  //!   indicator within the DoubleBuffer wrapper to reference which of the two
  //!   buffers now contains the sorted output sequence (a function of the
  //!   number of key bits specified and the targeted device architecture).
  //! * @devicestorageP
  //! * @devicestorage
  //!
  //! 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_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin custom-type
  //!     :end-before: example-end custom-type
  //!
  //! The following snippet shows how to sort an array of ``custom_t`` objects
  //! using ``cub::DeviceRadixSort::SortKeysDescending``:
  //!
  //! .. literalinclude:: ../../../cub/test/catch2_test_device_radix_sort_custom.cu
  //!     :language: c++
  //!     :dedent:
  //!     :start-after: example-begin keys-descending-bits-db
  //!     :end-before: example-end keys-descending-bits-db
  //!
  //! @endrst
  //!
  //! @tparam KeyT
  //!   **[inferred]** KeyT type
  //!
  //! @tparam NumItemsT
  //!   **[inferred]** Type of num_items
  //!
  //! @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] d_temp_storage
  //!   Device-accessible allocation of temporary storage. When `nullptr`, the
  //!   required allocation size is written to `temp_storage_bytes` and no work
  //!   is done.
  //!
  //! @param[in,out] temp_storage_bytes
  //!   Reference to size in bytes of `d_temp_storage` allocation
  //!
  //! @param[in,out] d_keys
  //!   Reference to the double-buffer of keys whose "current" device-accessible
  //!   buffer contains the unsorted input keys and, upon return, is updated to
  //!   point to the sorted output keys
  //!
  //! @param[in] num_items
  //!   Number of items 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
  //!   **[optional]** The least-significant bit index (inclusive) needed for
  //!   key comparison
  //!
  //! @param[in] end_bit
  //!   **[optional]** The most-significant bit index (exclusive) needed for key
  //!   comparison (e.g., `(sizeof(float) + sizeof(long long int)) * 8`)
  //!
  //! @param[in] stream
  //!   **[optional]** CUDA stream to launch kernels within.
  //!   Default is stream<sub>0</sub>.
  template <typename KeyT, typename NumItemsT, typename DecomposerT>
  CUB_RUNTIME_FUNCTION static //
    ::cuda::std::enable_if_t< //
      !::cuda::std::is_convertible_v<DecomposerT, int>, //
      cudaError_t>
    SortKeysDescending(
      void* d_temp_storage,
      size_t& temp_storage_bytes,
      DoubleBuffer<KeyT>& d_keys,
      NumItemsT num_items,
      DecomposerT decomposer,
      int begin_bit,
      int end_bit,
      cudaStream_t stream = 0)
  {
    CUB_DETAIL_NVTX_RANGE_SCOPE_IF(d_temp_storage, GetName());

    // unsigned integer type for global offsets
    using offset_t           = detail::choose_offset_t<NumItemsT>;
    using decomposer_check_t = detail::radix::decomposer_check_t<KeyT, DecomposerT>;

    static_assert(decomposer_check_t::value,
                  "DecomposerT must be a callable object returning a tuple of references to "
                  "arithmetic types");

    constexpr bool is_overwrite_okay = true;
    DoubleBuffer<NullType> d_values;

    return DeviceRadixSort::custom_radix_sort<SortOrder::Descending>(
      decomposer_check_t{},
      d_temp_storage,
      temp_storage_bytes,
      is_overwrite_okay,
      d_keys,
      d_values,
      static_cast<offset_t>(num_items),
      decomposer,
      begin_bit,
      end_bit,
      stream);
  }

  //! @}  end member group
};

CUB_NAMESPACE_END
