cuda_toolkit/include/cub/warp/warp_scan.cuh

/******************************************************************************
 * Copyright (c) 2011, Duane Merrill.  All rights reserved.
 * Copyright (c) 2011-2018, NVIDIA CORPORATION.  All rights reserved.
 *
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 * modification, are permitted provided that the following conditions are met:
 *     * Redistributions of source code must retain the above copyright
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 *     * Neither the name of the NVIDIA CORPORATION nor the
 *       names of its contributors may be used to endorse or promote products
 *       derived from this software without specific prior written permission.
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//! @file
//! @rst
//! The ``cub::WarpScan`` class provides :ref:`collective <collective-primitives>` methods for
//! computing a parallel prefix scan of items partitioned across a CUDA thread warp.
//! @endrst

#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/thread/thread_operators.cuh>
#include <cub/util_type.cuh>
#include <cub/warp/specializations/warp_scan_shfl.cuh>
#include <cub/warp/specializations/warp_scan_smem.cuh>

CUB_NAMESPACE_BEGIN

//! @rst
//! The WarpScan class provides :ref:`collective <collective-primitives>` methods for computing a
//! parallel prefix scan of items partitioned across a CUDA thread warp.
//!
//! .. image:: ../img/warp_scan_logo.png
//!     :align: center
//!
//! Overview
//! ++++++++++++++++++++++++++
//!
//! * Given a list of input elements and a binary reduction operator, a
//!   `prefix scan <http://en.wikipedia.org/wiki/Prefix_sum>`__ produces an output list where each
//!   element is computed to be the reduction of the elements occurring earlier in the input list.
//!   *Prefix sum* connotes a prefix scan with the addition operator. The term *inclusive*
//!   indicates that the *i*\ :sup:`th` output reduction incorporates the *i*\ :sup:`th` input.
//!   The term *exclusive* indicates the *i*\ :sup:`th` input is not incorporated into
//!   the *i*\ :sup:`th` output reduction.
//! * Supports non-commutative scan operators
//! * Supports "logical" warps smaller than the physical warp size
//!   (e.g., a logical warp of 8 threads)
//! * The number of entrant threads must be an multiple of ``LOGICAL_WARP_THREADS``
//!
//! Performance Considerations
//! ++++++++++++++++++++++++++
//!
//! * Uses special instructions when applicable (e.g., warp ``SHFL``)
//! * Uses synchronization-free communication between warp lanes when applicable
//! * Incurs zero bank conflicts for most types
//! * Computation is slightly more efficient (i.e., having lower instruction overhead) for:
//!
//!   * Summation (**vs.** generic scan)
//!   * The architecture's warp size is a whole multiple of ``LOGICAL_WARP_THREADS``
//!
//! Simple Examples
//! ++++++++++++++++++++++++++
//!
//! @warpcollective{WarpScan}
//!
//! The code snippet below illustrates four concurrent warp prefix sums within a block of
//! 128 threads (one per each of the 32-thread warps).
//!
//! .. code-block:: c++
//!
//!    #include <cub/cub.cuh>
//!
//!    __global__ void ExampleKernel(...)
//!    {
//!        // Specialize WarpScan for type int
//!        typedef cub::WarpScan<int> WarpScan;
//!
//!        // Allocate WarpScan shared memory for 4 warps
//!        __shared__ typename WarpScan::TempStorage temp_storage[4];
//!
//!        // Obtain one input item per thread
//!        int thread_data = ...
//!
//!        // Compute warp-wide prefix sums
//!        int warp_id = threadIdx.x / 32;
//!        WarpScan(temp_storage[warp_id]).ExclusiveSum(thread_data, thread_data);
//!
//! Suppose the set of input ``thread_data`` across the block of threads is
//! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` in each of the four warps of
//! threads will be ``0, 1, 2, 3, ..., 31}``.
//!
//! The code snippet below illustrates a single warp prefix sum within a block of
//! 128 threads.
//!
//! .. code-block:: c++
//!
//!    #include <cub/cub.cuh>
//!
//!    __global__ void ExampleKernel(...)
//!    {
//!        // Specialize WarpScan for type int
//!        typedef cub::WarpScan<int> WarpScan;
//!
//!        // Allocate WarpScan shared memory for one warp
//!        __shared__ typename WarpScan::TempStorage temp_storage;
//!        ...
//!
//!        // Only the first warp performs a prefix sum
//!        if (threadIdx.x < 32)
//!        {
//!            // Obtain one input item per thread
//!            int thread_data = ...
//!
//!            // Compute warp-wide prefix sums
//!            WarpScan(temp_storage).ExclusiveSum(thread_data, thread_data);
//!
//! Suppose the set of input ``thread_data`` across the warp of threads is
//! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` will be
//! ``{0, 1, 2, 3, ..., 31}``.
//! @endrst
//!
//! @tparam T
//!   The scan input/output element type
//!
//! @tparam LOGICAL_WARP_THREADS
//!   **[optional]** The number of threads per "logical" warp (may be less than the number of
//!   hardware warp threads). Default is the warp size associated with the CUDA Compute Capability
//!   targeted by the compiler (e.g., 32 threads for SM20).
//!
//! @tparam LEGACY_PTX_ARCH
//!   **[optional]** Unused.
template <typename T, int LOGICAL_WARP_THREADS = CUB_PTX_WARP_THREADS, int LEGACY_PTX_ARCH = 0>
class WarpScan
{
private:
  /******************************************************************************
   * Constants and type definitions
   ******************************************************************************/

  enum
  {
    /// Whether the logical warp size and the PTX warp size coincide
    IS_ARCH_WARP = (LOGICAL_WARP_THREADS == CUB_WARP_THREADS(0)),

    /// Whether the logical warp size is a power-of-two
    IS_POW_OF_TWO = ((LOGICAL_WARP_THREADS & (LOGICAL_WARP_THREADS - 1)) == 0),

    /// Whether the data type is an integer (which has fully-associative addition)
    IS_INTEGER = ((Traits<T>::CATEGORY == SIGNED_INTEGER) ||
                  (Traits<T>::CATEGORY == UNSIGNED_INTEGER))
  };

  /// Internal specialization.
  /// Use SHFL-based scan if LOGICAL_WARP_THREADS is a power-of-two
  using InternalWarpScan = cub::detail::conditional_t<IS_POW_OF_TWO,
                                                      WarpScanShfl<T, LOGICAL_WARP_THREADS>,
                                                      WarpScanSmem<T, LOGICAL_WARP_THREADS>>;

  /// Shared memory storage layout type for WarpScan
  using _TempStorage = typename InternalWarpScan::TempStorage;

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

  /// Shared storage reference
  _TempStorage &temp_storage;
  unsigned int lane_id;

  /******************************************************************************
   * Public types
   ******************************************************************************/

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

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

  //! @brief Collective constructor using the specified memory allocation as temporary storage.
  //!        Logical warp and lane identifiers are constructed from `threadIdx.x`.
  //!
  //! @param[in] temp_storage
  //!   Reference to memory allocation having layout type TempStorage
  __device__ __forceinline__ WarpScan(TempStorage &temp_storage)
      : temp_storage(temp_storage.Alias())
      , lane_id(IS_ARCH_WARP ? LaneId() : LaneId() % LOGICAL_WARP_THREADS)
  {}

  //! @}  end member group
  //! @name Inclusive prefix sums
  //! @{

  //! @rst
  //! Computes an inclusive prefix sum across the calling warp.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide inclusive prefix sums within a
  //! block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute inclusive warp-wide prefix sums
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).InclusiveSum(thread_data, thread_data);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` in each of the four warps
  //! of threads will be ``1, 2, 3, ..., 32}``.
  //! @endrst
  //!
  //! @param[in] input
  //!   Calling thread's input item.
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's output item. May be aliased with `input`.
  __device__ __forceinline__ void InclusiveSum(T input, T &inclusive_output)
  {
    InclusiveScan(input, inclusive_output, cub::Sum());
  }

  //! @rst
  //! Computes an inclusive prefix sum across the calling warp.
  //! Also provides every thread with the warp-wide ``warp_aggregate`` of all inputs.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide inclusive prefix sums within a
  //! block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute inclusive warp-wide prefix sums
  //!        int warp_aggregate;
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).InclusiveSum(thread_data,
  //!                                                     thread_data,
  //!                                                     warp_aggregate);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` in each of the four warps
  //! of threads will be ``1, 2, 3, ..., 32}``. Furthermore, ``warp_aggregate`` for all threads
  //! in all warps will be ``32``.
  //! @endrst
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[out] warp_aggregate
  //!   Warp-wide aggregate reduction of input items
  __device__ __forceinline__ void InclusiveSum(T input, T &inclusive_output, T &warp_aggregate)
  {
    InclusiveScan(input, inclusive_output, cub::Sum(), warp_aggregate);
  }

  //! @}  end member group
  //! @name Exclusive prefix sums
  //! @{

  //! @rst
  //! Computes an exclusive prefix sum across the calling warp. The value of 0 is applied as the
  //! initial value, and is assigned to ``exclusive_output`` in *lane*\ :sub:`0`.
  //!
  //! * @identityzero
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix sums within a
  //! block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix sums
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveSum(thread_data, thread_data);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` in each of the four warps
  //! of threads will be ``0, 1, 2, ..., 31}``.
  //! @endrst
  //!
  //! @param[in] input
  //!   Calling thread's input item.
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item. May be aliased with `input`.
  __device__ __forceinline__ void ExclusiveSum(T input, T &exclusive_output)
  {
    T initial_value{};
    ExclusiveScan(input, exclusive_output, initial_value, cub::Sum());
  }

  //! @rst
  //! Computes an exclusive prefix sum across the calling warp. The value of 0 is applied as the
  //! initial value, and is assigned to ``exclusive_output`` in *lane*\ :sub:`0`.
  //! Also provides every thread with the warp-wide ``warp_aggregate`` of all inputs.
  //!
  //! * @identityzero
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix sums within a
  //! block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix sums
  //!        int warp_aggregate;
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveSum(thread_data,
  //!                                                     thread_data,
  //!                                                     warp_aggregate);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{1, 1, 1, 1, ...}``. The corresponding output ``thread_data`` in each of the four warps
  //! of threads will be ``0, 1, 2, ..., 31}``. Furthermore, ``warp_aggregate`` for all threads
  //! in all warps will be ``32``.
  //! @endrst
  //!
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[out] warp_aggregate
  //!   Warp-wide aggregate reduction of input items
  __device__ __forceinline__ void ExclusiveSum(T input, T &exclusive_output, T &warp_aggregate)
  {
    T initial_value{};
    ExclusiveScan(input, exclusive_output, initial_value, cub::Sum(), warp_aggregate);
  }

  //! @}  end member group
  //! @name Inclusive prefix scans
  //! @{

  //! @rst
  //! Computes an inclusive prefix scan using the specified binary scan functor across the
  //! calling warp.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide inclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute inclusive warp-wide prefix max scans
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).InclusiveScan(thread_data, thread_data, cub::Max());
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``0, 0, 2, 2, ..., 30, 30``, the output for the second warp would be
  //! ``32, 32, 34, 34, ..., 62, 62``, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[in] can_op
  //!   Binary scan operator
  template <typename ScanOp>
  __device__ __forceinline__ void InclusiveScan(T input, T &inclusive_output, ScanOp scan_op)
  {
    InternalWarpScan(temp_storage).InclusiveScan(input, inclusive_output, scan_op);
  }

  //! @rst
  //! Computes an inclusive prefix scan using the specified binary scan functor across the
  //! calling warp. Also provides every thread with the warp-wide ``warp_aggregate`` of
  //! all inputs.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide inclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute inclusive warp-wide prefix max scans
  //!        int warp_aggregate;
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).InclusiveScan(
  //!            thread_data, thread_data, cub::Max(), warp_aggregate);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``0, 0, 2, 2, ..., 30, 30``, the output for the second warp would be
  //! ``32, 32, 34, 34, ..., 62, 62``, etc.  Furthermore, ``warp_aggregate`` would be assigned
  //! ``30`` for threads in the first warp, ``62`` for threads in the second warp, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's output item. May be aliased with ``input``
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  //!
  //! @param[out] warp_aggregate
  //!   Warp-wide aggregate reduction of input items.
  template <typename ScanOp>
  __device__ __forceinline__ void
  InclusiveScan(T input, T &inclusive_output, ScanOp scan_op, T &warp_aggregate)
  {
    InternalWarpScan(temp_storage).InclusiveScan(input, inclusive_output, scan_op, warp_aggregate);
  }

  //! @}  end member group
  //! @name Exclusive prefix scans
  //! @{

  //! @rst
  //! Computes an exclusive prefix scan using the specified binary scan functor across the
  //! calling warp. Because no initial value is supplied, the ``output`` computed for
  //! *lane*\ :sub:`0` is undefined.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix max scans
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveScan(thread_data, thread_data, cub::Max());
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``?, 0, 0, 2, ..., 28, 30``, the output for the second warp would be
  //! ``?, 32, 32, 34, ..., 60, 62``, etc.
  //! (The output ``thread_data`` in warp *lane*\ :sub:`0` is undefined.)
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  template <typename ScanOp>
  __device__ __forceinline__ void ExclusiveScan(T input, T &exclusive_output, ScanOp scan_op)
  {
    InternalWarpScan internal(temp_storage);

    T inclusive_output;
    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input, inclusive_output, exclusive_output, scan_op, Int2Type<IS_INTEGER>());
  }

  //! @rst
  //! Computes an exclusive prefix scan using the specified binary scan functor across the
  //! calling warp.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix max scans
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveScan(thread_data,
  //!                                                      thread_data,
  //!                                                      INT_MIN,
  //!                                                      cub::Max());
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``INT_MIN, 0, 0, 2, ..., 28, 30``, the output for the second warp would be
  //! ``30, 32, 32, 34, ..., 60, 62``, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[in] initial_value
  //!   Initial value to seed the exclusive scan
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  template <typename ScanOp>
  __device__ __forceinline__ void
  ExclusiveScan(T input, T &exclusive_output, T initial_value, ScanOp scan_op)
  {
    InternalWarpScan internal(temp_storage);

    T inclusive_output;
    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input,
                    inclusive_output,
                    exclusive_output,
                    scan_op,
                    initial_value,
                    Int2Type<IS_INTEGER>());
  }

  //! @rst
  //! Computes an exclusive prefix scan using the specified binary scan functor across the
  //! calling warp. Because no initial value is supplied, the ``output`` computed for
  //! *lane*\ :sub:`0` is undefined. Also provides every thread with the warp-wide
  //! ``warp_aggregate`` of all inputs.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix max scans
  //!        int warp_aggregate;
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveScan(thread_data,
  //!                                                      thread_data,
  //!                                                      cub::Max(),
  //!                                                      warp_aggregate);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``?, 0, 0, 2, ..., 28, 30``, the output for the second warp would be
  //! ``?, 32, 32, 34, ..., 60, 62``, etc. (The output ``thread_data`` in warp *lane*\ :sub:`0`
  //! is undefined). Furthermore, ``warp_aggregate`` would be assigned ``30`` for threads in the
  //! first warp, \p 62 for threads in the second warp, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item. May be aliased with `input`
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  //!
  //! @param[out] warp_aggregate
  //!   Warp-wide aggregate reduction of input items
  template <typename ScanOp>
  __device__ __forceinline__ void
  ExclusiveScan(T input, T &exclusive_output, ScanOp scan_op, T &warp_aggregate)
  {
    InternalWarpScan internal(temp_storage);

    T inclusive_output;
    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input,
                    inclusive_output,
                    exclusive_output,
                    warp_aggregate,
                    scan_op,
                    Int2Type<IS_INTEGER>());
  }

  //! @rst
  //! Computes an exclusive prefix scan using the specified binary scan functor across the
  //! calling warp. Also provides every thread with the warp-wide ``warp_aggregate`` of
  //! all inputs.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix max scans
  //!        int warp_aggregate;
  //!        int warp_id = threadIdx.x / 32;
  //!        WarpScan(temp_storage[warp_id]).ExclusiveScan(thread_data,
  //!                                                      thread_data,
  //!                                                      INT_MIN,
  //!                                                      cub::Max(),
  //!                                                      warp_aggregate);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``thread_data`` in the first
  //! warp would be ``INT_MIN, 0, 0, 2, ..., 28, 30``, the output for the second warp would be
  //! ``30, 32, 32, 34, ..., 60, 62``, etc. Furthermore, ``warp_aggregate`` would be assigned
  //! ``30`` for threads in the first warp, ``62`` for threads in the second warp, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's output item.  May be aliased with `input`
  //!
  //! @param[in] initial_value
  //!   Initial value to seed the exclusive scan
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  //!
  //! @param[out] warp_aggregate
  //!   Warp-wide aggregate reduction of input items
  //!
  template <typename ScanOp>
  __device__ __forceinline__ void
  ExclusiveScan(T input, T &exclusive_output, T initial_value, ScanOp scan_op, T &warp_aggregate)
  {
    InternalWarpScan internal(temp_storage);

    T inclusive_output;
    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input,
                    inclusive_output,
                    exclusive_output,
                    warp_aggregate,
                    scan_op,
                    initial_value,
                    Int2Type<IS_INTEGER>());
  }

  //! @}  end member group
  //! @name Combination (inclusive & exclusive) prefix scans
  //! @{

  //! @rst
  //! Computes both inclusive and exclusive prefix scans using the specified binary scan functor
  //! across the calling warp. Because no initial value is supplied, the ``exclusive_output``
  //! computed for *lane*\ :sub:`0` is undefined.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide exclusive prefix max scans
  //! within a block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute exclusive warp-wide prefix max scans
  //!        int inclusive_partial, exclusive_partial;
  //!        WarpScan(temp_storage[warp_id]).Scan(thread_data,
  //!                                             inclusive_partial,
  //!                                             exclusive_partial,
  //!                                             cub::Max());
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``inclusive_partial`` in the
  //! first warp would be ``0, 0, 2, 2, ..., 30, 30``, the output for the second warp would be
  //! ``32, 32, 34, 34, ..., 62, 62``, etc. The corresponding output ``exclusive_partial`` in the
  //! first warp would be ``?, 0, 0, 2, ..., 28, 30``, the output for the second warp would be
  //! ``?, 32, 32, 34, ..., 60, 62``, etc.
  //! (The output ``thread_data`` in warp *lane*\ :sub:`0` is undefined.)
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's inclusive-scan output item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's exclusive-scan output item
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  template <typename ScanOp>
  __device__ __forceinline__ void
  Scan(T input, T &inclusive_output, T &exclusive_output, ScanOp scan_op)
  {
    InternalWarpScan internal(temp_storage);

    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input, inclusive_output, exclusive_output, scan_op, Int2Type<IS_INTEGER>());
  }

  //! @rst
  //! Computes both inclusive and exclusive prefix scans using the specified binary scan functor
  //! across the calling warp.
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates four concurrent warp-wide prefix max scans within a
  //! block of 128 threads (one per each of the 32-thread warps).
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Compute inclusive warp-wide prefix max scans
  //!        int warp_id = threadIdx.x / 32;
  //!        int inclusive_partial, exclusive_partial;
  //!        WarpScan(temp_storage[warp_id]).Scan(thread_data,
  //!                                             inclusive_partial,
  //!                                             exclusive_partial,
  //!                                             INT_MIN,
  //!                                             cub::Max());
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, -1, 2, -3, ..., 126, -127}``. The corresponding output ``inclusive_partial`` in the
  //! first warp would be ``0, 0, 2, 2, ..., 30, 30``, the output for the second warp would be
  //! ``32, 32, 34, 34, ..., 62, 62``, etc. The corresponding output ``exclusive_partial`` in the
  //! first warp would be ``INT_MIN, 0, 0, 2, ..., 28, 30``, the output for the second warp would
  //! be ``30, 32, 32, 34, ..., 60, 62``, etc.
  //! @endrst
  //!
  //! @tparam ScanOp
  //!   **[inferred]** Binary scan operator type having member
  //!   `T operator()(const T &a, const T &b)`
  //!
  //! @param[in] input
  //!   Calling thread's input item
  //!
  //! @param[out] inclusive_output
  //!   Calling thread's inclusive-scan output item
  //!
  //! @param[out] exclusive_output
  //!   Calling thread's exclusive-scan output item
  //!
  //! @param[in] initial_value
  //!   Initial value to seed the exclusive scan
  //!
  //! @param[in] scan_op
  //!   Binary scan operator
  template <typename ScanOp>
  __device__ __forceinline__ void
  Scan(T input, T &inclusive_output, T &exclusive_output, T initial_value, ScanOp scan_op)
  {
    InternalWarpScan internal(temp_storage);

    internal.InclusiveScan(input, inclusive_output, scan_op);

    internal.Update(input,
                    inclusive_output,
                    exclusive_output,
                    scan_op,
                    initial_value,
                    Int2Type<IS_INTEGER>());
  }

  //! @}  end member group
  //! @name Data exchange
  //! @{

  //! @rst
  //! Broadcast the value ``input`` from *lane*\ :sub:`src_lane` to all lanes in the warp
  //!
  //! * @smemwarpreuse
  //!
  //! Snippet
  //! +++++++
  //!
  //! The code snippet below illustrates the warp-wide broadcasts of values from *lane*\ :sub:`0`
  //! in each of four warps to all other threads in those warps.
  //!
  //! .. code-block:: c++
  //!
  //!    #include <cub/cub.cuh>
  //!
  //!    __global__ void ExampleKernel(...)
  //!    {
  //!        // Specialize WarpScan for type int
  //!        typedef cub::WarpScan<int> WarpScan;
  //!
  //!        // Allocate WarpScan shared memory for 4 warps
  //!        __shared__ typename WarpScan::TempStorage temp_storage[4];
  //!
  //!        // Obtain one input item per thread
  //!        int thread_data = ...
  //!
  //!        // Broadcast from lane0 in each warp to all other threads in the warp
  //!        int warp_id = threadIdx.x / 32;
  //!        thread_data = WarpScan(temp_storage[warp_id]).Broadcast(thread_data, 0);
  //!
  //! Suppose the set of input ``thread_data`` across the block of threads is
  //! ``{0, 1, 2, 3, ..., 127}``. The corresponding output ``thread_data`` will be
  //! ``{0, 0, ..., 0}`` in warp\ :sub:`0`,
  //! ``{32, 32, ..., 32}`` in warp\ :sub:`1`,
  //! ``{64, 64, ..., 64}`` in warp\ :sub:`2`, etc.
  //! @endrst
  //!
  //! @param[in] input
  //!   The value to broadcast
  //!
  //! @param[in] src_lane
  //!   Which warp lane is to do the broadcasting
  __device__ __forceinline__ T Broadcast(T input, unsigned int src_lane)
  {
    return InternalWarpScan(temp_storage).Broadcast(input, src_lane);
  }

  //@}  end member group
};

CUB_NAMESPACE_END