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  /**
   * \file
   * The cub::BlockScan class provides [<em>collective</em>](index.html#sec0) methods for computing a parallel prefix sum/scan of items partitioned across a CUDA thread block.
   */
  
  #pragma once
  
  #include "specializations/block_scan_raking.cuh"
  #include "specializations/block_scan_warp_scans.cuh"
  #include "../util_arch.cuh"
  #include "../util_type.cuh"
  #include "../util_ptx.cuh"
  #include "../util_namespace.cuh"
  
  /// Optional outer namespace(s)
  CUB_NS_PREFIX
  
  /// CUB namespace
  namespace cub {
  
  
  /******************************************************************************
   * Algorithmic variants
   ******************************************************************************/
  
  /**
   * \brief BlockScanAlgorithm enumerates alternative algorithms for cub::BlockScan to compute a parallel prefix scan across a CUDA thread block.
   */
  enum BlockScanAlgorithm
  {
  
      /**
       * \par Overview
       * An efficient "raking reduce-then-scan" prefix scan algorithm.  Execution is comprised of five phases:
       * -# Upsweep sequential reduction in registers (if threads contribute more than one input each).  Each thread then places the partial reduction of its item(s) into shared memory.
       * -# Upsweep sequential reduction in shared memory.  Threads within a single warp rake across segments of shared partial reductions.
       * -# A warp-synchronous Kogge-Stone style exclusive scan within the raking warp.
       * -# Downsweep sequential exclusive scan in shared memory.  Threads within a single warp rake across segments of shared partial reductions, seeded with the warp-scan output.
       * -# Downsweep sequential scan in registers (if threads contribute more than one input), seeded with the raking scan output.
       *
       * \par
       * \image html block_scan_raking.png
       * <div class="centercaption">\p BLOCK_SCAN_RAKING data flow for a hypothetical 16-thread thread block and 4-thread raking warp.</div>
       *
       * \par Performance Considerations
       * - Although this variant may suffer longer turnaround latencies when the
       *   GPU is under-occupied, it can often provide higher overall throughput
       *   across the GPU when suitably occupied.
       */
      BLOCK_SCAN_RAKING,
  
  
      /**
       * \par Overview
       * Similar to cub::BLOCK_SCAN_RAKING, but with fewer shared memory reads at
       * the expense of higher register pressure.  Raking threads preserve their
       * "upsweep" segment of values in registers while performing warp-synchronous
       * scan, allowing the "downsweep" not to re-read them from shared memory.
       */
      BLOCK_SCAN_RAKING_MEMOIZE,
  
  
      /**
       * \par Overview
       * A quick "tiled warpscans" prefix scan algorithm.  Execution is comprised of four phases:
       * -# Upsweep sequential reduction in registers (if threads contribute more than one input each).  Each thread then places the partial reduction of its item(s) into shared memory.
       * -# Compute a shallow, but inefficient warp-synchronous Kogge-Stone style scan within each warp.
       * -# A propagation phase where the warp scan outputs in each warp are updated with the aggregate from each preceding warp.
       * -# Downsweep sequential scan in registers (if threads contribute more than one input), seeded with the raking scan output.
       *
       * \par
       * \image html block_scan_warpscans.png
       * <div class="centercaption">\p BLOCK_SCAN_WARP_SCANS data flow for a hypothetical 16-thread thread block and 4-thread raking warp.</div>
       *
       * \par Performance Considerations
       * - Although this variant may suffer lower overall throughput across the
       *   GPU because due to a heavy reliance on inefficient warpscans, it can
       *   often provide lower turnaround latencies when the GPU is under-occupied.
       */
      BLOCK_SCAN_WARP_SCANS,
  };
  
  
  /******************************************************************************
   * Block scan
   ******************************************************************************/
  
  /**
   * \brief The BlockScan class provides [<em>collective</em>](index.html#sec0) methods for computing a parallel prefix sum/scan of items partitioned across a CUDA thread block. ![](block_scan_logo.png)
   * \ingroup BlockModule
   *
   * \tparam T                Data type being scanned
   * \tparam BLOCK_DIM_X      The thread block length in threads along the X dimension
   * \tparam ALGORITHM        <b>[optional]</b> cub::BlockScanAlgorithm enumerator specifying the underlying algorithm to use (default: cub::BLOCK_SCAN_RAKING)
   * \tparam BLOCK_DIM_Y      <b>[optional]</b> The thread block length in threads along the Y dimension (default: 1)
   * \tparam BLOCK_DIM_Z      <b>[optional]</b> The thread block length in threads along the Z dimension (default: 1)
   * \tparam PTX_ARCH         <b>[optional]</b> \ptxversion
   *
   * \par Overview
   * - Given a list of input elements and a binary reduction operator, a [<em>prefix scan</em>](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.  <em>Prefix sum</em>
   *   connotes a prefix scan with the addition operator. The term \em inclusive indicates
   *   that the <em>i</em><sup>th</sup> output reduction incorporates the <em>i</em><sup>th</sup> input.
   *   The term \em exclusive indicates the <em>i</em><sup>th</sup> input is not incorporated into
   *   the <em>i</em><sup>th</sup> output reduction.
   * - \rowmajor
   * - BlockScan can be optionally specialized by algorithm to accommodate different workload profiles:
   *   -# <b>cub::BLOCK_SCAN_RAKING</b>.  An efficient (high throughput) "raking reduce-then-scan" prefix scan algorithm. [More...](\ref cub::BlockScanAlgorithm)
   *   -# <b>cub::BLOCK_SCAN_RAKING_MEMOIZE</b>.  Similar to cub::BLOCK_SCAN_RAKING, but having higher throughput at the expense of additional register pressure for intermediate storage. [More...](\ref cub::BlockScanAlgorithm)
   *   -# <b>cub::BLOCK_SCAN_WARP_SCANS</b>.  A quick (low latency) "tiled warpscans" prefix scan algorithm. [More...](\ref cub::BlockScanAlgorithm)
   *
   * \par Performance Considerations
   * - \granularity
   * - Uses special instructions when applicable (e.g., warp \p SHFL)
   * - Uses synchronization-free communication between warp lanes when applicable
   * - Invokes a minimal number of minimal block-wide synchronization barriers (only
   *   one or two depending on algorithm selection)
   * - Incurs zero bank conflicts for most types
   * - Computation is slightly more efficient (i.e., having lower instruction overhead) for:
   *   - Prefix sum variants (<b><em>vs.</em></b> generic scan)
   *   - \blocksize
   * - See cub::BlockScanAlgorithm for performance details regarding algorithmic alternatives
   *
   * \par A Simple Example
   * \blockcollective{BlockScan}
   * \par
   * The code snippet below illustrates an exclusive prefix sum of 512 integer items that
   * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
   * where each thread owns 4 consecutive items.
   * \par
   * \code
   * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
   *
   * __global__ void ExampleKernel(...)
   * {
   *     // Specialize BlockScan for a 1D block of 128 threads on type int
   *     typedef cub::BlockScan<int, 128> BlockScan;
   *
   *     // Allocate shared memory for BlockScan
   *     __shared__ typename BlockScan::TempStorage temp_storage;
   *
   *     // Obtain a segment of consecutive items that are blocked across threads
   *     int thread_data[4];
   *     ...
   *
   *     // Collectively compute the block-wide exclusive prefix sum
   *     BlockScan(temp_storage).ExclusiveSum(thread_data, thread_data);
   *
   * \endcode
   * \par
   * Suppose the set of input \p thread_data across the block of threads is
   * <tt>{[1,1,1,1], [1,1,1,1], ..., [1,1,1,1]}</tt>.
   * The corresponding output \p thread_data in those threads will be
   * <tt>{[0,1,2,3], [4,5,6,7], ..., [508,509,510,511]}</tt>.
   *
   */
  template <
      typename            T,
      int                 BLOCK_DIM_X,
      BlockScanAlgorithm  ALGORITHM       = BLOCK_SCAN_RAKING,
      int                 BLOCK_DIM_Y     = 1,
      int                 BLOCK_DIM_Z     = 1,
      int                 PTX_ARCH        = CUB_PTX_ARCH>
  class BlockScan
  {
  private:
  
      /******************************************************************************
       * Constants and type definitions
       ******************************************************************************/
  
      /// Constants
      enum
      {
          /// The thread block size in threads
          BLOCK_THREADS = BLOCK_DIM_X * BLOCK_DIM_Y * BLOCK_DIM_Z,
      };
  
      /**
       * Ensure the template parameterization meets the requirements of the
       * specified algorithm. Currently, the BLOCK_SCAN_WARP_SCANS policy
       * cannot be used with thread block sizes not a multiple of the
       * architectural warp size.
       */
      static const BlockScanAlgorithm SAFE_ALGORITHM =
          ((ALGORITHM == BLOCK_SCAN_WARP_SCANS) && (BLOCK_THREADS % CUB_WARP_THREADS(PTX_ARCH) != 0)) ?
              BLOCK_SCAN_RAKING :
              ALGORITHM;
  
      typedef BlockScanWarpScans<T, BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z, PTX_ARCH> WarpScans;
      typedef BlockScanRaking<T, BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z, (SAFE_ALGORITHM == BLOCK_SCAN_RAKING_MEMOIZE), PTX_ARCH> Raking;
  
      /// Define the delegate type for the desired algorithm
      typedef typename If<(SAFE_ALGORITHM == BLOCK_SCAN_WARP_SCANS),
          WarpScans,
          Raking>::Type InternalBlockScan;
  
      /// Shared memory storage layout type for BlockScan
      typedef typename InternalBlockScan::TempStorage _TempStorage;
  
  
      /******************************************************************************
       * Thread fields
       ******************************************************************************/
  
      /// Shared storage reference
      _TempStorage &temp_storage;
  
      /// Linear thread-id
      unsigned int linear_tid;
  
  
      /******************************************************************************
       * Utility methods
       ******************************************************************************/
  
      /// Internal storage allocator
      __device__ __forceinline__ _TempStorage& PrivateStorage()
      {
          __shared__ _TempStorage private_storage;
          return private_storage;
      }
  
  
      /******************************************************************************
       * Public types
       ******************************************************************************/
  public:
  
      /// \smemstorage{BlockScan}
      struct TempStorage : Uninitialized<_TempStorage> {};
  
  
      /******************************************************************//**
       * 
  ame Collective constructors
       *********************************************************************/
      //@{
  
      /**
       * \brief Collective constructor using a private static allocation of shared memory as temporary storage.
       */
      __device__ __forceinline__ BlockScan()
      :
          temp_storage(PrivateStorage()),
          linear_tid(RowMajorTid(BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z))
      {}
  
  
      /**
       * \brief Collective constructor using the specified memory allocation as temporary storage.
       */
      __device__ __forceinline__ BlockScan(
          TempStorage &temp_storage)             ///< [in] Reference to memory allocation having layout type TempStorage
      :
          temp_storage(temp_storage.Alias()),
          linear_tid(RowMajorTid(BLOCK_DIM_X, BLOCK_DIM_Y, BLOCK_DIM_Z))
      {}
  
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Exclusive prefix sum operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.  The value of 0 is applied as the initial value, and is assigned to \p output in <em>thread</em><sub>0</sub>.
       *
       * \par
       * - \identityzero
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix sum of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix sum
       *     BlockScan(temp_storage).ExclusiveSum(thread_data, thread_data);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>1, 1, ..., 1</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>0, 1, ..., 127</tt>.
       *
       */
      __device__ __forceinline__ void ExclusiveSum(
          T               input,                          ///< [in] Calling thread's input item
          T               &output)                        ///< [out] Calling thread's output item (may be aliased to \p input)
      {
          T initial_value = 0;
          ExclusiveScan(input, output, initial_value, cub::Sum());
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.  The value of 0 is applied as the initial value, and is assigned to \p output in <em>thread</em><sub>0</sub>.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \identityzero
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix sum of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix sum
       *     int block_aggregate;
       *     BlockScan(temp_storage).ExclusiveSum(thread_data, thread_data, block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>1, 1, ..., 1</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>0, 1, ..., 127</tt>.
       * Furthermore the value \p 128 will be stored in \p block_aggregate for all threads.
       *
       */
      __device__ __forceinline__ void ExclusiveSum(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          T initial_value = 0;
          ExclusiveScan(input, output, initial_value, cub::Sum(), block_aggregate);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.  Instead of using 0 as the block-wide prefix, the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \identityzero
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an exclusive prefix sum over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total += block_aggregate;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data = d_data[block_offset];
       *
       *         // Collectively compute the block-wide exclusive prefix sum
       *         BlockScan(temp_storage).ExclusiveSum(
       *             thread_data, thread_data, prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         d_data[block_offset] = thread_data;
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>1, 1, 1, 1, 1, 1, 1, 1, ...</tt>.
       * The corresponding output for the first segment will be <tt>0, 1, ..., 127</tt>.
       * The output for the second segment will be <tt>128, 129, ..., 255</tt>.
       *
       * \tparam BlockPrefixCallbackOp        <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void ExclusiveSum(
          T                       input,                          ///< [in] Calling thread's input item
          T                       &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          ExclusiveScan(input, output, cub::Sum(), block_prefix_callback_op);
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Exclusive prefix sum operations (multiple data per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.  The value of 0 is applied as the initial value, and is assigned to \p output[0] in <em>thread</em><sub>0</sub>.
       *
       * \par
       * - \identityzero
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix sum of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix sum
       *     BlockScan(temp_storage).ExclusiveSum(thread_data, thread_data);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>{ [1,1,1,1], [1,1,1,1], ..., [1,1,1,1] }</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>{ [0,1,2,3], [4,5,6,7], ..., [508,509,510,511] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       */
      template <int ITEMS_PER_THREAD>
      __device__ __forceinline__ void ExclusiveSum(
          T                 (&input)[ITEMS_PER_THREAD],   ///< [in] Calling thread's input items
          T                 (&output)[ITEMS_PER_THREAD])  ///< [out] Calling thread's output items (may be aliased to \p input)
      {
          T initial_value = 0;
          ExclusiveScan(input, output, initial_value, cub::Sum());
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.  The value of 0 is applied as the initial value, and is assigned to \p output[0] in <em>thread</em><sub>0</sub>.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \identityzero
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix sum of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix sum
       *     int block_aggregate;
       *     BlockScan(temp_storage).ExclusiveSum(thread_data, thread_data, block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>{ [1,1,1,1], [1,1,1,1], ..., [1,1,1,1] }</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>{ [0,1,2,3], [4,5,6,7], ..., [508,509,510,511] }</tt>.
       * Furthermore the value \p 512 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       */
      template <int ITEMS_PER_THREAD>
      __device__ __forceinline__ void ExclusiveSum(
          T                 (&input)[ITEMS_PER_THREAD],       ///< [in] Calling thread's input items
          T                 (&output)[ITEMS_PER_THREAD],      ///< [out] Calling thread's output items (may be aliased to \p input)
          T                 &block_aggregate)                 ///< [out] block-wide aggregate reduction of input items
      {
          // Reduce consecutive thread items in registers
          T initial_value = 0;
          ExclusiveScan(input, output, initial_value, cub::Sum(), block_aggregate);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.  Instead of using 0 as the block-wide prefix, the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \identityzero
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an exclusive prefix sum over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 512 integer items that are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3)
       * across 128 threads where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total += block_aggregate;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockLoad, BlockStore, and BlockScan for a 1D block of 128 threads, 4 ints per thread
       *     typedef cub::BlockLoad<int*, 128, 4, BLOCK_LOAD_TRANSPOSE>   BlockLoad;
       *     typedef cub::BlockStore<int, 128, 4, BLOCK_STORE_TRANSPOSE>  BlockStore;
       *     typedef cub::BlockScan<int, 128>                             BlockScan;
       *
       *     // Allocate aliased shared memory for BlockLoad, BlockStore, and BlockScan
       *     __shared__ union {
       *         typename BlockLoad::TempStorage     load;
       *         typename BlockScan::TempStorage     scan;
       *         typename BlockStore::TempStorage    store;
       *     } temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128 * 4)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data[4];
       *         BlockLoad(temp_storage.load).Load(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *
       *         // Collectively compute the block-wide exclusive prefix sum
       *         int block_aggregate;
       *         BlockScan(temp_storage.scan).ExclusiveSum(
       *             thread_data, thread_data, prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         BlockStore(temp_storage.store).Store(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>1, 1, 1, 1, 1, 1, 1, 1, ...</tt>.
       * The corresponding output for the first segment will be <tt>0, 1, 2, 3, ..., 510, 511</tt>.
       * The output for the second segment will be <tt>512, 513, 514, 515, ..., 1022, 1023</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam BlockPrefixCallbackOp        <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          int ITEMS_PER_THREAD,
          typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void ExclusiveSum(
          T                       (&input)[ITEMS_PER_THREAD],   ///< [in] Calling thread's input items
          T                       (&output)[ITEMS_PER_THREAD],  ///< [out] Calling thread's output items (may be aliased to \p input)
          BlockPrefixCallbackOp   &block_prefix_callback_op)    ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          ExclusiveScan(input, output, cub::Sum(), block_prefix_callback_op);
      }
  
  
  
      //@}  end member group        // Exclusive prefix sums
      /******************************************************************//**
       * 
  ame Exclusive prefix scan operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix max scan of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix max scan
       *     BlockScan(temp_storage).ExclusiveScan(thread_data, thread_data, INT_MIN, cub::Max());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>0, -1, 2, -3, ..., 126, -127</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>INT_MIN, 0, 0, 2, ..., 124, 126</tt>.
       *
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          T               initial_value,                  ///< [in] Initial value to seed the exclusive scan (and is assigned to \p output[0] in <em>thread</em><sub>0</sub>)
          ScanOp          scan_op)                        ///< [in] Binary scan functor 
      {
          InternalBlockScan(temp_storage).ExclusiveScan(input, output, initial_value, scan_op);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix max scan of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix max scan
       *     int block_aggregate;
       *     BlockScan(temp_storage).ExclusiveScan(thread_data, thread_data, INT_MIN, cub::Max(), block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>0, -1, 2, -3, ..., 126, -127</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>INT_MIN, 0, 0, 2, ..., 124, 126</tt>.
       * Furthermore the value \p 126 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ScanOp   <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T               input,              ///< [in] Calling thread's input items
          T               &output,            ///< [out] Calling thread's output items (may be aliased to \p input)
          T               initial_value,      ///< [in] Initial value to seed the exclusive scan (and is assigned to \p output[0] in <em>thread</em><sub>0</sub>)
          ScanOp          scan_op,            ///< [in] Binary scan functor 
          T               &block_aggregate)   ///< [out] block-wide aggregate reduction of input items
      {
          InternalBlockScan(temp_storage).ExclusiveScan(input, output, initial_value, scan_op, block_aggregate);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an exclusive prefix max scan over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total = (block_aggregate > old_prefix) ? block_aggregate : old_prefix;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(INT_MIN);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data = d_data[block_offset];
       *
       *         // Collectively compute the block-wide exclusive prefix max scan
       *         BlockScan(temp_storage).ExclusiveScan(
       *             thread_data, thread_data, INT_MIN, cub::Max(), prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         d_data[block_offset] = thread_data;
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>0, -1, 2, -3, 4, -5, ...</tt>.
       * The corresponding output for the first segment will be <tt>INT_MIN, 0, 0, 2, ..., 124, 126</tt>.
       * The output for the second segment will be <tt>126, 128, 128, 130, ..., 252, 254</tt>.
       *
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       * \tparam BlockPrefixCallbackOp        <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          typename ScanOp,
          typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void ExclusiveScan(
          T                       input,                          ///< [in] Calling thread's input item
          T                       &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp                  scan_op,                        ///< [in] Binary scan functor 
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          InternalBlockScan(temp_storage).ExclusiveScan(input, output, scan_op, block_prefix_callback_op);
      }
  
  
      //@}  end member group        // Inclusive prefix sums
      /******************************************************************//**
       * 
  ame Exclusive prefix scan operations (multiple data per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix max scan of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix max scan
       *     BlockScan(temp_storage).ExclusiveScan(thread_data, thread_data, INT_MIN, cub::Max());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,-1,2,-3], [4,-5,6,-7], ..., [508,-509,510,-511] }</tt>.
       * The corresponding output \p thread_data in those threads will be
       * <tt>{ [INT_MIN,0,0,2], [2,4,4,6], ..., [506,508,508,510] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T                 (&input)[ITEMS_PER_THREAD],   ///< [in] Calling thread's input items
          T                 (&output)[ITEMS_PER_THREAD],  ///< [out] Calling thread's output items (may be aliased to \p input)
          T                 initial_value,                ///< [in] Initial value to seed the exclusive scan (and is assigned to \p output[0] in <em>thread</em><sub>0</sub>)
          ScanOp            scan_op)                      ///< [in] Binary scan functor
      {
          // Reduce consecutive thread items in registers
          T thread_prefix = internal::ThreadReduce(input, scan_op);
  
          // Exclusive thread block-scan
          ExclusiveScan(thread_prefix, thread_prefix, initial_value, scan_op);
  
          // Exclusive scan in registers with prefix as seed
          internal::ThreadScanExclusive(input, output, scan_op, thread_prefix);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an exclusive prefix max scan of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide exclusive prefix max scan
       *     int block_aggregate;
       *     BlockScan(temp_storage).ExclusiveScan(thread_data, thread_data, INT_MIN, cub::Max(), block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>{ [0,-1,2,-3], [4,-5,6,-7], ..., [508,-509,510,-511] }</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>{ [INT_MIN,0,0,2], [2,4,4,6], ..., [506,508,508,510] }</tt>.
       * Furthermore the value \p 510 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T                 (&input)[ITEMS_PER_THREAD],   ///< [in] Calling thread's input items
          T                 (&output)[ITEMS_PER_THREAD],  ///< [out] Calling thread's output items (may be aliased to \p input)
          T                 initial_value,                ///< [in] Initial value to seed the exclusive scan (and is assigned to \p output[0] in <em>thread</em><sub>0</sub>)
          ScanOp            scan_op,                      ///< [in] Binary scan functor
          T                 &block_aggregate)             ///< [out] block-wide aggregate reduction of input items
      {
          // Reduce consecutive thread items in registers
          T thread_prefix = internal::ThreadReduce(input, scan_op);
  
          // Exclusive thread block-scan
          ExclusiveScan(thread_prefix, thread_prefix, initial_value, scan_op, block_aggregate);
  
          // Exclusive scan in registers with prefix as seed
          internal::ThreadScanExclusive(input, output, scan_op, thread_prefix);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an exclusive prefix max scan over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total = (block_aggregate > old_prefix) ? block_aggregate : old_prefix;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockLoad, BlockStore, and BlockScan for a 1D block of 128 threads, 4 ints per thread
       *     typedef cub::BlockLoad<int*, 128, 4, BLOCK_LOAD_TRANSPOSE>   BlockLoad;
       *     typedef cub::BlockStore<int, 128, 4, BLOCK_STORE_TRANSPOSE>  BlockStore;
       *     typedef cub::BlockScan<int, 128>                             BlockScan;
       *
       *     // Allocate aliased shared memory for BlockLoad, BlockStore, and BlockScan
       *     __shared__ union {
       *         typename BlockLoad::TempStorage     load;
       *         typename BlockScan::TempStorage     scan;
       *         typename BlockStore::TempStorage    store;
       *     } temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128 * 4)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data[4];
       *         BlockLoad(temp_storage.load).Load(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *
       *         // Collectively compute the block-wide exclusive prefix max scan
       *         BlockScan(temp_storage.scan).ExclusiveScan(
       *             thread_data, thread_data, INT_MIN, cub::Max(), prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         BlockStore(temp_storage.store).Store(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>0, -1, 2, -3, 4, -5, ...</tt>.
       * The corresponding output for the first segment will be <tt>INT_MIN, 0, 0, 2, 2, 4, ..., 508, 510</tt>.
       * The output for the second segment will be <tt>510, 512, 512, 514, 514, 516, ..., 1020, 1022</tt>.
       *
       * \tparam ITEMS_PER_THREAD         <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp                   <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       * \tparam BlockPrefixCallbackOp    <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp,
          typename        BlockPrefixCallbackOp>
      __device__ __forceinline__ void ExclusiveScan(
          T                       (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T                       (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp                  scan_op,                        ///< [in] Binary scan functor
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          // Reduce consecutive thread items in registers
          T thread_prefix = internal::ThreadReduce(input, scan_op);
  
          // Exclusive thread block-scan
          ExclusiveScan(thread_prefix, thread_prefix, scan_op, block_prefix_callback_op);
  
          // Exclusive scan in registers with prefix as seed
          internal::ThreadScanExclusive(input, output, scan_op, thread_prefix);
      }
  
  
      //@}  end member group
  #ifndef DOXYGEN_SHOULD_SKIP_THIS    // Do not document no-initial-value scans
  
      /******************************************************************//**
       * 
  ame Exclusive prefix scan operations (no initial value, single datum per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  With no initial value, the output computed for <em>thread</em><sub>0</sub> is undefined.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp          scan_op)                        ///< [in] Binary scan functor
      {
          InternalBlockScan(temp_storage).ExclusiveScan(input, output, scan_op);
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  Also provides every thread with the block-wide \p block_aggregate of all inputs.  With no initial value, the output computed for <em>thread</em><sub>0</sub> is undefined.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \tparam ScanOp   <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp          scan_op,                        ///< [in] Binary scan functor
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          InternalBlockScan(temp_storage).ExclusiveScan(input, output, scan_op, block_aggregate);
      }
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Exclusive prefix scan operations (no initial value, multiple data per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  With no initial value, the output computed for <em>thread</em><sub>0</sub> is undefined.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T                 (&input)[ITEMS_PER_THREAD],   ///< [in] Calling thread's input items
          T                 (&output)[ITEMS_PER_THREAD],  ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp            scan_op)                      ///< [in] Binary scan functor
      {
          // Reduce consecutive thread items in registers
          T thread_partial = internal::ThreadReduce(input, scan_op);
  
          // Exclusive thread block-scan
          ExclusiveScan(thread_partial, thread_partial, scan_op);
  
          // Exclusive scan in registers with prefix
          internal::ThreadScanExclusive(input, output, scan_op, thread_partial, (linear_tid != 0));
      }
  
  
      /**
       * \brief Computes an exclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  Also provides every thread with the block-wide \p block_aggregate of all inputs.  With no initial value, the output computed for <em>thread</em><sub>0</sub> is undefined.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp>
      __device__ __forceinline__ void ExclusiveScan(
          T               (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T               (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp          scan_op,                        ///< [in] Binary scan functor
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          // Reduce consecutive thread items in registers
          T thread_partial = internal::ThreadReduce(input, scan_op);
  
          // Exclusive thread block-scan
          ExclusiveScan(thread_partial, thread_partial, scan_op, block_aggregate);
  
          // Exclusive scan in registers with prefix
          internal::ThreadScanExclusive(input, output, scan_op, thread_partial, (linear_tid != 0));
      }
  
  
      //@}  end member group
  #endif // DOXYGEN_SHOULD_SKIP_THIS  // Do not document no-initial-value scans
  
      /******************************************************************//**
       * 
  ame Inclusive prefix sum operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.
       *
       * \par
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix sum of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix sum
       *     BlockScan(temp_storage).InclusiveSum(thread_data, thread_data);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>1, 1, ..., 1</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>1, 2, ..., 128</tt>.
       *
       */
      __device__ __forceinline__ void InclusiveSum(
          T               input,                          ///< [in] Calling thread's input item
          T               &output)                        ///< [out] Calling thread's output item (may be aliased to \p input)
      {
          InclusiveScan(input, output, cub::Sum());
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix sum of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix sum
       *     int block_aggregate;
       *     BlockScan(temp_storage).InclusiveSum(thread_data, thread_data, block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>1, 1, ..., 1</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>1, 2, ..., 128</tt>.
       * Furthermore the value \p 128 will be stored in \p block_aggregate for all threads.
       *
       */
      __device__ __forceinline__ void InclusiveSum(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          InclusiveScan(input, output, cub::Sum(), block_aggregate);
      }
  
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes one input element.  Instead of using 0 as the block-wide prefix, the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an inclusive prefix sum over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total += block_aggregate;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data = d_data[block_offset];
       *
       *         // Collectively compute the block-wide inclusive prefix sum
       *         BlockScan(temp_storage).InclusiveSum(
       *             thread_data, thread_data, prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         d_data[block_offset] = thread_data;
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>1, 1, 1, 1, 1, 1, 1, 1, ...</tt>.
       * The corresponding output for the first segment will be <tt>1, 2, ..., 128</tt>.
       * The output for the second segment will be <tt>129, 130, ..., 256</tt>.
       *
       * \tparam BlockPrefixCallbackOp          <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void InclusiveSum(
          T                       input,                          ///< [in] Calling thread's input item
          T                       &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          InclusiveScan(input, output, cub::Sum(), block_prefix_callback_op);
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Inclusive prefix sum operations (multiple data per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.
       *
       * \par
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix sum of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix sum
       *     BlockScan(temp_storage).InclusiveSum(thread_data, thread_data);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>{ [1,1,1,1], [1,1,1,1], ..., [1,1,1,1] }</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>{ [1,2,3,4], [5,6,7,8], ..., [509,510,511,512] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       */
      template <int ITEMS_PER_THREAD>
      __device__ __forceinline__ void InclusiveSum(
          T               (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T               (&output)[ITEMS_PER_THREAD])    ///< [out] Calling thread's output items (may be aliased to \p input)
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveSum(input[0], output[0]);
          }
          else
          {
              // Reduce consecutive thread items in registers
              Sum scan_op;
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan
              ExclusiveSum(thread_prefix, thread_prefix);
  
              // Inclusive scan in registers with prefix as seed
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix, (linear_tid != 0));
          }
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix sum of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix sum
       *     int block_aggregate;
       *     BlockScan(temp_storage).InclusiveSum(thread_data, thread_data, block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [1,1,1,1], [1,1,1,1], ..., [1,1,1,1] }</tt>.  The
       * corresponding output \p thread_data in those threads will be
       * <tt>{ [1,2,3,4], [5,6,7,8], ..., [509,510,511,512] }</tt>.
       * Furthermore the value \p 512 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <int ITEMS_PER_THREAD>
      __device__ __forceinline__ void InclusiveSum(
          T               (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T               (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveSum(input[0], output[0], block_aggregate);
          }
          else
          {
              // Reduce consecutive thread items in registers
              Sum scan_op;
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan
              ExclusiveSum(thread_prefix, thread_prefix, block_aggregate);
  
              // Inclusive scan in registers with prefix as seed
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix, (linear_tid != 0));
          }
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using addition (+) as the scan operator.  Each thread contributes an array of consecutive input elements.  Instead of using 0 as the block-wide prefix, the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an inclusive prefix sum over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 512 integer items that are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3)
       * across 128 threads where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total += block_aggregate;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockLoad, BlockStore, and BlockScan for a 1D block of 128 threads, 4 ints per thread
       *     typedef cub::BlockLoad<int*, 128, 4, BLOCK_LOAD_TRANSPOSE>   BlockLoad;
       *     typedef cub::BlockStore<int, 128, 4, BLOCK_STORE_TRANSPOSE>  BlockStore;
       *     typedef cub::BlockScan<int, 128>                             BlockScan;
       *
       *     // Allocate aliased shared memory for BlockLoad, BlockStore, and BlockScan
       *     __shared__ union {
       *         typename BlockLoad::TempStorage     load;
       *         typename BlockScan::TempStorage     scan;
       *         typename BlockStore::TempStorage    store;
       *     } temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128 * 4)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data[4];
       *         BlockLoad(temp_storage.load).Load(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *
       *         // Collectively compute the block-wide inclusive prefix sum
       *         BlockScan(temp_storage.scan).IncluisveSum(
       *             thread_data, thread_data, prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         BlockStore(temp_storage.store).Store(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>1, 1, 1, 1, 1, 1, 1, 1, ...</tt>.
       * The corresponding output for the first segment will be <tt>1, 2, 3, 4, ..., 511, 512</tt>.
       * The output for the second segment will be <tt>513, 514, 515, 516, ..., 1023, 1024</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam BlockPrefixCallbackOp        <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          int ITEMS_PER_THREAD,
          typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void InclusiveSum(
          T                       (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T                       (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveSum(input[0], output[0], block_prefix_callback_op);
          }
          else
          {
              // Reduce consecutive thread items in registers
              Sum scan_op;
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan
              ExclusiveSum(thread_prefix, thread_prefix, block_prefix_callback_op);
  
              // Inclusive scan in registers with prefix as seed
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix);
          }
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Inclusive prefix scan operations
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix max scan of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix max scan
       *     BlockScan(temp_storage).InclusiveScan(thread_data, thread_data, cub::Max());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>0, -1, 2, -3, ..., 126, -127</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>0, 0, 2, 2, ..., 126, 126</tt>.
       *
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void InclusiveScan(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp          scan_op)                        ///< [in] Binary scan functor 
      {
          InternalBlockScan(temp_storage).InclusiveScan(input, output, scan_op);
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix max scan of 128 integer items that
       * are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain input item for each thread
       *     int thread_data;
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix max scan
       *     int block_aggregate;
       *     BlockScan(temp_storage).InclusiveScan(thread_data, thread_data, cub::Max(), block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>0, -1, 2, -3, ..., 126, -127</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>0, 0, 2, 2, ..., 126, 126</tt>.
       * Furthermore the value \p 126 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ScanOp   <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <typename ScanOp>
      __device__ __forceinline__ void InclusiveScan(
          T               input,                          ///< [in] Calling thread's input item
          T               &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp          scan_op,                        ///< [in] Binary scan functor 
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          InternalBlockScan(temp_storage).InclusiveScan(input, output, scan_op, block_aggregate);
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes one input element.  the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - Supports non-commutative scan operators.
       * - \rowmajor
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an inclusive prefix max scan over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total = (block_aggregate > old_prefix) ? block_aggregate : old_prefix;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(INT_MIN);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data = d_data[block_offset];
       *
       *         // Collectively compute the block-wide inclusive prefix max scan
       *         BlockScan(temp_storage).InclusiveScan(
       *             thread_data, thread_data, cub::Max(), prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         d_data[block_offset] = thread_data;
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>0, -1, 2, -3, 4, -5, ...</tt>.
       * The corresponding output for the first segment will be <tt>0, 0, 2, 2, ..., 126, 126</tt>.
       * The output for the second segment will be <tt>128, 128, 130, 130, ..., 254, 254</tt>.
       *
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       * \tparam BlockPrefixCallbackOp        <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          typename ScanOp,
          typename BlockPrefixCallbackOp>
      __device__ __forceinline__ void InclusiveScan(
          T                       input,                          ///< [in] Calling thread's input item
          T                       &output,                        ///< [out] Calling thread's output item (may be aliased to \p input)
          ScanOp                  scan_op,                        ///< [in] Binary scan functor 
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          InternalBlockScan(temp_storage).InclusiveScan(input, output, scan_op, block_prefix_callback_op);
      }
  
  
      //@}  end member group
      /******************************************************************//**
       * 
  ame Inclusive prefix scan operations (multiple data per thread)
       *********************************************************************/
      //@{
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix max scan of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix max scan
       *     BlockScan(temp_storage).InclusiveScan(thread_data, thread_data, cub::Max());
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is <tt>{ [0,-1,2,-3], [4,-5,6,-7], ..., [508,-509,510,-511] }</tt>.  The
       * corresponding output \p thread_data in those threads will be <tt>{ [0,0,2,2], [4,4,6,6], ..., [508,508,510,510] }</tt>.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp>
      __device__ __forceinline__ void InclusiveScan(
          T               (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T               (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp          scan_op)                        ///< [in] Binary scan functor 
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveScan(input[0], output[0], scan_op);
          }
          else
          {
              // Reduce consecutive thread items in registers
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan
              ExclusiveScan(thread_prefix, thread_prefix, scan_op);
  
              // Inclusive scan in registers with prefix as seed (first thread does not seed)
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix, (linear_tid != 0));
          }
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates an inclusive prefix max scan of 512 integer items that
       * are partitioned in a [<em>blocked arrangement</em>](index.html#sec5sec3) across 128 threads
       * where each thread owns 4 consecutive items.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * __global__ void ExampleKernel(...)
       * {
       *     // Specialize BlockScan for a 1D block of 128 threads on type int
       *     typedef cub::BlockScan<int, 128> BlockScan;
       *
       *     // Allocate shared memory for BlockScan
       *     __shared__ typename BlockScan::TempStorage temp_storage;
       *
       *     // Obtain a segment of consecutive items that are blocked across threads
       *     int thread_data[4];
       *     ...
       *
       *     // Collectively compute the block-wide inclusive prefix max scan
       *     int block_aggregate;
       *     BlockScan(temp_storage).InclusiveScan(thread_data, thread_data, cub::Max(), block_aggregate);
       *
       * \endcode
       * \par
       * Suppose the set of input \p thread_data across the block of threads is
       * <tt>{ [0,-1,2,-3], [4,-5,6,-7], ..., [508,-509,510,-511] }</tt>.
       * The corresponding output \p thread_data in those threads will be
       * <tt>{ [0,0,2,2], [4,4,6,6], ..., [508,508,510,510] }</tt>.
       * Furthermore the value \p 510 will be stored in \p block_aggregate for all threads.
       *
       * \tparam ITEMS_PER_THREAD     <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp               <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename         ScanOp>
      __device__ __forceinline__ void InclusiveScan(
          T               (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T               (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp          scan_op,                        ///< [in] Binary scan functor 
          T               &block_aggregate)               ///< [out] block-wide aggregate reduction of input items
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveScan(input[0], output[0], scan_op, block_aggregate);
          }
          else
          {
              // Reduce consecutive thread items in registers
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan (with no initial value)
              ExclusiveScan(thread_prefix, thread_prefix, scan_op, block_aggregate);
  
              // Inclusive scan in registers with prefix as seed (first thread does not seed)
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix, (linear_tid != 0));
          }
      }
  
  
      /**
       * \brief Computes an inclusive block-wide prefix scan using the specified binary \p scan_op functor.  Each thread contributes an array of consecutive input elements.  the call-back functor \p block_prefix_callback_op is invoked by the first warp in the block, and the value returned by <em>lane</em><sub>0</sub> in that warp is used as the "seed" value that logically prefixes the thread block's scan inputs.  Also provides every thread with the block-wide \p block_aggregate of all inputs.
       *
       * \par
       * - The \p block_prefix_callback_op functor must implement a member function <tt>T operator()(T block_aggregate)</tt>.
       *   The functor's input parameter \p block_aggregate is the same value also returned by the scan operation.
       *   The functor will be invoked by the first warp of threads in the block, however only the return value from
       *   <em>lane</em><sub>0</sub> is applied as the block-wide prefix.  Can be stateful.
       * - Supports non-commutative scan operators.
       * - \blocked
       * - \granularity
       * - \smemreuse
       *
       * \par Snippet
       * The code snippet below illustrates a single thread block that progressively
       * computes an inclusive prefix max scan over multiple "tiles" of input using a
       * prefix functor to maintain a running total between block-wide scans.  Each tile consists
       * of 128 integer items that are partitioned across 128 threads.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/block/block_scan.cuh>
       *
       * // A stateful callback functor that maintains a running prefix to be applied
       * // during consecutive scan operations.
       * struct BlockPrefixCallbackOp
       * {
       *     // Running prefix
       *     int running_total;
       *
       *     // Constructor
       *     __device__ BlockPrefixCallbackOp(int running_total) : running_total(running_total) {}
       *
       *     // Callback operator to be entered by the first warp of threads in the block.
       *     // Thread-0 is responsible for returning a value for seeding the block-wide scan.
       *     __device__ int operator()(int block_aggregate)
       *     {
       *         int old_prefix = running_total;
       *         running_total = (block_aggregate > old_prefix) ? block_aggregate : old_prefix;
       *         return old_prefix;
       *     }
       * };
       *
       * __global__ void ExampleKernel(int *d_data, int num_items, ...)
       * {
       *     // Specialize BlockLoad, BlockStore, and BlockScan for a 1D block of 128 threads, 4 ints per thread
       *     typedef cub::BlockLoad<int*, 128, 4, BLOCK_LOAD_TRANSPOSE>   BlockLoad;
       *     typedef cub::BlockStore<int, 128, 4, BLOCK_STORE_TRANSPOSE>  BlockStore;
       *     typedef cub::BlockScan<int, 128>                             BlockScan;
       *
       *     // Allocate aliased shared memory for BlockLoad, BlockStore, and BlockScan
       *     __shared__ union {
       *         typename BlockLoad::TempStorage     load;
       *         typename BlockScan::TempStorage     scan;
       *         typename BlockStore::TempStorage    store;
       *     } temp_storage;
       *
       *     // Initialize running total
       *     BlockPrefixCallbackOp prefix_op(0);
       *
       *     // Have the block iterate over segments of items
       *     for (int block_offset = 0; block_offset < num_items; block_offset += 128 * 4)
       *     {
       *         // Load a segment of consecutive items that are blocked across threads
       *         int thread_data[4];
       *         BlockLoad(temp_storage.load).Load(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *
       *         // Collectively compute the block-wide inclusive prefix max scan
       *         BlockScan(temp_storage.scan).InclusiveScan(
       *             thread_data, thread_data, cub::Max(), prefix_op);
       *         CTA_SYNC();
       *
       *         // Store scanned items to output segment
       *         BlockStore(temp_storage.store).Store(d_data + block_offset, thread_data);
       *         CTA_SYNC();
       *     }
       * \endcode
       * \par
       * Suppose the input \p d_data is <tt>0, -1, 2, -3, 4, -5, ...</tt>.
       * The corresponding output for the first segment will be <tt>0, 0, 2, 2, 4, 4, ..., 510, 510</tt>.
       * The output for the second segment will be <tt>512, 512, 514, 514, 516, 516, ..., 1022, 1022</tt>.
       *
       * \tparam ITEMS_PER_THREAD         <b>[inferred]</b> The number of consecutive items partitioned onto each thread.
       * \tparam ScanOp                   <b>[inferred]</b> Binary scan functor  type having member <tt>T operator()(const T &a, const T &b)</tt>
       * \tparam BlockPrefixCallbackOp    <b>[inferred]</b> Call-back functor type having member <tt>T operator()(T block_aggregate)</tt>
       */
      template <
          int             ITEMS_PER_THREAD,
          typename        ScanOp,
          typename        BlockPrefixCallbackOp>
      __device__ __forceinline__ void InclusiveScan(
          T                       (&input)[ITEMS_PER_THREAD],     ///< [in] Calling thread's input items
          T                       (&output)[ITEMS_PER_THREAD],    ///< [out] Calling thread's output items (may be aliased to \p input)
          ScanOp                  scan_op,                        ///< [in] Binary scan functor 
          BlockPrefixCallbackOp   &block_prefix_callback_op)      ///< [in-out] <b>[<em>warp</em><sub>0</sub> only]</b> Call-back functor for specifying a block-wide prefix to be applied to the logical input sequence.
      {
          if (ITEMS_PER_THREAD == 1)
          {
              InclusiveScan(input[0], output[0], scan_op, block_prefix_callback_op);
          }
          else
          {
              // Reduce consecutive thread items in registers
              T thread_prefix = internal::ThreadReduce(input, scan_op);
  
              // Exclusive thread block-scan
              ExclusiveScan(thread_prefix, thread_prefix, scan_op, block_prefix_callback_op);
  
              // Inclusive scan in registers with prefix as seed
              internal::ThreadScanInclusive(input, output, scan_op, thread_prefix);
          }
      }
  
      //@}  end member group
  
  
  };
  
  /**
   * \example example_block_scan.cu
   */
  
  }               // CUB namespace
  CUB_NS_POSTFIX  // Optional outer namespace(s)