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     * 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 threadblock 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,
    };