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     *
     * \par
     * \image html block_reduce.png
     * <div class="centercaption">\p BLOCK_REDUCE_RAKING data flow for a hypothetical 16-thread threadblock and 4-thread raking warp.</div>
     *
     * \par Performance Considerations
     * - This variant performs less communication than BLOCK_REDUCE_RAKING_NON_COMMUTATIVE
     *   and is preferable when the reduction operator is commutative.  This variant
     *   applies fewer reduction operators  than BLOCK_REDUCE_WARP_REDUCTIONS, and can provide higher overall
     *   throughput across the GPU when suitably occupied.  However, turn-around latency may be
     *   higher than to BLOCK_REDUCE_WARP_REDUCTIONS and thus less-desirable
     *   when the GPU is under-occupied.
     */
    BLOCK_REDUCE_RAKING_COMMUTATIVE_ONLY,


    /**
     * \par Overview
     * An efficient "raking" reduction algorithm that supports commutative
     * (e.g., addition) and non-commutative (e.g., string concatenation) reduction
     * operators. \blocked.
     *
     * \par
     * Execution is comprised of three 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 reduction within the raking warp.
     *
     * \par
     * \image html block_reduce.png
     * <div class="centercaption">\p BLOCK_REDUCE_RAKING data flow for a hypothetical 16-thread threadblock and 4-thread raking warp.</div>
     *
     * \par Performance Considerations
     * - This variant performs more communication than BLOCK_REDUCE_RAKING
     *   and is only preferable when the reduction operator is non-commutative.  This variant
     *   applies fewer reduction operators than BLOCK_REDUCE_WARP_REDUCTIONS, and can provide higher overall
     *   throughput across the GPU when suitably occupied.  However, turn-around latency may be
     *   higher than to BLOCK_REDUCE_WARP_REDUCTIONS and thus less-desirable
     *   when the GPU is under-occupied.
     */
    BLOCK_REDUCE_RAKING,


    /**
     * \par Overview
     * A quick "tiled warp-reductions" reduction algorithm that supports commutative
     * (e.g., addition) and non-commutative (e.g., string concatenation) reduction
     * operators.
     *
     * \par
     * 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
     *    reduction within each warp.
     * -# A propagation phase where the warp reduction outputs in each warp are
     *    updated with the aggregate from each preceding warp.
     *
     * \par
     * \image html block_scan_warpscans.png
     * <div class="centercaption">\p BLOCK_REDUCE_WARP_REDUCTIONS data flow for a hypothetical 16-thread threadblock and 4-thread raking warp.</div>
     *
     * \par Performance Considerations
     * - This variant applies more reduction operators than BLOCK_REDUCE_RAKING
     *   or BLOCK_REDUCE_RAKING_NON_COMMUTATIVE, which may result in lower overall
     *   throughput across the GPU.  However turn-around latency may be lower and
     *   thus useful when the GPU is under-occupied.
     */
    BLOCK_REDUCE_WARP_REDUCTIONS,
};


/******************************************************************************
 * Block reduce
 ******************************************************************************/

/**
 * \brief The BlockReduce class provides [<em>collective</em>](index.html#sec0) methods for computing a parallel reduction of items partitioned across a CUDA thread block. ![](reduce_logo.png)
 * \ingroup BlockModule
 *
 * \tparam T                Data type being reduced
 * \tparam BLOCK_DIM_X      The thread block length in threads along the X dimension
 * \tparam ALGORITHM        <b>[optional]</b> cub::BlockReduceAlgorithm enumerator specifying the underlying algorithm to use (default: cub::BLOCK_REDUCE_WARP_REDUCTIONS)
 * \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
 * - A <a href="http://en.wikipedia.org/wiki/Reduce_(higher-order_function)"><em>reduction</em></a> (or <em>fold</em>)
 *   uses a binary combining operator to compute a single aggregate from a list of input elements.
 * - \rowmajor
 * - BlockReduce can be optionally specialized by algorithm to accommodate different latency/throughput workload profiles:
 *   -# <b>cub::BLOCK_REDUCE_RAKING_COMMUTATIVE_ONLY</b>.  An efficient "raking" reduction algorithm that only supports commutative reduction operators. [More...](\ref cub::BlockReduceAlgorithm)
 *   -# <b>cub::BLOCK_REDUCE_RAKING</b>.  An efficient "raking" reduction algorithm that supports commutative and non-commutative reduction operators. [More...](\ref cub::BlockReduceAlgorithm)
 *   -# <b>cub::BLOCK_REDUCE_WARP_REDUCTIONS</b>.  A quick "tiled warp-reductions" reduction algorithm that supports commutative and non-commutative reduction operators. [More...](\ref cub::BlockReduceAlgorithm)
 *
 * \par Performance Considerations
 * - \granularity
 * - Very efficient (only one synchronization barrier).
 * - Incurs zero bank conflicts for most types
 * - Computation is slightly more efficient (i.e., having lower instruction overhead) for:
 *   - Summation (<b><em>vs.</em></b> generic reduction)
 *   - \p BLOCK_THREADS is a multiple of the architecture's warp size
 *   - Every thread has a valid input (i.e., full <b><em>vs.</em></b> partial-tiles)
 * - See cub::BlockReduceAlgorithm for performance details regarding algorithmic alternatives
 *
 * \par A Simple Example
 * \blockcollective{BlockReduce}
 * \par
 * The code snippet below illustrates a sum reduction 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_reduce.cuh>
 *
 * __global__ void ExampleKernel(...)