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tools/cub-1.8.0/cub/device/device_segmented_reduce.cuh 35.7 KB
8dcb6dfcb   Yannick Estève   first commit
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  /******************************************************************************
   * Copyright (c) 2011, Duane Merrill.  All rights reserved.
   * Copyright (c) 2011-2018, NVIDIA CORPORATION.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions are met:
   *     * Redistributions of source code must retain the above copyright
   *       notice, this list of conditions and the following disclaimer.
   *     * Redistributions in binary form must reproduce the above copyright
   *       notice, this list of conditions and the following disclaimer in the
   *       documentation and/or other materials provided with the distribution.
   *     * Neither the name of the NVIDIA CORPORATION nor the
   *       names of its contributors may be used to endorse or promote products
   *       derived from this software without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
   * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE FOR ANY
   * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
   * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
   * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   *
   ******************************************************************************/
  
  /**
   * \file
   * cub::DeviceSegmentedReduce provides device-wide, parallel operations for computing a batched reduction across multiple sequences of data items residing within device-accessible memory.
   */
  
  #pragma once
  
  #include <stdio.h>
  #include <iterator>
  
  #include "../iterator/arg_index_input_iterator.cuh"
  #include "dispatch/dispatch_reduce.cuh"
  #include "dispatch/dispatch_reduce_by_key.cuh"
  #include "../util_type.cuh"
  #include "../util_namespace.cuh"
  
  /// Optional outer namespace(s)
  CUB_NS_PREFIX
  
  /// CUB namespace
  namespace cub {
  
  
  /**
   * \brief DeviceSegmentedReduce provides device-wide, parallel operations for computing a reduction across multiple sequences of data items residing within device-accessible memory. ![](reduce_logo.png)
   * \ingroup SegmentedModule
   *
   * \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 sequence of input elements.
   *
   * \par Usage Considerations
   * \cdp_class{DeviceSegmentedReduce}
   *
   */
  struct DeviceSegmentedReduce
  {
      /**
       * \brief Computes a device-wide segmented reduction using the specified binary \p reduction_op functor.
       *
       * \par
       * - Does not support binary reduction operators that are non-commutative.
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates a custom min-reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // CustomMin functor
       * struct CustomMin
       * {
       *     template <typename T>
       *     CUB_RUNTIME_FUNCTION __forceinline__
       *     T operator()(const T &a, const T &b) const {
       *         return (b < a) ? b : a;
       *     }
       * };
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int          num_segments;   // e.g., 3
       * int          *d_offsets;     // e.g., [0, 3, 3, 7]
       * int          *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int          *d_out;         // e.g., [-, -, -]
       * CustomMin    min_op;
       * int          initial_value;           // e.g., INT_MAX
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::Reduce(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1, min_op, initial_value);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run reduction
       * cub::DeviceSegmentedReduce::Reduce(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1, min_op, initial_value);
       *
       * // d_out <-- [6, INT_MAX, 0]
       *
       * \endcode
       *
       * \tparam InputIteratorT       <b>[inferred]</b> Random-access input iterator type for reading input items \iterator
       * \tparam OutputIteratorT      <b>[inferred]</b> Output iterator type for recording the reduced aggregate \iterator
       * \tparam OffsetIteratorT      <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       * \tparam ReductionOp          <b>[inferred]</b> Binary reduction functor type having member <tt>T operator()(const T &a, const T &b)</tt>
       * \tparam T                    <b>[inferred]</b> Data element type that is convertible to the \p value type of \p InputIteratorT
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT,
          typename            ReductionOp,
          typename            T>
      CUB_RUNTIME_FUNCTION
      static cudaError_t Reduce(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          ReductionOp         reduction_op,                       ///< [in] Binary reduction functor 
          T                   initial_value,                      ///< [in] Initial value of the reduction for each segment
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          return DispatchSegmentedReduce<InputIteratorT, OutputIteratorT, OffsetIteratorT, OffsetT, ReductionOp>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              reduction_op,
              initial_value,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Computes a device-wide segmented sum using the addition ('+') operator.
       *
       * \par
       * - Uses \p 0 as the initial value of the reduction for each segment.
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - Does not support \p + operators that are non-commutative..
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates the sum reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int num_segments;   // e.g., 3
       * int *d_offsets;     // e.g., [0, 3, 3, 7]
       * int *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int *d_out;         // e.g., [-, -, -]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::Sum(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run sum-reduction
       * cub::DeviceSegmentedReduce::Sum(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // d_out <-- [21, 0, 17]
       *
       * \endcode
       *
       * \tparam InputIteratorT     <b>[inferred]</b> Random-access input iterator type for reading input items \iterator
       * \tparam OutputIteratorT    <b>[inferred]</b> Output iterator type for recording the reduced aggregate \iterator
       * \tparam OffsetIteratorT      <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t Sum(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // The output value type
          typedef typename If<(Equals<typename std::iterator_traits<OutputIteratorT>::value_type, void>::VALUE),  // OutputT =  (if output iterator's value type is void) ?
              typename std::iterator_traits<InputIteratorT>::value_type,                                          // ... then the input iterator's value type,
              typename std::iterator_traits<OutputIteratorT>::value_type>::Type OutputT;                          // ... else the output iterator's value type
  
          return DispatchSegmentedReduce<InputIteratorT,  OutputIteratorT, OffsetIteratorT, OffsetT, cub::Sum>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              cub::Sum(),
              OutputT(),            // zero-initialize
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Computes a device-wide segmented minimum using the less-than ('<') operator.
       *
       * \par
       * - Uses <tt>std::numeric_limits<T>::max()</tt> as the initial value of the reduction for each segment.
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - Does not support \p < operators that are non-commutative.
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates the min-reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int num_segments;   // e.g., 3
       * int *d_offsets;     // e.g., [0, 3, 3, 7]
       * int *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int *d_out;         // e.g., [-, -, -]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::Min(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run min-reduction
       * cub::DeviceSegmentedReduce::Min(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // d_out <-- [6, INT_MAX, 0]
       *
       * \endcode
       *
       * \tparam InputIteratorT     <b>[inferred]</b> Random-access input iterator type for reading input items \iterator
       * \tparam OutputIteratorT    <b>[inferred]</b> Output iterator type for recording the reduced aggregate \iterator
       * \tparam OffsetIteratorT      <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t Min(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // The input value type
          typedef typename std::iterator_traits<InputIteratorT>::value_type InputT;
  
          return DispatchSegmentedReduce<InputIteratorT,  OutputIteratorT, OffsetIteratorT, OffsetT, cub::Min>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              cub::Min(),
              Traits<InputT>::Max(),    // replace with std::numeric_limits<T>::max() when C++11 support is more prevalent
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Finds the first device-wide minimum in each segment using the less-than ('<') operator, also returning the in-segment index of that item.
       *
       * \par
       * - The output value type of \p d_out is cub::KeyValuePair <tt><int, T></tt> (assuming the value type of \p d_in is \p T)
       *   - The minimum of the <em>i</em><sup>th</sup> segment is written to <tt>d_out[i].value</tt> and its offset in that segment is written to <tt>d_out[i].key</tt>.
       *   - The <tt>{1, std::numeric_limits<T>::max()}</tt> tuple is produced for zero-length inputs
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - Does not support \p < operators that are non-commutative.
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates the argmin-reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int                      num_segments;   // e.g., 3
       * int                      *d_offsets;     // e.g., [0, 3, 3, 7]
       * int                      *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * KeyValuePair<int, int>   *d_out;         // e.g., [{-,-}, {-,-}, {-,-}]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::ArgMin(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run argmin-reduction
       * cub::DeviceSegmentedReduce::ArgMin(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // d_out <-- [{1,6}, {1,INT_MAX}, {2,0}]
       *
       * \endcode
       *
       * \tparam InputIteratorT     <b>[inferred]</b> Random-access input iterator type for reading input items (of some type \p T) \iterator
       * \tparam OutputIteratorT    <b>[inferred]</b> Output iterator type for recording the reduced aggregate (having value type <tt>KeyValuePair<int, T></tt>) \iterator
       * \tparam OffsetIteratorT      <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t ArgMin(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // The input type
          typedef typename std::iterator_traits<InputIteratorT>::value_type InputValueT;
  
          // The output tuple type
          typedef typename If<(Equals<typename std::iterator_traits<OutputIteratorT>::value_type, void>::VALUE),  // OutputT =  (if output iterator's value type is void) ?
              KeyValuePair<OffsetT, InputValueT>,                                                                 // ... then the key value pair OffsetT + InputValueT
              typename std::iterator_traits<OutputIteratorT>::value_type>::Type OutputTupleT;                     // ... else the output iterator's value type
  
          // The output value type
          typedef typename OutputTupleT::Value OutputValueT;
  
          // Wrapped input iterator to produce index-value <OffsetT, InputT> tuples
          typedef ArgIndexInputIterator<InputIteratorT, OffsetT, OutputValueT> ArgIndexInputIteratorT;
          ArgIndexInputIteratorT d_indexed_in(d_in);
  
          // Initial value
          OutputTupleT initial_value(1, Traits<InputValueT>::Max());   // replace with std::numeric_limits<T>::max() when C++11 support is more prevalent
  
          return DispatchSegmentedReduce<ArgIndexInputIteratorT,  OutputIteratorT, OffsetIteratorT, OffsetT, cub::ArgMin>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_indexed_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              cub::ArgMin(),
              initial_value,
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Computes a device-wide segmented maximum using the greater-than ('>') operator.
       *
       * \par
       * - Uses <tt>std::numeric_limits<T>::lowest()</tt> as the initial value of the reduction.
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - Does not support \p > operators that are non-commutative.
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates the max-reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_radix_sort.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int num_segments;   // e.g., 3
       * int *d_offsets;     // e.g., [0, 3, 3, 7]
       * int *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * int *d_out;         // e.g., [-, -, -]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::Max(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run max-reduction
       * cub::DeviceSegmentedReduce::Max(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // d_out <-- [8, INT_MIN, 9]
       *
       * \endcode
       *
       * \tparam InputIteratorT     <b>[inferred]</b> Random-access input iterator type for reading input items \iterator
       * \tparam OutputIteratorT    <b>[inferred]</b> Output iterator type for recording the reduced aggregate \iterator
       * \tparam OffsetIteratorT      <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t Max(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // The input value type
          typedef typename std::iterator_traits<InputIteratorT>::value_type InputT;
  
          return DispatchSegmentedReduce<InputIteratorT,  OutputIteratorT, OffsetIteratorT, OffsetT, cub::Max>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              cub::Max(),
              Traits<InputT>::Lowest(),    // replace with std::numeric_limits<T>::lowest() when C++11 support is more prevalent
              stream,
              debug_synchronous);
      }
  
  
      /**
       * \brief Finds the first device-wide maximum in each segment using the greater-than ('>') operator, also returning the in-segment index of that item
       *
       * \par
       * - The output value type of \p d_out is cub::KeyValuePair <tt><int, T></tt> (assuming the value type of \p d_in is \p T)
       *   - The maximum of the <em>i</em><sup>th</sup> segment is written to <tt>d_out[i].value</tt> and its offset in that segment is written to <tt>d_out[i].key</tt>.
       *   - The <tt>{1, std::numeric_limits<T>::lowest()}</tt> tuple is produced for zero-length inputs
       * - When input a contiguous sequence of segments, a single sequence
       *   \p segment_offsets (of length <tt>num_segments+1</tt>) can be aliased
       *   for both the \p d_begin_offsets and \p d_end_offsets parameters (where
       *   the latter is specified as <tt>segment_offsets+1</tt>).
       * - Does not support \p > operators that are non-commutative.
       * - \devicestorage
       *
       * \par Snippet
       * The code snippet below illustrates the argmax-reduction of a device vector of \p int data elements.
       * \par
       * \code
       * #include <cub/cub.cuh>   // or equivalently <cub/device/device_reduce.cuh>
       *
       * // Declare, allocate, and initialize device-accessible pointers for input and output
       * int                      num_segments;   // e.g., 3
       * int                      *d_offsets;     // e.g., [0, 3, 3, 7]
       * int                      *d_in;          // e.g., [8, 6, 7, 5, 3, 0, 9]
       * KeyValuePair<int, int>   *d_out;         // e.g., [{-,-}, {-,-}, {-,-}]
       * ...
       *
       * // Determine temporary device storage requirements
       * void     *d_temp_storage = NULL;
       * size_t   temp_storage_bytes = 0;
       * cub::DeviceSegmentedReduce::ArgMax(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // Allocate temporary storage
       * cudaMalloc(&d_temp_storage, temp_storage_bytes);
       *
       * // Run argmax-reduction
       * cub::DeviceSegmentedReduce::ArgMax(d_temp_storage, temp_storage_bytes, d_in, d_out,
       *     num_segments, d_offsets, d_offsets + 1);
       *
       * // d_out <-- [{0,8}, {1,INT_MIN}, {3,9}]
       *
       * \endcode
       *
       * \tparam InputIteratorT     <b>[inferred]</b> Random-access input iterator type for reading input items (of some type \p T) \iterator
       * \tparam OutputIteratorT    <b>[inferred]</b> Output iterator type for recording the reduced aggregate (having value type <tt>KeyValuePair<int, T></tt>) \iterator
       * \tparam OffsetIteratorT    <b>[inferred]</b> Random-access input iterator type for reading segment offsets \iterator
       */
      template <
          typename            InputIteratorT,
          typename            OutputIteratorT,
          typename            OffsetIteratorT>
      CUB_RUNTIME_FUNCTION
      static cudaError_t ArgMax(
          void                *d_temp_storage,                    ///< [in] %Device-accessible allocation of temporary storage.  When NULL, the required allocation size is written to \p temp_storage_bytes and no work is done.
          size_t              &temp_storage_bytes,                ///< [in,out] Reference to size in bytes of \p d_temp_storage allocation
          InputIteratorT      d_in,                               ///< [in] Pointer to the input sequence of data items
          OutputIteratorT     d_out,                              ///< [out] Pointer to the output aggregate
          int                 num_segments,                       ///< [in] The number of segments that comprise the sorting data
          OffsetIteratorT     d_begin_offsets,                    ///< [in] Pointer to the sequence of beginning offsets of length \p num_segments, such that <tt>d_begin_offsets[i]</tt> is the first element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>
          OffsetIteratorT     d_end_offsets,                      ///< [in] Pointer to the sequence of ending offsets of length \p num_segments, such that <tt>d_end_offsets[i]-1</tt> is the last element of the <em>i</em><sup>th</sup> data segment in <tt>d_keys_*</tt> and <tt>d_values_*</tt>.  If <tt>d_end_offsets[i]-1</tt> <= <tt>d_begin_offsets[i]</tt>, the <em>i</em><sup>th</sup> is considered empty.
          cudaStream_t        stream              = 0,            ///< [in] <b>[optional]</b> CUDA stream to launch kernels within.  Default is stream<sub>0</sub>.
          bool                debug_synchronous   = false)        ///< [in] <b>[optional]</b> Whether or not to synchronize the stream after every kernel launch to check for errors.  Also causes launch configurations to be printed to the console.  Default is \p false.
      {
          // Signed integer type for global offsets
          typedef int OffsetT;
  
          // The input type
          typedef typename std::iterator_traits<InputIteratorT>::value_type InputValueT;
  
          // The output tuple type
          typedef typename If<(Equals<typename std::iterator_traits<OutputIteratorT>::value_type, void>::VALUE),  // OutputT =  (if output iterator's value type is void) ?
              KeyValuePair<OffsetT, InputValueT>,                                                                 // ... then the key value pair OffsetT + InputValueT
              typename std::iterator_traits<OutputIteratorT>::value_type>::Type OutputTupleT;                     // ... else the output iterator's value type
  
          // The output value type
          typedef typename OutputTupleT::Value OutputValueT;
  
          // Wrapped input iterator to produce index-value <OffsetT, InputT> tuples
          typedef ArgIndexInputIterator<InputIteratorT, OffsetT, OutputValueT> ArgIndexInputIteratorT;
          ArgIndexInputIteratorT d_indexed_in(d_in);
  
          // Initial value
          OutputTupleT initial_value(1, Traits<InputValueT>::Lowest());     // replace with std::numeric_limits<T>::lowest() when C++11 support is more prevalent
  
          return DispatchSegmentedReduce<ArgIndexInputIteratorT, OutputIteratorT, OffsetIteratorT, OffsetT, cub::ArgMax>::Dispatch(
              d_temp_storage,
              temp_storage_bytes,
              d_indexed_in,
              d_out,
              num_segments,
              d_begin_offsets,
              d_end_offsets,
              cub::ArgMax(),
              initial_value,
              stream,
              debug_synchronous);
      }
  
  };
  
  }               // CUB namespace
  CUB_NS_POSTFIX  // Optional outer namespace(s)