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Edit File : balanced_quicksort.h \| Size : 16.55 KB
// -- C++ -- // Copyright (C) 2007-2018 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the terms // of the GNU General Public License as published by the Free Software // Foundation; either version 3, or (at your option) any later // version. // This library is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // <http://www.gnu.org/licenses/>. /** @file parallel/balanced_quicksort.h * @brief Implementation of a dynamically load-balanced parallel quicksort. * * It works in-place and needs only logarithmic extra memory. * The algorithm is similar to the one proposed in * * P. Tsigas and Y. Zhang. * A simple, fast parallel implementation of quicksort and * its performance evaluation on SUN enterprise 10000. * In 11th Euromicro Conference on Parallel, Distributed and * Network-Based Processing, page 372, 2003. * * This file is a GNU parallel extension to the Standard C++ Library. / // Written by Johannes Singler. #ifndef _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H #define _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H 1 #include <parallel/basic_iterator.h> #include <bits/stl_algo.h> #include <bits/stl_function.h> #include <parallel/settings.h> #include <parallel/partition.h> #include <parallel/random_number.h> #include <parallel/queue.h> #if _GLIBCXX_PARALLEL_ASSERTIONS #include <parallel/checkers.h> #ifdef _GLIBCXX_HAVE_UNISTD_H #include <unistd.h> #endif #endif namespace __gnu_parallel { /* @brief Information local to one thread in the parallel quicksort run. / template<typename _RAIter> struct _QSBThreadLocal { typedef std::iterator_traits<_RAIter> _TraitsType; typedef typename _TraitsType::difference_type _DifferenceType; /* @brief Continuous part of the sequence, described by an iterator pair. / typedef std::pair<_RAIter, _RAIter> _Piece; /* @brief Initial piece to work on. / _Piece _M_initial; /* @brief Work-stealing queue. / _RestrictedBoundedConcurrentQueue<_Piece> _M_leftover_parts; /* @brief Number of threads involved in this algorithm. / _ThreadIndex _M_num_threads; /* @brief Pointer to a counter of elements left over to sort. / volatile _DifferenceType _M_elements_leftover; /** @brief The complete sequence to sort. / _Piece _M_global; /* @brief Constructor. * @param __queue_size size of the work-stealing queue. / _QSBThreadLocal(int __queue_size) : _M_leftover_parts(__queue_size) { } }; /* @brief Balanced quicksort divide step. * @param __begin Begin iterator of subsequence. * @param __end End iterator of subsequence. * @param __comp Comparator. * @param __num_threads Number of threads that are allowed to work on * this part. * @pre @c (__end-__begin)>=1 / template<typename _RAIter, typename _Compare> typename std::iterator_traits<_RAIter>::difference_type __qsb_divide(_RAIter __begin, _RAIter __end, _Compare __comp, _ThreadIndex __num_threads) { _GLIBCXX_PARALLEL_ASSERT(__num_threads > 0); typedef std::iterator_traits<_RAIter> _TraitsType; typedef typename _TraitsType::value_type _ValueType; typedef typename _TraitsType::difference_type _DifferenceType; _RAIter __pivot_pos = __median_of_three_iterators(__begin, __begin + (__end - __begin) / 2, __end - 1, __comp); #if defined(_GLIBCXX_PARALLEL_ASSERTIONS) // Must be in between somewhere. _DifferenceType __n = __end - __begin; _GLIBCXX_PARALLEL_ASSERT((!__comp(__pivot_pos, __begin) && !__comp((__begin + __n / 2), __pivot_pos)) \|\| (!__comp(__pivot_pos, __begin) && !__comp((__end - 1), __pivot_pos)) \|\| (!__comp(__pivot_pos, (__begin + __n / 2)) && !__comp(__begin, __pivot_pos)) \|\| (!__comp(__pivot_pos, (__begin + __n / 2)) && !__comp((__end - 1), __pivot_pos)) \|\| (!__comp(__pivot_pos, (__end - 1)) && !__comp(__begin, __pivot_pos)) \|\| (!__comp(__pivot_pos, (__end - 1)) && !__comp((__begin + __n / 2), __pivot_pos))); #endif // Swap pivot value to end. if (__pivot_pos != (__end - 1)) std::iter_swap(__pivot_pos, __end - 1); __pivot_pos = __end - 1; __gnu_parallel::__binder2nd<_Compare, _ValueType, _ValueType, bool> __pred(__comp, __pivot_pos); // Divide, returning __end - __begin - 1 in the worst case. _DifferenceType __split_pos = __parallel_partition(__begin, __end - 1, __pred, __num_threads); // Swap back pivot to middle. std::iter_swap(__begin + __split_pos, __pivot_pos); __pivot_pos = __begin + __split_pos; #if _GLIBCXX_PARALLEL_ASSERTIONS _RAIter __r; for (__r = __begin; __r != __pivot_pos; ++__r) _GLIBCXX_PARALLEL_ASSERT(__comp(__r, __pivot_pos)); for (; __r != __end; ++__r) _GLIBCXX_PARALLEL_ASSERT(!__comp(__r, __pivot_pos)); #endif return __split_pos; } /** @brief Quicksort conquer step. * @param __tls Array of thread-local storages. * @param __begin Begin iterator of subsequence. * @param __end End iterator of subsequence. * @param __comp Comparator. * @param __iam Number of the thread processing this function. * @param __num_threads * Number of threads that are allowed to work on this part. / template<typename _RAIter, typename _Compare> void __qsb_conquer(_QSBThreadLocal<_RAIter>* __tls, _RAIter __begin, _RAIter __end, _Compare __comp, _ThreadIndex __iam, _ThreadIndex __num_threads, bool __parent_wait) { typedef std::iterator_traits<_RAIter> _TraitsType; typedef typename _TraitsType::value_type _ValueType; typedef typename _TraitsType::difference_type _DifferenceType; _DifferenceType __n = __end - __begin; if (__num_threads <= 1 \|\| __n <= 1) { __tls[__iam]->_M_initial.first = __begin; __tls[__iam]->_M_initial.second = __end; __qsb_local_sort_with_helping(__tls, __comp, __iam, __parent_wait); return; } // Divide step. _DifferenceType __split_pos = __qsb_divide(__begin, __end, __comp, __num_threads); #if _GLIBCXX_PARALLEL_ASSERTIONS _GLIBCXX_PARALLEL_ASSERT(0 <= __split_pos && __split_pos < (__end - __begin)); #endif _ThreadIndex __num_threads_leftside = std::max<_ThreadIndex> (1, std::min<_ThreadIndex>(__num_threads - 1, __split_pos * __num_threads / __n)); # pragma omp atomic __tls[__iam]->_M_elements_leftover -= (_DifferenceType)1; // Conquer step. # pragma omp parallel num_threads(2) { bool __wait; if(omp_get_num_threads() < 2) __wait = false; else __wait = __parent_wait; # pragma omp sections { # pragma omp section { __qsb_conquer(__tls, __begin, __begin + __split_pos, __comp, __iam, __num_threads_leftside, __wait); __wait = __parent_wait; } // The pivot_pos is left in place, to ensure termination. # pragma omp section { __qsb_conquer(__tls, __begin + __split_pos + 1, __end, __comp, __iam + __num_threads_leftside, __num_threads - __num_threads_leftside, __wait); __wait = __parent_wait; } } } } /* * @brief Quicksort step doing load-balanced local sort. * @param __tls Array of thread-local storages. * @param __comp Comparator. * @param __iam Number of the thread processing this function. / template<typename _RAIter, typename _Compare> void __qsb_local_sort_with_helping(_QSBThreadLocal<_RAIter>* __tls, _Compare& __comp, _ThreadIndex __iam, bool __wait) { typedef std::iterator_traits<_RAIter> _TraitsType; typedef typename _TraitsType::value_type _ValueType; typedef typename _TraitsType::difference_type _DifferenceType; typedef std::pair<_RAIter, _RAIter> _Piece; _QSBThreadLocal<_RAIter>& __tl = __tls[__iam]; _DifferenceType __base_case_n = _Settings::get().sort_qsb_base_case_maximal_n; if (__base_case_n < 2) __base_case_n = 2; _ThreadIndex __num_threads = __tl._M_num_threads; // Every thread has its own random number generator. _RandomNumber __rng(__iam + 1); _Piece __current = __tl._M_initial; _DifferenceType __elements_done = 0; #if _GLIBCXX_PARALLEL_ASSERTIONS _DifferenceType __total_elements_done = 0; #endif for (;;) { // Invariant: __current must be a valid (maybe empty) range. _RAIter __begin = __current.first, __end = __current.second; _DifferenceType __n = __end - __begin; if (__n > __base_case_n) { // Divide. _RAIter __pivot_pos = __begin + __rng(__n); // Swap __pivot_pos value to end. if (__pivot_pos != (__end - 1)) std::iter_swap(__pivot_pos, __end - 1); __pivot_pos = __end - 1; __gnu_parallel::__binder2nd <_Compare, _ValueType, _ValueType, bool> __pred(__comp, __pivot_pos); // Divide, leave pivot unchanged in last place. _RAIter __split_pos1, __split_pos2; __split_pos1 = __gnu_sequential::partition(__begin, __end - 1, __pred); // Left side: < __pivot_pos; __right side: >= __pivot_pos. #if _GLIBCXX_PARALLEL_ASSERTIONS _GLIBCXX_PARALLEL_ASSERT(__begin <= __split_pos1 && __split_pos1 < __end); #endif // Swap pivot back to middle. if (__split_pos1 != __pivot_pos) std::iter_swap(__split_pos1, __pivot_pos); __pivot_pos = __split_pos1; // In case all elements are equal, __split_pos1 == 0. if ((__split_pos1 + 1 - __begin) < (__n >> 7) \|\| (__end - __split_pos1) < (__n >> 7)) { // Very unequal split, one part smaller than one 128th // elements not strictly larger than the pivot. __gnu_parallel::__unary_negate<__gnu_parallel::__binder1st <_Compare, _ValueType, _ValueType, bool>, _ValueType> __pred(__gnu_parallel::__binder1st <_Compare, _ValueType, _ValueType, bool> (__comp, __pivot_pos)); // Find other end of pivot-equal range. __split_pos2 = __gnu_sequential::partition(__split_pos1 + 1, __end, __pred); } else // Only skip the pivot. __split_pos2 = __split_pos1 + 1; // Elements equal to pivot are done. __elements_done += (__split_pos2 - __split_pos1); #if _GLIBCXX_PARALLEL_ASSERTIONS __total_elements_done += (__split_pos2 - __split_pos1); #endif // Always push larger part onto stack. if (((__split_pos1 + 1) - __begin) < (__end - (__split_pos2))) { // Right side larger. if ((__split_pos2) != __end) __tl._M_leftover_parts.push_front (std::make_pair(__split_pos2, __end)); //__current.first = __begin; //already set anyway __current.second = __split_pos1; continue; } else { // Left side larger. if (__begin != __split_pos1) __tl._M_leftover_parts.push_front(std::make_pair (__begin, __split_pos1)); __current.first = __split_pos2; //__current.second = __end; //already set anyway continue; } } else { __gnu_sequential::sort(__begin, __end, __comp); __elements_done += __n; #if _GLIBCXX_PARALLEL_ASSERTIONS __total_elements_done += __n; #endif // Prefer own stack, small pieces. if (__tl._M_leftover_parts.pop_front(__current)) continue; # pragma omp atomic __tl._M_elements_leftover -= __elements_done; __elements_done = 0; #if _GLIBCXX_PARALLEL_ASSERTIONS double __search_start = omp_get_wtime(); #endif // Look for new work. bool __successfully_stolen = false; while (__wait && __tl._M_elements_leftover > 0 && !__successfully_stolen #if _GLIBCXX_PARALLEL_ASSERTIONS // Possible dead-lock. && (omp_get_wtime() < (__search_start + 1.0)) #endif ) { _ThreadIndex __victim; __victim = __rng(__num_threads); // Large pieces. __successfully_stolen = (__victim != __iam) && __tls[__victim]->_M_leftover_parts.pop_back(__current); if (!__successfully_stolen) __yield(); #if !defined(__ICC) && !defined(__ECC) # pragma omp flush #endif } #if _GLIBCXX_PARALLEL_ASSERTIONS if (omp_get_wtime() >= (__search_start + 1.0)) { sleep(1); _GLIBCXX_PARALLEL_ASSERT(omp_get_wtime() < (__search_start + 1.0)); } #endif if (!__successfully_stolen) { #if _GLIBCXX_PARALLEL_ASSERTIONS _GLIBCXX_PARALLEL_ASSERT(__tl._M_elements_leftover == 0); #endif return; } } } } /** @brief Top-level quicksort routine. * @param __begin Begin iterator of sequence. * @param __end End iterator of sequence. * @param __comp Comparator. * @param __num_threads Number of threads that are allowed to work on * this part. / template<typename _RAIter, typename _Compare> void __parallel_sort_qsb(_RAIter __begin, _RAIter __end, _Compare __comp, _ThreadIndex __num_threads) { _GLIBCXX_CALL(__end - __begin) typedef std::iterator_traits<_RAIter> _TraitsType; typedef typename _TraitsType::value_type _ValueType; typedef typename _TraitsType::difference_type _DifferenceType; typedef std::pair<_RAIter, _RAIter> _Piece; typedef _QSBThreadLocal<_RAIter> _TLSType; _DifferenceType __n = __end - __begin; if (__n <= 1) return; // At least one element per processor. if (__num_threads > __n) __num_threads = static_cast<_ThreadIndex>(__n); // Initialize thread local storage _TLSType* __tls = new _TLSType[__num_threads]; _DifferenceType __queue_size = (__num_threads (_ThreadIndex)(__rd_log2(__n) + 1)); for (_ThreadIndex __t = 0; __t < __num_threads; ++__t) __tls[__t] = new _QSBThreadLocal<_RAIter>(__queue_size); // There can never be more than ceil(__rd_log2(__n)) ranges on the // stack, because // 1. Only one processor pushes onto the stack // 2. The largest range has at most length __n // 3. Each range is larger than half of the range remaining volatile _DifferenceType __elements_leftover = __n; for (_ThreadIndex __i = 0; __i < __num_threads; ++__i) { __tls[__i]->_M_elements_leftover = &__elements_leftover; __tls[__i]->_M_num_threads = __num_threads; __tls[__i]->_M_global = std::make_pair(__begin, __end); // Just in case nothing is left to assign. __tls[__i]->_M_initial = std::make_pair(__end, __end); } // Main recursion call. __qsb_conquer(__tls, __begin, __begin + __n, __comp, 0, __num_threads, true); #if _GLIBCXX_PARALLEL_ASSERTIONS // All stack must be empty. _Piece __dummy; for (_ThreadIndex __i = 1; __i < __num_threads; ++__i) _GLIBCXX_PARALLEL_ASSERT( !__tls[__i]->_M_leftover_parts.pop_back(__dummy)); #endif for (_ThreadIndex __i = 0; __i < __num_threads; ++__i) delete __tls[__i]; delete[] __tls; } } // namespace __gnu_parallel #endif /* _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H */ Back

Edit File : balanced_quicksort.h | Size : 16.55 KB

// -*- C++ -*-

// Copyright (C) 2007-2018 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the terms
// of the GNU General Public License as published by the Free Software
// Foundation; either version 3, or (at your option) any later
// version.

// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file parallel/balanced_quicksort.h
 *  @brief Implementation of a dynamically load-balanced parallel quicksort.
 *
 *  It works in-place and needs only logarithmic extra memory.
 *  The algorithm is similar to the one proposed in
 *
 *  P. Tsigas and Y. Zhang.
 *  A simple, fast parallel implementation of quicksort and
 *  its performance evaluation on SUN enterprise 10000.
 *  In 11th Euromicro Conference on Parallel, Distributed and
 *  Network-Based Processing, page 372, 2003.
 *
 *  This file is a GNU parallel extension to the Standard C++ Library.
 */

// Written by Johannes Singler.

#ifndef _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H
#define _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H 1

#include <parallel/basic_iterator.h>
#include <bits/stl_algo.h>
#include <bits/stl_function.h>

#include <parallel/settings.h>
#include <parallel/partition.h>
#include <parallel/random_number.h>
#include <parallel/queue.h>

#if _GLIBCXX_PARALLEL_ASSERTIONS
#include <parallel/checkers.h>
#ifdef _GLIBCXX_HAVE_UNISTD_H
#include <unistd.h>
#endif
#endif

namespace __gnu_parallel
{
  /** @brief Information local to one thread in the parallel quicksort run. */
  template<typename _RAIter>
    struct _QSBThreadLocal
    {
      typedef std::iterator_traits<_RAIter> _TraitsType;
      typedef typename _TraitsType::difference_type _DifferenceType;

/** @brief Continuous part of the sequence, described by an
      iterator pair. */
      typedef std::pair<_RAIter, _RAIter> _Piece;

/** @brief Initial piece to work on. */
      _Piece _M_initial;

/** @brief Work-stealing queue. */
      _RestrictedBoundedConcurrentQueue<_Piece> _M_leftover_parts;

/** @brief Number of threads involved in this algorithm. */
      _ThreadIndex _M_num_threads;

/** @brief Pointer to a counter of elements left over to sort. */
      volatile _DifferenceType* _M_elements_leftover;

/** @brief The complete sequence to sort. */
      _Piece _M_global;

/** @brief Constructor.
       *  @param __queue_size size of the work-stealing queue. */
      _QSBThreadLocal(int __queue_size) : _M_leftover_parts(__queue_size) { }
    };

/** @brief Balanced quicksort divide step.
    *  @param __begin Begin iterator of subsequence.
    *  @param __end End iterator of subsequence.
    *  @param __comp Comparator.
    *  @param __num_threads Number of threads that are allowed to work on
    *  this part.
    *  @pre @c (__end-__begin)>=1 */
  template<typename _RAIter, typename _Compare>
    typename std::iterator_traits<_RAIter>::difference_type
    __qsb_divide(_RAIter __begin, _RAIter __end,
		 _Compare __comp, _ThreadIndex __num_threads)
    {
      _GLIBCXX_PARALLEL_ASSERT(__num_threads > 0);

typedef std::iterator_traits<_RAIter> _TraitsType;
      typedef typename _TraitsType::value_type _ValueType;
      typedef typename _TraitsType::difference_type _DifferenceType;

_RAIter __pivot_pos =
	__median_of_three_iterators(__begin, __begin + (__end - __begin) / 2,
				    __end  - 1, __comp);

#if defined(_GLIBCXX_PARALLEL_ASSERTIONS)
      // Must be in between somewhere.
      _DifferenceType __n = __end - __begin;

_GLIBCXX_PARALLEL_ASSERT((!__comp(*__pivot_pos, *__begin)
				&& !__comp(*(__begin + __n / 2),
					   *__pivot_pos))
			       || (!__comp(*__pivot_pos, *__begin)
				   && !__comp(*(__end - 1), *__pivot_pos))
			       || (!__comp(*__pivot_pos, *(__begin + __n / 2))
				   && !__comp(*__begin, *__pivot_pos))
			       || (!__comp(*__pivot_pos, *(__begin + __n / 2))
				   && !__comp(*(__end - 1), *__pivot_pos))
			       || (!__comp(*__pivot_pos, *(__end - 1))
				   && !__comp(*__begin, *__pivot_pos))
			       || (!__comp(*__pivot_pos, *(__end - 1))
				   && !__comp(*(__begin + __n / 2),
					      *__pivot_pos)));
#endif

// Swap pivot value to end.
      if (__pivot_pos != (__end - 1))
	std::iter_swap(__pivot_pos, __end - 1);
      __pivot_pos = __end - 1;

__gnu_parallel::__binder2nd<_Compare, _ValueType, _ValueType, bool>
	__pred(__comp, *__pivot_pos);

// Divide, returning __end - __begin - 1 in the worst case.
      _DifferenceType __split_pos = __parallel_partition(__begin, __end - 1,
							 __pred,
							 __num_threads);

// Swap back pivot to middle.
      std::iter_swap(__begin + __split_pos, __pivot_pos);
      __pivot_pos = __begin + __split_pos;

#if _GLIBCXX_PARALLEL_ASSERTIONS
      _RAIter __r;
      for (__r = __begin; __r != __pivot_pos; ++__r)
	_GLIBCXX_PARALLEL_ASSERT(__comp(*__r, *__pivot_pos));
      for (; __r != __end; ++__r)
	_GLIBCXX_PARALLEL_ASSERT(!__comp(*__r, *__pivot_pos));
#endif

return __split_pos;
    }

/** @brief Quicksort conquer step.
    *  @param __tls Array of thread-local storages.
    *  @param __begin Begin iterator of subsequence.
    *  @param __end End iterator of subsequence.
    *  @param __comp Comparator.
    *  @param __iam Number of the thread processing this function.
    *  @param __num_threads
    *          Number of threads that are allowed to work on this part. */
  template<typename _RAIter, typename _Compare>
    void
    __qsb_conquer(_QSBThreadLocal<_RAIter>** __tls,
		  _RAIter __begin, _RAIter __end,
		  _Compare __comp,
		  _ThreadIndex __iam, _ThreadIndex __num_threads,
		  bool __parent_wait)
    {
      typedef std::iterator_traits<_RAIter> _TraitsType;
      typedef typename _TraitsType::value_type _ValueType;
      typedef typename _TraitsType::difference_type _DifferenceType;

_DifferenceType __n = __end - __begin;

if (__num_threads <= 1 || __n <= 1)
	{
          __tls[__iam]->_M_initial.first  = __begin;
          __tls[__iam]->_M_initial.second = __end;

__qsb_local_sort_with_helping(__tls, __comp, __iam, __parent_wait);

return;
	}

// Divide step.
      _DifferenceType __split_pos =
	__qsb_divide(__begin, __end, __comp, __num_threads);

#if _GLIBCXX_PARALLEL_ASSERTIONS
      _GLIBCXX_PARALLEL_ASSERT(0 <= __split_pos &&
                               __split_pos < (__end - __begin));
#endif

_ThreadIndex
	__num_threads_leftside = std::max<_ThreadIndex>
	(1, std::min<_ThreadIndex>(__num_threads - 1, __split_pos
				   * __num_threads / __n));

#     pragma omp atomic
      *__tls[__iam]->_M_elements_leftover -= (_DifferenceType)1;

// Conquer step.
#     pragma omp parallel num_threads(2)
      {
	bool __wait;
	if(omp_get_num_threads() < 2)
          __wait = false;
	else
          __wait = __parent_wait;

#       pragma omp sections
	{
#         pragma omp section
	  {
	    __qsb_conquer(__tls, __begin, __begin + __split_pos, __comp,
			  __iam, __num_threads_leftside, __wait);
	    __wait = __parent_wait;
	  }
	  // The pivot_pos is left in place, to ensure termination.
#         pragma omp section
	  {
	    __qsb_conquer(__tls, __begin + __split_pos + 1, __end, __comp,
			  __iam + __num_threads_leftside,
			  __num_threads - __num_threads_leftside, __wait);
	    __wait = __parent_wait;
	  }
	}
      }
    }

/**
    *  @brief Quicksort step doing load-balanced local sort.
    *  @param __tls Array of thread-local storages.
    *  @param __comp Comparator.
    *  @param __iam Number of the thread processing this function.
    */
  template<typename _RAIter, typename _Compare>
    void
    __qsb_local_sort_with_helping(_QSBThreadLocal<_RAIter>** __tls,
				  _Compare& __comp, _ThreadIndex __iam,
				  bool __wait)
    {
      typedef std::iterator_traits<_RAIter> _TraitsType;
      typedef typename _TraitsType::value_type _ValueType;
      typedef typename _TraitsType::difference_type _DifferenceType;
      typedef std::pair<_RAIter, _RAIter> _Piece;

_QSBThreadLocal<_RAIter>& __tl = *__tls[__iam];

_DifferenceType
	__base_case_n = _Settings::get().sort_qsb_base_case_maximal_n;
      if (__base_case_n < 2)
	__base_case_n = 2;
      _ThreadIndex __num_threads = __tl._M_num_threads;

// Every thread has its own random number generator.
      _RandomNumber __rng(__iam + 1);

_Piece __current = __tl._M_initial;

_DifferenceType __elements_done = 0;
#if _GLIBCXX_PARALLEL_ASSERTIONS
      _DifferenceType __total_elements_done = 0;
#endif

for (;;)
	{
          // Invariant: __current must be a valid (maybe empty) range.
          _RAIter __begin = __current.first, __end = __current.second;
          _DifferenceType __n = __end - __begin;

if (__n > __base_case_n)
            {
              // Divide.
              _RAIter __pivot_pos = __begin +  __rng(__n);

// Swap __pivot_pos value to end.
              if (__pivot_pos != (__end - 1))
        	std::iter_swap(__pivot_pos, __end - 1);
              __pivot_pos = __end - 1;

__gnu_parallel::__binder2nd
		<_Compare, _ValueType, _ValueType, bool>
		__pred(__comp, *__pivot_pos);

// Divide, leave pivot unchanged in last place.
              _RAIter __split_pos1, __split_pos2;
              __split_pos1 = __gnu_sequential::partition(__begin, __end - 1,
							 __pred);

// Left side: < __pivot_pos; __right side: >= __pivot_pos.
#if _GLIBCXX_PARALLEL_ASSERTIONS
              _GLIBCXX_PARALLEL_ASSERT(__begin <= __split_pos1
                                       && __split_pos1 < __end);
#endif
              // Swap pivot back to middle.
              if (__split_pos1 != __pivot_pos)
        	std::iter_swap(__split_pos1, __pivot_pos);
              __pivot_pos = __split_pos1;

// In case all elements are equal, __split_pos1 == 0.
              if ((__split_pos1 + 1 - __begin) < (__n >> 7)
		  || (__end - __split_pos1) < (__n >> 7))
        	{
                  // Very unequal split, one part smaller than one 128th
                  // elements not strictly larger than the pivot.
                  __gnu_parallel::__unary_negate<__gnu_parallel::__binder1st
                    <_Compare, _ValueType, _ValueType, bool>, _ValueType>
                    __pred(__gnu_parallel::__binder1st
                	 <_Compare, _ValueType, _ValueType, bool>
			   (__comp, *__pivot_pos));

// Find other end of pivot-equal range.
                  __split_pos2 = __gnu_sequential::partition(__split_pos1 + 1,
							     __end, __pred);
        	}
              else
        	// Only skip the pivot.
        	__split_pos2 = __split_pos1 + 1;

// Elements equal to pivot are done.
              __elements_done += (__split_pos2 - __split_pos1);
#if _GLIBCXX_PARALLEL_ASSERTIONS
              __total_elements_done += (__split_pos2 - __split_pos1);
#endif
              // Always push larger part onto stack.
              if (((__split_pos1 + 1) - __begin) < (__end - (__split_pos2)))
        	{
                  // Right side larger.
                  if ((__split_pos2) != __end)
                    __tl._M_leftover_parts.push_front
		      (std::make_pair(__split_pos2, __end));

//__current.first = __begin;    //already set anyway
                  __current.second = __split_pos1;
                  continue;
        	}
              else
        	{
                  // Left side larger.
                  if (__begin != __split_pos1)
                    __tl._M_leftover_parts.push_front(std::make_pair
						      (__begin, __split_pos1));

__current.first = __split_pos2;
                  //__current.second = __end;     //already set anyway
                  continue;
        	}
            }
          else
            {
              __gnu_sequential::sort(__begin, __end, __comp);
              __elements_done += __n;
#if _GLIBCXX_PARALLEL_ASSERTIONS
              __total_elements_done += __n;
#endif

// Prefer own stack, small pieces.
              if (__tl._M_leftover_parts.pop_front(__current))
        	continue;

#             pragma omp atomic
              *__tl._M_elements_leftover -= __elements_done;

__elements_done = 0;

#if _GLIBCXX_PARALLEL_ASSERTIONS
              double __search_start = omp_get_wtime();
#endif

// Look for new work.
              bool __successfully_stolen = false;
              while (__wait && *__tl._M_elements_leftover > 0
                     && !__successfully_stolen
#if _GLIBCXX_PARALLEL_ASSERTIONS
                      // Possible dead-lock.
                     && (omp_get_wtime() < (__search_start + 1.0))
#endif
		     )
        	{
                  _ThreadIndex __victim;
                  __victim = __rng(__num_threads);

// Large pieces.
                  __successfully_stolen = (__victim != __iam)
		    && __tls[__victim]->_M_leftover_parts.pop_back(__current);
                  if (!__successfully_stolen)
                    __yield();
#if !defined(__ICC) && !defined(__ECC)
#                 pragma omp flush
#endif
        	}

#if _GLIBCXX_PARALLEL_ASSERTIONS
              if (omp_get_wtime() >= (__search_start + 1.0))
        	{
                  sleep(1);
                  _GLIBCXX_PARALLEL_ASSERT(omp_get_wtime()
                                           < (__search_start + 1.0));
        	}
#endif
              if (!__successfully_stolen)
        	{
#if _GLIBCXX_PARALLEL_ASSERTIONS
                  _GLIBCXX_PARALLEL_ASSERT(*__tl._M_elements_leftover == 0);
#endif
                  return;
        	}
            }
	}
    }

/** @brief Top-level quicksort routine.
    *  @param __begin Begin iterator of sequence.
    *  @param __end End iterator of sequence.
    *  @param __comp Comparator.
    *  @param __num_threads Number of threads that are allowed to work on
    *  this part.
    */
  template<typename _RAIter, typename _Compare>
    void
    __parallel_sort_qsb(_RAIter __begin, _RAIter __end,
			_Compare __comp, _ThreadIndex __num_threads)
    {
      _GLIBCXX_CALL(__end - __begin)

typedef std::iterator_traits<_RAIter> _TraitsType;
      typedef typename _TraitsType::value_type _ValueType;
      typedef typename _TraitsType::difference_type _DifferenceType;
      typedef std::pair<_RAIter, _RAIter> _Piece;

typedef _QSBThreadLocal<_RAIter> _TLSType;

_DifferenceType __n = __end - __begin;

if (__n <= 1)
	return;

// At least one element per processor.
      if (__num_threads > __n)
	__num_threads = static_cast<_ThreadIndex>(__n);

// Initialize thread local storage
      _TLSType** __tls = new _TLSType*[__num_threads];
      _DifferenceType __queue_size = (__num_threads
				      * (_ThreadIndex)(__rd_log2(__n) + 1));
      for (_ThreadIndex __t = 0; __t < __num_threads; ++__t)
	__tls[__t] = new _QSBThreadLocal<_RAIter>(__queue_size);

// There can never be more than ceil(__rd_log2(__n)) ranges on the
      // stack, because
      // 1. Only one processor pushes onto the stack
      // 2. The largest range has at most length __n
      // 3. Each range is larger than half of the range remaining
      volatile _DifferenceType __elements_leftover = __n;
      for (_ThreadIndex __i = 0; __i < __num_threads; ++__i)
	{
          __tls[__i]->_M_elements_leftover = &__elements_leftover;
          __tls[__i]->_M_num_threads = __num_threads;
          __tls[__i]->_M_global = std::make_pair(__begin, __end);

// Just in case nothing is left to assign.
          __tls[__i]->_M_initial = std::make_pair(__end, __end);
	}

// Main recursion call.
      __qsb_conquer(__tls, __begin, __begin + __n, __comp, 0,
		    __num_threads, true);

#if _GLIBCXX_PARALLEL_ASSERTIONS
      // All stack must be empty.
      _Piece __dummy;
      for (_ThreadIndex __i = 1; __i < __num_threads; ++__i)
	_GLIBCXX_PARALLEL_ASSERT(
          !__tls[__i]->_M_leftover_parts.pop_back(__dummy));
#endif

for (_ThreadIndex __i = 0; __i < __num_threads; ++__i)
	delete __tls[__i];
      delete[] __tls;
    }
} // namespace __gnu_parallel

#endif /* _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H */

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