# balanced_quicksort.h

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    00001 // -*- C++ -*-
    00002
    00003 // Copyright (C) 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
    00004 //
    00005 // This file is part of the GNU ISO C++ Library.  This library is free
    00006 // software; you can redistribute it and/or modify it under the terms
    00007 // of the GNU General Public License as published by the Free Software
    00008 // Foundation; either version 3, or (at your option) any later
    00009 // version.
    00010
    00011 // This library is distributed in the hope that it will be useful, but
    00012 // WITHOUT ANY WARRANTY; without even the implied warranty of
    00013 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    00014 // General Public License for more details.
    00015
    00016 // Under Section 7 of GPL version 3, you are granted additional
    00017 // permissions described in the GCC Runtime Library Exception, version
    00018 // 3.1, as published by the Free Software Foundation.
    00019
    00020 // You should have received a copy of the GNU General Public License and
    00021 // a copy of the GCC Runtime Library Exception along with this program;
    00022 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
    00023 // <http://www.gnu.org/licenses/>.
    00024
    00025 /** @file parallel/balanced_quicksort.h
    00026  *  @brief Implementation of a dynamically load-balanced parallel quicksort.
    00027  *
    00028  *  It works in-place and needs only logarithmic extra memory.
    00029  *  The algorithm is similar to the one proposed in
    00030  *
    00031  *  P. Tsigas and Y. Zhang.
    00032  *  A simple, fast parallel implementation of quicksort and
    00033  *  its performance evaluation on SUN enterprise 10000.
    00034  *  In 11th Euromicro Conference on Parallel, Distributed and
    00035  *  Network-Based Processing, page 372, 2003.
    00036  *
    00037  *  This file is a GNU parallel extension to the Standard C++ Library.
    00038  */
    00039
    00040 // Written by Johannes Singler.
    00041
    00042 #ifndef _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H
    00043 #define _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H 1
    00044
    00045 #include <parallel/basic_iterator.h>
    00046 #include <bits/stl_algo.h>
    00047 #include <bits/stl_function.h>
    00048
    00049 #include <parallel/settings.h>
    00050 #include <parallel/partition.h>
    00051 #include <parallel/random_number.h>
    00052 #include <parallel/queue.h>
    00053
    00054 #if _GLIBCXX_ASSERTIONS
    00055 #include <parallel/checkers.h>
    00056 #endif
    00057
    00058 namespace __gnu_parallel
    00059 {
    00060   /** @brief Information local to one thread in the parallel quicksort run. */
    00061   template<typename _RAIter>
    00062     struct _QSBThreadLocal
    00063     {
    00064       typedef std::iterator_traits<_RAIter> _TraitsType;
    00065       typedef typename _TraitsType::difference_type _DifferenceType;
    00066
    00067       /** @brief Continuous part of the sequence, described by an
    00068       iterator pair. */
    00069       typedef std::pair<_RAIter, _RAIter> _Piece;
    00070
    00071       /** @brief Initial piece to work on. */
    00072       _Piece _M_initial;
    00073
    00074       /** @brief Work-stealing queue. */
    00075       _RestrictedBoundedConcurrentQueue<_Piece> _M_leftover_parts;
    00076
    00077       /** @brief Number of threads involved in this algorithm. */
    00078       _ThreadIndex _M_num_threads;
    00079
    00080       /** @brief Pointer to a counter of elements left over to sort. */
    00081       volatile _DifferenceType* _M_elements_leftover;
    00082
    00083       /** @brief The complete sequence to sort. */
    00084       _Piece _M_global;
    00085
    00086       /** @brief Constructor.
    00087        *  @param __queue_size size of the work-stealing queue. */
    00088       _QSBThreadLocal(int __queue_size) : _M_leftover_parts(__queue_size) { }
    00089     };
    00090
    00091   /** @brief Balanced quicksort divide step.
    00092     *  @param __begin Begin iterator of subsequence.
    00093     *  @param __end End iterator of subsequence.
    00094     *  @param __comp Comparator.
    00095     *  @param __num_threads Number of threads that are allowed to work on
    00096     *  this part.
    00097     *  @pre @c (__end-__begin)>=1 */
    00098   template<typename _RAIter, typename _Compare>
    00099     typename std::iterator_traits<_RAIter>::difference_type
    00100     __qsb_divide(_RAIter __begin, _RAIter __end,
    00101          _Compare __comp, _ThreadIndex __num_threads)
    00102     {
    00103       _GLIBCXX_PARALLEL_ASSERT(__num_threads > 0);
    00104
    00105       typedef std::iterator_traits<_RAIter> _TraitsType;
    00106       typedef typename _TraitsType::value_type _ValueType;
    00107       typedef typename _TraitsType::difference_type _DifferenceType;
    00108
    00109       _RAIter __pivot_pos =
    00110     __median_of_three_iterators(__begin, __begin + (__end - __begin) / 2,
    00111                     __end  - 1, __comp);
    00112
    00113 #if defined(_GLIBCXX_ASSERTIONS)
    00114       // Must be in between somewhere.
    00115       _DifferenceType __n = __end - __begin;
    00116
    00117       _GLIBCXX_PARALLEL_ASSERT((!__comp(*__pivot_pos, *__begin)
    00118                 && !__comp(*(__begin + __n / 2),
    00119                        *__pivot_pos))
    00120                    || (!__comp(*__pivot_pos, *__begin)
    00121                    && !__comp(*(__end - 1), *__pivot_pos))
    00122                    || (!__comp(*__pivot_pos, *(__begin + __n / 2))
    00123                    && !__comp(*__begin, *__pivot_pos))
    00124                    || (!__comp(*__pivot_pos, *(__begin + __n / 2))
    00125                    && !__comp(*(__end - 1), *__pivot_pos))
    00126                    || (!__comp(*__pivot_pos, *(__end - 1))
    00127                    && !__comp(*__begin, *__pivot_pos))
    00128                    || (!__comp(*__pivot_pos, *(__end - 1))
    00129                    && !__comp(*(__begin + __n / 2),
    00130                           *__pivot_pos)));
    00131 #endif
    00132
    00133       // Swap pivot value to end.
    00134       if (__pivot_pos != (__end - 1))
    00135     std::swap(*__pivot_pos, *(__end - 1));
    00136       __pivot_pos = __end - 1;
    00137
    00138       __gnu_parallel::__binder2nd<_Compare, _ValueType, _ValueType, bool>
    00139     __pred(__comp, *__pivot_pos);
    00140
    00141       // Divide, returning __end - __begin - 1 in the worst case.
    00142       _DifferenceType __split_pos = __parallel_partition(__begin, __end - 1,
    00143                              __pred,
    00144                              __num_threads);
    00145
    00146       // Swap back pivot to middle.
    00147       std::swap(*(__begin + __split_pos), *__pivot_pos);
    00148       __pivot_pos = __begin + __split_pos;
    00149
    00150 #if _GLIBCXX_ASSERTIONS
    00151       _RAIter __r;
    00152       for (__r = __begin; __r != __pivot_pos; ++__r)
    00153     _GLIBCXX_PARALLEL_ASSERT(__comp(*__r, *__pivot_pos));
    00154       for (; __r != __end; ++__r)
    00155     _GLIBCXX_PARALLEL_ASSERT(!__comp(*__r, *__pivot_pos));
    00156 #endif
    00157
    00158       return __split_pos;
    00159     }
    00160
    00161   /** @brief Quicksort conquer step.
    00162     *  @param __tls Array of thread-local storages.
    00163     *  @param __begin Begin iterator of subsequence.
    00164     *  @param __end End iterator of subsequence.
    00165     *  @param __comp Comparator.
    00166     *  @param __iam Number of the thread processing this function.
    00167     *  @param __num_threads
    00168     *          Number of threads that are allowed to work on this part. */
    00169   template<typename _RAIter, typename _Compare>
    00170     void
    00171     __qsb_conquer(_QSBThreadLocal<_RAIter>** __tls,
    00172           _RAIter __begin, _RAIter __end,
    00173           _Compare __comp,
    00174           _ThreadIndex __iam, _ThreadIndex __num_threads,
    00175           bool __parent_wait)
    00176     {
    00177       typedef std::iterator_traits<_RAIter> _TraitsType;
    00178       typedef typename _TraitsType::value_type _ValueType;
    00179       typedef typename _TraitsType::difference_type _DifferenceType;
    00180
    00181       _DifferenceType __n = __end - __begin;
    00182
    00183       if (__num_threads <= 1 || __n <= 1)
    00184     {
    00185           __tls[__iam]->_M_initial.first  = __begin;
    00186           __tls[__iam]->_M_initial.second = __end;
    00187
    00188           __qsb_local_sort_with_helping(__tls, __comp, __iam, __parent_wait);
    00189
    00190           return;
    00191     }
    00192
    00193       // Divide step.
    00194       _DifferenceType __split_pos =
    00195     __qsb_divide(__begin, __end, __comp, __num_threads);
    00196
    00197 #if _GLIBCXX_ASSERTIONS
    00198       _GLIBCXX_PARALLEL_ASSERT(0 <= __split_pos &&
    00199                                __split_pos < (__end - __begin));
    00200 #endif
    00201
    00202       _ThreadIndex
    00203     __num_threads_leftside = std::max<_ThreadIndex>
    00204     (1, std::min<_ThreadIndex>(__num_threads - 1, __split_pos
    00205                    * __num_threads / __n));
    00206
    00207 #     pragma omp atomic
    00208       *__tls[__iam]->_M_elements_leftover -= (_DifferenceType)1;
    00209
    00210       // Conquer step.
    00211 #     pragma omp parallel num_threads(2)
    00212       {
    00213     bool __wait;
    00214     if(omp_get_num_threads() < 2)
    00215           __wait = false;
    00216     else
    00217           __wait = __parent_wait;
    00218
    00219 #       pragma omp sections
    00220     {
    00221 #         pragma omp section
    00222       {
    00223         __qsb_conquer(__tls, __begin, __begin + __split_pos, __comp,
    00224               __iam, __num_threads_leftside, __wait);
    00225         __wait = __parent_wait;
    00226       }
    00227       // The pivot_pos is left in place, to ensure termination.
    00228 #         pragma omp section
    00229       {
    00230         __qsb_conquer(__tls, __begin + __split_pos + 1, __end, __comp,
    00231               __iam + __num_threads_leftside,
    00232               __num_threads - __num_threads_leftside, __wait);
    00233         __wait = __parent_wait;
    00234       }
    00235     }
    00236       }
    00237     }
    00238
    00239   /**
    00240     *  @brief Quicksort step doing load-balanced local sort.
    00241     *  @param __tls Array of thread-local storages.
    00242     *  @param __comp Comparator.
    00243     *  @param __iam Number of the thread processing this function.
    00244     */
    00245   template<typename _RAIter, typename _Compare>
    00246     void
    00247     __qsb_local_sort_with_helping(_QSBThreadLocal<_RAIter>** __tls,
    00248                   _Compare& __comp, _ThreadIndex __iam,
    00249                   bool __wait)
    00250     {
    00251       typedef std::iterator_traits<_RAIter> _TraitsType;
    00252       typedef typename _TraitsType::value_type _ValueType;
    00253       typedef typename _TraitsType::difference_type _DifferenceType;
    00254       typedef std::pair<_RAIter, _RAIter> _Piece;
    00255
    00256       _QSBThreadLocal<_RAIter>& __tl = *__tls[__iam];
    00257
    00258       _DifferenceType
    00259     __base_case_n = _Settings::get().sort_qsb_base_case_maximal_n;
    00260       if (__base_case_n < 2)
    00261     __base_case_n = 2;
    00262       _ThreadIndex __num_threads = __tl._M_num_threads;
    00263
    00264       // Every thread has its own random number generator.
    00265       _RandomNumber __rng(__iam + 1);
    00266
    00267       _Piece __current = __tl._M_initial;
    00268
    00269       _DifferenceType __elements_done = 0;
    00270 #if _GLIBCXX_ASSERTIONS
    00271       _DifferenceType __total_elements_done = 0;
    00272 #endif
    00273
    00274       for (;;)
    00275     {
    00276           // Invariant: __current must be a valid (maybe empty) range.
    00277           _RAIter __begin = __current.first, __end = __current.second;
    00278           _DifferenceType __n = __end - __begin;
    00279
    00280           if (__n > __base_case_n)
    00281             {
    00282               // Divide.
    00283               _RAIter __pivot_pos = __begin +  __rng(__n);
    00284
    00285               // Swap __pivot_pos value to end.
    00286               if (__pivot_pos != (__end - 1))
    00287             std::swap(*__pivot_pos, *(__end - 1));
    00288               __pivot_pos = __end - 1;
    00289
    00290               __gnu_parallel::__binder2nd
    00291         <_Compare, _ValueType, _ValueType, bool>
    00292         __pred(__comp, *__pivot_pos);
    00293
    00294               // Divide, leave pivot unchanged in last place.
    00295               _RAIter __split_pos1, __split_pos2;
    00296               __split_pos1 = __gnu_sequential::partition(__begin, __end - 1,
    00297                              __pred);
    00298
    00299               // Left side: < __pivot_pos; __right side: >= __pivot_pos.
    00300 #if _GLIBCXX_ASSERTIONS
    00301               _GLIBCXX_PARALLEL_ASSERT(__begin <= __split_pos1
    00302                                        && __split_pos1 < __end);
    00303 #endif
    00304               // Swap pivot back to middle.
    00305               if (__split_pos1 != __pivot_pos)
    00306             std::swap(*__split_pos1, *__pivot_pos);
    00307               __pivot_pos = __split_pos1;
    00308
    00309               // In case all elements are equal, __split_pos1 == 0.
    00310               if ((__split_pos1 + 1 - __begin) < (__n >> 7)
    00311           || (__end - __split_pos1) < (__n >> 7))
    00312             {
    00313                   // Very unequal split, one part smaller than one 128th
    00314                   // elements not strictly larger than the pivot.
    00315                   __gnu_parallel::__unary_negate<__gnu_parallel::__binder1st
    00316                     <_Compare, _ValueType, _ValueType, bool>, _ValueType>
    00317                     __pred(__gnu_parallel::__binder1st
    00318                      <_Compare, _ValueType, _ValueType, bool>
    00319                (__comp, *__pivot_pos));
    00320
    00321                   // Find other end of pivot-equal range.
    00322                   __split_pos2 = __gnu_sequential::partition(__split_pos1 + 1,
    00323                                  __end, __pred);
    00324             }
    00325               else
    00326             // Only skip the pivot.
    00327             __split_pos2 = __split_pos1 + 1;
    00328
    00329               // Elements equal to pivot are done.
    00330               __elements_done += (__split_pos2 - __split_pos1);
    00331 #if _GLIBCXX_ASSERTIONS
    00332               __total_elements_done += (__split_pos2 - __split_pos1);
    00333 #endif
    00334               // Always push larger part onto stack.
    00335               if (((__split_pos1 + 1) - __begin) < (__end - (__split_pos2)))
    00336             {
    00337                   // Right side larger.
    00338                   if ((__split_pos2) != __end)
    00339                     __tl._M_leftover_parts.push_front
    00340               (std::make_pair(__split_pos2, __end));
    00341
    00342                   //__current.first = __begin;    //already set anyway
    00343                   __current.second = __split_pos1;
    00344                   continue;
    00345             }
    00346               else
    00347             {
    00348                   // Left side larger.
    00349                   if (__begin != __split_pos1)
    00350                     __tl._M_leftover_parts.push_front(std::make_pair
    00351                               (__begin, __split_pos1));
    00352
    00353                   __current.first = __split_pos2;
    00354                   //__current.second = __end;     //already set anyway
    00355                   continue;
    00356             }
    00357             }
    00358           else
    00359             {
    00360               __gnu_sequential::sort(__begin, __end, __comp);
    00361               __elements_done += __n;
    00362 #if _GLIBCXX_ASSERTIONS
    00363               __total_elements_done += __n;
    00364 #endif
    00365
    00366               // Prefer own stack, small pieces.
    00367               if (__tl._M_leftover_parts.pop_front(__current))
    00368             continue;
    00369
    00370 #             pragma omp atomic
    00371               *__tl._M_elements_leftover -= __elements_done;
    00372
    00373               __elements_done = 0;
    00374
    00375 #if _GLIBCXX_ASSERTIONS
    00376               double __search_start = omp_get_wtime();
    00377 #endif
    00378
    00379               // Look for new work.
    00380               bool __successfully_stolen = false;
    00381               while (__wait && *__tl._M_elements_leftover > 0
    00382                      && !__successfully_stolen
    00383 #if _GLIBCXX_ASSERTIONS
    00384                       // Possible dead-lock.
    00385                      && (omp_get_wtime() < (__search_start + 1.0))
    00386 #endif
    00387              )
    00388             {
    00389                   _ThreadIndex __victim;
    00390                   __victim = __rng(__num_threads);
    00391
    00392                   // Large pieces.
    00393                   __successfully_stolen = (__victim != __iam)
    00394             && __tls[__victim]->_M_leftover_parts.pop_back(__current);
    00395                   if (!__successfully_stolen)
    00396                     __yield();
    00397 #if !defined(__ICC) && !defined(__ECC)
    00398 #                 pragma omp flush
    00399 #endif
    00400             }
    00401
    00402 #if _GLIBCXX_ASSERTIONS
    00403               if (omp_get_wtime() >= (__search_start + 1.0))
    00404             {
    00405                   sleep(1);
    00406                   _GLIBCXX_PARALLEL_ASSERT(omp_get_wtime()
    00407                                            < (__search_start + 1.0));
    00408             }
    00409 #endif
    00410               if (!__successfully_stolen)
    00411             {
    00412 #if _GLIBCXX_ASSERTIONS
    00413                   _GLIBCXX_PARALLEL_ASSERT(*__tl._M_elements_leftover == 0);
    00414 #endif
    00415                   return;
    00416             }
    00417             }
    00418     }
    00419     }
    00420
    00421   /** @brief Top-level quicksort routine.
    00422     *  @param __begin Begin iterator of sequence.
    00423     *  @param __end End iterator of sequence.
    00424     *  @param __comp Comparator.
    00425     *  @param __num_threads Number of threads that are allowed to work on
    00426     *  this part.
    00427     */
    00428   template<typename _RAIter, typename _Compare>
    00429     void
    00430     __parallel_sort_qsb(_RAIter __begin, _RAIter __end,
    00431             _Compare __comp, _ThreadIndex __num_threads)
    00432     {
    00433       _GLIBCXX_CALL(__end - __begin)
    00434
    00435       typedef std::iterator_traits<_RAIter> _TraitsType;
    00436       typedef typename _TraitsType::value_type _ValueType;
    00437       typedef typename _TraitsType::difference_type _DifferenceType;
    00438       typedef std::pair<_RAIter, _RAIter> _Piece;
    00439
    00440       typedef _QSBThreadLocal<_RAIter> _TLSType;
    00441
    00442       _DifferenceType __n = __end - __begin;
    00443
    00444       if (__n <= 1)
    00445     return;
    00446
    00447       // At least one element per processor.
    00448       if (__num_threads > __n)
    00449     __num_threads = static_cast<_ThreadIndex>(__n);
    00450
    00451       // Initialize thread local storage
    00452       _TLSType** __tls = new _TLSType*[__num_threads];
    00453       _DifferenceType __queue_size = (__num_threads
    00454                       * (_ThreadIndex)(__rd_log2(__n) + 1));
    00455       for (_ThreadIndex __t = 0; __t < __num_threads; ++__t)
    00456     __tls[__t] = new _QSBThreadLocal<_RAIter>(__queue_size);
    00457
    00458       // There can never be more than ceil(__rd_log2(__n)) ranges on the
    00459       // stack, because
    00460       // 1. Only one processor pushes onto the stack
    00461       // 2. The largest range has at most length __n
    00462       // 3. Each range is larger than half of the range remaining
    00463       volatile _DifferenceType __elements_leftover = __n;
    00464       for (_ThreadIndex __i = 0; __i < __num_threads; ++__i)
    00465     {
    00466           __tls[__i]->_M_elements_leftover = &__elements_leftover;
    00467           __tls[__i]->_M_num_threads = __num_threads;
    00468           __tls[__i]->_M_global = std::make_pair(__begin, __end);
    00469
    00470           // Just in case nothing is left to assign.
    00471           __tls[__i]->_M_initial = std::make_pair(__end, __end);
    00472     }
    00473
    00474       // Main recursion call.
    00475       __qsb_conquer(__tls, __begin, __begin + __n, __comp, 0,
    00476             __num_threads, true);
    00477
    00478 #if _GLIBCXX_ASSERTIONS
    00479       // All stack must be empty.
    00480       _Piece __dummy;
    00481       for (_ThreadIndex __i = 1; __i < __num_threads; ++__i)
    00482     _GLIBCXX_PARALLEL_ASSERT(
    00483           !__tls[__i]->_M_leftover_parts.pop_back(__dummy));
    00484 #endif
    00485
    00486       for (_ThreadIndex __i = 0; __i < __num_threads; ++__i)
    00487     delete __tls[__i];
    00488       delete[] __tls;
    00489     }
    00490 } // namespace __gnu_parallel
    00491
    00492 #endif /* _GLIBCXX_PARALLEL_BALANCED_QUICKSORT_H */