gcc/libstdc++-v3/include/parallel/multiway_merge.h

// -*- C++ -*-

// Copyright (C) 2007 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 2, or (at your option) any later
// version.

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// 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.

// You should have received a copy of the GNU General Public License
// along with this library; see the file COPYING.  If not, write to
// the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
// MA 02111-1307, USA.

// As a special exception, you may use this file as part of a free
// software library without restriction.  Specifically, if other files
// instantiate templates or use macros or inline functions from this
// file, or you compile this file and link it with other files to
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/** @file parallel/multiway_merge.h
 *  @brief Implementation of sequential and parallel multiway merge.
 *
 *  Explanations on the high-speed merging routines in the appendix of
 *
 *  P. Sanders.
 *  Fast priority queues for cached memory.
 *  ACM Journal of Experimental Algorithmics, 5, 2000.
 *
 *  This file is a GNU parallel extension to the Standard C++ Library.
 */

// Written by Johannes Singler.

#ifndef _GLIBCXX_PARALLEL_MULTIWAY_MERGE_H
#define _GLIBCXX_PARALLEL_MULTIWAY_MERGE_H

#include <vector>

#include <bits/stl_algo.h>
#include <parallel/features.h>
#include <parallel/parallel.h>
#include <parallel/merge.h>
#include <parallel/losertree.h>
#if _GLIBCXX_ASSERTIONS
#include <parallel/checkers.h>
#endif

/** @brief Length of a sequence described by a pair of iterators. */
#define LENGTH(s) ((s).second - (s).first)

// XXX need iterator typedefs
namespace __gnu_parallel
{
  template<typename RandomAccessIterator, typename Comparator>
  class guarded_iterator;

  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<(guarded_iterator<RandomAccessIterator, Comparator>& bi1,
	    guarded_iterator<RandomAccessIterator, Comparator>& bi2);

  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<=(guarded_iterator<RandomAccessIterator, Comparator>& bi1,
	     guarded_iterator<RandomAccessIterator, Comparator>& bi2);

  /** @brief Iterator wrapper supporting an implicit supremum at the end
      of the sequence, dominating all comparisons.
      *  Deriving from RandomAccessIterator is not possible since
      *  RandomAccessIterator need not be a class.
      */
  template<typename RandomAccessIterator, typename Comparator>
  class guarded_iterator
  {
  private:
    /** @brief Current iterator position. */
    RandomAccessIterator current;

    /** @brief End iterator of the sequence. */
    RandomAccessIterator end;

    /** @brief Comparator. */
    Comparator& comp;

  public:
    /** @brief Constructor. Sets iterator to beginning of sequence.
     *  @param begin Begin iterator of sequence.
     *  @param end End iterator of sequence.
     *  @param comp Comparator provided for associated overloaded
     *  compare operators. */
    inline guarded_iterator(RandomAccessIterator begin, 
			    RandomAccessIterator end, Comparator& comp) 
    : current(begin), end(end), comp(comp)
    { }

    /** @brief Pre-increment operator.
     *  @return This. */
    inline guarded_iterator<RandomAccessIterator, Comparator>&
    operator++()
    {
      ++current;
      return *this;
    }

    /** @brief Dereference operator.
     *  @return Referenced element. */
    inline typename std::iterator_traits<RandomAccessIterator>::value_type
    operator*()
    { return *current; }

    /** @brief Convert to wrapped iterator.
     *  @return Wrapped iterator. */
    inline operator RandomAccessIterator()
    { return current; }

    friend bool
    operator< <RandomAccessIterator, Comparator>(guarded_iterator<RandomAccessIterator, Comparator>& bi1, guarded_iterator<RandomAccessIterator, Comparator>& bi2);

    friend bool
    operator<= <RandomAccessIterator, Comparator>(guarded_iterator<RandomAccessIterator, Comparator>& bi1, guarded_iterator<RandomAccessIterator, Comparator>& bi2);
  };

  /** @brief Compare two elements referenced by guarded iterators.
   *  @param bi1 First iterator.
   *  @param bi2 Second iterator.
   *  @return @c True if less. */
  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<(guarded_iterator<RandomAccessIterator, Comparator>& bi1,
	    guarded_iterator<RandomAccessIterator, Comparator>& bi2)
  {
    if (bi1.current == bi1.end)	//bi1 is sup
      return bi2.current == bi2.end;	//bi2 is not sup
    if (bi2.current == bi2.end)	//bi2 is sup
      return true;
    return (bi1.comp)(*bi1, *bi2);	//normal compare
  }

  /** @brief Compare two elements referenced by guarded iterators.
   *  @param bi1 First iterator.
   *  @param bi2 Second iterator.
   *  @return @c True if less equal. */
  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<=(guarded_iterator<RandomAccessIterator, Comparator>& bi1,
	     guarded_iterator<RandomAccessIterator, Comparator>& bi2)
  {
    if (bi2.current == bi2.end)	//bi1 is sup
      return bi1.current != bi1.end;	//bi2 is not sup
    if (bi1.current == bi1.end)	//bi2 is sup
      return false;
    return !(bi1.comp)(*bi2, *bi1);	//normal compare
  }

  template<typename RandomAccessIterator, typename Comparator>
  class unguarded_iterator;

  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<(unguarded_iterator<RandomAccessIterator, Comparator>& bi1,
	    unguarded_iterator<RandomAccessIterator, Comparator>& bi2);

  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<=(unguarded_iterator<RandomAccessIterator, Comparator>& bi1,
	     unguarded_iterator<RandomAccessIterator, Comparator>& bi2);

  template<typename RandomAccessIterator, typename Comparator>
  class unguarded_iterator
  {
  private:
    /** @brief Current iterator position. */
    RandomAccessIterator& current;
    /** @brief Comparator. */
    mutable Comparator& comp;

  public:
    /** @brief Constructor. Sets iterator to beginning of sequence.
     *  @param begin Begin iterator of sequence.
     *  @param end Unused, only for compatibility.
     *  @param comp Unused, only for compatibility. */
    inline unguarded_iterator(RandomAccessIterator begin, 
			      RandomAccessIterator end, Comparator& comp) 
    : current(begin), comp(comp)
    { }

    /** @brief Pre-increment operator.
     *  @return This. */
    inline  unguarded_iterator<RandomAccessIterator, Comparator>&
    operator++()
    {
      current++;
      return *this;
    }

    /** @brief Dereference operator.
     *  @return Referenced element. */
    inline typename std::iterator_traits<RandomAccessIterator>::value_type 
    operator*()
    { return *current; }

    /** @brief Convert to wrapped iterator.
     *  @return Wrapped iterator. */
    inline
    operator RandomAccessIterator()
    { return current; }

    friend bool
    operator< <RandomAccessIterator, Comparator>(unguarded_iterator<RandomAccessIterator, Comparator>& bi1, unguarded_iterator<RandomAccessIterator, Comparator>& bi2);

    friend bool
    operator<= <RandomAccessIterator, Comparator>(unguarded_iterator<RandomAccessIterator, Comparator>& bi1, unguarded_iterator<RandomAccessIterator, Comparator>& bi2);
  };

  /** @brief Compare two elements referenced by unguarded iterators.
   *  @param bi1 First iterator.
   *  @param bi2 Second iterator.
   *  @return @c True if less. */
  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<(unguarded_iterator<RandomAccessIterator, Comparator>& bi1,
	    unguarded_iterator<RandomAccessIterator, Comparator>& bi2)
  {
    // Normal compare.
    return (bi1.comp)(*bi1, *bi2);
  }

  /** @brief Compare two elements referenced by unguarded iterators.
   *  @param bi1 First iterator.
   *  @param bi2 Second iterator.
   *  @return @c True if less equal. */
  template<typename RandomAccessIterator, typename Comparator>
  inline bool
  operator<=(unguarded_iterator<RandomAccessIterator, Comparator>& bi1,
	     unguarded_iterator<RandomAccessIterator, Comparator>& bi2)
  {
    // Normal compare.
    return !(bi1.comp)(*bi2, *bi1);
  }

  /** Prepare a set of sequences to be merged without a (end) guard
   *  @param seqs_begin
   *  @param seqs_end
   *  @param comp
   *  @param min_sequence
   *  @param stable
   *  @pre (seqs_end - seqs_begin > 0) */
  template<typename RandomAccessIteratorIterator, typename Comparator>
  typename std::iterator_traits<typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type>::difference_type
  prepare_unguarded(RandomAccessIteratorIterator seqs_begin,
		    RandomAccessIteratorIterator seqs_end, Comparator comp,
		    int& min_sequence, bool stable)
  {
    _GLIBCXX_CALL(seqs_end - seqs_begin)

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;
    typedef typename std::iterator_traits<RandomAccessIterator1>::difference_type
      difference_type;

    if ((*seqs_begin).first == (*seqs_begin).second)
      {
	// Empty sequence found, it's the first one.
	min_sequence = 0;
	return -1;
      }

    // Last element in sequence.
    value_type min = *((*seqs_begin).second - 1);
    min_sequence = 0;
    for (RandomAccessIteratorIterator s = seqs_begin + 1; s != seqs_end; s++)
      {
	if ((*s).first == (*s).second)
	  {
	    // Empty sequence found.
	    min_sequence = static_cast<int>(s - seqs_begin);
	    return -1;
	  }

	// Last element in sequence.
	const value_type& v = *((*s).second - 1);
	if (comp(v, min))	//strictly smaller
	  {
	    min = v;
	    min_sequence = static_cast<int>(s - seqs_begin);
	  }
      }

    difference_type overhang_size = 0;

    int s = 0;
    for (s = 0; s <= min_sequence; s++)
      {
	RandomAccessIterator1 split;
	if (stable)
	  split = std::upper_bound(seqs_begin[s].first, seqs_begin[s].second,
				   min, comp);
	else
	  split = std::lower_bound(seqs_begin[s].first, seqs_begin[s].second,
				   min, comp);

	overhang_size += seqs_begin[s].second - split;
      }

    for (; s < (seqs_end - seqs_begin); s++)
      {
	RandomAccessIterator1 split = std::lower_bound(seqs_begin[s].first, seqs_begin[s].second, min, comp);
	overhang_size += seqs_begin[s].second - split;
      }

    // So many elements will be left over afterwards.
    return overhang_size;
  }

  /** Prepare a set of sequences to be merged with a (end) guard (sentinel)
   *  @param seqs_begin
   *  @param seqs_end
   *  @param comp */
  template<typename RandomAccessIteratorIterator, typename Comparator>
  typename std::iterator_traits<typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type>::difference_type
  prepare_unguarded_sentinel(RandomAccessIteratorIterator seqs_begin,
			     RandomAccessIteratorIterator seqs_end,
			     Comparator comp)
  {
    _GLIBCXX_CALL(seqs_end - seqs_begin)

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;
    typedef typename std::iterator_traits<RandomAccessIterator1>::difference_type
      difference_type;

    // Last element in sequence.
    value_type* max = NULL;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; s++)
      {
	if ((*s).first == (*s).second)
	  continue;

	// Last element in sequence.
	value_type& v = *((*s).second - 1);

	// Strictly greater.
	if (!max || comp(*max, v))
	  max = &v;
      }

    difference_type overhang_size = 0;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; s++)
      {
	RandomAccessIterator1 split = std::lower_bound((*s).first, (*s).second,
						       *max, comp);
	overhang_size += (*s).second - split;

	// Set sentinel.
	*((*s).second) = *max;
      }

    // So many elements will be left over afterwards.
    return overhang_size;
  }

  /** @brief Highly efficient 3-way merging procedure.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Unused, stable anyway.
   *  @return End iterator of output sequence. */
  template<template<typename RAI, typename C> class iterator, typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_3_variant(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length);
    
    typedef _DifferenceTp difference_type;

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    if (length == 0)
      return target;

    iterator<RandomAccessIterator1, Comparator>
      seq0(seqs_begin[0].first, seqs_begin[0].second, comp),
      seq1(seqs_begin[1].first, seqs_begin[1].second, comp),
      seq2(seqs_begin[2].first, seqs_begin[2].second, comp);

    if (seq0 <= seq1)
      {
	if (seq1 <= seq2)
	  goto s012;
	else
	  if (seq2 <  seq0)
	    goto s201;
	  else
	    goto s021;
      }
    else
      {
	if (seq1 <= seq2)
	  {
	    if (seq0 <= seq2)
	      goto s102;
	    else
	      goto s120;
	  }
	else
	  goto s210;
      }

#define Merge3Case(a,b,c,c0,c1)				\
    s ## a ## b ## c :					\
      *target = *seq ## a;				\
    ++target;						\
    length--;						\
    ++seq ## a;						\
    if (length == 0) goto finish;			\
    if (seq ## a c0 seq ## b) goto s ## a ## b ## c;	\
    if (seq ## a c1 seq ## c) goto s ## b ## a ## c;	\
    goto s ## b ## c ## a;

    Merge3Case(0, 1, 2, <=, <=);
    Merge3Case(1, 2, 0, <=, < );
    Merge3Case(2, 0, 1, < , < );
    Merge3Case(1, 0, 2, < , <=);
    Merge3Case(0, 2, 1, <=, <=);
    Merge3Case(2, 1, 0, < , < );

#undef Merge3Case

  finish:
    ;

    seqs_begin[0].first = seq0;
    seqs_begin[1].first = seq1;
    seqs_begin[2].first = seq2;

    return target;
  }

  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_3_combined(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length);
    
    typedef _DifferenceTp difference_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    int min_seq;
    RandomAccessIterator3 target_end;

    // Stable anyway.
    difference_type overhang = prepare_unguarded(seqs_begin, seqs_end, comp, min_seq, true);

    difference_type total_length = 0;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; ++s)
      total_length += LENGTH(*s);

    if (overhang != -1)
      {
	difference_type unguarded_length = std::min(length, total_length - overhang);
	target_end = multiway_merge_3_variant<unguarded_iterator>
	  (seqs_begin, seqs_end, target, comp, unguarded_length, stable);
	overhang = length - unguarded_length;
      }
    else
      {
	// Empty sequence found.
	overhang = length;
	target_end = target;
      }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length - overhang);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    switch (min_seq)
      {
      case 0:
	// Iterators will be advanced accordingly.
	target_end = merge_advance(seqs_begin[1].first, seqs_begin[1].second,
				   seqs_begin[2].first, seqs_begin[2].second,
				   target_end, overhang, comp);
	break;
      case 1:
	target_end = merge_advance(seqs_begin[0].first, seqs_begin[0].second,
				   seqs_begin[2].first, seqs_begin[2].second,
				   target_end, overhang, comp);
	break;
      case 2:
	target_end = merge_advance(seqs_begin[0].first, seqs_begin[0].second,
				   seqs_begin[1].first, seqs_begin[1].second,
				   target_end, overhang, comp);
	break;
      default:
	_GLIBCXX_PARALLEL_ASSERT(false);
      }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    return target_end;
  }

  /** @brief Highly efficient 4-way merging procedure.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Unused, stable anyway.
   *  @return End iterator of output sequence. */
  template<template<typename RAI, typename C> class iterator, typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_4_variant(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length);
    typedef _DifferenceTp difference_type;

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    iterator<RandomAccessIterator1, Comparator>
      seq0(seqs_begin[0].first, seqs_begin[0].second, comp),
      seq1(seqs_begin[1].first, seqs_begin[1].second, comp),
      seq2(seqs_begin[2].first, seqs_begin[2].second, comp),
      seq3(seqs_begin[3].first, seqs_begin[3].second, comp);

#define Decision(a,b,c,d) {					\
      if (seq ## d < seq ## a) goto s ## d ## a ## b ## c;	\
      if (seq ## d < seq ## b) goto s ## a ## d ## b ## c;	\
      if (seq ## d < seq ## c) goto s ## a ## b ## d ## c;	\
      goto s ## a ## b ## c ## d;  }

    if (seq0 <= seq1)
      {
	if (seq1 <= seq2)
	  Decision(0,1,2,3)
	  else
	    if (seq2 < seq0)
	      Decision(2,0,1,3)
	      else
		Decision(0,2,1,3)
		  }
    else
      {
	if (seq1 <= seq2)
	  {
	    if (seq0 <= seq2)
	      Decision(1,0,2,3)
	      else
		Decision(1,2,0,3)
		  }
	else
	  Decision(2,1,0,3)
	    }

#define Merge4Case(a,b,c,d,c0,c1,c2)				\
    s ## a ## b ## c ## d:					\
      if (length == 0) goto finish;				\
    *target = *seq ## a;					\
    ++target;							\
    length--;							\
    ++seq ## a;							\
    if (seq ## a c0 seq ## b) goto s ## a ## b ## c ## d;	\
    if (seq ## a c1 seq ## c) goto s ## b ## a ## c ## d;	\
    if (seq ## a c2 seq ## d) goto s ## b ## c ## a ## d;	\
    goto s ## b ## c ## d ## a;

    Merge4Case(0, 1, 2, 3, <=, <=, <=);
    Merge4Case(0, 1, 3, 2, <=, <=, <=);
    Merge4Case(0, 2, 1, 3, <=, <=, <=);
    Merge4Case(0, 2, 3, 1, <=, <=, <=);
    Merge4Case(0, 3, 1, 2, <=, <=, <=);
    Merge4Case(0, 3, 2, 1, <=, <=, <=);
    Merge4Case(1, 0, 2, 3, < , <=, <=);
    Merge4Case(1, 0, 3, 2, < , <=, <=);
    Merge4Case(1, 2, 0, 3, <=, < , <=);
    Merge4Case(1, 2, 3, 0, <=, <=, < );
    Merge4Case(1, 3, 0, 2, <=, < , <=);
    Merge4Case(1, 3, 2, 0, <=, <=, < );
    Merge4Case(2, 0, 1, 3, < , < , <=);
    Merge4Case(2, 0, 3, 1, < , <=, < );
    Merge4Case(2, 1, 0, 3, < , < , <=);
    Merge4Case(2, 1, 3, 0, < , <=, < );
    Merge4Case(2, 3, 0, 1, <=, < , < );
    Merge4Case(2, 3, 1, 0, <=, < , < );
    Merge4Case(3, 0, 1, 2, < , < , < );
    Merge4Case(3, 0, 2, 1, < , < , < );
    Merge4Case(3, 1, 0, 2, < , < , < );
    Merge4Case(3, 1, 2, 0, < , < , < );
    Merge4Case(3, 2, 0, 1, < , < , < );
    Merge4Case(3, 2, 1, 0, < , < , < );

#undef Merge4Case
#undef Decision

  finish:
    ;

    seqs_begin[0].first = seq0;
    seqs_begin[1].first = seq1;
    seqs_begin[2].first = seq2;
    seqs_begin[3].first = seq3;

    return target;
  }

  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_4_combined(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length);
    typedef _DifferenceTp difference_type;

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    int min_seq;
    RandomAccessIterator3 target_end;

    // Stable anyway.
    difference_type overhang = prepare_unguarded(seqs_begin, seqs_end, comp, min_seq, true);

    difference_type total_length = 0;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; ++s)
      total_length += LENGTH(*s);

    if (overhang != -1)
      {
	difference_type unguarded_length = std::min(length, total_length - overhang);
	target_end = multiway_merge_4_variant<unguarded_iterator>
	  (seqs_begin, seqs_end, target, comp, unguarded_length, stable);
	overhang = length - unguarded_length;
      }
    else
      {
	// Empty sequence found.
	overhang = length;
	target_end = target;
      }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length - overhang);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    std::vector<std::pair<RandomAccessIterator1, RandomAccessIterator1> > one_missing(seqs_begin, seqs_end);
    one_missing.erase(one_missing.begin() + min_seq);	//remove

    target_end = multiway_merge_3_variant<guarded_iterator>(one_missing.begin(), one_missing.end(), target_end, comp, overhang, stable);

    // Insert back again.
    one_missing.insert(one_missing.begin() + min_seq, seqs_begin[min_seq]);
    // Write back modified iterators.
    copy(one_missing.begin(), one_missing.end(), seqs_begin);

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    return target_end;
  }

  /** @brief Basic multi-way merging procedure.
   *
   *  The head elements are kept in a sorted array, new heads are
   *  inserted linearly.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @return End iterator of output sequence. 
   */
  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_bubble(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    // Num remaining pieces.
    int k = static_cast<int>(seqs_end - seqs_begin), nrp;

    value_type* pl = static_cast<value_type*>(::operator new(sizeof(value_type) * k));
    int* source = new int[k];
    difference_type total_length = 0;

#define POS(i) seqs_begin[(i)].first
#define STOPS(i) seqs_begin[(i)].second

    // Write entries into queue.
    nrp = 0;
    for (int pi = 0; pi < k; pi++)
      {
	if (STOPS(pi) != POS(pi))
	  {
	    pl[nrp] = *(POS(pi));
	    source[nrp] = pi;
	    nrp++;
	    total_length += LENGTH(seqs_begin[pi]);
	  }
      }

    if (stable)
      {
	for (int k = 0; k < nrp - 1; k++)
	  for (int pi = nrp - 1; pi > k; pi--)
	    if (comp(pl[pi], pl[pi - 1]) ||
		(!comp(pl[pi - 1], pl[pi]) && source[pi] < source[pi - 1]))
	      {
		std::swap(pl[pi - 1], pl[pi]);
		std::swap(source[pi - 1], source[pi]);
	      }
      }
    else
      {
	for (int k = 0; k < nrp - 1; k++)
	  for (int pi = nrp - 1; pi > k; pi--)
	    if (comp(pl[pi], pl[pi-1]))
	      {
		std::swap(pl[pi-1], pl[pi]);
		std::swap(source[pi-1], source[pi]);
	      }
      }

    // Iterate.
    if (stable)
      {
	int j;
	while (nrp > 0 && length > 0)
	  {
	    if (source[0] < source[1])
	      {
		// pl[0] <= pl[1]
		while ((nrp == 1 || !(comp(pl[1], pl[0]))) && length > 0)
		  {
		    *target = pl[0];
		    ++target;
		    ++POS(source[0]);
		    length--;
		    if (POS(source[0]) == STOPS(source[0]))
		      {
			// Move everything to the left.
			for (int s = 0; s < nrp - 1; s++)
			  {
			    pl[s] = pl[s + 1];
			    source[s] = source[s + 1];
			  }
			nrp--;
			break;
		      }
		    else
		      pl[0] = *(POS(source[0]));
		  }
	      }
	    else
	      {
		// pl[0] < pl[1]
		while ((nrp == 1 || comp(pl[0], pl[1])) && length > 0)
		  {
		    *target = pl[0];
		    ++target;
		    ++POS(source[0]);
		    length--;
		    if (POS(source[0]) == STOPS(source[0]))
		      {
			for (int s = 0; s < nrp - 1; s++)
			  {
			    pl[s] = pl[s + 1];
			    source[s] = source[s + 1];
			  }
			nrp--;
			break;
		      }
		    else
		      pl[0] = *(POS(source[0]));
		  }
	      }

	    // Sink down.
	    j = 1;
	    while ((j < nrp) && (comp(pl[j], pl[j - 1]) ||
				 (!comp(pl[j - 1], pl[j]) && (source[j] < source[j - 1]))))
	      {
		std::swap(pl[j - 1], pl[j]);
		std::swap(source[j - 1], source[j]);
		j++;
	      }
	  }
      }
    else
      {
	int j;
	while (nrp > 0 && length > 0)
	  {
	    // pl[0] <= pl[1]
	    while (nrp == 1 || (!comp(pl[1], pl[0])) && length > 0)
	      {
		*target = pl[0];
		++target;
		++POS(source[0]);
		length--;
		if (POS(source[0]) == STOPS(source[0]))
		  {
		    for (int s = 0; s < (nrp - 1); s++)
		      {
			pl[s] = pl[s + 1];
			source[s] = source[s + 1];
		      }
		    nrp--;
		    break;
		  }
		else
		  pl[0] = *(POS(source[0]));
	      }

	    // Sink down.
	    j = 1;
	    while ((j < nrp) && comp(pl[j], pl[j - 1]))
	      {
		std::swap(pl[j - 1], pl[j]);
		std::swap(source[j - 1], source[j]);
		j++;
	      }
	  }
      }

    delete[] pl;
    delete[] source;

    return target;
  }

  /** @brief Multi-way merging procedure for a high branching factor,
   * guarded case.
   *
   *  The head elements are kept in a loser tree.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @return End iterator of output sequence. 
   */
  template<typename LT, typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_loser_tree(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    int k = static_cast<int>(seqs_end - seqs_begin);

    LT lt(k, comp);

    difference_type total_length = 0;

    // Default value for potentially non-default-constructible types.
    value_type* arbitrary_element = NULL;

    for (int t = 0; t < k; t++)
      {
        if(arbitrary_element == NULL && LENGTH(seqs_begin[t]) > 0)
          arbitrary_element = &(*seqs_begin[t].first);
        total_length += LENGTH(seqs_begin[t]);
      }

    if(total_length == 0)
      return target;

    for (int t = 0; t < k; t++)
      {
        if (stable)
          {
            if (seqs_begin[t].first == seqs_begin[t].second)
              lt.insert_start_stable(*arbitrary_element, t, true);
            else
              lt.insert_start_stable(*seqs_begin[t].first, t, false);
          }
        else
          {
            if (seqs_begin[t].first == seqs_begin[t].second)
              lt.insert_start(*arbitrary_element, t, true);
            else
              lt.insert_start(*seqs_begin[t].first, t, false);
          }
      }

    if (stable)
      lt.init_stable();
    else
      lt.init();

    total_length = std::min(total_length, length);

    int source;

    if (stable)
      {
	for (difference_type i = 0; i < total_length; i++)
	  {
	    // Take out.
	    source = lt.get_min_source();

	    *(target++) = *(seqs_begin[source].first++);

	    // Feed.
	    if (seqs_begin[source].first == seqs_begin[source].second)
	      lt.delete_min_insert_stable(*arbitrary_element, true);
	    else
	      // Replace from same source.
	      lt.delete_min_insert_stable(*seqs_begin[source].first, false);

	  }
      }
    else
      {
	for (difference_type i = 0; i < total_length; i++)
	  {
	    //take out
	    source = lt.get_min_source();

	    *(target++) = *(seqs_begin[source].first++);

	    // Feed.
	    if (seqs_begin[source].first == seqs_begin[source].second)
	      lt.delete_min_insert(*arbitrary_element, true);
	    else
	      // Replace from same source.
	      lt.delete_min_insert(*seqs_begin[source].first, false);
	  }
      }

    return target;
  }

  /** @brief Multi-way merging procedure for a high branching factor,
   * unguarded case.
   *
   *  The head elements are kept in a loser tree.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @return End iterator of output sequence.
   *  @pre No input will run out of elements during the merge. 
   */
  template<typename LT, typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_loser_tree_unguarded(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length)
    typedef _DifferenceTp difference_type;

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    int k = seqs_end - seqs_begin;

    LT lt(k, comp);

    difference_type total_length = 0;

    for (int t = 0; t < k; t++)
      {
#if _GLIBCXX_ASSERTIONS
	_GLIBCXX_PARALLEL_ASSERT(seqs_begin[t].first != seqs_begin[t].second);
#endif
	if (stable)
	  lt.insert_start_stable(*seqs_begin[t].first, t, false);
	else
	  lt.insert_start(*seqs_begin[t].first, t, false);

	total_length += LENGTH(seqs_begin[t]);
      }

    if (stable)
      lt.init_stable();
    else
      lt.init();

    // Do not go past end.
    length = std::min(total_length, length);

    int source;

#if _GLIBCXX_ASSERTIONS
    difference_type i = 0;
#endif

    if (stable)
      {
	RandomAccessIterator3 target_end = target + length;
	while (target < target_end)
	  {
	    // Take out.
	    source = lt.get_min_source();

#if _GLIBCXX_ASSERTIONS
	    _GLIBCXX_PARALLEL_ASSERT(i == 0 || !comp(*(seqs_begin[source].first), *(target - 1)));
#endif

	    *(target++) = *(seqs_begin[source].first++);

#if _GLIBCXX_ASSERTIONS
	    _GLIBCXX_PARALLEL_ASSERT((seqs_begin[source].first != seqs_begin[source].second) || (i == length - 1));
	    i++;
#endif
	    // Feed.
	    // Replace from same source.
	    lt.delete_min_insert_stable(*seqs_begin[source].first, false);

	  }
      }
    else
      {
	RandomAccessIterator3 target_end = target + length;
	while (target < target_end)
	  {
	    // Take out.
	    source = lt.get_min_source();

#if _GLIBCXX_ASSERTIONS
	    if (i > 0 && comp(*(seqs_begin[source].first), *(target - 1)))
	      printf("         %i %i %i\n", length, i, source);
	    _GLIBCXX_PARALLEL_ASSERT(i == 0 || !comp(*(seqs_begin[source].first), *(target - 1)));
#endif

	    *(target++) = *(seqs_begin[source].first++);

#if _GLIBCXX_ASSERTIONS
	    if (!((seqs_begin[source].first != seqs_begin[source].second) || (i >= length - 1)))
	      printf("         %i %i %i\n", length, i, source);
	    _GLIBCXX_PARALLEL_ASSERT((seqs_begin[source].first != seqs_begin[source].second) || (i >= length - 1));
	    i++;
#endif
	    // Feed.
	    // Replace from same source.
	    lt.delete_min_insert(*seqs_begin[source].first, false);
	  }
      }

    return target;
  }

  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_loser_tree_combined(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;

    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

    int min_seq;
    RandomAccessIterator3 target_end;
    difference_type overhang = prepare_unguarded(seqs_begin, seqs_end,
					  comp, min_seq, stable);

    difference_type total_length = 0;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; s++)
      total_length += LENGTH(*s);

    if (overhang != -1)
      {
	difference_type unguarded_length = std::min(length, total_length - overhang);
	target_end = multiway_merge_loser_tree_unguarded
	  <typename loser_tree_unguarded_traits<value_type, Comparator>::LT>
	  (seqs_begin, seqs_end, target, comp, unguarded_length, stable);
	overhang = length - unguarded_length;
      }
    else
      {
	// Empty sequence found.
	overhang = length;
	target_end = target;
      }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length - overhang);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    target_end = multiway_merge_loser_tree
      <typename loser_tree_traits<value_type, Comparator>::LT>
      (seqs_begin, seqs_end, target_end, comp, overhang, stable);

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    return target_end;
  }

  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_loser_tree_sentinel(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;
    typedef std::iterator_traits<RandomAccessIteratorIterator> traits_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;

    RandomAccessIterator3 target_end;
    difference_type overhang = prepare_unguarded_sentinel(seqs_begin, seqs_end, comp);

    difference_type total_length = 0;
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; s++)
      {
	total_length += LENGTH(*s);

	// Sentinel spot.
	(*s).second++;
      }

    difference_type unguarded_length = std::min(length, total_length - overhang);
    target_end = multiway_merge_loser_tree_unguarded
      <typename loser_tree_unguarded_traits<value_type, Comparator>::LT>
      (seqs_begin, seqs_end, target, comp, unguarded_length, stable);
    overhang = length - unguarded_length;

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length - overhang);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    // Copy rest stable.
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end && overhang > 0; s++)
      {
	// Restore.
	(*s).second--;
	difference_type local_length = std::min((difference_type)overhang, (difference_type)LENGTH(*s));
	target_end = std::copy((*s).first, (*s).first + local_length, target_end);
	(*s).first += local_length;
	overhang -= local_length;
      }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(overhang == 0);
    _GLIBCXX_PARALLEL_ASSERT(target_end == target + length);
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target_end, comp));
#endif

    return target_end;
  }

  /** @brief Sequential multi-way merging switch.
   *
   *  The decision if based on the branching factor and runtime settings.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @param sentinel The sequences have a sentinel element.
   *  @return End iterator of output sequence. */
  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable, bool sentinel, sequential_tag)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

#if _GLIBCXX_ASSERTIONS
    for (RandomAccessIteratorIterator s = seqs_begin; s != seqs_end; s++)
      _GLIBCXX_PARALLEL_ASSERT(is_sorted((*s).first, (*s).second, comp));
#endif

    RandomAccessIterator3 return_target = target;
    int k = static_cast<int>(seqs_end - seqs_begin);

    Settings::MultiwayMergeAlgorithm mwma = Settings::multiway_merge_algorithm;

    if (!sentinel && mwma == Settings::LOSER_TREE_SENTINEL)
      mwma = Settings::LOSER_TREE_COMBINED;

    switch (k)
      {
      case 0:
	break;
      case 1:
	return_target = std::copy(seqs_begin[0].first, seqs_begin[0].first + length, target);
	seqs_begin[0].first += length;
	break;
      case 2:
	return_target = merge_advance(seqs_begin[0].first, seqs_begin[0].second, seqs_begin[1].first, seqs_begin[1].second, target, length, comp);
	break;
      case 3:
	switch (mwma)
	  {
	  case Settings::LOSER_TREE_COMBINED:
	    return_target = multiway_merge_3_combined(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  case Settings::LOSER_TREE_SENTINEL:
	    return_target = multiway_merge_3_variant<unguarded_iterator>(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  default:
	    return_target = multiway_merge_3_variant<guarded_iterator>(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  }
	break;
      case 4:
	switch (mwma)
	  {
	  case Settings::LOSER_TREE_COMBINED:
	    return_target = multiway_merge_4_combined(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  case Settings::LOSER_TREE_SENTINEL:
	    return_target = multiway_merge_4_variant<unguarded_iterator>(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  default:
	    return_target = multiway_merge_4_variant<guarded_iterator>(seqs_begin, seqs_end, target, comp, length, stable);
	    break;
	  }
	break;
      default:
	{
	  switch (mwma)
	    {
	    case Settings::BUBBLE:
	      return_target = multiway_merge_bubble(seqs_begin, seqs_end, target, comp, length, stable);
	      break;
#if _GLIBCXX_LOSER_TREE_EXPLICIT
	    case Settings::LOSER_TREE_EXPLICIT:
	      return_target = multiway_merge_loser_tree<LoserTreeExplicit<value_type, Comparator> >(seqs_begin, seqs_end, target, comp, length, stable);
	      break;
#endif
#if _GLIBCXX_LOSER_TREE
	    case Settings::LOSER_TREE:
	      return_target = multiway_merge_loser_tree<LoserTree<value_type, Comparator> >(seqs_begin, seqs_end, target, comp, length, stable);
	      break;
#endif
#if _GLIBCXX_LOSER_TREE_COMBINED
	    case Settings::LOSER_TREE_COMBINED:
	      return_target = multiway_merge_loser_tree_combined(seqs_begin, seqs_end, target, comp, length, stable);
	      break;
#endif
#if _GLIBCXX_LOSER_TREE_SENTINEL
	    case Settings::LOSER_TREE_SENTINEL:
	      return_target = multiway_merge_loser_tree_sentinel(seqs_begin, seqs_end, target, comp, length, stable);
	      break;
#endif
	    default:
	      // multiway_merge algorithm not implemented.
	      _GLIBCXX_PARALLEL_ASSERT(0);
	      break;
	    }
	}
      }
#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target + length, comp));
#endif

    return return_target;
  }

  /** @brief Parallel multi-way merge routine.
   *
   *  The decision if based on the branching factor and runtime settings.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @param sentinel Ignored.
   *  @return End iterator of output sequence. 
   */
  template<typename RandomAccessIteratorIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  parallel_multiway_merge(RandomAccessIteratorIterator seqs_begin, RandomAccessIteratorIterator seqs_end, RandomAccessIterator3 target, Comparator comp, _DifferenceTp length, bool stable, bool sentinel)
  {
    _GLIBCXX_CALL(length)

    typedef _DifferenceTp difference_type;
    typedef typename std::iterator_traits<RandomAccessIteratorIterator>::value_type::first_type
      RandomAccessIterator1;
    typedef typename std::iterator_traits<RandomAccessIterator1>::value_type
      value_type;

#if _GLIBCXX_ASSERTIONS
    for (RandomAccessIteratorIterator rii = seqs_begin; rii != seqs_end; rii++)
      _GLIBCXX_PARALLEL_ASSERT(is_sorted((*rii).first, (*rii).second, comp));
#endif

    // k sequences.
    int k = static_cast<int>(seqs_end - seqs_begin);

    difference_type total_length = 0;
    for (RandomAccessIteratorIterator raii = seqs_begin; raii != seqs_end; raii++)
      total_length += LENGTH(*raii);

    _GLIBCXX_CALL(total_length)

    if (total_length == 0 || k == 0)
      return target;

    thread_index_t num_threads = static_cast<thread_index_t>(std::min(static_cast<difference_type>(get_max_threads()), total_length));

    bool tight = (total_length == length);

    // Thread t will have to merge pieces[iam][0..k - 1]
    std::vector<std::pair<difference_type, difference_type> >* pieces = new std::vector<std::pair<difference_type, difference_type> >[num_threads];
    for (int s = 0; s < num_threads; s++)
      pieces[s].resize(k);

    difference_type num_samples = Settings::merge_oversampling * num_threads;

    if (Settings::multiway_merge_splitting == Settings::SAMPLING)
      {
	value_type* samples = static_cast<value_type*>(::operator new(sizeof(value_type) * k * num_samples));
	// Sample.
	for (int s = 0; s < k; s++)
	  for (int i = 0; (difference_type)i < num_samples; i++)
	    {
	      difference_type sample_index = static_cast<difference_type>(LENGTH(seqs_begin[s]) * (double(i + 1) / (num_samples + 1)) * (double(length) / total_length));
	      samples[s * num_samples + i] = seqs_begin[s].first[sample_index];
	    }

	if (stable)
	  __gnu_sequential::stable_sort(samples, samples + (num_samples * k), comp);
	else
	  __gnu_sequential::sort(samples, samples + (num_samples * k), comp);

	for (int slab = 0; slab < num_threads; slab++)
	  // For each slab / processor.
	  for (int seq = 0; seq < k; seq++)
	    {
	      // For each sequence.
	      if (slab > 0)
		pieces[slab][seq].first = std::upper_bound(seqs_begin[seq].first, seqs_begin[seq].second, samples[num_samples * k * slab / num_threads], comp) - seqs_begin[seq].first;
	      else
		{
		  // Absolute beginning.
		  pieces[slab][seq].first = 0;
		}
	      if ((slab + 1) < num_threads)
		pieces[slab][seq].second = std::upper_bound(seqs_begin[seq].first, seqs_begin[seq].second, samples[num_samples * k * (slab + 1) / num_threads], comp) - seqs_begin[seq].first;
	      else
		pieces[slab][seq].second = LENGTH(seqs_begin[seq]);	//absolute ending
	    }
	delete[] samples;
      }
    else
      {
	// (Settings::multiway_merge_splitting == Settings::EXACT).
	std::vector<RandomAccessIterator1>* offsets = new std::vector<RandomAccessIterator1>[num_threads];
	std::vector<std::pair<RandomAccessIterator1, RandomAccessIterator1> > se(k);

	copy(seqs_begin, seqs_end, se.begin());

	difference_type* borders = static_cast<difference_type*>(__builtin_alloca(sizeof(difference_type) * (num_threads + 1)));
	equally_split(length, num_threads, borders);

	for (int s = 0; s < (num_threads - 1); s++)
	  {
	    offsets[s].resize(k);
	    multiseq_partition(se.begin(), se.end(), borders[s + 1],
			       offsets[s].begin(), comp);

	    // Last one also needed and available.
	    if (!tight)
	      {
		offsets[num_threads - 1].resize(k);
		multiseq_partition(se.begin(), se.end(), 
				   difference_type(length), 
				   offsets[num_threads - 1].begin(),  comp);
	      }
	  }


	for (int slab = 0; slab < num_threads; slab++)
	  {
	    // For each slab / processor.
	    for (int seq = 0; seq < k; seq++)
	      {
		// For each sequence.
		if (slab == 0)
		  {
		    // Absolute beginning.
		    pieces[slab][seq].first = 0;
		  }
		else
		  pieces[slab][seq].first = pieces[slab - 1][seq].second;
		if (!tight || slab < (num_threads - 1))
		  pieces[slab][seq].second = offsets[slab][seq] - seqs_begin[seq].first;
		else
		  {
		    // slab == num_threads - 1
		    pieces[slab][seq].second = LENGTH(seqs_begin[seq]);
		  }
	      }
	  }
	delete[] offsets;
      }

#	pragma omp parallel num_threads(num_threads)
    {
      thread_index_t iam = omp_get_thread_num();

      difference_type target_position = 0;

      for (int c = 0; c < k; c++)
	target_position += pieces[iam][c].first;

      if (k > 2)
	{
	  std::pair<RandomAccessIterator1, RandomAccessIterator1>* chunks = new std::pair<RandomAccessIterator1, RandomAccessIterator1>[k];

	  difference_type local_length = 0;
	  for (int s = 0; s < k; s++)
	    {
	      chunks[s] = std::make_pair(seqs_begin[s].first + pieces[iam][s].first, seqs_begin[s].first + pieces[iam][s].second);
	      local_length += LENGTH(chunks[s]);
	    }

	  multiway_merge(chunks, chunks + k, target + target_position, comp,
			 std::min(local_length, length - target_position),
			 stable, false, sequential_tag());

	  delete[] chunks;
	}
      else if (k == 2)
	{
	  RandomAccessIterator1 begin0 = seqs_begin[0].first + pieces[iam][0].first, begin1 = seqs_begin[1].first + pieces[iam][1].first;
	  merge_advance(begin0,
			seqs_begin[0].first + pieces[iam][0].second,
			begin1,
			seqs_begin[1].first + pieces[iam][1].second,
			target + target_position,
			(pieces[iam][0].second - pieces[iam][0].first) + (pieces[iam][1].second - pieces[iam][1].first),
			comp);
	}
    }

#if _GLIBCXX_ASSERTIONS
    _GLIBCXX_PARALLEL_ASSERT(is_sorted(target, target + length, comp));
#endif

    // Update ends of sequences.
    for (int s = 0; s < k; s++)
      seqs_begin[s].first += pieces[num_threads - 1][s].second;

    delete[] pieces;

    return target + length;
  }

  /** 
   *  @brief Multi-way merging front-end.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @return End iterator of output sequence. 
   */
  template<typename RandomAccessIteratorPairIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge(RandomAccessIteratorPairIterator seqs_begin,
		 RandomAccessIteratorPairIterator seqs_end,
		 RandomAccessIterator3 target, Comparator comp,
		 _DifferenceTp length, bool stable)
  {
    typedef _DifferenceTp difference_type;
    _GLIBCXX_CALL(seqs_end - seqs_begin)

    if (seqs_begin == seqs_end)
      return target;

    RandomAccessIterator3 target_end;
    if (_GLIBCXX_PARALLEL_CONDITION(((seqs_end - seqs_begin) >= Settings::multiway_merge_minimal_k) && ((sequence_index_t)length >= Settings::multiway_merge_minimal_n)))
      target_end = parallel_multiway_merge(seqs_begin, seqs_end, target, comp, (difference_type)length, stable, false);
    else
      target_end = multiway_merge(seqs_begin, seqs_end, target, comp, length, stable, false, sequential_tag());

    return target_end;
  }

  /** @brief Multi-way merging front-end.
   *  @param seqs_begin Begin iterator of iterator pair input sequence.
   *  @param seqs_end End iterator of iterator pair input sequence.
   *  @param target Begin iterator out output sequence.
   *  @param comp Comparator.
   *  @param length Maximum length to merge.
   *  @param stable Stable merging incurs a performance penalty.
   *  @return End iterator of output sequence.
   *  @pre For each @c i, @c seqs_begin[i].second must be the end
   *  marker of the sequence, but also reference the one more sentinel
   *  element. */
  template<typename RandomAccessIteratorPairIterator, typename RandomAccessIterator3, typename _DifferenceTp, typename Comparator>
  RandomAccessIterator3
  multiway_merge_sentinel(RandomAccessIteratorPairIterator seqs_begin,
			  RandomAccessIteratorPairIterator seqs_end,
			  RandomAccessIterator3 target,
			  Comparator comp,
			  _DifferenceTp length,
			  bool stable)
  {
    typedef _DifferenceTp difference_type;

    if (seqs_begin == seqs_end)
      return target;

    _GLIBCXX_CALL(seqs_end - seqs_begin)

    if (_GLIBCXX_PARALLEL_CONDITION(((seqs_end - seqs_begin) >= Settings::multiway_merge_minimal_k) && ((sequence_index_t)length >= Settings::multiway_merge_minimal_n)))
      return parallel_multiway_merge(seqs_begin, seqs_end, target, comp, (typename std::iterator_traits<RandomAccessIterator3>::difference_type)length, stable, true);
    else
      return multiway_merge(seqs_begin, seqs_end, target, comp, length, stable, true, sequential_tag());
  }
}

#endif