urns true are removed from the range
   *  @p [first,last).
   *
   *  remove_if() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<typename _ForwardIterator, typename _Predicate>
    _ForwardIterator
    remove_if(_ForwardIterator __first, _ForwardIterator __last,
	      _Predicate __pred)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
	    typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      __first = _GLIBCXX_STD_P::find_if(__first, __last, __pred);
      if(__first == __last)
        return __first;
      _ForwardIterator __result = __first;
      ++__first;
      for(; __first != __last; ++__first)
        if(!bool(__pred(*__first)))
          {
            *__result = _GLIBCXX_MOVE(*__first);
            ++__result;
          }
      return __result;
    }

  /**
   *  @brief Remove consecutive duplicate values from a sequence.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Removes all but the first element from each group of consecutive
   *  values that compare equal.
   *  unique() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<typename _ForwardIterator>
    _ForwardIterator
    unique(_ForwardIterator __first, _ForwardIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_function_requires(_EqualityComparableConcept<
		     typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      // Skip the beginning, if already unique.
      __first = _GLIBCXX_STD_P::adjacent_find(__first, __last);
      if (__first == __last)
	return __last;

      // Do the real copy work.
      _ForwardIterator __dest = __first;
      ++__first;
      while (++__first != __last)
	if (!(*__dest == *__first))
	  *++__dest = _GLIBCXX_MOVE(*__first);
      return ++__dest;
    }

  /**
   *  @brief Remove consecutive values from a sequence using a predicate.
   *  @param  first        A forward iterator.
   *  @param  last         A forward iterator.
   *  @param  binary_pred  A binary predicate.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Removes all but the first element from each group of consecutive
   *  values for which @p binary_pred returns true.
   *  unique() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<typename _ForwardIterator, typename _BinaryPredicate>
    _ForwardIterator
    unique(_ForwardIterator __first, _ForwardIterator __last,
           _BinaryPredicate __binary_pred)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
		typename iterator_traits<_ForwardIterator>::value_type,
		typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      // Skip the beginning, if already unique.
      __first = _GLIBCXX_STD_P::adjacent_find(__first, __last, __binary_pred);
      if (__first == __last)
	return __last;

      // Do the real copy work.
      _ForwardIterator __dest = __first;
      ++__first;
      while (++__first != __last)
	if (!bool(__binary_pred(*__dest, *__first)))
	  *++__dest = _GLIBCXX_MOVE(*__first);
      return ++__dest;
    }

  /**
   *  This is an uglified unique_copy(_InputIterator, _InputIterator,
   *                                  _OutputIterator)
   *  overloaded for forward iterators and output iterator as result.
  */
  template<typename _ForwardIterator, typename _OutputIterator>
    _OutputIterator
    __unique_copy(_ForwardIterator __first, _ForwardIterator __last,
		  _OutputIterator __result,
		  forward_iterator_tag, output_iterator_tag)
    {
      // concept requirements -- taken care of in dispatching function
      _ForwardIterator __next = __first;
      *__result = *__first;
      while (++__next != __last)
	if (!(*__first == *__next))
	  {
	    __first = __next;
	    *++__result = *__first;
	  }
      return ++__result;
    }

  /**
   *  This is an uglified unique_copy(_InputIterator, _InputIterator,
   *                                  _OutputIterator)
   *  overloaded for input iterators and output iterator as result.
  */
  template<typename _InputIterator, typename _OutputIterator>
    _OutputIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
		  _OutputIterator __result,
		  input_iterator_tag, output_iterator_tag)
    {
      // concept requirements -- taken care of in dispatching function
      typename iterator_traits<_InputIterator>::value_type __value = *__first;
      *__result = __value;
      while (++__first != __last)
	if (!(__value == *__first))
	  {
	    __value = *__first;
	    *++__result = __value;
	  }
      return ++__result;
    }

  /**
   *  This is an uglified unique_copy(_InputIterator, _InputIterator,
   *                                  _OutputIterator)
   *  overloaded for input iterators and forward iterator as result.
  */
  template<typename _InputIterator, typename _ForwardIterator>
    _ForwardIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
		  _ForwardIterator __result,
		  input_iterator_tag, forward_iterator_tag)
    {
      // concept requirements -- taken care of in dispatching function
      *__result = *__first;
      while (++__first != __last)
	if (!(*__result == *__first))
	  *++__result = *__first;
      return ++__result;
    }

  /**
   *  This is an uglified
   *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
   *              _BinaryPredicate)
   *  overloaded for forward iterators and output iterator as result.
  */
  template<typename _ForwardIterator, typename _OutputIterator,
	   typename _BinaryPredicate>
    _OutputIterator
    __unique_copy(_ForwardIterator __first, _ForwardIterator __last,
		  _OutputIterator __result, _BinaryPredicate __binary_pred,
		  forward_iterator_tag, output_iterator_tag)
    {
      // concept requirements -- iterators already checked
      __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
	  typename iterator_traits<_ForwardIterator>::value_type,
	  typename iterator_traits<_ForwardIterator>::value_type>)

      _ForwardIterator __next = __first;
      *__result = *__first;
      while (++__next != __last)
	if (!bool(__binary_pred(*__first, *__next)))
	  {
	    __first = __next;
	    *++__result = *__first;
	  }
      return ++__result;
    }

  /**
   *  This is an uglified
   *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
   *              _BinaryPredicate)
   *  overloaded for input iterators and output iterator as result.
  */
  template<typename _InputIterator, typename _OutputIterator,
	   typename _BinaryPredicate>
    _OutputIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
		  _OutputIterator __result, _BinaryPredicate __binary_pred,
		  input_iterator_tag, output_iterator_tag)
    {
      // concept requirements -- iterators already checked
      __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
	  typename iterator_traits<_InputIterator>::value_type,
	  typename iterator_traits<_InputIterator>::value_type>)

      typename iterator_traits<_InputIterator>::value_type __value = *__first;
      *__result = __value;
      while (++__first != __last)
	if (!bool(__binary_pred(__value, *__first)))
	  {
	    __value = *__first;
	    *++__result = __value;
	  }
      return ++__result;
    }

  /**
   *  This is an uglified
   *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
   *              _BinaryPredicate)
   *  overloaded for input iterators and forward iterator as result.
  */
  template<typename _InputIterator, typename _ForwardIterator,
	   typename _BinaryPredicate>
    _ForwardIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
		  _ForwardIterator __result, _BinaryPredicate __binary_pred,
		  input_iterator_tag, forward_iterator_tag)
    {
      // concept requirements -- iterators already checked
      __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
	  typename iterator_traits<_ForwardIterator>::value_type,
	  typename iterator_traits<_InputIterator>::value_type>)

      *__result = *__first;
      while (++__first != __last)
	if (!bool(__binary_pred(*__result, *__first)))
	  *++__result = *__first;
      return ++__result;
    }

  /**
   *  This is an uglified reverse(_BidirectionalIterator,
   *                              _BidirectionalIterator)
   *  overloaded for bidirectional iterators.
  */
  template<typename _BidirectionalIterator>
    void
    __reverse(_BidirectionalIterator __first, _BidirectionalIterator __last,
	      bidirectional_iterator_tag)
    {
      while (true)
	if (__first == __last || __first == --__last)
	  return;
	else
	  {
	    std::iter_swap(__first, __last);
	    ++__first;
	  }
    }

  /**
   *  This is an uglified reverse(_BidirectionalIterator,
   *                              _BidirectionalIterator)
   *  overloaded for random access iterators.
  */
  template<typename _RandomAccessIterator>
    void
    __reverse(_RandomAccessIterator __first, _RandomAccessIterator __last,
	      random_access_iterator_tag)
    {
      if (__first == __last)
	return;
      --__last;
      while (__first < __last)
	{
	  std::iter_swap(__first, __last);
	  ++__first;
	  --__last;
	}
    }

  /**
   *  @brief Reverse a sequence.
   *  @param  first  A bidirectional iterator.
   *  @param  last   A bidirectional iterator.
   *  @return   reverse() returns no value.
   *
   *  Reverses the order of the elements in the range @p [first,last),
   *  so that the first element becomes the last etc.
   *  For every @c i such that @p 0<=i<=(last-first)/2), @p reverse()
   *  swaps @p *(first+i) and @p *(last-(i+1))
  */
  template<typename _BidirectionalIterator>
    inline void
    reverse(_BidirectionalIterator __first, _BidirectionalIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)
      __glibcxx_requires_valid_range(__first, __last);
      std::__reverse(__first, __last, std::__iterator_category(__first));
    }

  /**
   *  @brief Copy a sequence, reversing its elements.
   *  @param  first   A bidirectional iterator.
   *  @param  last    A bidirectional iterator.
   *  @param  result  An output iterator.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements in the range @p [first,last) to the range
   *  @p [result,result+(last-first)) such that the order of the
   *  elements is reversed.
   *  For every @c i such that @p 0<=i<=(last-first), @p reverse_copy()
   *  performs the assignment @p *(result+(last-first)-i) = *(first+i).
   *  The ranges @p [first,last) and @p [result,result+(last-first))
   *  must not overlap.
  */
  template<typename _BidirectionalIterator, typename _OutputIterator>
    _OutputIterator
    reverse_copy(_BidirectionalIterator __first, _BidirectionalIterator __last,
			     _OutputIterator __result)
    {
      // concept requirements
      __glibcxx_function_requires(_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)
      __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
		typename iterator_traits<_BidirectionalIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      while (__first != __last)
	{
	  --__last;
	  *__result = *__last;
	  ++__result;
	}
      return __result;
    }

  /**
   *  This is a helper function for the rotate algorithm specialized on RAIs.
   *  It returns the greatest common divisor of two integer values.
  */
  template<typename _EuclideanRingElement>
    _EuclideanRingElement
    __gcd(_EuclideanRingElement __m, _EuclideanRingElement __n)
    {
      while (__n != 0)
	{
	  _EuclideanRingElement __t = __m % __n;
	  __m = __n;
	  __n = __t;
	}
      return __m;
    }

  /// This is a helper function for the rotate algorithm.
  template<typename _ForwardIterator>
    void
    __rotate(_ForwardIterator __first,
	     _ForwardIterator __middle,
	     _ForwardIterator __last,
	     forward_iterator_tag)
    {
      if (__first == __middle || __last  == __middle)
	return;

      _ForwardIterator __first2 = __middle;
      do
	{
	  std::iter_swap(__first, __first2);
	  ++__first;
	  ++__first2;
	  if (__first == __middle)
	    __middle = __first2;
	}
      while (__first2 != __last);

      __first2 = __middle;

      while (__first2 != __last)
	{
	  std::iter_swap(__first, __first2);
	  ++__first;
	  ++__first2;
	  if (__first == __middle)
	    __middle = __first2;
	  else if (__first2 == __last)
	    __first2 = __middle;
	}
    }

   /// This is a helper function for the rotate algorithm.
  template<typename _BidirectionalIterator>
    void
    __rotate(_BidirectionalIterator __first,
	     _BidirectionalIterator __middle,
	     _BidirectionalIterator __last,
	      bidirectional_iterator_tag)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
				  _BidirectionalIterator>)

      if (__first == __middle || __last  == __middle)
	return;

      std::__reverse(__first,  __middle, bidirectional_iterator_tag());
      std::__reverse(__middle, __last,   bidirectional_iterator_tag());

      while (__first != __middle && __middle != __last)
	{
	  std::iter_swap(__first, --__last);
	  ++__first;
	}

      if (__first == __middle)
	std::__reverse(__middle, __last,   bidirectional_iterator_tag());
      else
	std::__reverse(__first,  __middle, bidirectional_iterator_tag());
    }

  /// This is a helper function for the rotate algorithm.
  template<typename _RandomAccessIterator>
    void
    __rotate(_RandomAccessIterator __first,
	     _RandomAccessIterator __middle,
	     _RandomAccessIterator __last,
	     random_access_iterator_tag)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
				  _RandomAccessIterator>)

      if (__first == __middle || __last  == __middle)
	return;

      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
	_Distance;
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      const _Distance __n = __last   - __first;
      const _Distance __k = __middle - __first;
      const _Distance __l = __n - __k;

      if (__k == __l)
	{
	  std::swap_ranges(__first, __middle, __middle);
	  return;
	}

      const _Distance __d = std::__gcd(__n, __k);

      for (_Distance __i = 0; __i < __d; __i++)
	{
	  _ValueType __tmp = _GLIBCXX_MOVE(*__first);
	  _RandomAccessIterator __p = __first;

	  if (__k < __l)
	    {
	      for (_Distance __j = 0; __j < __l / __d; __j++)
		{
		  if (__p > __first + __l)
		    {
		      *__p = _GLIBCXX_MOVE(*(__p - __l));
		      __p -= __l;
		    }

		  *__p = _GLIBCXX_MOVE(*(__p + __k));
		  __p += __k;
		}
	    }
	  else
	    {
	      for (_Distance __j = 0; __j < __k / __d - 1; __j ++)
		{
		  if (__p < __last - __k)
		    {
		      *__p = _GLIBCXX_MOVE(*(__p + __k));
		      __p += __k;
		    }
		  *__p = _GLIBCXX_MOVE(*(__p - __l));
		  __p -= __l;
		}
	    }

	  *__p = _GLIBCXX_MOVE(__tmp);
	  ++__first;
	}
    }

  /**
   *  @brief Rotate the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Rotates the elements of the range @p [first,last) by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p first, the
   *  element at @p middle+1 is moved to @first+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  This effectively swaps the ranges @p [first,middle) and
   *  @p [middle,last).
   *
   *  Performs @p *(first+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<typename _ForwardIterator>
    inline void
    rotate(_ForwardIterator __first, _ForwardIterator __middle,
	   _ForwardIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      typedef typename iterator_traits<_ForwardIterator>::iterator_category
	_IterType;
      std::__rotate(__first, __middle, __last, _IterType());
    }

  /**
   *  @brief Copy a sequence, rotating its elements.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements of the range @p [first,last) to the range
   *  beginning at @result, rotating the copied elements by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p result, the
   *  element at @p middle+1 is moved to @result+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  Performs @p *(result+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<typename _ForwardIterator, typename _OutputIterator>
    _OutputIterator
    rotate_copy(_ForwardIterator __first, _ForwardIterator __middle,
                _ForwardIterator __last, _OutputIterator __result)
    {
      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
		typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      return std::copy(__first, __middle,
                       std::copy(__middle, __last, __result));
    }

  /// This is a helper function...
  template<typename _ForwardIterator, typename _Predicate>
    _ForwardIterator
    __partition(_ForwardIterator __first, _ForwardIterator __last,
		_Predicate __pred, forward_iterator_tag)
    {
      if (__first == __last)
	return __first;

      while (__pred(*__first))
	if (++__first == __last)
	  return __first;

      _ForwardIterator __next = __first;

      while (++__next != __last)
	if (__pred(*__next))
	  {
	    std::iter_swap(__first, __next);
	    ++__first;
	  }

      return __first;
    }

  /// This is a helper function...
  template<typename _BidirectionalIterator, typename _Predicate>
    _BidirectionalIterator
    __partition(_BidirectionalIterator __first, _BidirectionalIterator __last,
		_Predicate __pred, bidirectional_iterator_tag)
    {
      while (true)
	{
	  while (true)
	    if (__first == __last)
	      return __first;
	    else if (__pred(*__first))
	      ++__first;
	    else
	      break;
	  --__last;
	  while (true)
	    if (__first == __last)
	      return __first;
	    else if (!bool(__pred(*__last)))
	      --__last;
	    else
	      break;
	  std::iter_swap(__first, __last);
	  ++__first;
	}
    }

  // partition

  /// This is a helper function...
  template<typename _ForwardIterator, typename _Predicate, typename _Distance>
    _ForwardIterator
    __inplace_stable_partition(_ForwardIterator __first,
			       _ForwardIterator __last,
			       _Predicate __pred, _Distance __len)
    {
      if (__len == 1)
	return __pred(*__first) ? __last : __first;
      _ForwardIterator __middle = __first;
      std::advance(__middle, __len / 2);
      _ForwardIterator __begin = std::__inplace_stable_partition(__first,
								 __middle,
								 __pred,
								 __len / 2);
      _ForwardIterator __end = std::__inplace_stable_partition(__middle, __last,
							       __pred,
							       __len
							       - __len / 2);
      std::rotate(__begin, __middle, __end);
      std::advance(__begin, std::distance(__middle, __end));
      return __begin;
    }

  /// This is a helper function...
  template<typename _ForwardIterator, typename _Pointer, typename _Predicate,
	   typename _Distance>
    _ForwardIterator
    __stable_partition_adaptive(_ForwardIterator __first,
				_ForwardIterator __last,
				_Predicate __pred, _Distance __len,
				_Pointer __buffer,
				_Distance __buffer_size)
    {
      if (__len <= __buffer_size)
	{
	  _ForwardIterator __result1 = __first;
	  _Pointer __result2 = __buffer;
	  for (; __first != __last; ++__first)
	    if (__pred(*__first))
	      {
		*__result1 = *__first;
		++__result1;
	      }
	    else
	      {
		*__result2 = *__first;
		++__result2;
	      }
	  std::copy(__buffer, __result2, __result1);
	  return __result1;
	}
      else
	{
	  _ForwardIterator __middle = __first;
	  std::advance(__middle, __len / 2);
	  _ForwardIterator __begin =
	    std::__stable_partition_adaptive(__first, __middle, __pred,
					     __len / 2, __buffer,
					     __buffer_size);
	  _ForwardIterator __end =
	    std::__stable_partition_adaptive(__middle, __last, __pred,
					     __len - __len / 2,
					     __buffer, __buffer_size);
	  std::rotate(__begin, __middle, __end);
	  std::advance(__begin, std::distance(__middle, __end));
	  return __begin;
	}
    }

  /**
   *  @brief Move elements for which a predicate is true to the beginning
   *         of a sequence, preserving relative ordering.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  pred    A predicate functor.
   *  @return  An iterator @p middle such that @p pred(i) is true for each
   *  iterator @p i in the range @p [first,middle) and false for each @p i
   *  in the range @p [middle,last).
   *
   *  Performs the same function as @p partition() with the additional
   *  guarantee that the relative ordering of elements in each group is
   *  preserved, so any two elements @p x and @p y in the range
   *  @p [first,last) such that @p pred(x)==pred(y) will have the same
   *  relative ordering after calling @p stable_partition().
  */
  template<typename _ForwardIterator, typename _Predicate>
    _ForwardIterator
    stable_partition(_ForwardIterator __first, _ForwardIterator __last,
		     _Predicate __pred)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
				  _ForwardIterator>)
      __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
	    typename iterator_traits<_ForwardIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
	return __first;
      else
	{
	  typedef typename iterator_traits<_ForwardIterator>::value_type
	    _ValueType;
	  typedef typename iterator_traits<_ForwardIterator>::difference_type
	    _DistanceType;

	  _Temporary_buffer<_ForwardIterator, _ValueType> __buf(__first,
								__last);
	if (__buf.size() > 0)
	  return
	    std::__stable_partition_adaptive(__first, __last, __pred,
					  _DistanceType(__buf.requested_size()),
					  __buf.begin(),
					  _DistanceType(__buf.size()));
	else
	  return
	    std::__inplace_stable_partition(__first, __last, __pred,
					 _DistanceType(__buf.requested_size()));
	}
    }

  /// This is a helper function for the sort routines.
  template<typename _RandomAccessIterator>
    void
    __heap_select(_RandomAccessIterator __first,
		  _RandomAccessIterator __middle,
		  _RandomAccessIterator __last)
    {
      std::make_heap(__first, __middle);
      for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
	if (*__i < *__first)
	  std::__pop_heap(__first, __middle, __i);
    }

  /// This is a helper function for the sort routines.
  template<typename _RandomAccessIterator, typename _Compare>
    void
    __heap_select(_RandomAccessIterator __first,
		  _RandomAccessIterator __middle,
		  _RandomAccessIterator __last, _Compare __comp)
    {
      std::make_heap(__first, __middle, __comp);
      for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
	if (__comp(*__i, *__first))
	  std::__pop_heap(__first, __middle, __i, __comp);
    }

  // partial_sort

  /**
   *  @brief Copy the smallest elements of a sequence.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  result_first   A random-access iterator.
   *  @param  result_last    Another random-access iterator.
   *  @return   An iterator indicating the end of the resulting sequence.
   *
   *  Copies and sorts the smallest N values from the range @p [first,last)
   *  to the range beginning at @p result_first, where the number of
   *  elements to be copied, @p N, is the smaller of @p (last-first) and
   *  @p (result_last-result_first).
   *  After the sort if @p i and @j are iterators in the range
   *  @p [result_first,result_first+N) such that @i precedes @j then
   *  @p *j<*i is false.
   *  The value returned is @p result_first+N.
  */
  template<typename _InputIterator, typename _RandomAccessIterator>
    _RandomAccessIterator
    partial_sort_copy(_InputIterator __first, _InputIterator __last,
		      _RandomAccessIterator __result_first,
		      _RandomAccessIterator __result_last)
    {
      typedef typename iterator_traits<_InputIterator>::value_type
	_InputValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_OutputValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
      __glibcxx_function_requires(_ConvertibleConcept<_InputValueType,
				  _OutputValueType>)
      __glibcxx_function_requires(_LessThanOpConcept<_InputValueType,
				                     _OutputValueType>)
      __glibcxx_function_requires(_LessThanComparableConcept<_OutputValueType>)
      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_valid_range(__result_first, __result_last);

      if (__result_first == __result_last)
	return __result_last;
      _RandomAccessIterator __result_real_last = __result_first;
      while(__first != __last && __result_real_last != __result_last)
	{
	  *__result_real_last = *__first;
	  ++__result_real_last;
	  ++__first;
	}
      std::make_heap(__result_first, __result_real_last);
      while (__first != __last)
	{
	  if (*__first < *__result_first)
	    std::__adjust_heap(__result_first, _DistanceType(0),
			       _DistanceType(__result_real_last
					     - __result_first),
			       _InputValueType(*__first));
	  ++__first;
	}
      std::sort_heap(__result_first, __result_real_last);
      return __result_real_last;
    }

  /**
   *  @brief Copy the smallest elements of a sequence using a predicate for
   *         comparison.
   *  @param  first   An input iterator.
   *  @param  last    Another input iterator.
   *  @param  result_first   A random-access iterator.
   *  @param  result_last    Another random-access iterator.
   *  @param  comp    A comparison functor.
   *  @return   An iterator indicating the end of the resulting sequence.
   *
   *  Copies and sorts the smallest N values from the range @p [first,last)
   *  to the range beginning at @p result_first, where the number of
   *  elements to be copied, @p N, is the smaller of @p (last-first) and
   *  @p (result_last-result_first).
   *  After the sort if @p i and @j are iterators in the range
   *  @p [result_first,result_first+N) such that @i precedes @j then
   *  @p comp(*j,*i) is false.
   *  The value returned is @p result_first+N.
  */
  template<typename _InputIterator, typename _RandomAccessIterator, typename _Compare>
    _RandomAccessIterator
    partial_sort_copy(_InputIterator __first, _InputIterator __last,
		      _RandomAccessIterator __result_first,
		      _RandomAccessIterator __result_last,
		      _Compare __comp)
    {
      typedef typename iterator_traits<_InputIterator>::value_type
	_InputValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_OutputValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
				  _RandomAccessIterator>)
      __glibcxx_function_requires(_ConvertibleConcept<_InputValueType,
				  _OutputValueType>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _InputValueType, _OutputValueType>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _OutputValueType, _OutputValueType>)
      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_valid_range(__result_first, __result_last);

      if (__result_first == __result_last)
	return __result_last;
      _RandomAccessIterator __result_real_last = __result_first;
      while(__first != __last && __result_real_last != __result_last)
	{
	  *__result_real_last = *__first;
	  ++__result_real_last;
	  ++__first;
	}
      std::make_heap(__result_first, __result_real_last, __comp);
      while (__first != __last)
	{
	  if (__comp(*__first, *__result_first))
	    std::__adjust_heap(__result_first, _DistanceType(0),
			       _DistanceType(__result_real_last
					     - __result_first),
			       _InputValueType(*__first),
			       __comp);
	  ++__first;
	}
      std::sort_heap(__result_first, __result_real_last, __comp);
      return __result_real_last;
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Tp>
    void
    __unguarded_linear_insert(_RandomAccessIterator __last, _Tp __val)
    {
      _RandomAccessIterator __next = __last;
      --__next;
      while (__val < *__next)
	{
	  *__last = *__next;
	  __last = __next;
	  --__next;
	}
      *__last = __val;
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Tp, typename _Compare>
    void
    __unguarded_linear_insert(_RandomAccessIterator __last, _Tp __val,
			      _Compare __comp)
    {
      _RandomAccessIterator __next = __last;
      --__next;
      while (__comp(__val, *__next))
	{
	  *__last = *__next;
	  __last = __next;
	  --__next;
	}
      *__last = __val;
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator>
    void
    __insertion_sort(_RandomAccessIterator __first,
		     _RandomAccessIterator __last)
    {
      if (__first == __last)
	return;

      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
	{
	  typename iterator_traits<_RandomAccessIterator>::value_type
	    __val = *__i;
	  if (__val < *__first)
	    {
	      std::copy_backward(__first, __i, __i + 1);
	      *__first = __val;
	    }
	  else
	    std::__unguarded_linear_insert(__i, __val);
	}
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Compare>
    void
    __insertion_sort(_RandomAccessIterator __first,
		     _RandomAccessIterator __last, _Compare __comp)
    {
      if (__first == __last) return;

      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
	{
	  typename iterator_traits<_RandomAccessIterator>::value_type
	    __val = *__i;
	  if (__comp(__val, *__first))
	    {
	      std::copy_backward(__first, __i, __i + 1);
	      *__first = __val;
	    }
	  else
	    std::__unguarded_linear_insert(__i, __val, __comp);
	}
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator>
    inline void
    __unguarded_insertion_sort(_RandomAccessIterator __first,
			       _RandomAccessIterator __last)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      for (_RandomAccessIterator __i = __first; __i != __last; ++__i)
	std::__unguarded_linear_insert(__i, _ValueType(*__i));
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Compare>
    inline void
    __unguarded_insertion_sort(_RandomAccessIterator __first,
			       _RandomAccessIterator __last, _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      for (_RandomAccessIterator __i = __first; __i != __last; ++__i)
	std::__unguarded_linear_insert(__i, _ValueType(*__i), __comp);
    }

  /**
   *  @doctodo
   *  This controls some aspect of the sort routines.
  */
  enum { _S_threshold = 16 };

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator>
    void
    __final_insertion_sort(_RandomAccessIterator __first,
			   _RandomAccessIterator __last)
    {
      if (__last - __first > int(_S_threshold))
	{
	  std::__insertion_sort(__first, __first + int(_S_threshold));
	  std::__unguarded_insertion_sort(__first + int(_S_threshold), __last);
	}
      else
	std::__insertion_sort(__first, __last);
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Compare>
    void
    __final_insertion_sort(_RandomAccessIterator __first,
			   _RandomAccessIterator __last, _Compare __comp)
    {
      if (__last - __first > int(_S_threshold))
	{
	  std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
	  std::__unguarded_insertion_sort(__first + int(_S_threshold), __last,
					  __comp);
	}
      else
	std::__insertion_sort(__first, __last, __comp);
    }

  /// This is a helper function...
  template<typename _RandomAccessIterator, typename _Tp>
    _RandomAccessIterator
    __unguarded_partition(_RandomAccessIterator __first,
			  _RandomAccessIterator __last, _Tp __pivot)
    {
      while (true)
	{
	  while (*__first < __pivot)
	    ++__first;
	  --__last;
	  while (__pivot < *__last)
	    --__last;
	  if (!(__first < __last))
	    return __first;
	  std::iter_swap(__first, __last);
	  ++__first;
	}
    }

  /// This is a helper function...
  template<typename _RandomAccessIterator, typename _Tp, typename _Compare>
    _RandomAccessIterator
    __unguarded_partition(_RandomAccessIterator __first,
			  _RandomAccessIterator __last,
			  _Tp __pivot, _Compare __comp)
    {
      while (true)
	{
	  while (__comp(*__first, __pivot))
	    ++__first;
	  --__last;
	  while (__comp(__pivot, *__last))
	    --__last;
	  if (!(__first < __last))
	    return __first;
	  std::iter_swap(__first, __last);
	  ++__first;
	}
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Size>
    void
    __introsort_loop(_RandomAccessIterator __first,
		     _RandomAccessIterator __last,
		     _Size __depth_limit)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > int(_S_threshold))
	{
	  if (__depth_limit == 0)
	    {
	      _GLIBCXX_STD_P::partial_sort(__first, __last, __last);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last
								  - 1))));
	  std::__introsort_loop(__cut, __last, __depth_limit);
	  __last = __cut;
	}
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Size, typename _Compare>
    void
    __introsort_loop(_RandomAccessIterator __first,
		     _RandomAccessIterator __last,
		     _Size __depth_limit, _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > int(_S_threshold))
	{
	  if (__depth_limit == 0)
	    {
	      _GLIBCXX_STD_P::partial_sort(__first, __last, __last, __comp);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last - 1),
								__comp)),
				       __comp);
	  std::__introsort_loop(__cut, __last, __depth_limit, __comp);
	  __last = __cut;
	}
    }

  /// This is a helper function for the sort routines.  Precondition: __n > 0.
  template<typename _Size>
    inline _Size
    __lg(_Size __n)
    {
      _Size __k;
      for (__k = 0; __n != 0; __n >>= 1)
	++__k;
      return __k - 1;
    }

  inline int
  __lg(int __n)
  { return sizeof(int) * __CHAR_BIT__  - 1 - __builtin_clz(__n); }

  inline long
  __lg(long __n)
  { return sizeof(long) * __CHAR_BIT__ - 1 - __builtin_clzl(__n); }

  inline long long
  __lg(long long __n)
  { return sizeof(long long) * __CHAR_BIT__ - 1 - __builtin_clzll(__n); }

  // sort

  template<typename _RandomAccessIterator, typename _Size>
    void
    __introselect(_RandomAccessIterator __first, _RandomAccessIterator __nth,
		  _RandomAccessIterator __last, _Size __depth_limit)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > 3)
	{
	  if (__depth_limit == 0)
	    {
	      std::__heap_select(__first, __nth + 1, __last);

	      // Place the nth largest element in its final position.
	      std::iter_swap(__first, __nth);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last
								  - 1))));
	  if (__cut <= __nth)
	    __first = __cut;
	  else
	    __last = __cut;
	}
      std::__insertion_sort(__first, __last);
    }

  template<typename _RandomAccessIterator, typename _Size, typename _Compare>
    void
    __introselect(_RandomAccessIterator __first, _RandomAccessIterator __nth,
		  _RandomAccessIterator __last, _Size __depth_limit,
		  _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > 3)
	{
	  if (__depth_limit == 0)
	    {
	      std::__heap_select(__first, __nth + 1, __last, __comp);
	      // Place the nth largest element in its final position.
	      std::iter_swap(__first, __nth);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last - 1),
								__comp)),
				       __comp);
	  if (__cut <= __nth)
	    __first = __cut;
	  else
	    __last = __cut;
	}
      std::__insertion_sort(__first, __last, __comp);
    }

  // nth_element

  /**
   *  @brief Finds the first position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return         An iterator pointing to the first element "not less
   *                  than" @a val, or end() if every element is less than 
   *                  @a val.
   *  @ingroup binarysearch
  */
  template<typename _ForwardIterator, typename _Tp>
    _ForwardIterator
    lower_bound(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_LessThanOpConcept<_ValueType, _Tp>)
      __glibcxx_requires_partitioned_lower(__first, __last, __val);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (*__middle < __val)
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	  else
	    __len = __half;
	}
      return __first;
    }

  /**
   *  @brief Finds the first position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An iterator pointing to the first element "not less than" @a val,
   *           or end() if every element is less than @a val.
   *  @ingroup binarysearch
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<typename _ForwardIterator, typename _Tp, typename _Compare>
    _ForwardIterator
    lower_bound(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val, _Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _ValueType, _Tp>)
      __glibcxx_requires_partitioned_lower_pred(__first, __last,
						__val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (__comp(*__middle, __val))
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	  else
	    __len = __half;
	}
      return __first;
    }

  /**
   *  @brief Finds the last position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  An iterator pointing to the first element greater than @a val,
   *           or end() if no elements are greater than @a val.
   *  @ingroup binarysearch
  */
  template<typename _ForwardIterator, typename _Tp>
    _ForwardIterator
    upper_bound(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)
      __glibcxx_requires_partitioned_upper(__first, __last, __val);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (__val < *__middle)
	    __len = __half;
	  else
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	}
      return __first;
    }

  /**
   *  @brief Finds the last position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An iterator pointing to the first element greater than @a val,
   *           or end() if no elements are greater than @a val.
   *  @ingroup binarysearch
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<typename _ForwardIterator, typename _Tp, typename _Compare>
    _ForwardIterator
    upper_bound(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val, _Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _Tp, _ValueType>)
      __glibcxx_requires_partitioned_upper_pred(__first, __last,
						__val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (__comp(__val, *__middle))
	    __len = __half;
	  else
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	}
      return __first;
    }

  /**
   *  @brief Finds the largest subrange in which @a val could be inserted
   *         at any place in it without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  An pair of iterators defining the subrange.
   *  @ingroup binarysearch
   *
   *  This is equivalent to
   *  @code
   *    std::make_pair(lower_bound(first, last, val),
   *                   upper_bound(first, last, val))
   *  @endcode
   *  but does not actually call those functions.
  */
  template<typename _ForwardIterator, typename _Tp>
    pair<_ForwardIterator, _ForwardIterator>
    equal_range(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_LessThanOpConcept<_ValueType, _Tp>)
      __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)	
      __glibcxx_requires_partitioned_lower(__first, __last, __val);
      __glibcxx_requires_partitioned_upper(__first, __last, __val);      

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle, __left, __right;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (*__middle < __val)
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	  else if (__val < *__middle)
	    __len = __half;
	  else
	    {
	      __left = std::lower_bound(__first, __middle, __val);
	      std::advance(__first, __len);
	      __right = std::upper_bound(++__middle, __first, __val);
	      return pair<_ForwardIterator, _ForwardIterator>(__left, __right);
	    }
	}
      return pair<_ForwardIterator, _ForwardIterator>(__first, __first);
    }

  /**
   *  @brief Finds the largest subrange in which @a val could be inserted
   *         at any place in it without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An pair of iterators defining the subrange.
   *  @ingroup binarysearch
   *
   *  This is equivalent to
   *  @code
   *    std::make_pair(lower_bound(first, last, val, comp),
   *                   upper_bound(first, last, val, comp))
   *  @endcode
   *  but does not actually call those functions.
  */
  template<typename _ForwardIterator, typename _Tp, typename _Compare>
    pair<_ForwardIterator, _ForwardIterator>
    equal_range(_ForwardIterator __first, _ForwardIterator __last,
		const _Tp& __val,
		_Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
	_DistanceType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _ValueType, _Tp>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _Tp, _ValueType>)
      __glibcxx_requires_partitioned_lower_pred(__first, __last,
						__val, __comp);
      __glibcxx_requires_partitioned_upper_pred(__first, __last,
						__val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _ForwardIterator __middle, __left, __right;

      while (__len > 0)
	{
	  __half = __len >> 1;
	  __middle = __first;
	  std::advance(__middle, __half);
	  if (__comp(*__middle, __val))
	    {
	      __first = __middle;
	      ++__first;
	      __len = __len - __half - 1;
	    }
	  else if (__comp(__val, *__middle))
	    __len = __half;
	  else
	    {
	      __left = std::lower_bound(__first, __middle, __val, __comp);
	      std::advance(__first, __len);
	      __right = std::upper_bound(++__middle, __first, __val, __comp);
	      return pair<_ForwardIterator, _ForwardIterator>(__left, __right);
	    }
	}
      return pair<_ForwardIterator, _ForwardIterator>(__first, __first);
    }

  /**
   *  @brief Determines whether an element exists in a range.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  True if @a val (or its equivalent) is in [@a first,@a last ].
   *  @ingroup binarysearch
   *
   *  Note that this does not actually return an iterator to @a val.  For
   *  that, use std::find or a container's specialized find member functions.
  */
  template<typename _ForwardIterator, typename _Tp>
    bool
    binary_search(_ForwardIterator __first, _ForwardIterator __last,
                  const _Tp& __val)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)
      __glibcxx_requires_partitioned_lower(__first, __last, __val);
      __glibcxx_requires_partitioned_upper(__first, __last, __val);

      _ForwardIterator __i = std::lower_bound(__first, __last, __val);
      return __i != __last && !(__val < *__i);
    }

  /**
   *  @brief Determines whether an element exists in a range.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  True if @a val (or its equivalent) is in [@a first,@a last ].
   *  @ingroup binarysearch
   *
   *  Note that this does not actually return an iterator to @a val.  For
   *  that, use std::find or a container's specialized find member functions.
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<typename _ForwardIterator, typename _Tp, typename _Compare>
    bool
    binary_search(_ForwardIterator __first, _ForwardIterator __last,
                  const _Tp& __val, _Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
	_ValueType;

      // concept requirements
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
				  _Tp, _ValueType>)
      __glibcxx_requires_partitioned_lower_pred(__first, __last,
						__val, __comp);
      __glibcxx_requires_partitioned_upper_pred(__first, __last,
						__val, __comp);

      _ForwardIterator __i = std::lower_bound(__first, __last, __val, __comp);
      return __i != __last && !bool(__comp(__val, *__i));
    }

  // merge

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
	   typename _BidirectionalIterator3>
    _BidirectionalIterator3
    __merge_backward(_BidirectionalIterator1 __first1,
		     _BidirectionalIterator1 __last1,
		     _BidirectionalIterator2 __first2,
		     _BidirectionalIterator2 __last2,
		     _BidirectionalIterator3 __result)
    {
      if (__first1 == __last1)
	return std::copy_backward(__first2, __last2, __result);
      if (__first2 == __last2)
	return std::copy_backward(__first1, __last1, __result);
      --__last1;
      --__last2;
      while (true)
	{
	  if (*__last2 < *__last1)
	    {
	      *--__result = *__last1;
	      if (__first1 == __last1)
		return std::copy_backward(__first2, ++__last2, __result);
	      --__last1;
	    }
	  else
	    {
	      *--__result = *__last2;
	      if (__first2 == __last2)
		return std::copy_backward(__first1, ++__last1, __result);
	      --__last2;
	    }
	}
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
	   typename _BidirectionalIterator3, typename _Compare>
    _BidirectionalIterator3
    __merge_backward(_BidirectionalIterator1 __first1,
		     _BidirectionalIterator1 __last1,
		     _BidirectionalIterator2 __first2,
		     _BidirectionalIterator2 __last2,
		     _BidirectionalIterator3 __result,
		     _Compare __comp)
    {
      if (__first1 == __last1)
	return std::copy_backward(__first2, __last2, __result);
      if (__first2 == __last2)
	return std::copy_backward(__first1, __last1, __result);
      --__last1;
      --__last2;
      while (true)
	{
	  if (__comp(*__last2, *__last1))
	    {
	      *--__result = *__last1;
	      if (__first1 == __last1)
		return std::copy_backward(__first2, ++__last2, __result);
	      --__last1;
	    }
	  else
	    {
	      *--__result = *__last2;
	      if (__first2 == __last2)
		return std::copy_backward(__first1, ++__last1, __result);
	      --__last2;
	    }
	}
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
	   typename _Distance>
    _BidirectionalIterator1
    __rotate_adaptive(_BidirectionalIterator1 __first,
		      _BidirectionalIterator1 __middle,
		      _BidirectionalIterator1 __last,
		      _Distance __len1, _Distance __len2,
		      _BidirectionalIterator2 __buffer,
		      _Distance __buffer_size)
    {
      _BidirectionalIterator2 __buffer_end;
      if (__len1 > __len2 && __len2 <= __buffer_size)
	{
	  __buffer_end = std::copy(__middle, __last, __buffer);
	  std::copy_backward(__first, __middle, __last);
	  return std::copy(__buffer, __buffer_end, __first);
	}
      else if (__len1 <= __buffer_size)
	{
	  __buffer_end = std::copy(__first, __middle, __buffer);
	  std::copy(__middle, __last, __first);
	  return std::copy_backward(__buffer, __buffer_end, __last);
	}
      else
	{
	  std::rotate(__first, __middle, __last);
	  std::advance(__first, std::distance(__middle, __last));
	  return __first;
	}
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator, typename _Distance,
	   typename _Pointer>
    void
    __merge_adaptive(_BidirectionalIterator __first,
                     _BidirectionalIterator __middle,
		     _BidirectionalIterator __last,
		     _Distance __len1, _Distance __len2,
		     _Pointer __buffer, _Distance __buffer_size)
    {
      if (__len1 <= __len2 && __len1 <= __buffer_size)
	{
	  _Pointer __buffer_end = std::copy(__first, __middle, __buffer);
	  _GLIBCXX_STD_P::merge(__buffer, __buffer_end, __middle, __last, 
				__first);
	}
      else if (__len2 <= __buffer_size)
	{
	  _Pointer __buffer_end = std::copy(__middle, __last, __buffer);
	  std::__merge_backward(__first, __middle, __buffer,
				__buffer_end, __last);
	}
      else
	{
	  _BidirectionalIterator __first_cut = __first;
	  _BidirectionalIterator __second_cut = __middle;
	  _Distance __len11 = 0;
	  _Distance __len22 = 0;
	  if (__len1 > __len2)
	    {
	      __len11 = __len1 / 2;
	      std::advance(__first_cut, __len11);
	      __second_cut = std::lower_bound(__middle, __last,
					      *__first_cut);
	      __len22 = std::distance(__middle, __second_cut);
	    }
	  else
	    {
	      __len22 = __len2 / 2;
	      std::advance(__second_cut, __len22);
	      __first_cut = std::upper_bound(__first, __middle,
					     *__second_cut);
	      __len11 = std::distance(__first, __first_cut);
	    }
	  _BidirectionalIterator __new_middle =
	    std::__rotate_adaptive(__first_cut, __middle, __second_cut,
				   __len1 - __len11, __len22, __buffer,
				   __buffer_size);
	  std::__merge_adaptive(__first, __first_cut, __new_middle, __len11,
				__len22, __buffer, __buffer_size);
	  std::__merge_adaptive(__new_middle, __second_cut, __last,
				__len1 - __len11,
				__len2 - __len22, __buffer, __buffer_size);
	}
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator, typename _Distance, 
	   typename _Pointer, typename _Compare>
    void
    __merge_adaptive(_BidirectionalIterator __first,
                     _BidirectionalIterator __middle,
		     _BidirectionalIterator __last,
		     _Distance __len1, _Distance __len2,
		     _Pointer __buffer, _Distance __buffer_size,
		     _Compare __comp)
    {
      if (__len1 <= __len2 && __len1 <= __buffer_size)
	{
	  _Pointer __buffer_end = std::copy(__first, __middle, __buffer);
	  _GLIBCXX_STD_P::merge(__buffer, __buffer_end, __middle, __last,
				__first, __comp);
	}
      else if (__len2 <= __buffer_size)
	{
	  _Pointer __buffer_end = std::copy(__middle, __last, __buffer);
	  std::__merge_backward(__first, __middle, __buffer, __buffer_end,
				__last, __comp);
	}
      else
	{
	  _BidirectionalIterator __first_cut = __first;
	  _BidirectionalIterator __second_cut = __middle;
	  _Distance __len11 = 0;
	  _Distance __len22 = 0;
	  if (__len1 > __len2)
	    {
	      __len11 = __len1 / 2;
	      std::advance(__first_cut, __len11);
	      __second_cut = std::lower_bound(__middle, __last, *__first_cut,
					      __comp);
	      __len22 = std::distance(__middle, __second_cut);
	    }
	  else
	    {
	      __len22 = __len2 / 2;
	      std::advance(__second_cut, __len22);
	      __first_cut = std::upper_bound(__first, __middle, *__second_cut,
					     __comp);
	      __len11 = std::distance(__first, __first_cut);
	    }
	  _BidirectionalIterator __new_middle =
	    std::__rotate_adaptive(__first_cut, __middle, __second_cut,
				   __len1 - __len11, __len22, __buffer,
				   __buffer_size);
	  std::__merge_adaptive(__first, __first_cut, __new_middle, __len11,
				__len22, __buffer, __buffer_size, __comp);
	  std::__merge_adaptive(__new_middle, __second_cut, __last,
				__len1 - __len11,
				__len2 - __len22, __buffer,
				__buffer_size, __comp);
	}
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator, typename _Distance>
    void
    __merge_without_buffer(_BidirectionalIterator __first,
			   _BidirectionalIterator __middle,
			   _BidirectionalIterator __last,
			   _Distance __len1, _Distance __len2)
    {
      if (__len1 == 0 || __len2 == 0)
	return;
      if (__len1 + __len2 == 2)
	{
	  if (*__middle < *__first)
	    std::iter_swap(__first, __middle);
	  return;
	}
      _BidirectionalIterator __first_cut = __first;
      _BidirectionalIterator __second_cut = __middle;
      _Distance __len11 = 0;
      _Distance __len22 = 0;
      if (__len1 > __len2)
	{
	  __len11 = __len1 / 2;
	  std::advance(__first_cut, __len11);
	  __second_cut = std::lower_bound(__middle, __last, *__first_cut);
	  __len22 = std::distance(__middle, __second_cut);
	}
      else
	{
	  __len22 = __len2 / 2;
	  std::advance(__second_cut, __len22);
	  __first_cut = std::upper_bound(__first, __middle, *__second_cut);
	  __len11 = std::distance(__first, __first_cut);
	}
      std::rotate(__first_cut, __middle, __second_cut);
      _BidirectionalIterator __new_middle = __first_cut;
      std::advance(__new_middle, std::distance(__middle, __second_cut));
      std::__merge_without_buffer(__first, __first_cut, __new_middle,
				  __len11, __len22);
      std::__merge_without_buffer(__new_middle, __second_cut, __last,
				  __len1 - __len11, __len2 - __len22);
    }

  /// This is a helper function for the merge routines.
  template<typename _BidirectionalIterator, typename _Distance,
	   typename _Compare>
    void
    __merge_without_buffer(_BidirectionalIterator __first,
                           _BidirectionalIterator __middle,
			   _BidirectionalIterator __last,
			   _Distance __len1, _Distance __len2,
			   _Compare __comp)
    {
      if (__len1 == 0 || __len2 == 0)
	return;
      if (__len1 + __len2 == 2)
	{
	  if (__comp(*__middle, *__first))
	    std::iter_swap(__first, __middle);
	  return;
	}
      _BidirectionalIterator __first_cut = __first;
      _BidirectionalIterator __second_cut = __middle;
      _Distance __len11 = 0;
      _Distance __len22 = 0;
      if (__len1 > __len2)
	{
	  __len11 = __len1 / 2;
	  std::advance(__first_cut, __len11);
	  __second_cut = std::lower_bound(__middle, __last, *__first_cut,
					  __comp);
	  __len22 = std::distance(__middle, __second_cut);
	}
      else
	{
	  __len22 = __len2 / 2;
	  std::advance(__second_cut, __len22);
	  __first_cut = std::upper_bound(__first, __middle, *__second_cut,
					 __comp);
	  __len11 = std::distance(__first, __first_cut);
	}
      std::rotate(__first_cut, __middle, __second_cut);
      _BidirectionalIterator __new_middle = __first_cut;
      std::advance(__new_middle, std::distance(__middle, __second_cut));
      std::__merge_without_buffer(__first, __first_cut, __new_middle,
				  __len11, __len22, __comp);
      std::__merge_without_buffer(__new_middle, __second_cut, __last,
				  __len1 - __len11, __len2 - __len22, __comp);
    }

  /**
   *  @brief Merges two sorted ranges in place.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Merges two sorted and consecutive ranges, [first,middle) and
   *  [middle,last), and puts the result in [first,last).  The output will
   *  be sorted.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
   *
   *  If enough additional memory is available, this takes (last-first)-1
   *  comparisons.  Otherwise an NlogN algorithm is used, where N is
   *  distance(first,last).
  */
  template<typename _BidirectionalIterator>
    void
    inplace_merge(_BidirectionalIterator __first,
		  _BidirectionalIterator __middle,
		  _BidirectionalIterator __last)
    {
      typedef typename iterator_traits<_BidirectionalIterator>::value_type
          _ValueType;
      typedef typename iterator_traits<_BidirectionalIterator>::difference_type
          _DistanceType;

      // concept requirements
      __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
	    _BidirectionalIterator>)
      __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
      __glibcxx_requires_sorted(__first, __middle);
      __glibcxx_requires_sorted(__middle, __last);

      if (__first == __middle || __middle == __last)
	return;

      _DistanceType __len1 = std::distance(__first, __middle);
      _DistanceType __len2 = std::distance(__middle, __last);

      _Temporary_buffer<_BidirectionalIterator, _ValueType> __buf(__first,
								  __last);
      if (__buf.begin() == 0)
	std::__merge_without_buffer(__first, __middle, __last, __len1, __len2);
      else
	std::__merge_adaptive(__first, __middle, __last, __len1, __len2,
			      __buf.begin(), _DistanceType(__buf.size()));
    }

  /**
   *  @brief Merges two sorted ranges in place.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A functor to use for comparisons.
   *  @return  Nothing.
   *
   *  Merges two sorted and consecutive ranges, [first,middle) and
   *  [middle,last), and puts the result in [first,last).  The output will
   *  be sorted.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
   *