ble @a v.  It does so
       *  by calling num_get::do_get().
       *
       *  The input characters are parsed like the scanf %p specifier.
       *
       *  Digit grouping is interpreted according to numpunct::grouping() and
       *  numpunct::thousands_sep().  If the pattern of digit groups isn't
       *  consistent, sets err to ios_base::failbit.
       *
       *  Note that the digit grouping effect for pointers is a bit ambiguous
       *  in the standard and shouldn't be relied on.  See DR 344.
       *
       *  If parsing the string yields a valid value for @a v, @a v is set.
       *  Otherwise, sets err to ios_base::failbit and leaves @a v unaltered.
       *  Sets err to ios_base::eofbit if the stream is emptied.
       *
       *  @param  in  Start of input stream.
       *  @param  end  End of input stream.
       *  @param  io  Source of locale and flags.
       *  @param  err  Error flags to set.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after reading.
      */
      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
	  ios_base::iostate& __err, void*& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

    protected:
      /// Destructor.
      virtual ~num_get() { }

      iter_type
      _M_extract_float(iter_type, iter_type, ios_base&, ios_base::iostate&,
		       string& __xtrc) const;

      template<typename _ValueT>
        iter_type
        _M_extract_int(iter_type, iter_type, ios_base&, ios_base::iostate&,
		       _ValueT& __v) const;

      template<typename _CharT2>
      typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value, int>::__type
        _M_find(const _CharT2*, size_t __len, _CharT2 __c) const
        {
	  int __ret = -1;
	  if (__len <= 10)
	    {
	      if (__c >= _CharT2('0') && __c < _CharT2(_CharT2('0') + __len))
		__ret = __c - _CharT2('0');
	    }
	  else
	    {
	      if (__c >= _CharT2('0') && __c <= _CharT2('9'))
		__ret = __c - _CharT2('0');
	      else if (__c >= _CharT2('a') && __c <= _CharT2('f'))
		__ret = 10 + (__c - _CharT2('a'));
	      else if (__c >= _CharT2('A') && __c <= _CharT2('F'))
		__ret = 10 + (__c - _CharT2('A'));
	    }
	  return __ret;
	}

      template<typename _CharT2>
      typename __gnu_cxx::__enable_if<!__is_char<_CharT2>::__value, 
				      int>::__type
        _M_find(const _CharT2* __zero, size_t __len, _CharT2 __c) const
        {
	  int __ret = -1;
	  const char_type* __q = char_traits<_CharT2>::find(__zero, __len, __c);
	  if (__q)
	    {
	      __ret = __q - __zero;
	      if (__ret > 15)
		__ret -= 6;
	    }
	  return __ret;
	}

      //@{
      /**
       *  @brief  Numeric parsing.
       *
       *  Parses the input stream into the variable @a v.  This function is a
       *  hook for derived classes to change the value returned.  @see get()
       *  for more details.
       *
       *  @param  in  Start of input stream.
       *  @param  end  End of input stream.
       *  @param  io  Source of locale and flags.
       *  @param  err  Error flags to set.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after reading.
      */
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&, bool&) const;


      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&, long&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	      unsigned short&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     unsigned int&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     unsigned long&) const;

#ifdef _GLIBCXX_USE_LONG_LONG
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     long long&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     unsigned long long&) const;
#endif

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     float&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     double&) const;

      // XXX GLIBCXX_ABI Deprecated
#if defined _GLIBCXX_LONG_DOUBLE_COMPAT && defined __LONG_DOUBLE_128__
      virtual iter_type
      __do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	       double&) const;
#else
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     long double&) const;
#endif

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     void*&) const;

      // XXX GLIBCXX_ABI Deprecated
#if defined _GLIBCXX_LONG_DOUBLE_COMPAT && defined __LONG_DOUBLE_128__
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate& __err,
	     long double&) const;
#endif
      //@}
    };

  template<typename _CharT, typename _InIter>
    locale::id num_get<_CharT, _InIter>::id;


  /**
   *  @brief  Facet for converting numbers to strings.
   *
   *  This facet encapsulates the code to convert a number to a string.  It is
   *  used by the ostream numeric insertion operators.
   *
   *  The num_put template uses protected virtual functions to provide the
   *  actual results.  The public accessors forward the call to the virtual
   *  functions.  These virtual functions are hooks for developers to
   *  implement the behavior they require from the num_put facet.
  */
  template<typename _CharT, typename _OutIter>
    class num_put : public locale::facet
    {
    public:
      // Types:
      //@{
      /// Public typedefs
      typedef _CharT		char_type;
      typedef _OutIter		iter_type;
      //@}

      /// Numpunct facet id.
      static locale::id		id;

      /**
       *  @brief  Constructor performs initialization.
       *
       *  This is the constructor provided by the standard.
       *
       *  @param refs  Passed to the base facet class.
      */
      explicit
      num_put(size_t __refs = 0) : facet(__refs) { }

      /**
       *  @brief  Numeric formatting.
       *
       *  Formats the boolean @a v and inserts it into a stream.  It does so
       *  by calling num_put::do_put().
       *
       *  If ios_base::boolalpha is set, writes ctype<CharT>::truename() or
       *  ctype<CharT>::falsename().  Otherwise formats @a v as an int.
       *
       *  @param  s  Stream to write to.
       *  @param  io  Source of locale and flags.
       *  @param  fill  Char_type to use for filling.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after writing.
      */
      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill, bool __v) const
      { return this->do_put(__s, __f, __fill, __v); }

      //@{
      /**
       *  @brief  Numeric formatting.
       *
       *  Formats the integral value @a v and inserts it into a
       *  stream.  It does so by calling num_put::do_put().
       *
       *  Formatting is affected by the flag settings in @a io.
       *
       *  The basic format is affected by the value of io.flags() &
       *  ios_base::basefield.  If equal to ios_base::oct, formats like the
       *  printf %o specifier.  Else if equal to ios_base::hex, formats like
       *  %x or %X with ios_base::uppercase unset or set respectively.
       *  Otherwise, formats like %d, %ld, %lld for signed and %u, %lu, %llu
       *  for unsigned values.  Note that if both oct and hex are set, neither
       *  will take effect.
       *
       *  If ios_base::showpos is set, '+' is output before positive values.
       *  If ios_base::showbase is set, '0' precedes octal values (except 0)
       *  and '0[xX]' precedes hex values.
       *
       *  Thousands separators are inserted according to numpunct::grouping()
       *  and numpunct::thousands_sep().  The decimal point character used is
       *  numpunct::decimal_point().
       *
       *  If io.width() is non-zero, enough @a fill characters are inserted to
       *  make the result at least that wide.  If
       *  (io.flags() & ios_base::adjustfield) == ios_base::left, result is
       *  padded at the end.  If ios_base::internal, then padding occurs
       *  immediately after either a '+' or '-' or after '0x' or '0X'.
       *  Otherwise, padding occurs at the beginning.
       *
       *  @param  s  Stream to write to.
       *  @param  io  Source of locale and flags.
       *  @param  fill  Char_type to use for filling.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after writing.
      */
      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill, long __v) const
      { return this->do_put(__s, __f, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill,
	  unsigned long __v) const
      { return this->do_put(__s, __f, __fill, __v); }

#ifdef _GLIBCXX_USE_LONG_LONG
      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill, long long __v) const
      { return this->do_put(__s, __f, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill,
	  unsigned long long __v) const
      { return this->do_put(__s, __f, __fill, __v); }
#endif
      //@}

      //@{
      /**
       *  @brief  Numeric formatting.
       *
       *  Formats the floating point value @a v and inserts it into a stream.
       *  It does so by calling num_put::do_put().
       *
       *  Formatting is affected by the flag settings in @a io.
       *
       *  The basic format is affected by the value of io.flags() &
       *  ios_base::floatfield.  If equal to ios_base::fixed, formats like the
       *  printf %f specifier.  Else if equal to ios_base::scientific, formats
       *  like %e or %E with ios_base::uppercase unset or set respectively.
       *  Otherwise, formats like %g or %G depending on uppercase.  Note that
       *  if both fixed and scientific are set, the effect will also be like
       *  %g or %G.
       *
       *  The output precision is given by io.precision().  This precision is
       *  capped at numeric_limits::digits10 + 2 (different for double and
       *  long double).  The default precision is 6.
       *
       *  If ios_base::showpos is set, '+' is output before positive values.
       *  If ios_base::showpoint is set, a decimal point will always be
       *  output.
       *
       *  Thousands separators are inserted according to numpunct::grouping()
       *  and numpunct::thousands_sep().  The decimal point character used is
       *  numpunct::decimal_point().
       *
       *  If io.width() is non-zero, enough @a fill characters are inserted to
       *  make the result at least that wide.  If
       *  (io.flags() & ios_base::adjustfield) == ios_base::left, result is
       *  padded at the end.  If ios_base::internal, then padding occurs
       *  immediately after either a '+' or '-' or after '0x' or '0X'.
       *  Otherwise, padding occurs at the beginning.
       *
       *  @param  s  Stream to write to.
       *  @param  io  Source of locale and flags.
       *  @param  fill  Char_type to use for filling.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after writing.
      */
      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill, double __v) const
      { return this->do_put(__s, __f, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill,
	  long double __v) const
      { return this->do_put(__s, __f, __fill, __v); }
      //@}

      /**
       *  @brief  Numeric formatting.
       *
       *  Formats the pointer value @a v and inserts it into a stream.  It
       *  does so by calling num_put::do_put().
       *
       *  This function formats @a v as an unsigned long with ios_base::hex
       *  and ios_base::showbase set.
       *
       *  @param  s  Stream to write to.
       *  @param  io  Source of locale and flags.
       *  @param  fill  Char_type to use for filling.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after writing.
      */
      iter_type
      put(iter_type __s, ios_base& __f, char_type __fill,
	  const void* __v) const
      { return this->do_put(__s, __f, __fill, __v); }

    protected:
      template<typename _ValueT>
        iter_type
        _M_insert_float(iter_type, ios_base& __io, char_type __fill,
			char __mod, _ValueT __v) const;

      void
      _M_group_float(const char* __grouping, size_t __grouping_size,
		     char_type __sep, const char_type* __p, char_type* __new,
		     char_type* __cs, int& __len) const;

      template<typename _ValueT>
        iter_type
        _M_insert_int(iter_type, ios_base& __io, char_type __fill,
		      _ValueT __v) const;

      void
      _M_group_int(const char* __grouping, size_t __grouping_size,
		   char_type __sep, ios_base& __io, char_type* __new,
		   char_type* __cs, int& __len) const;

      void
      _M_pad(char_type __fill, streamsize __w, ios_base& __io,
	     char_type* __new, const char_type* __cs, int& __len) const;

      /// Destructor.
      virtual
      ~num_put() { };

      //@{
      /**
       *  @brief  Numeric formatting.
       *
       *  These functions do the work of formatting numeric values and
       *  inserting them into a stream. This function is a hook for derived
       *  classes to change the value returned.
       *
       *  @param  s  Stream to write to.
       *  @param  io  Source of locale and flags.
       *  @param  fill  Char_type to use for filling.
       *  @param  v  Value to format and insert.
       *  @return  Iterator after writing.
      */
      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, bool __v) const;

      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, long __v) const;

      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, unsigned long) const;

#ifdef _GLIBCXX_USE_LONG_LONG
      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, long long __v) const;

      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, unsigned long long) const;
#endif

      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, double __v) const;

      // XXX GLIBCXX_ABI Deprecated
#if defined _GLIBCXX_LONG_DOUBLE_COMPAT && defined __LONG_DOUBLE_128__
      virtual iter_type
      __do_put(iter_type, ios_base&, char_type __fill, double __v) const;
#else
      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, long double __v) const;
#endif

      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, const void* __v) const;

      // XXX GLIBCXX_ABI Deprecated
#if defined _GLIBCXX_LONG_DOUBLE_COMPAT && defined __LONG_DOUBLE_128__
      virtual iter_type
      do_put(iter_type, ios_base&, char_type __fill, long double __v) const;
#endif
      //@}
    };

  template <typename _CharT, typename _OutIter>
    locale::id num_put<_CharT, _OutIter>::id;

_GLIBCXX_END_LDBL_NAMESPACE

  // Subclause convenience interfaces, inlines.
  // NB: These are inline because, when used in a loop, some compilers
  // can hoist the body out of the loop; then it's just as fast as the
  // C is*() function.

  /// Convenience interface to ctype.is(ctype_base::space, __c).
  template<typename _CharT>
    inline bool
    isspace(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::space, __c); }

  /// Convenience interface to ctype.is(ctype_base::print, __c).
  template<typename _CharT>
    inline bool
    isprint(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::print, __c); }

  /// Convenience interface to ctype.is(ctype_base::cntrl, __c).
  template<typename _CharT>
    inline bool
    iscntrl(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::cntrl, __c); }

  /// Convenience interface to ctype.is(ctype_base::upper, __c).
  template<typename _CharT>
    inline bool
    isupper(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::upper, __c); }

  /// Convenience interface to ctype.is(ctype_base::lower, __c).
  template<typename _CharT>
    inline bool 
    islower(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::lower, __c); }

  /// Convenience interface to ctype.is(ctype_base::alpha, __c).
  template<typename _CharT>
    inline bool
    isalpha(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::alpha, __c); }

  /// Convenience interface to ctype.is(ctype_base::digit, __c).
  template<typename _CharT>
    inline bool
    isdigit(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::digit, __c); }

  /// Convenience interface to ctype.is(ctype_base::punct, __c).
  template<typename _CharT>
    inline bool
    ispunct(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::punct, __c); }

  /// Convenience interface to ctype.is(ctype_base::xdigit, __c).
  template<typename _CharT>
    inline bool
    isxdigit(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::xdigit, __c); }

  /// Convenience interface to ctype.is(ctype_base::alnum, __c).
  template<typename _CharT>
    inline bool
    isalnum(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::alnum, __c); }

  /// Convenience interface to ctype.is(ctype_base::graph, __c).
  template<typename _CharT>
    inline bool
    isgraph(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::graph, __c); }

  /// Convenience interface to ctype.toupper(__c).
  template<typename _CharT>
    inline _CharT
    toupper(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).toupper(__c); }

  /// Convenience interface to ctype.tolower(__c).
  template<typename _CharT>
    inline _CharT
    tolower(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).tolower(__c); }

_GLIBCXX_END_NAMESPACE

#ifndef _GLIBCXX_EXPORT_TEMPLATE
# include <bits/locale_facets.tcc>
#endif

#endif
// The template and inlines for the -*- C++ -*- slice_array class.

// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006
// 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.

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

// 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, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// 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 produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

/** @file slice_array.h
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

// Written by Gabriel Dos Reis <Gabriel.Dos-Reis@DPTMaths.ENS-Cachan.Fr>

#ifndef _SLICE_ARRAY_H
#define _SLICE_ARRAY_H 1

#pragma GCC system_header

_GLIBCXX_BEGIN_NAMESPACE(std)

  /**
   *  @brief  Class defining one-dimensional subset of an array.
   *
   *  The slice class represents a one-dimensional subset of an array,
   *  specified by three parameters: start offset, size, and stride.  The
   *  start offset is the index of the first element of the array that is part
   *  of the subset.  The size is the total number of elements in the subset.
   *  Stride is the distance between each successive array element to include
   *  in the subset.
   *
   *  For example, with an array of size 10, and a slice with offset 1, size 3
   *  and stride 2, the subset consists of array elements 1, 3, and 5.
   */
  class slice
  {
  public:
    ///  Construct an empty slice.
    slice();

    /**
     *  @brief  Construct a slice.
     *
     *  @param  o  Offset in array of first element.
     *  @param  d  Number of elements in slice.
     *  @param  s  Stride between array elements.
     */
    slice(size_t, size_t, size_t);

    ///  Return array offset of first slice element.
    size_t start() const;
    ///  Return size of slice.
    size_t size() const;
    ///  Return array stride of slice.
    size_t stride() const;

  private:
    size_t _M_off;                      // offset
    size_t _M_sz;			// size
    size_t _M_st;			// stride unit
  };

  // _GLIBCXX_RESOLVE_LIB_DEFECTS
  // 543. valarray slice default constructor
  inline
  slice::slice() 
  : _M_off(0), _M_sz(0), _M_st(0) {}

  inline
  slice::slice(size_t __o, size_t __d, size_t __s)
  : _M_off(__o), _M_sz(__d), _M_st(__s) {}

  inline size_t
  slice::start() const
  { return _M_off; }

  inline size_t
  slice::size() const
  { return _M_sz; }

  inline size_t
  slice::stride() const
  { return _M_st; }

  /**
   *  @brief  Reference to one-dimensional subset of an array.
   *
   *  A slice_array is a reference to the actual elements of an array
   *  specified by a slice.  The way to get a slice_array is to call
   *  operator[](slice) on a valarray.  The returned slice_array then permits
   *  carrying operations out on the referenced subset of elements in the
   *  original valarray.  For example, operator+=(valarray) will add values
   *  to the subset of elements in the underlying valarray this slice_array
   *  refers to.
   *
   *  @param  Tp  Element type.
   */
  template<typename _Tp>
    class slice_array
    {
    public:
      typedef _Tp value_type;

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 253. valarray helper functions are almost entirely useless

      ///  Copy constructor.  Both slices refer to the same underlying array.
      slice_array(const slice_array&);

      ///  Assignment operator.  Assigns slice elements to corresponding
      ///  elements of @a a.
      slice_array& operator=(const slice_array&);

      ///  Assign slice elements to corresponding elements of @a v.
      void operator=(const valarray<_Tp>&) const;
      ///  Multiply slice elements by corresponding elements of @a v.
      void operator*=(const valarray<_Tp>&) const;
      ///  Divide slice elements by corresponding elements of @a v.
      void operator/=(const valarray<_Tp>&) const;
      ///  Modulo slice elements by corresponding elements of @a v.
      void operator%=(const valarray<_Tp>&) const;
      ///  Add corresponding elements of @a v to slice elements.
      void operator+=(const valarray<_Tp>&) const;
      ///  Subtract corresponding elements of @a v from slice elements.
      void operator-=(const valarray<_Tp>&) const;
      ///  Logical xor slice elements with corresponding elements of @a v.
      void operator^=(const valarray<_Tp>&) const;
      ///  Logical and slice elements with corresponding elements of @a v.
      void operator&=(const valarray<_Tp>&) const;
      ///  Logical or slice elements with corresponding elements of @a v.
      void operator|=(const valarray<_Tp>&) const;
      ///  Left shift slice elements by corresponding elements of @a v.
      void operator<<=(const valarray<_Tp>&) const;
      ///  Right shift slice elements by corresponding elements of @a v.
      void operator>>=(const valarray<_Tp>&) const;
      ///  Assign all slice elements to @a t.
      void operator=(const _Tp &) const;
      //        ~slice_array ();

      template<class _Dom>
        void operator=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator*=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator/=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator%=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator+=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator-=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator^=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator&=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator|=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator<<=(const _Expr<_Dom, _Tp>&) const;
      template<class _Dom>
	void operator>>=(const _Expr<_Dom, _Tp>&) const;

    private:
      friend class valarray<_Tp>;
      slice_array(_Array<_Tp>, const slice&);

      const size_t      _M_sz;
      const size_t      _M_stride;
      const _Array<_Tp> _M_array;

      // not implemented
      slice_array();
    };

  template<typename _Tp>
    inline
    slice_array<_Tp>::slice_array(_Array<_Tp> __a, const slice& __s)
    : _M_sz(__s.size()), _M_stride(__s.stride()),
      _M_array(__a.begin() + __s.start()) {}

  template<typename _Tp>
    inline
    slice_array<_Tp>::slice_array(const slice_array<_Tp>& a)
    : _M_sz(a._M_sz), _M_stride(a._M_stride), _M_array(a._M_array) {}

  //    template<typename _Tp>
  //    inline slice_array<_Tp>::~slice_array () {}

  template<typename _Tp>
    inline slice_array<_Tp>&
    slice_array<_Tp>::operator=(const slice_array<_Tp>& __a)
    {
      std::__valarray_copy(__a._M_array, __a._M_sz, __a._M_stride,
			   _M_array, _M_stride);
      return *this;
    }

  template<typename _Tp>
    inline void
    slice_array<_Tp>::operator=(const _Tp& __t) const
    { std::__valarray_fill(_M_array, _M_sz, _M_stride, __t); }

  template<typename _Tp>
    inline void
    slice_array<_Tp>::operator=(const valarray<_Tp>& __v) const
    { std::__valarray_copy(_Array<_Tp>(__v), _M_array, _M_sz, _M_stride); }

  template<typename _Tp>
  template<class _Dom>
    inline void
    slice_array<_Tp>::operator=(const _Expr<_Dom,_Tp>& __e) const
    { std::__valarray_copy(__e, _M_sz, _M_array, _M_stride); }

#undef _DEFINE_VALARRAY_OPERATOR
#define _DEFINE_VALARRAY_OPERATOR(_Op,_Name)				\
  template<typename _Tp>						\
    inline void								\
    slice_array<_Tp>::operator _Op##=(const valarray<_Tp>& __v) const	\
    {									\
      _Array_augmented_##_Name(_M_array, _M_sz, _M_stride, _Array<_Tp>(__v));\
    }									\
									\
  template<typename _Tp>                                                \
    template<class _Dom>				                \
      inline void							\
      slice_array<_Tp>::operator _Op##=(const _Expr<_Dom,_Tp>& __e) const\
      {									\
	  _Array_augmented_##_Name(_M_array, _M_stride, __e, _M_sz);	\
      }


_DEFINE_VALARRAY_OPERATOR(*, __multiplies)
_DEFINE_VALARRAY_OPERATOR(/, __divides)
_DEFINE_VALARRAY_OPERATOR(%, __modulus)
_DEFINE_VALARRAY_OPERATOR(+, __plus)
_DEFINE_VALARRAY_OPERATOR(-, __minus)
_DEFINE_VALARRAY_OPERATOR(^, __bitwise_xor)
_DEFINE_VALARRAY_OPERATOR(&, __bitwise_and)
_DEFINE_VALARRAY_OPERATOR(|, __bitwise_or)
_DEFINE_VALARRAY_OPERATOR(<<, __shift_left)
_DEFINE_VALARRAY_OPERATOR(>>, __shift_right)

#undef _DEFINE_VALARRAY_OPERATOR

_GLIBCXX_END_NAMESPACE

#endif /* _SLICE_ARRAY_H */
// RB tree implementation -*- C++ -*-

// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 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.

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

// 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, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// 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 produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

/*
 *
 * Copyright (c) 1996,1997
 * Silicon Graphics Computer Systems, Inc.
 *
 * Permission to use, copy, modify, distribute and sell this software
 * and its documentation for any purpose is hereby granted without fee,
 * provided that the above copyright notice appear in all copies and
 * that both that copyright notice and this permission notice appear
 * in supporting documentation.  Silicon Graphics makes no
 * representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied warranty.
 *
 *
 * Copyright (c) 1994
 * Hewlett-Packard Company
 *
 * Permission to use, copy, modify, distribute and sell this software
 * and its documentation for any purpose is hereby granted without fee,
 * provided that the above copyright notice appear in all copies and
 * that both that copyright notice and this permission notice appear
 * in supporting documentation.  Hewlett-Packard Company makes no
 * representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied warranty.
 *
 *
 */

/** @file stl_tree.h
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

#ifndef _STL_TREE_H
#define _STL_TREE_H 1

#include <bits/stl_algobase.h>
#include <bits/allocator.h>
#include <bits/stl_function.h>
#include <bits/cpp_type_traits.h>

_GLIBCXX_BEGIN_NAMESPACE(std)

  // Red-black tree class, designed for use in implementing STL
  // associative containers (set, multiset, map, and multimap). The
  // insertion and deletion algorithms are based on those in Cormen,
  // Leiserson, and Rivest, Introduction to Algorithms (MIT Press,
  // 1990), except that
  //
  // (1) the header cell is maintained with links not only to the root
  // but also to the leftmost node of the tree, to enable constant
  // time begin(), and to the rightmost node of the tree, to enable
  // linear time performance when used with the generic set algorithms
  // (set_union, etc.)
  // 
  // (2) when a node being deleted has two children its successor node
  // is relinked into its place, rather than copied, so that the only
  // iterators invalidated are those referring to the deleted node.

  enum _Rb_tree_color { _S_red = false, _S_black = true };

  struct _Rb_tree_node_base
  {
    typedef _Rb_tree_node_base* _Base_ptr;
    typedef const _Rb_tree_node_base* _Const_Base_ptr;

    _Rb_tree_color	_M_color;
    _Base_ptr		_M_parent;
    _Base_ptr		_M_left;
    _Base_ptr		_M_right;

    static _Base_ptr
    _S_minimum(_Base_ptr __x)
    {
      while (__x->_M_left != 0) __x = __x->_M_left;
      return __x;
    }

    static _Const_Base_ptr
    _S_minimum(_Const_Base_ptr __x)
    {
      while (__x->_M_left != 0) __x = __x->_M_left;
      return __x;
    }

    static _Base_ptr
    _S_maximum(_Base_ptr __x)
    {
      while (__x->_M_right != 0) __x = __x->_M_right;
      return __x;
    }

    static _Const_Base_ptr
    _S_maximum(_Const_Base_ptr __x)
    {
      while (__x->_M_right != 0) __x = __x->_M_right;
      return __x;
    }
  };

  template<typename _Val>
    struct _Rb_tree_node : public _Rb_tree_node_base
    {
      typedef _Rb_tree_node<_Val>* _Link_type;
      _Val _M_value_field;
    };

  _Rb_tree_node_base*
  _Rb_tree_increment(_Rb_tree_node_base* __x);

  const _Rb_tree_node_base*
  _Rb_tree_increment(const _Rb_tree_node_base* __x);

  _Rb_tree_node_base*
  _Rb_tree_decrement(_Rb_tree_node_base* __x);

  const _Rb_tree_node_base*
  _Rb_tree_decrement(const _Rb_tree_node_base* __x);

  template<typename _Tp>
    struct _Rb_tree_iterator
    {
      typedef _Tp  value_type;
      typedef _Tp& reference;
      typedef _Tp* pointer;

      typedef bidirectional_iterator_tag iterator_category;
      typedef ptrdiff_t                  difference_type;

      typedef _Rb_tree_iterator<_Tp>        _Self;
      typedef _Rb_tree_node_base::_Base_ptr _Base_ptr;
      typedef _Rb_tree_node<_Tp>*           _Link_type;

      _Rb_tree_iterator()
      : _M_node() { }

      explicit
      _Rb_tree_iterator(_Link_type __x)
      : _M_node(__x) { }

      reference
      operator*() const
      { return static_cast<_Link_type>(_M_node)->_M_value_field; }

      pointer
      operator->() const
      { return &static_cast<_Link_type>(_M_node)->_M_value_field; }

      _Self&
      operator++()
      {
	_M_node = _Rb_tree_increment(_M_node);
	return *this;
      }

      _Self
      operator++(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_increment(_M_node);
	return __tmp;
      }

      _Self&
      operator--()
      {
	_M_node = _Rb_tree_decrement(_M_node);
	return *this;
      }

      _Self
      operator--(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_decrement(_M_node);
	return __tmp;
      }

      bool
      operator==(const _Self& __x) const
      { return _M_node == __x._M_node; }

      bool
      operator!=(const _Self& __x) const
      { return _M_node != __x._M_node; }

      _Base_ptr _M_node;
  };

  template<typename _Tp>
    struct _Rb_tree_const_iterator
    {
      typedef _Tp        value_type;
      typedef const _Tp& reference;
      typedef const _Tp* pointer;

      typedef _Rb_tree_iterator<_Tp> iterator;

      typedef bidirectional_iterator_tag iterator_category;
      typedef ptrdiff_t                  difference_type;

      typedef _Rb_tree_const_iterator<_Tp>        _Self;
      typedef _Rb_tree_node_base::_Const_Base_ptr _Base_ptr;
      typedef const _Rb_tree_node<_Tp>*           _Link_type;

      _Rb_tree_const_iterator()
      : _M_node() { }

      explicit
      _Rb_tree_const_iterator(_Link_type __x)
      : _M_node(__x) { }

      _Rb_tree_const_iterator(const iterator& __it)
      : _M_node(__it._M_node) { }

      reference
      operator*() const
      { return static_cast<_Link_type>(_M_node)->_M_value_field; }

      pointer
      operator->() const
      { return &static_cast<_Link_type>(_M_node)->_M_value_field; }

      _Self&
      operator++()
      {
	_M_node = _Rb_tree_increment(_M_node);
	return *this;
      }

      _Self
      operator++(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_increment(_M_node);
	return __tmp;
      }

      _Self&
      operator--()
      {
	_M_node = _Rb_tree_decrement(_M_node);
	return *this;
      }

      _Self
      operator--(int)
      {
	_Self __tmp = *this;
	_M_node = _Rb_tree_decrement(_M_node);
	return __tmp;
      }

      bool
      operator==(const _Self& __x) const
      { return _M_node == __x._M_node; }

      bool
      operator!=(const _Self& __x) const
      { return _M_node != __x._M_node; }

      _Base_ptr _M_node;
    };

  template<typename _Val>
    inline bool
    operator==(const _Rb_tree_iterator<_Val>& __x,
               const _Rb_tree_const_iterator<_Val>& __y)
    { return __x._M_node == __y._M_node; }

  template<typename _Val>
    inline bool
    operator!=(const _Rb_tree_iterator<_Val>& __x,
               const _Rb_tree_const_iterator<_Val>& __y)
    { return __x._M_node != __y._M_node; }

  void
  _Rb_tree_insert_and_rebalance(const bool __insert_left,
                                _Rb_tree_node_base* __x,
                                _Rb_tree_node_base* __p,
                                _Rb_tree_node_base& __header);

  _Rb_tree_node_base*
  _Rb_tree_rebalance_for_erase(_Rb_tree_node_base* const __z,
			       _Rb_tree_node_base& __header);


  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc = allocator<_Val> >
    class _Rb_tree
    {
      typedef typename _Alloc::template rebind<_Rb_tree_node<_Val> >::other
              _Node_allocator;

    protected:
      typedef _Rb_tree_node_base* _Base_ptr;
      typedef const _Rb_tree_node_base* _Const_Base_ptr;

    public:
      typedef _Key key_type;
      typedef _Val value_type;
      typedef value_type* pointer;
      typedef const value_type* const_pointer;
      typedef value_type& reference;
      typedef const value_type& const_reference;
      typedef _Rb_tree_node<_Val>* _Link_type;
      typedef const _Rb_tree_node<_Val>* _Const_Link_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;
      typedef _Alloc allocator_type;

      _Node_allocator&
      _M_get_Node_allocator()
      { return *static_cast<_Node_allocator*>(&this->_M_impl); }
      
      const _Node_allocator&
      _M_get_Node_allocator() const
      { return *static_cast<const _Node_allocator*>(&this->_M_impl); }

      allocator_type
      get_allocator() const
      { return allocator_type(_M_get_Node_allocator()); }

    protected:
      _Link_type
      _M_get_node()
      { return _M_impl._Node_allocator::allocate(1); }

      void
      _M_put_node(_Link_type __p)
      { _M_impl._Node_allocator::deallocate(__p, 1); }

      _Link_type
      _M_create_node(const value_type& __x)
      {
	_Link_type __tmp = _M_get_node();
	try
	  { get_allocator().construct(&__tmp->_M_value_field, __x); }
	catch(...)
	  {
	    _M_put_node(__tmp);
	    __throw_exception_again;
	  }
	return __tmp;
      }

      _Link_type
      _M_clone_node(_Const_Link_type __x)
      {
	_Link_type __tmp = _M_create_node(__x->_M_value_field);
	__tmp->_M_color = __x->_M_color;
	__tmp->_M_left = 0;
	__tmp->_M_right = 0;
	return __tmp;
      }

      void
      _M_destroy_node(_Link_type __p)
      {
	get_allocator().destroy(&__p->_M_value_field);
	_M_put_node(__p);
      }

    protected:
      template<typename _Key_compare, 
	       bool _Is_pod_comparator = __is_pod(_Key_compare)>
        struct _Rb_tree_impl : public _Node_allocator
        {
	  _Key_compare		_M_key_compare;
	  _Rb_tree_node_base 	_M_header;
	  size_type 		_M_node_count; // Keeps track of size of tree.

	  _Rb_tree_impl()
	  : _Node_allocator(), _M_key_compare(), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	  _Rb_tree_impl(const _Key_compare& __comp, const _Node_allocator& __a)
	  : _Node_allocator(__a), _M_key_compare(__comp), _M_header(),
	    _M_node_count(0)
	  { _M_initialize(); }

	private:
	  void
	  _M_initialize()
	  {
	    this->_M_header._M_color = _S_red;
	    this->_M_header._M_parent = 0;
	    this->_M_header._M_left = &this->_M_header;
	    this->_M_header._M_right = &this->_M_header;
	  }	    
	};

      _Rb_tree_impl<_Compare> _M_impl;

    protected:
      _Base_ptr&
      _M_root()
      { return this->_M_impl._M_header._M_parent; }

      _Const_Base_ptr
      _M_root() const
      { return this->_M_impl._M_header._M_parent; }

      _Base_ptr&
      _M_leftmost()
      { return this->_M_impl._M_header._M_left; }

      _Const_Base_ptr
      _M_leftmost() const
      { return this->_M_impl._M_header._M_left; }

      _Base_ptr&
      _M_rightmost()
*'+','-'.'/'0'1'2'3'4'5'6'7'8'9':';'<'='>'?'@'A'B'C'D'E'F'G'H'      { return this->_M_impl._M_header._M_right; }

      _Const_Base_ptr
      _M_rightmost() const
      { return this->_M_impl._M_header._M_right; }

      _Link_type
      _M_begin()
      { return static_cast<_Link_type>(this->_M_impl._M_header._M_parent); }

      _Const_Link_type
      _M_begin() const
      {
	return static_cast<_Const_Link_type>
	  (this->_M_impl._M_header._M_parent);
      }

      _Link_type
      _M_end()
      { return static_cast<_Link_type>(&this->_M_impl._M_header); }

      _Const_Link_type
      _M_end() const
      { return static_cast<_Const_Link_type>(&this->_M_impl._M_header); }

      static const_reference
      _S_value(_Const_Link_type __x)
      { return __x->_M_value_field; }

      static const _Key&
      _S_key(_Const_Link_type __x)
      { return _KeyOfValue()(_S_value(__x)); }

      static _Link_type
      _S_left(_Base_ptr __x)
      { return static_cast<_Link_type>(__x->_M_left); }

      static _Const_Link_type
      _S_left(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x->_M_left); }

      static _Link_type
      _S_right(_Base_ptr __x)
      { return static_cast<_Link_type>(__x->_M_right); }

      static _Const_Link_type
      _S_right(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x->_M_right); }

      static const_reference
      _S_value(_Const_Base_ptr __x)
      { return static_cast<_Const_Link_type>(__x)->_M_value_field; }

      static const _Key&
      _S_key(_Const_Base_ptr __x)
      { return _KeyOfValue()(_S_value(__x)); }

      static _Base_ptr
      _S_minimum(_Base_ptr __x)
      { return _Rb_tree_node_base::_S_minimum(__x); }

      static _Const_Base_ptr
      _S_minimum(_Const_Base_ptr __x)
      { return _Rb_tree_node_base::_S_minimum(__x); }

      static _Base_ptr
      _S_maximum(_Base_ptr __x)
      { return _Rb_tree_node_base::_S_maximum(__x); }

      static _Const_Base_ptr
      _S_maximum(_Const_Base_ptr __x)
      { return _Rb_tree_node_base::_S_maximum(__x); }

    public:
      typedef _Rb_tree_iterator<value_type>       iterator;
      typedef _Rb_tree_const_iterator<value_type> const_iterator;

      typedef std::reverse_iterator<iterator>       reverse_iterator;
      typedef std::reverse_iterator<const_iterator> const_reverse_iterator;

    private:
      iterator
      _M_insert_(_Const_Base_ptr __x, _Const_Base_ptr __y,
		 const value_type& __v);

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 233. Insertion hints in associative containers.
      iterator
      _M_insert_lower(_Base_ptr __x, _Base_ptr __y, const value_type& __v);

      iterator
      _M_insert_equal_lower(const value_type& __x);

      _Link_type
      _M_copy(_Const_Link_type __x, _Link_type __p);

      void
      _M_erase(_Link_type __x);

      iterator
      _M_lower_bound(_Link_type __x, _Link_type __y,
		     const _Key& __k);

      const_iterator
      _M_lower_bound(_Const_Link_type __x, _Const_Link_type __y,
		     const _Key& __k) const;

      iterator
      _M_upper_bound(_Link_type __x, _Link_type __y,
		     const _Key& __k);

      const_iterator
      _M_upper_bound(_Const_Link_type __x, _Const_Link_type __y,
		     const _Key& __k) const;

    public:
      // allocation/deallocation
      _Rb_tree() { }

      _Rb_tree(const _Compare& __comp,
	       const allocator_type& __a = allocator_type())
      : _M_impl(__comp, __a) { }

      _Rb_tree(const _Rb_tree& __x)
      : _M_impl(__x._M_impl._M_key_compare, __x._M_get_Node_allocator())
      {
	if (__x._M_root() != 0)
	  {
	    _M_root() = _M_copy(__x._M_begin(), _M_end());
	    _M_leftmost() = _S_minimum(_M_root());
	    _M_rightmost() = _S_maximum(_M_root());
	    _M_impl._M_node_count = __x._M_impl._M_node_count;
	  }
      }

#ifdef __GXX_EXPERIMENTAL_CXX0X__
      _Rb_tree(_Rb_tree&& __x);
#endif

      ~_Rb_tree()
      { _M_erase(_M_begin()); }

      _Rb_tree&
      operator=(const _Rb_tree& __x);

      // Accessors.
      _Compare
      key_comp() const
      { return _M_impl._M_key_compare; }

      iterator
      begin()
      { 
	return iterator(static_cast<_Link_type>
			(this->_M_impl._M_header._M_left));
      }

      const_iterator
      begin() const
      { 
	return const_iterator(static_cast<_Const_Link_type>
			      (this->_M_impl._M_header._M_left));
      }

      iterator
      end()
      { return iterator(static_cast<_Link_type>(&this->_M_impl._M_header)); }

      const_iterator
      end() const
      { 
	return const_iterator(static_cast<_Const_Link_type>
			      (&this->_M_impl._M_header));
      }

      reverse_iterator
      rbegin()
      { return reverse_iterator(end()); }

      const_reverse_iterator
      rbegin() const
      { return const_reverse_iterator(end()); }

      reverse_iterator
      rend()
      { return reverse_iterator(begin()); }

      const_reverse_iterator
      rend() const
      { return const_reverse_iterator(begin()); }

      bool
      empty() const
      { return _M_impl._M_node_count == 0; }

      size_type
      size() const
      { return _M_impl._M_node_count; }

      size_type
      max_size() const
      { return get_allocator().max_size(); }

      void
#ifdef __GXX_EXPERIMENTAL_CXX0X__
      swap(_Rb_tree&& __t);
#else
      swap(_Rb_tree& __t);      
#endif

      // Insert/erase.
      pair<iterator, bool>
      _M_insert_unique(const value_type& __x);

      iterator
      _M_insert_equal(const value_type& __x);

      iterator
      _M_insert_unique_(const_iterator __position, const value_type& __x);

      iterator
      _M_insert_equal_(const_iterator __position, const value_type& __x);

      template<typename _InputIterator>
        void
        _M_insert_unique(_InputIterator __first, _InputIterator __last);

      template<typename _InputIterator>
        void
        _M_insert_equal(_InputIterator __first, _InputIterator __last);

      void
      erase(iterator __position);

      void
      erase(const_iterator __position);

      size_type
      erase(const key_type& __x);

      void
      erase(iterator __first, iterator __last);

      void
      erase(const_iterator __first, const_iterator __last);

      void
      erase(const key_type* __first, const key_type* __last);

      void
      clear()
      {
        _M_erase(_M_begin());
        _M_leftmost() = _M_end();
        _M_root() = 0;
        _M_rightmost() = _M_end();
        _M_impl._M_node_count = 0;
      }

      // Set operations.
      iterator
      find(const key_type& __k);

      const_iterator
      find(const key_type& __k) const;

      size_type
      count(const key_type& __k) const;

      iterator
      lower_bound(const key_type& __k)
      { return _M_lower_bound(_M_begin(), _M_end(), __k); }

      const_iterator
      lower_bound(const key_type& __k) const
      { return _M_lower_bound(_M_begin(), _M_end(), __k); }

      iterator
      upper_bound(const key_type& __k)
      { return _M_upper_bound(_M_begin(), _M_end(), __k); }

      const_iterator
      upper_bound(const key_type& __k) const
      { return _M_upper_bound(_M_begin(), _M_end(), __k); }

      pair<iterator, iterator>
      equal_range(const key_type& __k);

      pair<const_iterator, const_iterator>
      equal_range(const key_type& __k) const;

      // Debugging.
      bool
      __rb_verify() const;
    };

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator==(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	       const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    {
      return __x.size() == __y.size()
	     && std::equal(__x.begin(), __x.end(), __y.begin());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator<(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	      const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    {
      return std::lexicographical_compare(__x.begin(), __x.end(), 
					  __y.begin(), __y.end());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator!=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	       const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    { return !(__x == __y); }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator>(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	      const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    { return __y < __x; }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator<=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	       const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    { return !(__y < __x); }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline bool
    operator>=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	       const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    { return !(__x < __y); }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    inline void
    swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x,
	 _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __y)
    { __x.swap(__y); }

#ifdef __GXX_EXPERIMENTAL_CXX0X__
  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _Rb_tree(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&& __x)
    : _M_impl(__x._M_impl._M_key_compare, __x._M_get_Node_allocator())
    {
      if (__x._M_root() != 0)
	{
	  _M_root() = __x._M_root();
	  _M_leftmost() = __x._M_leftmost();
	  _M_rightmost() = __x._M_rightmost();
	  _M_root()->_M_parent = _M_end();

	  __x._M_root() = 0;
	  __x._M_leftmost() = __x._M_end();
	  __x._M_rightmost() = __x._M_end();

	  this->_M_impl._M_node_count = __x._M_impl._M_node_count;
	  __x._M_impl._M_node_count = 0;
	}
    }
#endif

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    operator=(const _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __x)
    {
      if (this != &__x)
	{
	  // Note that _Key may be a constant type.
	  clear();
	  _M_impl._M_key_compare = __x._M_impl._M_key_compare;
	  if (__x._M_root() != 0)
	    {
	      _M_root() = _M_copy(__x._M_begin(), _M_end());
	      _M_leftmost() = _S_minimum(_M_root());
	      _M_rightmost() = _S_maximum(_M_root());
	      _M_impl._M_node_count = __x._M_impl._M_node_count;
	    }
	}
      return *this;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_(_Const_Base_ptr __x, _Const_Base_ptr __p, const _Val& __v)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
			    || _M_impl._M_key_compare(_KeyOfValue()(__v), 
						      _S_key(__p)));

      _Link_type __z = _M_create_node(__v);

      _Rb_tree_insert_and_rebalance(__insert_left, __z,
				    const_cast<_Base_ptr>(__p),  
				    this->_M_impl._M_header);
      ++_M_impl._M_node_count;
      return iterator(__z);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_lower(_Base_ptr __x, _Base_ptr __p, const _Val& __v)
    {
      bool __insert_left = (__x != 0 || __p == _M_end()
			    || !_M_impl._M_key_compare(_S_key(__p),
						       _KeyOfValue()(__v)));

      _Link_type __z = _M_create_node(__v);

      _Rb_tree_insert_and_rebalance(__insert_left, __z, __p,  
				    this->_M_impl._M_header);
      ++_M_impl._M_node_count;
      return iterator(__z);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_equal_lower(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      while (__x != 0)
	{
	  __y = __x;
	  __x = !_M_impl._M_key_compare(_S_key(__x), _KeyOfValue()(__v)) ?
	        _S_left(__x) : _S_right(__x);
	}
      return _M_insert_lower(__x, __y, __v);
    }

  template<typename _Key, typename _Val, typename _KoV,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::_Link_type
    _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::
    _M_copy(_Const_Link_type __x, _Link_type __p)
    {
      // Structural copy.  __x and __p must be non-null.
      _Link_type __top = _M_clone_node(__x);
      __top->_M_parent = __p;

      try
	{
	  if (__x->_M_right)
	    __top->_M_right = _M_copy(_S_right(__x), __top);
	  __p = __top;
	  __x = _S_left(__x);

	  while (__x != 0)
	    {
	      _Link_type __y = _M_clone_node(__x);
	      __p->_M_left = __y;
	      __y->_M_parent = __p;
	      if (__x->_M_right)
		__y->_M_right = _M_copy(_S_right(__x), __y);
	      __p = __y;
	      __x = _S_left(__x);
	    }
	}
      catch(...)
	{
	  _M_erase(__top);
	  __throw_exception_again;
	}
      return __top;
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_erase(_Link_type __x)
    {
      // Erase without rebalancing.
      while (__x != 0)
	{
	  _M_erase(_S_right(__x));
	  _Link_type __y = _S_left(__x);
	  _M_destroy_node(__x);
	  __x = __y;
	}
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue,
		      _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_lower_bound(_Link_type __x, _Link_type __y,
		   const _Key& __k)
    {
      while (__x != 0)
	if (!_M_impl._M_key_compare(_S_key(__x), __k))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      return iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue,
		      _Compare, _Alloc>::const_iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_lower_bound(_Const_Link_type __x, _Const_Link_type __y,
		   const _Key& __k) const
    {
      while (__x != 0)
	if (!_M_impl._M_key_compare(_S_key(__x), __k))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      return const_iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue,
		      _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_upper_bound(_Link_type __x, _Link_type __y,
		   const _Key& __k)
    {
      while (__x != 0)
	if (_M_impl._M_key_compare(__k, _S_key(__x)))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      return iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue,
		      _Compare, _Alloc>::const_iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_upper_bound(_Const_Link_type __x, _Const_Link_type __y,
		   const _Key& __k) const
    {
      while (__x != 0)
	if (_M_impl._M_key_compare(__k, _S_key(__x)))
	  __y = __x, __x = _S_left(__x);
	else
	  __x = _S_right(__x);
      return const_iterator(__y);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
			   _Compare, _Alloc>::iterator,
	 typename _Rb_tree<_Key, _Val, _KeyOfValue,
			   _Compare, _Alloc>::iterator>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    equal_range(const _Key& __k)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      while (__x != 0)
	{
	  if (_M_impl._M_key_compare(_S_key(__x), __k))
	    __x = _S_right(__x);
	  else if (_M_impl._M_key_compare(__k, _S_key(__x)))
	    __y = __x, __x = _S_left(__x);
	  else
	    {
	      _Link_type __xu(__x), __yu(__y);
	      __y = __x, __x = _S_left(__x);
	      __xu = _S_right(__xu);
	      return pair<iterator,
		          iterator>(_M_lower_bound(__x, __y, __k),
				    _M_upper_bound(__xu, __yu, __k));
	    }
	}
      return pair<iterator, iterator>(iterator(__y),
				      iterator(__y));
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
			   _Compare, _Alloc>::const_iterator,
	 typename _Rb_tree<_Key, _Val, _KeyOfValue,
			   _Compare, _Alloc>::const_iterator>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    equal_range(const _Key& __k) const
    {
      _Const_Link_type __x = _M_begin();
      _Const_Link_type __y = _M_end();
      while (__x != 0)
	{
	  if (_M_impl._M_key_compare(_S_key(__x), __k))
	    __x = _S_right(__x);
	  else if (_M_impl._M_key_compare(__k, _S_key(__x)))
	    __y = __x, __x = _S_left(__x);
	  else
	    {
	      _Const_Link_type __xu(__x), __yu(__y);
	      __y = __x, __x = _S_left(__x);
	      __xu = _S_right(__xu);
	      return pair<const_iterator,
		          const_iterator>(_M_lower_bound(__x, __y, __k),
					  _M_upper_bound(__xu, __yu, __k));
	    }
	}
      return pair<const_iterator, const_iterator>(const_iterator(__y),
						  const_iterator(__y));
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    void
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
#ifdef __GXX_EXPERIMENTAL_CXX0X__
    swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>&& __t)
#else
    swap(_Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>& __t)
#endif
    {
      if (_M_root() == 0)
	{
	  if (__t._M_root() != 0)
	    {
	      _M_root() = __t._M_root();
	      _M_leftmost() = __t._M_leftmost();
	      _M_rightmost() = __t._M_rightmost();
	      _M_root()->_M_parent = _M_end();
	      
	      __t._M_root() = 0;
	      __t._M_leftmost() = __t._M_end();
	      __t._M_rightmost() = __t._M_end();
	    }
	}
      else if (__t._M_root() == 0)
	{
	  __t._M_root() = _M_root();
	  __t._M_leftmost() = _M_leftmost();
	  __t._M_rightmost() = _M_rightmost();
	  __t._M_root()->_M_parent = __t._M_end();
	  
	  _M_root() = 0;
	  _M_leftmost() = _M_end();
	  _M_rightmost() = _M_end();
	}
      else
	{
	  std::swap(_M_root(),__t._M_root());
	  std::swap(_M_leftmost(),__t._M_leftmost());
	  std::swap(_M_rightmost(),__t._M_rightmost());
	  
	  _M_root()->_M_parent = _M_end();
	  __t._M_root()->_M_parent = __t._M_end();
	}
      // No need to swap header's color as it does not change.
      std::swap(this->_M_impl._M_node_count, __t._M_impl._M_node_count);
      std::swap(this->_M_impl._M_key_compare, __t._M_impl._M_key_compare);
      
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 431. Swapping containers with unequal allocators.
      std::__alloc_swap<_Node_allocator>::
	_S_do_it(_M_get_Node_allocator(), __t._M_get_Node_allocator());
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    pair<typename _Rb_tree<_Key, _Val, _KeyOfValue,
			   _Compare, _Alloc>::iterator, bool>
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_unique(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      bool __comp = true;
      while (__x != 0)
	{
	  __y = __x;
	  __comp = _M_impl._M_key_compare(_KeyOfValue()(__v), _S_key(__x));
	  __x = __comp ? _S_left(__x) : _S_right(__x);
	}
      iterator __j = iterator(__y);
      if (__comp)
	{
	  if (__j == begin())
	    return pair<iterator, bool>(_M_insert_(__x, __y, __v), true);
	  else
	    --__j;
	}
      if (_M_impl._M_key_compare(_S_key(__j._M_node), _KeyOfValue()(__v)))
	return pair<iterator, bool>(_M_insert_(__x, __y, __v), true);
      return pair<iterator, bool>(__j, false);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_equal(const _Val& __v)
    {
      _Link_type __x = _M_begin();
      _Link_type __y = _M_end();
      while (__x != 0)
	{
	  __y = __x;
	  __x = _M_impl._M_key_compare(_KeyOfValue()(__v), _S_key(__x)) ?
	        _S_left(__x) : _S_right(__x);
	}
      return _M_insert_(__x, __y, __v);
    }

  template<typename _Key, typename _Val, typename _KeyOfValue,
           typename _Compare, typename _Alloc>
    typename _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::iterator
    _Rb_tree<_Key, _Val, _KeyOfValue, _Compare, _Alloc>::
    _M_insert_unique_(const_iterator __position, const _Val& __v)
    {
      // end()
      if (__position._M_node == _M_end())
	{
	  if (size() > 0
	      && _M_impl._M_key_compare(_S_key(_M_rightmost()), 
					_KeyOfValue()(__v)))
	    return _M_insert_(0, _M_rightmost(), __v);
	  else
	    return _M_insert_unique(__v).first;
	}
      else if (_M_impl._M_key_compare(_KeyOfValue()(__v),
				      _S_key(__position._M_node)))
	{
	  // First, try before...
	  const_iterator __before = __position;
	  if (__position._M_node == _M_leftmost()) // begin()
	    return _M_insert_(_M_leftmost(), _M_leftmost(), __v);
	  else if (_M_impl._M_key_compare(_S_key((--__before)._M_node), 
					  _KeyOfValue()(__v)))
	    {
	      if (_S_right(__before._M_node) == 0)
		return _M_inser