text: //  Boost operators.hpp header file  ----------------------------------------//
  
  //  (C) Copyright David Abrahams, Jeremy Siek, Daryle Walker 1999-2001.
  //  Distributed under the Boost Software License, Version 1.0. (See
  //  accompanying file LICENSE_1_0.txt or copy at
  //  http://www.boost.org/LICENSE_1_0.txt)
  
  //  See http://www.boost.org/libs/utility/operators.htm for documentation.
  
  //  Revision History
  //  16 Dec 10 Limit warning suppression for 4284 to older versions of VC++
  //            (Matthew Bradbury, fixes #4432)
  //  07 Aug 08 Added "euclidean" spelling. (Daniel Frey)
  //  03 Apr 08 Make sure "convertible to bool" is sufficient
  //            for T::operator<, etc. (Daniel Frey)
  //  24 May 07 Changed empty_base to depend on T, see
  //            http://svn.boost.org/trac/boost/ticket/979
  //  21 Oct 02 Modified implementation of operators to allow compilers with a
  //            correct named return value optimization (NRVO) to produce optimal
  //            code.  (Daniel Frey)
  //  02 Dec 01 Bug fixed in random_access_iteratable.  (Helmut Zeisel)
  //  28 Sep 01 Factored out iterator operator groups.  (Daryle Walker)
  //  27 Aug 01 'left' form for non commutative operators added;
  //            additional classes for groups of related operators added;
  //            workaround for empty base class optimization
  //            bug of GCC 3.0 (Helmut Zeisel)
  //  25 Jun 01 output_iterator_helper changes: removed default template 
  //            parameters, added support for self-proxying, additional 
  //            documentation and tests (Aleksey Gurtovoy)
  //  29 May 01 Added operator classes for << and >>.  Added input and output
  //            iterator helper classes.  Added classes to connect equality and
  //            relational operators.  Added classes for groups of related
  //            operators.  Reimplemented example operator and iterator helper
  //            classes in terms of the new groups.  (Daryle Walker, with help
  //            from Alexy Gurtovoy)
  //  11 Feb 01 Fixed bugs in the iterator helpers which prevented explicitly
  //            supplied arguments from actually being used (Dave Abrahams)
  //  04 Jul 00 Fixed NO_OPERATORS_IN_NAMESPACE bugs, major cleanup and
  //            refactoring of compiler workarounds, additional documentation
  //            (Alexy Gurtovoy and Mark Rodgers with some help and prompting from
  //            Dave Abrahams) 
  //  28 Jun 00 General cleanup and integration of bugfixes from Mark Rodgers and
  //            Jeremy Siek (Dave Abrahams)
  //  20 Jun 00 Changes to accommodate Borland C++Builder 4 and Borland C++ 5.5
  //            (Mark Rodgers)
  //  20 Jun 00 Minor fixes to the prior revision (Aleksey Gurtovoy)
  //  10 Jun 00 Support for the base class chaining technique was added
  //            (Aleksey Gurtovoy). See documentation and the comments below 
  //            for the details. 
  //  12 Dec 99 Initial version with iterator operators (Jeremy Siek)
  //  18 Nov 99 Change name "divideable" to "dividable", remove unnecessary
  //            specializations of dividable, subtractable, modable (Ed Brey) 
  //  17 Nov 99 Add comments (Beman Dawes)
  //            Remove unnecessary specialization of operators<> (Ed Brey)
  //  15 Nov 99 Fix less_than_comparable<T,U> second operand type for first two
  //            operators.(Beman Dawes)
  //  12 Nov 99 Add operators templates (Ed Brey)
  //  11 Nov 99 Add single template parameter version for compilers without
  //            partial specialization (Beman Dawes)
  //  10 Nov 99 Initial version
  
  // 10 Jun 00:
  // An additional optional template parameter was added to most of 
  // operator templates to support the base class chaining technique (see 
  // documentation for the details). Unfortunately, a straightforward
  // implementation of this change would have broken compatibility with the
  // previous version of the library by making it impossible to use the same
  // template name (e.g. 'addable') for both the 1- and 2-argument versions of
  // an operator template. This implementation solves the backward-compatibility
  // issue at the cost of some simplicity.
  //
  // One of the complications is an existence of special auxiliary class template
  // 'is_chained_base<>' (see 'detail' namespace below), which is used
  // to determine whether its template parameter is a library's operator template
  // or not. You have to specialize 'is_chained_base<>' for each new 
  // operator template you add to the library.
  //
  // However, most of the non-trivial implementation details are hidden behind 
  // several local macros defined below, and as soon as you understand them,
  // you understand the whole library implementation. 
  
  #ifndef BOOST_OPERATORS_HPP
  #define BOOST_OPERATORS_HPP
  
  #include <boost/config.hpp>
  #include <boost/iterator.hpp>
  #include <boost/detail/workaround.hpp>
  
  #if defined(__sgi) && !defined(__GNUC__)
  #   pragma set woff 1234
  #endif
  
  #if BOOST_WORKAROUND(BOOST_MSVC, < 1600)
  #   pragma warning( disable : 4284 ) // complaint about return type of 
  #endif                               // operator-> not begin a UDT
  
  namespace boost {
  namespace detail {
  
  template <typename T> class empty_base {};
  
  } // namespace detail
  } // namespace boost
  
  // In this section we supply the xxxx1 and xxxx2 forms of the operator
  // templates, which are explicitly targeted at the 1-type-argument and
  // 2-type-argument operator forms, respectively. Some compilers get confused
  // when inline friend functions are overloaded in namespaces other than the
  // global namespace. When BOOST_NO_OPERATORS_IN_NAMESPACE is defined, all of
  // these templates must go in the global namespace.
  
  #ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
  namespace boost
  {
  #endif
  
  //  Basic operator classes (contributed by Dave Abrahams) ------------------//
  
  //  Note that friend functions defined in a class are implicitly inline.
  //  See the C++ std, 11.4 [class.friend] paragraph 5
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct less_than_comparable2 : B
  {
       friend bool operator<=(const T& x, const U& y) { return !static_cast<bool>(x > y); }
       friend bool operator>=(const T& x, const U& y) { return !static_cast<bool>(x < y); }
       friend bool operator>(const U& x, const T& y)  { return y < x; }
       friend bool operator<(const U& x, const T& y)  { return y > x; }
       friend bool operator<=(const U& x, const T& y) { return !static_cast<bool>(y < x); }
       friend bool operator>=(const U& x, const T& y) { return !static_cast<bool>(y > x); }
  };
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct less_than_comparable1 : B
  {
       friend bool operator>(const T& x, const T& y)  { return y < x; }
       friend bool operator<=(const T& x, const T& y) { return !static_cast<bool>(y < x); }
       friend bool operator>=(const T& x, const T& y) { return !static_cast<bool>(x < y); }
  };
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct equality_comparable2 : B
  {
       friend bool operator==(const U& y, const T& x) { return x == y; }
       friend bool operator!=(const U& y, const T& x) { return !static_cast<bool>(x == y); }
       friend bool operator!=(const T& y, const U& x) { return !static_cast<bool>(y == x); }
  };
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct equality_comparable1 : B
  {
       friend bool operator!=(const T& x, const T& y) { return !static_cast<bool>(x == y); }
  };
  
  // A macro which produces "name_2left" from "name".
  #define BOOST_OPERATOR2_LEFT(name) name##2##_##left
  
  //  NRVO-friendly implementation (contributed by Daniel Frey) ---------------//
  
  #if defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  // This is the optimal implementation for ISO/ANSI C++,
  // but it requires the compiler to implement the NRVO.
  // If the compiler has no NRVO, this is the best symmetric
  // implementation available.
  
  #define BOOST_BINARY_OPERATOR_COMMUTATIVE( NAME, OP )                         \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >        \
  struct NAME##2 : B                                                            \
  {                                                                             \
    friend T operator OP( const T& lhs, const U& rhs )                          \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                              \
    friend T operator OP( const U& lhs, const T& rhs )                          \
      { T nrv( rhs ); nrv OP##= lhs; return nrv; }                              \
  };                                                                            \
                                                                                \
  template <class T, class B = ::boost::detail::empty_base<T> >                 \
  struct NAME##1 : B                                                            \
  {                                                                             \
    friend T operator OP( const T& lhs, const T& rhs )                          \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                              \
  };
  
  #define BOOST_BINARY_OPERATOR_NON_COMMUTATIVE( NAME, OP )               \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >  \
  struct NAME##2 : B                                                      \
  {                                                                       \
    friend T operator OP( const T& lhs, const U& rhs )                    \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                        \
  };                                                                      \
                                                                          \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >  \
  struct BOOST_OPERATOR2_LEFT(NAME) : B                                   \
  {                                                                       \
    friend T operator OP( const U& lhs, const T& rhs )                    \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                        \
  };                                                                      \
                                                                          \
  template <class T, class B = ::boost::detail::empty_base<T> >           \
  struct NAME##1 : B                                                      \
  {                                                                       \
    friend T operator OP( const T& lhs, const T& rhs )                    \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                        \
  };
  
  #else // defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  // For compilers without NRVO the following code is optimal, but not
  // symmetric!  Note that the implementation of
  // BOOST_OPERATOR2_LEFT(NAME) only looks cool, but doesn't provide
  // optimization opportunities to the compiler :)
  
  #define BOOST_BINARY_OPERATOR_COMMUTATIVE( NAME, OP )                   \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >  \
  struct NAME##2 : B                                                      \
  {                                                                       \
    friend T operator OP( T lhs, const U& rhs ) { return lhs OP##= rhs; } \
    friend T operator OP( const U& lhs, T rhs ) { return rhs OP##= lhs; } \
  };                                                                      \
                                                                          \
  template <class T, class B = ::boost::detail::empty_base<T> >           \
  struct NAME##1 : B                                                      \
  {                                                                       \
    friend T operator OP( T lhs, const T& rhs ) { return lhs OP##= rhs; } \
  };
  
  #define BOOST_BINARY_OPERATOR_NON_COMMUTATIVE( NAME, OP )               \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >  \
  struct NAME##2 : B                                                      \
  {                                                                       \
    friend T operator OP( T lhs, const U& rhs ) { return lhs OP##= rhs; } \
  };                                                                      \
                                                                          \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >  \
  struct BOOST_OPERATOR2_LEFT(NAME) : B                                   \
  {                                                                       \
    friend T operator OP( const U& lhs, const T& rhs )                    \
      { return T( lhs ) OP##= rhs; }                                      \
  };                                                                      \
                                                                          \
  template <class T, class B = ::boost::detail::empty_base<T> >           \
  struct NAME##1 : B                                                      \
  {                                                                       \
    friend T operator OP( T lhs, const T& rhs ) { return lhs OP##= rhs; } \
  };
  
  #endif // defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  BOOST_BINARY_OPERATOR_COMMUTATIVE( multipliable, * )
  BOOST_BINARY_OPERATOR_COMMUTATIVE( addable, + )
  BOOST_BINARY_OPERATOR_NON_COMMUTATIVE( subtractable, - )
  BOOST_BINARY_OPERATOR_NON_COMMUTATIVE( dividable, / )
  BOOST_BINARY_OPERATOR_NON_COMMUTATIVE( modable, % )
  BOOST_BINARY_OPERATOR_COMMUTATIVE( xorable, ^ )
  BOOST_BINARY_OPERATOR_COMMUTATIVE( andable, & )
  BOOST_BINARY_OPERATOR_COMMUTATIVE( orable, | )
  
  #undef BOOST_BINARY_OPERATOR_COMMUTATIVE
  #undef BOOST_BINARY_OPERATOR_NON_COMMUTATIVE
  #undef BOOST_OPERATOR2_LEFT
  
  //  incrementable and decrementable contributed by Jeremy Siek
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct incrementable : B
  {
    friend T operator++(T& x, int)
    {
      incrementable_type nrv(x);
      ++x;
      return nrv;
    }
  private: // The use of this typedef works around a Borland bug
    typedef T incrementable_type;
  };
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct decrementable : B
  {
    friend T operator--(T& x, int)
    {
      decrementable_type nrv(x);
      --x;
      return nrv;
    }
  private: // The use of this typedef works around a Borland bug
    typedef T decrementable_type;
  };
  
  //  Iterator operator classes (contributed by Jeremy Siek) ------------------//
  
  template <class T, class P, class B = ::boost::detail::empty_base<T> >
  struct dereferenceable : B
  {
    P operator->() const
    { 
      return &*static_cast<const T&>(*this); 
    }
  };
  
  template <class T, class I, class R, class B = ::boost::detail::empty_base<T> >
  struct indexable : B
  {
    R operator[](I n) const
    {
      return *(static_cast<const T&>(*this) + n);
    }
  };
  
  //  More operator classes (contributed by Daryle Walker) --------------------//
  //  (NRVO-friendly implementation contributed by Daniel Frey) ---------------//
  
  #if defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  #define BOOST_BINARY_OPERATOR( NAME, OP )                                     \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >        \
  struct NAME##2 : B                                                            \
  {                                                                             \
    friend T operator OP( const T& lhs, const U& rhs )                          \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                              \
  };                                                                            \
                                                                                \
  template <class T, class B = ::boost::detail::empty_base<T> >                 \
  struct NAME##1 : B                                                            \
  {                                                                             \
    friend T operator OP( const T& lhs, const T& rhs )                          \
      { T nrv( lhs ); nrv OP##= rhs; return nrv; }                              \
  };
  
  #else // defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  #define BOOST_BINARY_OPERATOR( NAME, OP )                                     \
  template <class T, class U, class B = ::boost::detail::empty_base<T> >        \
  struct NAME##2 : B                                                            \
  {                                                                             \
    friend T operator OP( T lhs, const U& rhs ) { return lhs OP##= rhs; }       \
  };                                                                            \
                                                                                \
  template <class T, class B = ::boost::detail::empty_base<T> >                 \
  struct NAME##1 : B                                                            \
  {                                                                             \
    friend T operator OP( T lhs, const T& rhs ) { return lhs OP##= rhs; }       \
  };
  
  #endif // defined(BOOST_HAS_NRVO) || defined(BOOST_FORCE_SYMMETRIC_OPERATORS)
  
  BOOST_BINARY_OPERATOR( left_shiftable, << )
  BOOST_BINARY_OPERATOR( right_shiftable, >> )
  
  #undef BOOST_BINARY_OPERATOR
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct equivalent2 : B
  {
    friend bool operator==(const T& x, const U& y)
    {
      return !static_cast<bool>(x < y) && !static_cast<bool>(x > y);
    }
  };
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct equivalent1 : B
  {
    friend bool operator==(const T&x, const T&y)
    {
      return !static_cast<bool>(x < y) && !static_cast<bool>(y < x);
    }
  };
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct partially_ordered2 : B
  {
    friend bool operator<=(const T& x, const U& y)
      { return static_cast<bool>(x < y) || static_cast<bool>(x == y); }
    friend bool operator>=(const T& x, const U& y)
      { return static_cast<bool>(x > y) || static_cast<bool>(x == y); }
    friend bool operator>(const U& x, const T& y)
      { return y < x; }
    friend bool operator<(const U& x, const T& y)
      { return y > x; }
    friend bool operator<=(const U& x, const T& y)
      { return static_cast<bool>(y > x) || static_cast<bool>(y == x); }
    friend bool operator>=(const U& x, const T& y)
      { return static_cast<bool>(y < x) || static_cast<bool>(y == x); }
  };
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct partially_ordered1 : B
  {
    friend bool operator>(const T& x, const T& y)
      { return y < x; }
    friend bool operator<=(const T& x, const T& y)
      { return static_cast<bool>(x < y) || static_cast<bool>(x == y); }
    friend bool operator>=(const T& x, const T& y)
      { return static_cast<bool>(y < x) || static_cast<bool>(x == y); }
  };
  
  //  Combined operator classes (contributed by Daryle Walker) ----------------//
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct totally_ordered2
      : less_than_comparable2<T, U
      , equality_comparable2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct totally_ordered1
      : less_than_comparable1<T
      , equality_comparable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct additive2
      : addable2<T, U
      , subtractable2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct additive1
      : addable1<T
      , subtractable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct multiplicative2
      : multipliable2<T, U
      , dividable2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct multiplicative1
      : multipliable1<T
      , dividable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct integer_multiplicative2
      : multiplicative2<T, U
      , modable2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct integer_multiplicative1
      : multiplicative1<T
      , modable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct arithmetic2
      : additive2<T, U
      , multiplicative2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct arithmetic1
      : additive1<T
      , multiplicative1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct integer_arithmetic2
      : additive2<T, U
      , integer_multiplicative2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct integer_arithmetic1
      : additive1<T
      , integer_multiplicative1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct bitwise2
      : xorable2<T, U
      , andable2<T, U
      , orable2<T, U, B
        > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct bitwise1
      : xorable1<T
      , andable1<T
      , orable1<T, B
        > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct unit_steppable
      : incrementable<T
      , decrementable<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct shiftable2
      : left_shiftable2<T, U
      , right_shiftable2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct shiftable1
      : left_shiftable1<T
      , right_shiftable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct ring_operators2
      : additive2<T, U
      , subtractable2_left<T, U
      , multipliable2<T, U, B
        > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct ring_operators1
      : additive1<T
      , multipliable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct ordered_ring_operators2
      : ring_operators2<T, U
      , totally_ordered2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct ordered_ring_operators1
      : ring_operators1<T
      , totally_ordered1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct field_operators2
      : ring_operators2<T, U
      , dividable2<T, U
      , dividable2_left<T, U, B
        > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct field_operators1
      : ring_operators1<T
      , dividable1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct ordered_field_operators2
      : field_operators2<T, U
      , totally_ordered2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct ordered_field_operators1
      : field_operators1<T
      , totally_ordered1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct euclidian_ring_operators2
      : ring_operators2<T, U
      , dividable2<T, U
      , dividable2_left<T, U
      , modable2<T, U
      , modable2_left<T, U, B
        > > > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct euclidian_ring_operators1
      : ring_operators1<T
      , dividable1<T
      , modable1<T, B
        > > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct ordered_euclidian_ring_operators2
      : totally_ordered2<T, U
      , euclidian_ring_operators2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct ordered_euclidian_ring_operators1
      : totally_ordered1<T
      , euclidian_ring_operators1<T, B
        > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct euclidean_ring_operators2
      : ring_operators2<T, U
      , dividable2<T, U
      , dividable2_left<T, U
      , modable2<T, U
      , modable2_left<T, U, B
        > > > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct euclidean_ring_operators1
      : ring_operators1<T
      , dividable1<T
      , modable1<T, B
        > > > {};
  
  template <class T, class U, class B = ::boost::detail::empty_base<T> >
  struct ordered_euclidean_ring_operators2
      : totally_ordered2<T, U
      , euclidean_ring_operators2<T, U, B
        > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct ordered_euclidean_ring_operators1
      : totally_ordered1<T
      , euclidean_ring_operators1<T, B
        > > {};
  
  template <class T, class P, class B = ::boost::detail::empty_base<T> >
  struct input_iteratable
      : equality_comparable1<T
      , incrementable<T
      , dereferenceable<T, P, B
        > > > {};
  
  template <class T, class B = ::boost::detail::empty_base<T> >
  struct output_iteratable
      : incrementable<T, B
        > {};
  
  template <class T, class P, class B = ::boost::detail::empty_base<T> >
  struct forward_iteratable
      : input_iteratable<T, P, B
        > {};
  
  template <class T, class P, class B = ::boost::detail::empty_base<T> >
  struct bidirectional_iteratable
      : forward_iteratable<T, P
      , decrementable<T, B
        > > {};
  
  //  To avoid repeated derivation from equality_comparable,
  //  which is an indirect base class of bidirectional_iterable,
  //  random_access_iteratable must not be derived from totally_ordered1
  //  but from less_than_comparable1 only. (Helmut Zeisel, 02-Dec-2001)
  template <class T, class P, class D, class R, class B = ::boost::detail::empty_base<T> >
  struct random_access_iteratable
      : bidirectional_iteratable<T, P
      , less_than_comparable1<T
      , additive2<T, D
      , indexable<T, D, R, B
        > > > > {};
  
  #ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
  } // namespace boost
  #endif // BOOST_NO_OPERATORS_IN_NAMESPACE
  
  
  // BOOST_IMPORT_TEMPLATE1 .. BOOST_IMPORT_TEMPLATE4 -
  //
  // When BOOST_NO_OPERATORS_IN_NAMESPACE is defined we need a way to import an
  // operator template into the boost namespace. BOOST_IMPORT_TEMPLATE1 is used
  // for one-argument forms of operator templates; BOOST_IMPORT_TEMPLATE2 for
  // two-argument forms. Note that these macros expect to be invoked from within
  // boost.
  
  #ifndef BOOST_NO_OPERATORS_IN_NAMESPACE
  
    // The template is already in boost so we have nothing to do.
  # define BOOST_IMPORT_TEMPLATE4(template_name)
  # define BOOST_IMPORT_TEMPLATE3(template_name)
  # define BOOST_IMPORT_TEMPLATE2(template_name)
  # define BOOST_IMPORT_TEMPLATE1(template_name)
  
  #else // BOOST_NO_OPERATORS_IN_NAMESPACE
  
  #  ifndef BOOST_NO_USING_TEMPLATE
  
       // Bring the names in with a using-declaration
       // to avoid stressing the compiler.
  #    define BOOST_IMPORT_TEMPLATE4(template_name) using ::template_name;
  #    define BOOST_IMPORT_TEMPLATE3(template_name) using ::template_name;
  #    define BOOST_IMPORT_TEMPLATE2(template_name) using ::template_name;
  #    define BOOST_IMPORT_TEMPLATE1(template_name) using ::template_name;
  
  #  else
  
       // Otherwise, because a Borland C++ 5.5 bug prevents a using declaration
       // from working, we are forced to use inheritance for that compiler.
  #    define BOOST_IMPORT_TEMPLATE4(template_name)                                             \
       template <class T, class U, class V, class W, class B = ::boost::detail::empty_base<T> > \
       struct template_name : ::template_name<T, U, V, W, B> {};
  
  #    define BOOST_IMPORT_TEMPLATE3(template_name)                                    \
       template <class T, class U, class V, class B = ::boost::detail::empty_base<T> > \
       struct template_name : ::template_name<T, U, V, B> {};
  
  #    define BOOST_IMPORT_TEMPLATE2(template_name)                           \
       template <class T, class U, class B = ::boost::detail::empty_base<T> > \
       struct template_name : ::template_name<T, U, B> {};
  
  #    define BOOST_IMPORT_TEMPLATE1(template_name)                  \
       template <class T, class B = ::boost::detail::empty_base<T> > \
       struct template_name : ::template_name<T, B> {};
  
  #  endif // BOOST_NO_USING_TEMPLATE
  
  #endif // BOOST_NO_OPERATORS_IN_NAMESPACE
  
  //
  // Here's where we put it all together, defining the xxxx forms of the templates
  // in namespace boost. We also define specializations of is_chained_base<> for
  // the xxxx, xxxx1, and xxxx2 templates, importing them into boost:: as
  // necessary.
  //
  
  // is_chained_base<> - a traits class used to distinguish whether an operator
  // template argument is being used for base class chaining, or is specifying a
  // 2nd argument type.
  
  namespace boost {
  // A type parameter is used instead of a plain bool because Borland's compiler
  // didn't cope well with the more obvious non-type template parameter.
  namespace detail {
    struct true_t {};
    struct false_t {};
  } // namespace detail
  
  // Unspecialized version assumes that most types are not being used for base
  // class chaining. We specialize for the operator templates defined in this
  // library.
  template<class T> struct is_chained_base {
    typedef ::boost::detail::false_t value;
  };
  
  } // namespace boost
  
  // Import a 4-type-argument operator template into boost (if necessary) and
  // provide a specialization of 'is_chained_base<>' for it.
  # define BOOST_OPERATOR_TEMPLATE4(template_name4)                     \
    BOOST_IMPORT_TEMPLATE4(template_name4)                              \
    template<class T, class U, class V, class W, class B>               \
    struct is_chained_base< ::boost::template_name4<T, U, V, W, B> > {  \
      typedef ::boost::detail::true_t value;                            \
    };
  
  // Import a 3-type-argument operator template into boost (if necessary) and
  // provide a specialization of 'is_chained_base<>' for it.
  # define BOOST_OPERATOR_TEMPLATE3(template_name3)                     \
    BOOST_IMPORT_TEMPLATE3(template_name3)                              \
    template<class T, class U, class V, class B>                        \
    struct is_chained_base< ::boost::template_name3<T, U, V, B> > {     \
      typedef ::boost::detail::true_t value;                            \
    };
  
  // Import a 2-type-argument operator template into boost (if necessary) and
  // provide a specialization of 'is_chained_base<>' for it.
  # define BOOST_OPERATOR_TEMPLATE2(template_name2)                  \
    BOOST_IMPORT_TEMPLATE2(template_name2)                           \
    template<class T, class U, class B>                              \
    struct is_chained_base< ::boost::template_name2<T, U, B> > {     \
      typedef ::boost::detail::true_t value;                         \
    };
  
  // Import a 1-type-argument operator template into boost (if necessary) and
  // provide a specialization of 'is_chained_base<>' for it.
  # define BOOST_OPERATOR_TEMPLATE1(template_name1)                  \
    BOOST_IMPORT_TEMPLATE1(template_name1)                           \
    template<class T, class B>                                       \
    struct is_chained_base< ::boost::template_name1<T, B> > {        \
      typedef ::boost::detail::true_t value;                         \
    };
  
  // BOOST_OPERATOR_TEMPLATE(template_name) defines template_name<> such that it
  // can be used for specifying both 1-argument and 2-argument forms. Requires the
  // existence of two previously defined class templates named '<template_name>1'
  // and '<template_name>2' which must implement the corresponding 1- and 2-
  // argument forms.
  //
  // The template type parameter O == is_chained_base<U>::value is used to
  // distinguish whether the 2nd argument to <template_name> is being used for
  // base class chaining from another boost operator template or is describing a
  // 2nd operand type. O == true_t only when U is actually an another operator
  // template from the library. Partial specialization is used to select an
  // implementation in terms of either '<template_name>1' or '<template_name>2'.
  //
  
  # define BOOST_OPERATOR_TEMPLATE(template_name)                    \
  template <class T                                                  \
           ,class U = T                                              \
           ,class B = ::boost::detail::empty_base<T>                 \
           ,class O = typename is_chained_base<U>::value             \
           >                                                         \
  struct template_name : template_name##2<T, U, B> {};               \
                                                                     \
  template<class T, class U, class B>                                \
  struct template_name<T, U, B, ::boost::detail::true_t>             \
    : template_name##1<T, U> {};                                     \
                                                                     \
  template <class T, class B>                                        \
  struct template_name<T, T, B, ::boost::detail::false_t>            \
    : template_name##1<T, B> {};                                     \
                                                                     \
  template<class T, class U, class B, class O>                       \
  struct is_chained_base< ::boost::template_name<T, U, B, O> > {     \
    typedef ::boost::detail::true_t value;                           \
  };                                                                 \
                                                                     \
  BOOST_OPERATOR_TEMPLATE2(template_name##2)                         \
  BOOST_OPERATOR_TEMPLATE1(template_name##1)
  
  
  
  namespace boost {
      
  BOOST_OPERATOR_TEMPLATE(less_than_comparable)
  BOOST_OPERATOR_TEMPLATE(equality_comparable)
  BOOST_OPERATOR_TEMPLATE(multipliable)
  BOOST_OPERATOR_TEMPLATE(addable)
  BOOST_OPERATOR_TEMPLATE(subtractable)
  BOOST_OPERATOR_TEMPLATE2(subtractable2_left)
  BOOST_OPERATOR_TEMPLATE(dividable)
  BOOST_OPERATOR_TEMPLATE2(dividable2_left)
  BOOST_OPERATOR_TEMPLATE(modable)
  BOOST_OPERATOR_TEMPLATE2(modable2_left)
  BOOST_OPERATOR_TEMPLATE(xorable)
  BOOST_OPERATOR_TEMPLATE(andable)
  BOOST_OPERATOR_TEMPLATE(orable)
  
  BOOST_OPERATOR_TEMPLATE1(incrementable)
  BOOST_OPERATOR_TEMPLATE1(decrementable)
  
  BOOST_OPERATOR_TEMPLATE2(dereferenceable)
  BOOST_OPERATOR_TEMPLATE3(indexable)
  
  BOOST_OPERATOR_TEMPLATE(left_shiftable)
  BOOST_OPERATOR_TEMPLATE(right_shiftable)
  BOOST_OPERATOR_TEMPLATE(equivalent)
  BOOST_OPERATOR_TEMPLATE(partially_ordered)
  
  BOOST_OPERATOR_TEMPLATE(totally_ordered)
  BOOST_OPERATOR_TEMPLATE(additive)
  BOOST_OPERATOR_TEMPLATE(multiplicative)
  BOOST_OPERATOR_TEMPLATE(integer_multiplicative)
  BOOST_OPERATOR_TEMPLATE(arithmetic)
  BOOST_OPERATOR_TEMPLATE(integer_arithmetic)
  BOOST_OPERATOR_TEMPLATE(bitwise)
  BOOST_OPERATOR_TEMPLATE1(unit_steppable)
  BOOST_OPERATOR_TEMPLATE(shiftable)
  BOOST_OPERATOR_TEMPLATE(ring_operators)
  BOOST_OPERATOR_TEMPLATE(ordered_ring_operators)
  BOOST_OPERATOR_TEMPLATE(field_operators)
  BOOST_OPERATOR_TEMPLATE(ordered_field_operators)
  BOOST_OPERATOR_TEMPLATE(euclidian_ring_operators)
  BOOST_OPERATOR_TEMPLATE(ordered_euclidian_ring_operators)
  BOOST_OPERATOR_TEMPLATE(euclidean_ring_operators)
  BOOST_OPERATOR_TEMPLATE(ordered_euclidean_ring_operators)
  BOOST_OPERATOR_TEMPLATE2(input_iteratable)
  BOOST_OPERATOR_TEMPLATE1(output_iteratable)
  BOOST_OPERATOR_TEMPLATE2(forward_iteratable)
  BOOST_OPERATOR_TEMPLATE2(bidirectional_iteratable)
  BOOST_OPERATOR_TEMPLATE4(random_access_iteratable)
  
  #undef BOOST_OPERATOR_TEMPLATE
  #undef BOOST_OPERATOR_TEMPLATE4
  #undef BOOST_OPERATOR_TEMPLATE3
  #undef BOOST_OPERATOR_TEMPLATE2
  #undef BOOST_OPERATOR_TEMPLATE1
  #undef BOOST_IMPORT_TEMPLATE1
  #undef BOOST_IMPORT_TEMPLATE2
  #undef BOOST_IMPORT_TEMPLATE3
  #undef BOOST_IMPORT_TEMPLATE4
  
  // The following 'operators' classes can only be used portably if the derived class
  // declares ALL of the required member operators.
  template <class T, class U>
  struct operators2
      : totally_ordered2<T,U
      , integer_arithmetic2<T,U
      , bitwise2<T,U
        > > > {};
  
  template <class T, class U = T>
  struct operators : operators2<T, U> {};
  
  template <class T> struct operators<T, T>
      : totally_ordered<T
      , integer_arithmetic<T
      , bitwise<T
      , unit_steppable<T
        > > > > {};
  
  //  Iterator helper classes (contributed by Jeremy Siek) -------------------//
  //  (Input and output iterator helpers contributed by Daryle Walker) -------//
  //  (Changed to use combined operator classes by Daryle Walker) ------------//
  template <class T,
            class V,
            class D = std::ptrdiff_t,
            class P = V const *,
            class R = V const &>
  struct input_iterator_helper
    : input_iteratable<T, P
    , boost::iterator<std::input_iterator_tag, V, D, P, R
      > > {};
  
  template<class T>
  struct output_iterator_helper
    : output_iteratable<T
    , boost::iterator<std::output_iterator_tag, void, void, void, void
    > >
  {
    T& operator*()  { return static_cast<T&>(*this); }
    T& operator++() { return static_cast<T&>(*this); }
  };
  
  template <class T,
            class V,
            class D = std::ptrdiff_t,
            class P = V*,
            class R = V&>
  struct forward_iterator_helper
    : forward_iteratable<T, P
    , boost::iterator<std::forward_iterator_tag, V, D, P, R
      > > {};
  
  template <class T,
            class V,
            class D = std::ptrdiff_t,
            class P = V*,
            class R = V&>
  struct bidirectional_iterator_helper
    : bidirectional_iteratable<T, P
    , boost::iterator<std::bidirectional_iterator_tag, V, D, P, R
      > > {};
  
  template <class T,
            class V, 
            class D = std::ptrdiff_t,
            class P = V*,
            class R = V&>
  struct random_access_iterator_helper
    : random_access_iteratable<T, P, D, R
    , boost::iterator<std::random_access_iterator_tag, V, D, P, R
      > >
  {
    friend D requires_difference_operator(const T& x, const T& y) {
      return x - y;
    }
  }; // random_access_iterator_helper
  
  } // namespace boost
  
  #if defined(__sgi) && !defined(__GNUC__)
  #pragma reset woff 1234
  #endif
  
  #endif // BOOST_OPERATORS_HPP
  