//  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

//  22 Feb 16 Preserve old work-arounds. (Daniel Frey)

//  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_V1_HPP

#define BOOST_OPERATORS_V1_HPP

#include <cstddef>

#include <iterator>

#include <boost/config.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

    , equality_comparable2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct totally_ordered1

    : less_than_comparable1

    , equality_comparable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct additive2

    : addable2

    , subtractable2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct additive1

    : addable1

    , subtractable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct multiplicative2

    : multipliable2

    , dividable2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct multiplicative1

    : multipliable1

    , dividable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct integer_multiplicative2

    : multiplicative2

    , modable2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct integer_multiplicative1

    : multiplicative1

    , modable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct arithmetic2

    : additive2

    , multiplicative2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct arithmetic1

    : additive1

    , multiplicative1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct integer_arithmetic2

    : additive2

    , integer_multiplicative2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct integer_arithmetic1

    : additive1

    , integer_multiplicative1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct bitwise2

    : xorable2

    , andable2

    , orable2

      > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct bitwise1

    : xorable1

    , andable1

    , orable1

      > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct unit_steppable

    : incrementable

    , decrementable

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct shiftable2

    : left_shiftable2

    , right_shiftable2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct shiftable1

    : left_shiftable1

    , right_shiftable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct ring_operators2

    : additive2

    , subtractable2_left

    , multipliable2

      > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct ring_operators1

    : additive1

    , multipliable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct ordered_ring_operators2

    : ring_operators2

    , totally_ordered2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct ordered_ring_operators1

    : ring_operators1

    , totally_ordered1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct field_operators2

    : ring_operators2

    , dividable2

    , dividable2_left

      > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct field_operators1

    : ring_operators1

    , dividable1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct ordered_field_operators2

    : field_operators2

    , totally_ordered2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct ordered_field_operators1

    : field_operators1

    , totally_ordered1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct euclidian_ring_operators2

    : ring_operators2

    , dividable2

    , dividable2_left

    , modable2

    , modable2_left

      > > > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct euclidian_ring_operators1

    : ring_operators1

    , dividable1

    , modable1

      > > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct ordered_euclidian_ring_operators2

    : totally_ordered2

    , euclidian_ring_operators2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct ordered_euclidian_ring_operators1

    : totally_ordered1

    , euclidian_ring_operators1

      > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct euclidean_ring_operators2

    : ring_operators2

    , dividable2

    , dividable2_left

    , modable2

    , modable2_left

      > > > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct euclidean_ring_operators1

    : ring_operators1

    , dividable1

    , modable1

      > > > {};

template <class T, class U, class B = ::boost::detail::empty_base<T> >

struct ordered_euclidean_ring_operators2

    : totally_ordered2

    , euclidean_ring_operators2

      > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct ordered_euclidean_ring_operators1

    : totally_ordered1

    , euclidean_ring_operators1

      > > {};

template <class T, class P, class B = ::boost::detail::empty_base<T> >

struct input_iteratable

    : equality_comparable1

    , incrementable

    , dereferenceable

      > > > {};

template <class T, class B = ::boost::detail::empty_base<T> >

struct output_iteratable

    : incrementable

      > {};

template <class T, class P, class B = ::boost::detail::empty_base<T> >

struct forward_iteratable

    : input_iteratable

      > {};

template <class T, class P, class B = ::boost::detail::empty_base<T> >

struct bidirectional_iteratable

    : forward_iteratable

    , decrementable

      > > {};

//  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

    , less_than_comparable1

    , additive2

    , indexable

      > > > > {};

#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 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

    , integer_arithmetic2

    , bitwise2

      > > > {};

template <class T, class U = T>

struct operators : operators2<T, U> {};

template <class T> struct operators<T, T>