//  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

//  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 defined(BOOST_MSVC)

#   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 {

// Helmut Zeisel, empty base class optimization bug with GCC 3.0.0

#if defined(__GNUC__) && __GNUC__==3 && __GNUC_MINOR__==0 && __GNU_PATCHLEVEL__==0

  bool dummy; 

#endif

};

} // 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 !(x > y); }

     friend bool operator>=(const T& x, const U& y) { return !(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 !(y < x); }

     friend bool operator>=(const U& x, const T& y) { return !(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 !(y < x); }

     friend bool operator>=(const T& x, const T& y) { return !(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 !(x == y); }

     friend bool operator!=(const T& y, const U& x) { return !(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 !(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 !(x < y) && !(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 !(x < y) && !(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 (x < y) || (x == y); }

  friend bool operator>=(const T& x, const U& y)

    { return (x > y) || (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 (y > x) || (y == x); }

  friend bool operator>=(const U& x, const T& y)

    { return (y < x) || (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 (x < y) || (x == y); }

  friend bool operator>=(const T& x, const T& y)

    { return (y < x) || (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