Chris@16: /*-----------------------------------------------------------------------------+
Chris@16: Copyright (c) 2010-2010: Joachim Faulhaber
Chris@16: +------------------------------------------------------------------------------+
Chris@16:    Distributed under the Boost Software License, Version 1.0.
Chris@16:       (See accompanying file LICENCE.txt or copy at
Chris@16:            http://www.boost.org/LICENSE_1_0.txt)
Chris@16: +-----------------------------------------------------------------------------*/
Chris@16: #ifndef BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
Chris@16: #define BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
Chris@16: 
Chris@16: #include <boost/assert.hpp> 
Chris@16: #include <boost/utility/enable_if.hpp>
Chris@16: #include <boost/mpl/and.hpp>
Chris@16: #include <boost/mpl/or.hpp>
Chris@16: #include <boost/mpl/not.hpp>
Chris@16: #include <boost/icl/detail/design_config.hpp>
Chris@16: #include <boost/icl/type_traits/unit_element.hpp>
Chris@16: #include <boost/icl/type_traits/identity_element.hpp>
Chris@16: #include <boost/icl/type_traits/infinity.hpp>
Chris@16: #include <boost/icl/type_traits/succ_pred.hpp>
Chris@16: #include <boost/icl/type_traits/is_numeric.hpp>
Chris@16: #include <boost/icl/type_traits/is_discrete.hpp>
Chris@16: #include <boost/icl/type_traits/is_continuous.hpp>
Chris@16: #include <boost/icl/type_traits/is_asymmetric_interval.hpp>
Chris@16: #include <boost/icl/type_traits/is_discrete_interval.hpp>
Chris@16: #include <boost/icl/type_traits/is_continuous_interval.hpp>
Chris@16: 
Chris@16: #include <boost/icl/concept/interval_bounds.hpp>
Chris@16: #include <boost/icl/interval_traits.hpp>
Chris@16: #include <boost/icl/dynamic_interval_traits.hpp>
Chris@16: 
Chris@16: 
Chris@16: namespace boost{namespace icl
Chris@16: {
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Ordering
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, bool>::type
Chris@16: domain_less(const typename interval_traits<Type>::domain_type& left, 
Chris@16:             const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     return typename interval_traits<Type>::domain_compare()(left, right);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, bool>::type
Chris@16: domain_less_equal(const typename interval_traits<Type>::domain_type& left, 
Chris@16:                   const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     return !(typename interval_traits<Type>::domain_compare()(right, left));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, bool>::type
Chris@16: domain_equal(const typename interval_traits<Type>::domain_type& left, 
Chris@16:              const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     return !(domain_compare()(left, right)) && !(domain_compare()(right, left));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if< is_interval<Type>
Chris@16:                          , typename interval_traits<Type>::domain_type>::type
Chris@16: domain_next(const typename interval_traits<Type>::domain_type value) 
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     return icl::successor<domain_type,domain_compare>::apply(value);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if< is_interval<Type>
Chris@16:                          , typename interval_traits<Type>::domain_type>::type
Chris@16: domain_prior(const typename interval_traits<Type>::domain_type value) 
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     return icl::predecessor<domain_type,domain_compare>::apply(value);
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Construct<Interval> singleton
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_right_open<Type>
Chris@16:              , is_discrete<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: singleton(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     //ASSERT: This always creates an interval with exactly one element
Chris@16:     return interval_traits<Type>::construct(value, domain_next<Type>(value));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_left_open<Type>
Chris@16:              , is_discrete<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: singleton(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     //ASSERT: This always creates an interval with exactly one element
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than(value) )); 
Chris@16: 
Chris@16:     return interval_traits<Type>::construct(domain_prior<Type>(value), value);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_discrete_static_open<Type>, Type>::type
Chris@16: singleton(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     //ASSERT: This always creates an interval with exactly one element
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than(value))); 
Chris@16: 
Chris@16:     return interval_traits<Type>::construct( domain_prior<Type>(value)
Chris@16:                                            , domain_next<Type>(value));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_discrete_static_closed<Type>, Type>::type
Chris@16: singleton(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     //ASSERT: This always creates an interval with exactly one element
Chris@16:     return interval_traits<Type>::construct(value, value);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: singleton(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
Chris@16: }
Chris@16: 
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Construct<Interval> unit_trail == generalized singleton
Chris@16: // The smallest interval on an incrementable (and decrementable) type that can 
Chris@16: // be constructed using ++ and -- and such that it contains a given value.
Chris@16: // If 'Type' is discrete, 'unit_trail' and 'singleton' are identical. So we 
Chris@16: // can view 'unit_trail' as a generalized singleton for static intervals of 
Chris@16: // continuous types.
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_right_open<Type>
Chris@16:              , boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: unit_trail(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     return interval_traits<Type>::construct(value, domain_next<Type>(value));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_left_open<Type>
Chris@16:              , boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: unit_trail(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than(value) )); 
Chris@16: 
Chris@16:     return interval_traits<Type>::construct(domain_prior<Type>(value), value);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_open<Type>
Chris@16:              , is_discrete<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: unit_trail(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than(value))); 
Chris@16: 
Chris@16:     return interval_traits<Type>::construct( domain_prior<Type>(value)
Chris@16:                                            ,  domain_next<Type>(value));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if
Chris@16: <
Chris@16:     mpl::and_< is_static_closed<Type>
Chris@16:              , is_discrete<typename interval_traits<Type>::domain_type> >
Chris@16:   , Type
Chris@16: >::type
Chris@16: unit_trail(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     return interval_traits<Type>::construct(value, value);
Chris@16: }
Chris@16: 
Chris@16: //NOTE: statically bounded closed or open intervals of continuous domain types
Chris@16: // are NOT supported by ICL. They can not be used with interval containers
Chris@16: // consistently.
Chris@16: 
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: unit_trail(const typename interval_traits<Type>::domain_type& value)
Chris@16: {
Chris@16:     return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
Chris@16: }
Chris@16: 
Chris@16: } //namespace detail
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Construct<Interval> multon
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename enable_if<has_static_bounds<Type>, Type>::type
Chris@16: construct(const typename interval_traits<Type>::domain_type& low,
Chris@16:           const typename interval_traits<Type>::domain_type& up  )
Chris@16: {
Chris@16:     return interval_traits<Type>::construct(low, up);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: construct(const typename interval_traits<Type>::domain_type& low,
Chris@16:           const typename interval_traits<Type>::domain_type& up,
Chris@16:           interval_bounds bounds = interval_bounds::right_open())
Chris@16: {
Chris@16:     return dynamic_interval_traits<Type>::construct(low, up, bounds);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //- construct form bounded values ----------------------------------------------
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: construct(const typename Type::bounded_domain_type& low,
Chris@16:           const typename Type::bounded_domain_type& up)
Chris@16: {
Chris@16:     return dynamic_interval_traits<Type>::construct_bounded(low, up);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_interval<Type>, Type>::type
Chris@16: span(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:         return construct<Type>(left, right);
Chris@16:     else
Chris@16:         return construct<Type>(right, left);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename enable_if<is_static_right_open<Type>, Type>::type
Chris@16: hull(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:         return construct<Type>(left, domain_next<Type>(right));
Chris@16:     else
Chris@16:         return construct<Type>(right, domain_next<Type>(left));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_static_left_open<Type>, Type>::type
Chris@16: hull(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:     {
Chris@16:         BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                      ::is_less_than(left) )); 
Chris@16:         return construct<Type>(domain_prior<Type>(left), right);
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:         BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                      ::is_less_than(right) )); 
Chris@16:         return construct<Type>(domain_prior<Type>(right), left);
Chris@16:     }
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_static_closed<Type>, Type>::type
Chris@16: hull(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:         return construct<Type>(left, right);
Chris@16:     else
Chris@16:         return construct<Type>(right, left);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<is_static_open<Type>, Type>::type
Chris@16: hull(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:     {
Chris@16:         BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                      ::is_less_than(left) )); 
Chris@16:         return construct<Type>( domain_prior<Type>(left)
Chris@16:                               ,  domain_next<Type>(right));
Chris@16:     }
Chris@16:     else
Chris@16:     {
Chris@16:         BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                      ::is_less_than(right) )); 
Chris@16:         return construct<Type>( domain_prior<Type>(right)
Chris@16:                               ,  domain_next<Type>(left));
Chris@16:     }
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: hull(const typename interval_traits<Type>::domain_type& left,
Chris@16:      const typename interval_traits<Type>::domain_type& right)
Chris@16: {
Chris@16:     if(interval_traits<Type>::domain_compare()(left,right))
Chris@16:         return construct<Type>(left, right, interval_bounds::closed());
Chris@16:     else
Chris@16:         return construct<Type>(right, left, interval_bounds::closed());
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Selection
Chris@16: //==============================================================================
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, 
Chris@16:                           typename interval_traits<Type>::domain_type>::type
Chris@16: lower(const Type& object)
Chris@16: { 
Chris@16:     return interval_traits<Type>::lower(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, 
Chris@16:                           typename interval_traits<Type>::domain_type>::type
Chris@16: upper(const Type& object)
Chris@16: { 
Chris@16:     return interval_traits<Type>::upper(object);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //- first ----------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::or_<is_static_right_open<Type>, is_static_closed<Type> >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: first(const Type& object)
Chris@16: { 
Chris@16:     return lower(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_open<Type> >
Chris@16:                     , is_discrete<typename interval_traits<Type>::domain_type> >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: first(const Type& object)
Chris@16: { 
Chris@16:     return domain_next<Type>(lower(object));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_discrete_interval<Type>, 
Chris@16:                           typename interval_traits<Type>::domain_type>::type
Chris@16: first(const Type& object)
Chris@16: { 
Chris@16:     return is_left_closed(object.bounds()) ? 
Chris@16:                                  lower(object) : 
Chris@16:                domain_next<Type>(lower(object));
Chris@16: }
Chris@16: 
Chris@16: //- last -----------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: last(const Type& object)
Chris@16: { 
Chris@16:     return upper(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
Chris@16:                     , is_discrete<typename interval_traits<Type>::domain_type>  >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: last(const Type& object)
Chris@16: { 
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than(upper(object)) )); 
Chris@16:     return domain_prior<Type>(upper(object));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_discrete_interval<Type>, 
Chris@16:                           typename interval_traits<Type>::domain_type>::type
Chris@16: last(const Type& object)
Chris@16: { 
Chris@16:     typedef typename interval_traits<Type>::domain_type    domain_type;
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16:     BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
Chris@16:                                  ::is_less_than_or(upper(object), is_right_closed(object.bounds())) )); 
Chris@16:     return is_right_closed(object.bounds()) ? 
Chris@16:                                   upper(object) : 
Chris@16:                domain_prior<Type>(upper(object));
Chris@16: }
Chris@16: 
Chris@16: //- last_next ------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
Chris@16:                     , is_discrete<typename interval_traits<Type>::domain_type>  >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: last_next(const Type& object)
Chris@16: { 
Chris@16:     return domain_next<Type>(upper(object));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename 
Chris@16: enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
Chris@16:                     , is_discrete<typename interval_traits<Type>::domain_type>  >
Chris@16:          , typename interval_traits<Type>::domain_type>::type
Chris@16: last_next(const Type& object)
Chris@16: { 
Chris@16:     typedef typename interval_traits<Type>::domain_type domain_type;
Chris@16:     return upper(object); // NOTE: last_next is implemented to avoid calling pred(object)
Chris@16: }                         // For unsigned integral types this may cause underflow.
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_discrete_interval<Type>, 
Chris@16:                           typename interval_traits<Type>::domain_type>::type
Chris@16: last_next(const Type& object)
Chris@16: { 
Chris@16:     return is_right_closed(object.bounds()) ? 
Chris@16:                domain_next<Type>(upper(object)): 
Chris@16:                                  upper(object) ;
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, 
Chris@16:                    typename Type::bounded_domain_type>::type
Chris@16: bounded_lower(const Type& object)
Chris@16: { 
Chris@16:     return typename 
Chris@16:         Type::bounded_domain_type(lower(object), object.bounds().left()); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, 
Chris@16:                    typename Type::bounded_domain_type>::type
Chris@16: reverse_bounded_lower(const Type& object)
Chris@16: { 
Chris@16:     return typename 
Chris@16:         Type::bounded_domain_type(lower(object), 
Chris@16:                                   object.bounds().reverse_left()); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, 
Chris@16:                    typename Type::bounded_domain_type>::type
Chris@16: bounded_upper(const Type& object)
Chris@16: { 
Chris@16:     return typename 
Chris@16:         Type::bounded_domain_type(upper(object), 
Chris@16:                                   object.bounds().right()); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename enable_if<has_dynamic_bounds<Type>, 
Chris@16:                    typename Type::bounded_domain_type>::type
Chris@16: reverse_bounded_upper(const Type& object)
Chris@16: { 
Chris@16:     return typename 
Chris@16:         Type::bounded_domain_type(upper(object), 
Chris@16:                                   object.bounds().reverse_right()); 
Chris@16: }
Chris@16: 
Chris@16: //- bounds ---------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename enable_if<has_dynamic_bounds<Type>, interval_bounds>::type
Chris@16: bounds(const Type& object)
Chris@16: {
Chris@16:     return object.bounds();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename enable_if<has_static_bounds<Type>, interval_bounds>::type
Chris@16: bounds(const Type&)
Chris@16: {
Chris@16:     return interval_bounds(interval_bound_type<Type>::value);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Emptieness
Chris@16: //==============================================================================
Chris@16: /** Is the interval empty? */
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16: is_empty(const Type& object)
Chris@16: { 
Chris@16:     return domain_less_equal<Type>(upper(object), lower(object)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_closed<Type>, bool>::type
Chris@16: is_empty(const Type& object)
Chris@16: { 
Chris@16:     return domain_less<Type>(upper(object), lower(object)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_open<Type>, bool>::type
Chris@16: is_empty(const Type& object)
Chris@16: { 
Chris@16:     return domain_less_equal<Type>(upper(object),                   lower(object) ) 
Chris@16:         || domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object)));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: is_empty(const Type& object)
Chris@16: { 
Chris@16:     if(object.bounds() == interval_bounds::closed())
Chris@16:         return domain_less<Type>(upper(object), lower(object)); 
Chris@16:     else if(object.bounds() == interval_bounds::open())
Chris@16:         return domain_less_equal<Type>(upper(object),                   lower(object) )
Chris@16:             || domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object)));
Chris@16:     else
Chris@16:         return domain_less_equal<Type>(upper(object), lower(object)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: is_empty(const Type& object)
Chris@16: {
Chris@16:     return     domain_less<Type>(upper(object), lower(object))
Chris@16:         || (   domain_equal<Type>(upper(object), lower(object))
Chris@16:             && object.bounds() != interval_bounds::closed()    );
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Orderings, containedness (non empty)
Chris@16: //==============================================================================
Chris@16: namespace non_empty
Chris@16: {
Chris@16: 
Chris@16:     template<class Type>
Chris@16:     inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16:     exclusive_less(const Type& left, const Type& right)
Chris@16:     { 
Chris@16:         BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
Chris@16:         return domain_less_equal<Type>(upper(left), lower(right)); 
Chris@16:     }
Chris@16: 
Chris@16:     template<class Type>
Chris@16:     inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16:     exclusive_less(const Type& left, const Type& right)
Chris@16:     { 
Chris@16:         BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
Chris@16:         return domain_less<Type>(last(left), first(right)); 
Chris@16:     }
Chris@16: 
Chris@16:     template<class Type>
Chris@16:     inline typename boost::
Chris@16:     enable_if<has_symmetric_bounds<Type>, bool>::type
Chris@16:     exclusive_less(const Type& left, const Type& right)
Chris@16:     { 
Chris@16:         BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
Chris@16:         return domain_less<Type>(last(left), first(right)); 
Chris@16:     }
Chris@16: 
Chris@16:     template<class Type>
Chris@16:     inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16:     exclusive_less(const Type& left, const Type& right)
Chris@16:     { 
Chris@16:         BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
Chris@16:         return     domain_less <Type>(upper(left), lower(right))
Chris@16:             || (   domain_equal<Type>(upper(left), lower(right))
Chris@16:                 && inner_bounds(left,right) != interval_bounds::open() );
Chris@16:     }
Chris@16: 
Chris@16:     template<class Type>
Chris@16:     inline typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16:     contains(const Type& super, const Type& sub)
Chris@16:     { 
Chris@16:         return lower_less_equal(super,sub) && upper_less_equal(sub,super);
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16: } //namespace non_empty
Chris@16: 
Chris@16: 
Chris@16: //- contains -------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: contains(const Type& super, const Type& sub)
Chris@16: { 
Chris@16:     return icl::is_empty(sub) || non_empty::contains(super, sub);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_static<Type>, bool>::type
Chris@16: contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
Chris@16: {
Chris@16:     return domain_less_equal<Type>(icl::first(super), element                  ) 
Chris@16:         && domain_less_equal<Type>(                   element, icl::last(super));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_left_open<Type>, bool>::type
Chris@16: contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
Chris@16: {
Chris@16:     return domain_less      <Type>(icl::lower(super), element                   ) 
Chris@16:         && domain_less_equal<Type>(                   element, icl::upper(super));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_right_open<Type>, bool>::type
Chris@16: contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
Chris@16: {
Chris@16:     return domain_less_equal<Type>(icl::lower(super), element                   ) 
Chris@16:         && domain_less      <Type>(                   element, icl::upper(super));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, bool>::type
Chris@16: contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
Chris@16: {
Chris@16:     return
Chris@16:         (is_left_closed(super.bounds())  
Chris@16:             ? domain_less_equal<Type>(lower(super), element) 
Chris@16:             :       domain_less<Type>(lower(super), element))
Chris@16:     &&
Chris@16:         (is_right_closed(super.bounds()) 
Chris@16:             ? domain_less_equal<Type>(element, upper(super)) 
Chris@16:             :       domain_less<Type>(element, upper(super)));
Chris@16: }
Chris@16: 
Chris@16: //- within ---------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: within(const Type& sub, const Type& super)
Chris@16: { 
Chris@16:     return contains(super,sub);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Equivalences and Orderings
Chris@16: //==============================================================================
Chris@16: //- exclusive_less -------------------------------------------------------------
Chris@16: /** Maximal element of <tt>left</tt> is less than the minimal element of 
Chris@16:     <tt>right</tt> */
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16: exclusive_less(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return icl::is_empty(left) || icl::is_empty(right)
Chris@16:         || domain_less_equal<Type>(upper(left), lower(right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: exclusive_less(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return icl::is_empty(left) || icl::is_empty(right)
Chris@16:         || domain_less<Type>(last(left), first(right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::
Chris@16: enable_if<has_symmetric_bounds<Type>, bool>::type
Chris@16: exclusive_less(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return icl::is_empty(left) || icl::is_empty(right)
Chris@16:         || domain_less<Type>(last(left), first(right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: exclusive_less(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return     icl::is_empty(left) || icl::is_empty(right)
Chris@16:         ||     domain_less<Type>(upper(left), lower(right))
Chris@16:         || (   domain_equal<Type>(upper(left), lower(right))
Chris@16:             && inner_bounds(left,right) != interval_bounds::open() );
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_static_bounds<Type>, bool>::type
Chris@16: lower_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_less<Type>(lower(left), lower(right));
Chris@16: }
Chris@16:     
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: lower_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_less<Type>(first(left), first(right));
Chris@16: }
Chris@16:     
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: lower_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(left_bounds(left,right) == interval_bounds::right_open())  //'[(' == 10
Chris@16:         return domain_less_equal<Type>(lower(left), lower(right));
Chris@16:     else 
Chris@16:         return domain_less<Type>(lower(left), lower(right));
Chris@16: }
Chris@16:     
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_static_bounds<Type>, bool>::type
Chris@16: upper_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_less<Type>(upper(left), upper(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: upper_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_less<Type>(last(left), last(right));
Chris@16: }
Chris@16:     
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: upper_less(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(right_bounds(left,right) == interval_bounds::left_open())
Chris@16:         return domain_less_equal<Type>(upper(left), upper(right));
Chris@16:     else
Chris@16:         return domain_less<Type>(upper(left), upper(right));
Chris@16: }
Chris@16:     
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, 
Chris@16:                           typename Type::bounded_domain_type   >::type
Chris@16: lower_min(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return lower_less(left, right) ? bounded_lower(left) : bounded_lower(right);
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, 
Chris@16:                           typename Type::bounded_domain_type   >::type
Chris@16: lower_max(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return lower_less(left, right) ? bounded_lower(right) : bounded_lower(left);
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, 
Chris@16:                           typename Type::bounded_domain_type   >::type
Chris@16: upper_max(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return upper_less(left, right) ? bounded_upper(right) : bounded_upper(left);
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, 
Chris@16:                           typename Type::bounded_domain_type   >::type
Chris@16: upper_min(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return upper_less(left, right) ? bounded_upper(left) : bounded_upper(right);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16: lower_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(lower(left), lower(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
Chris@16: lower_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(first(left), first(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: lower_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(first(left), first(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: lower_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return (left.bounds().left()==right.bounds().left())
Chris@16:         && domain_equal<Type>(lower(left), lower(right));
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16: upper_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(upper(left), upper(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
Chris@16: upper_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(last(left), last(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: upper_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(last(left), last(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: upper_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return (left.bounds().right()==right.bounds().right())
Chris@16:         && domain_equal<Type>(upper(left), upper(right));
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: lower_less_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return lower_less(left,right) || lower_equal(left,right);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: upper_less_equal(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return upper_less(left,right) || upper_equal(left,right);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //- operator == ----------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: operator == (const Type& left, const Type& right)
Chris@16: {
Chris@16:     return (icl::is_empty(left) && icl::is_empty(right)) 
Chris@16:         || (lower_equal(left,right) && upper_equal(left,right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: operator != (const Type& left, const Type& right)
Chris@16: {
Chris@16:     return !(left == right);
Chris@16: }
Chris@16: 
Chris@16: //- operator < -----------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: operator < (const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left)) 
Chris@16:         return !icl::is_empty(right);
Chris@16:     else 
Chris@16:         return lower_less(left,right) 
Chris@16:             || (lower_equal(left,right) && upper_less(left,right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: operator > (const Type& left, const Type& right)
Chris@16: {
Chris@16:     return right < left;
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
Chris@16: touches(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return domain_equal<Type>(upper(left), lower(right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
Chris@16: touches(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return domain_equal<Type>(last_next(left), first(right)); 
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, bool>::type
Chris@16: touches(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return domain_equal<Type>(domain_next<Type>(last(left)), first(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, bool>::type
Chris@16: touches(const Type& left, const Type& right)
Chris@16: {
Chris@16:     return is_complementary(inner_bounds(left,right))
Chris@16:         && domain_equal<Type>(upper(left), lower(right));
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Size
Chris@16: //==============================================================================
Chris@16: //- cardinality ----------------------------------------------------------------
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_interval<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: cardinality(const Type& object)
Chris@16: {
Chris@16:     typedef typename size_type_of<interval_traits<Type> >::type SizeT;
Chris@16:     if(icl::is_empty(object))
Chris@16:         return icl::identity_element<SizeT>::value();
Chris@16:     else if(   object.bounds() == interval_bounds::closed() 
Chris@16:             && domain_equal<Type>(lower(object), upper(object)))
Chris@16:         return icl::unit_element<SizeT>::value();
Chris@16:     else 
Chris@16:         return icl::infinity<SizeT>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_interval<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: cardinality(const Type& object)
Chris@16: {
Chris@16:     typedef typename size_type_of<interval_traits<Type> >::type SizeT;
Chris@16:     return icl::is_empty(object) ? identity_element<SizeT>::value()
Chris@16:                                  : static_cast<SizeT>(last_next(object) - first(object));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_asymmetric<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: cardinality(const Type& object)
Chris@16: {
Chris@16:     typedef typename size_type_of<interval_traits<Type> >::type SizeT;
Chris@16:     if(icl::is_empty(object))
Chris@16:         return icl::identity_element<SizeT>::value();
Chris@16:     else 
Chris@16:         return icl::infinity<SizeT>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_asymmetric<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: cardinality(const Type& object)
Chris@16: {
Chris@16:     typedef typename size_type_of<interval_traits<Type> >::type SizeT;
Chris@16:     return icl::is_empty(object) ? identity_element<SizeT>::value()
Chris@16:                                  : static_cast<SizeT>(last_next(object) - first(object));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_symmetric_bounds<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: cardinality(const Type& object)
Chris@16: {
Chris@16:     typedef typename size_type_of<interval_traits<Type> >::type SizeT;
Chris@16:     return icl::is_empty(object) ? identity_element<SizeT>::value()
Chris@16:                                  : static_cast<SizeT>(last_next(object) - first(object));
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: //- size -----------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: size(const Type& object)
Chris@16: {
Chris@16:     return cardinality(object);
Chris@16: }
Chris@16: 
Chris@16: //- length ---------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_continuous_interval<Type>, 
Chris@16:     typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: length(const Type& object)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
Chris@16:     return icl::is_empty(object) ? identity_element<DiffT>::value()
Chris@16:                                  : upper(object) - lower(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_discrete_interval<Type>, 
Chris@16:     typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: length(const Type& object)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
Chris@16:     return icl::is_empty(object) ? identity_element<DiffT>::value()
Chris@16:                                  : last_next(object) - first(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_continuous_asymmetric<Type>, 
Chris@16:     typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: length(const Type& object)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
Chris@16:     return icl::is_empty(object) ? identity_element<DiffT>::value()
Chris@16:                                  : upper(object) - lower(object);
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_discrete_static<Type>, 
Chris@16:     typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: length(const Type& object)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
Chris@16:     return icl::is_empty(object) ? identity_element<DiffT>::value()
Chris@16:                                  : last_next(object) - first(object);
Chris@16: }
Chris@16: 
Chris@16: //- iterative_size -------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: inline typename enable_if<is_interval<Type>, 
Chris@16:     typename size_type_of<interval_traits<Type> >::type>::type
Chris@16: iterative_size(const Type&)
Chris@16: {
Chris@16:     return 2;
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Addition
Chris@16: //==============================================================================
Chris@16: //- hull -----------------------------------------------------------------------
Chris@16: /** \c hull returns the smallest interval containing \c left and \c right. */
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_static_bounds<Type>, Type>::type
Chris@16: hull(Type left, const Type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16: 
Chris@16:     if(icl::is_empty(right))
Chris@16:         return left;
Chris@16:     else if(icl::is_empty(left))
Chris@16:         return right;
Chris@16: 
Chris@16:     return 
Chris@16:         construct<Type>
Chris@16:         (
Chris@16:             (std::min)(lower(left), lower(right), domain_compare()), 
Chris@16:             (std::max)(upper(left), upper(right), domain_compare())
Chris@16:         );
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: hull(Type left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(right))
Chris@16:         return left;
Chris@16:     else if(icl::is_empty(left))
Chris@16:         return right;
Chris@16: 
Chris@16:     return  dynamic_interval_traits<Type>::construct_bounded
Chris@16:             (
Chris@16:                 lower_min(left, right), 
Chris@16:                 upper_max(left, right)
Chris@16:             );
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Subtraction
Chris@16: //==============================================================================
Chris@16: //- left_subtract --------------------------------------------------------------
Chris@16: /** subtract \c left_minuend from the \c right interval on it's left side. 
Chris@16:     Return the difference: The part of \c right right of \c left_minuend.
Chris@16: \code
Chris@16: right_over = right - left_minuend; //on the left.
Chris@16: ...      d) : right
Chris@16: ... c)      : left_minuend
Chris@16:      [c  d) : right_over
Chris@16: \endcode
Chris@16: */
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
Chris@16: left_subtract(Type right, const Type& left_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left_minuend, right))
Chris@16:         return right; 
Chris@16: 
Chris@16:     return construct<Type>(upper(left_minuend), upper(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_closed<Type>, Type>::type
Chris@16: left_subtract(Type right, const Type& left_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left_minuend, right))
Chris@16:         return right; 
Chris@16: 
Chris@16:     return construct<Type>(domain_next<Type>(upper(left_minuend)), upper(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_open<Type>, Type>::type
Chris@16: left_subtract(Type right, const Type& left_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left_minuend, right))
Chris@16:         return right; 
Chris@16: 
Chris@16:     return construct<Type>(domain_prior<Type>(upper(left_minuend)), upper(right));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: left_subtract(Type right, const Type& left_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left_minuend, right))
Chris@16:         return right; 
Chris@16:     return  dynamic_interval_traits<Type>::construct_bounded
Chris@16:             ( reverse_bounded_upper(left_minuend), bounded_upper(right) );
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //- right_subtract -------------------------------------------------------------
Chris@16: /** subtract \c right_minuend from the \c left interval on it's right side. 
Chris@16:     Return the difference: The part of \c left right of \c right_minuend.
Chris@16: \code
Chris@16: left_over = left - right_minuend; //on the right side.
Chris@16: [a      ...  : left
Chris@16:      [b ...  : right_minuend
Chris@16: [a  b)       : left_over
Chris@16: \endcode
Chris@16: */
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
Chris@16: right_subtract(Type left, const Type& right_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left, right_minuend))
Chris@16:         return left; 
Chris@16:     return construct<Type>(lower(left), lower(right_minuend));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_closed<Type>, Type>::type
Chris@16: right_subtract(Type left, const Type& right_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left, right_minuend))
Chris@16:         return left;
Chris@16:     else if(lower_less_equal(right_minuend, left))
Chris@16:         return identity_element<Type>::value();
Chris@16: 
Chris@16:     return construct<Type>(lower(left), domain_prior<Type>(lower(right_minuend)));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_static_open<Type>, Type>::type
Chris@16: right_subtract(Type left, const Type& right_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left, right_minuend))
Chris@16:         return left;
Chris@16: 
Chris@16:     return construct<Type>(lower(left), domain_next<Type>(lower(right_minuend)));
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: right_subtract(Type left, const Type& right_minuend)
Chris@16: {
Chris@16:     if(exclusive_less(left, right_minuend))
Chris@16:         return left; 
Chris@16: 
Chris@16:     return  dynamic_interval_traits<Type>::construct_bounded
Chris@16:             ( bounded_lower(left), reverse_bounded_lower(right_minuend) );
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Intersection
Chris@16: //==============================================================================
Chris@16: //- operator & -----------------------------------------------------------------
Chris@16: /** Returns the intersection of \c left and \c right interval. */
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
Chris@16: operator & (Type left, const Type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16: 
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return identity_element<Type>::value();
Chris@16:     else
Chris@16:         return
Chris@16:         construct<Type>
Chris@16:         (
Chris@16:             (std::max)(icl::lower(left), icl::lower(right), domain_compare()),
Chris@16:             (std::min)(icl::upper(left), icl::upper(right), domain_compare())
Chris@16:         );
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_symmetric_bounds<Type>, Type>::type
Chris@16: operator & (Type left, const Type& right)
Chris@16: {
Chris@16:     typedef typename interval_traits<Type>::domain_compare domain_compare;
Chris@16: 
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return identity_element<Type>::value();
Chris@16:     else
Chris@16:         return
Chris@16:         construct<Type>
Chris@16:         (
Chris@16:             (std::max)(icl::lower(left), icl::lower(right), domain_compare()),
Chris@16:             (std::min)(icl::upper(left), icl::upper(right), domain_compare())
Chris@16:         );
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: operator & (Type left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return identity_element<Type>::value();
Chris@16:     else 
Chris@16:         return  dynamic_interval_traits<Type>::construct_bounded
Chris@16:                 (
Chris@16:                     lower_max(left, right), 
Chris@16:                     upper_min(left, right) 
Chris@16:                 );
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: //- intersects -----------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: intersects(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return !(   icl::is_empty(left) || icl::is_empty(right) 
Chris@16:              || exclusive_less(left,right) || exclusive_less(right,left)); 
Chris@16: }
Chris@16: 
Chris@16: //- disjoint -------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, bool>::type
Chris@16: disjoint(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return icl::is_empty(left) || icl::is_empty(right) 
Chris@16:         || exclusive_less(left,right) || exclusive_less(right,left); 
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Complement
Chris@16: //==============================================================================
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
Chris@16: inner_complement(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return  identity_element<Type>::value();
Chris@16:     else if(exclusive_less(left, right))
Chris@16:         return construct<Type>(upper(left), lower(right));
Chris@16:     else if(exclusive_less(right, left))
Chris@16:         return construct<Type>(upper(right), lower(left));
Chris@16:     else
Chris@16:         return identity_element<Type>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_static_closed<Type>, Type>::type
Chris@16: inner_complement(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return  identity_element<Type>::value();
Chris@16:     else if(exclusive_less(left, right))
Chris@16:         return construct<Type>(domain_next<Type>(upper(left)), domain_prior<Type>(lower(right)));
Chris@16:     else if(exclusive_less(right, left))
Chris@16:         return construct<Type>(domain_next<Type>(upper(right)), domain_prior<Type>(lower(left)));
Chris@16:     else
Chris@16:         return identity_element<Type>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<is_discrete_static_open<Type>, Type>::type
Chris@16: inner_complement(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return  identity_element<Type>::value();
Chris@16:     else if(exclusive_less(left, right))
Chris@16:         return construct<Type>(last(left), first(right));
Chris@16:     else if(exclusive_less(right, left))
Chris@16:         return construct<Type>(last(right), first(left));
Chris@16:     else
Chris@16:         return identity_element<Type>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
Chris@16: inner_complement(const Type& left, const Type& right)
Chris@16: {
Chris@16:     if(icl::is_empty(left) || icl::is_empty(right))
Chris@16:         return  identity_element<Type>::value();
Chris@16:     else if(exclusive_less(left, right))
Chris@16:         return right_subtract(left_subtract(hull(left, right), left), right);
Chris@16:     else if(exclusive_less(right, left))
Chris@16:         return right_subtract(left_subtract(hull(right, left), right), left);
Chris@16:     else
Chris@16:         return identity_element<Type>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: inline typename boost::enable_if<is_interval<Type>, Type>::type
Chris@16: between(const Type& left, const Type& right)
Chris@16: { 
Chris@16:     return inner_complement(left, right);
Chris@16: }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Distance
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16: enable_if< mpl::and_< is_interval<Type>
Chris@16:                     , has_difference<typename interval_traits<Type>::domain_type>
Chris@16:                     , is_discrete<typename interval_traits<Type>::domain_type>        
Chris@16:                     >
Chris@16:          , typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: distance(const Type& x1, const Type& x2)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type difference_type;
Chris@16: 
Chris@16:     if(icl::is_empty(x1) || icl::is_empty(x2))
Chris@16:         return icl::identity_element<difference_type>::value();
Chris@16:     else if(domain_less<Type>(last(x1), first(x2)))
Chris@16:         return static_cast<difference_type>(icl::pred(first(x2) - last(x1)));
Chris@16:     else if(domain_less<Type>(last(x2), first(x1)))
Chris@16:         return static_cast<difference_type>(icl::pred(first(x1) - last(x2)));
Chris@16:     else
Chris@16:         return icl::identity_element<difference_type>::value();
Chris@16: }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16: enable_if< mpl::and_< is_interval<Type>
Chris@16:                     , has_difference<typename interval_traits<Type>::domain_type>
Chris@16:                     , is_continuous<typename interval_traits<Type>::domain_type>        
Chris@16:                     >
Chris@16:          , typename difference_type_of<interval_traits<Type> >::type>::type
Chris@16: distance(const Type& x1, const Type& x2)
Chris@16: {
Chris@16:     typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
Chris@16: 
Chris@16:     if(icl::is_empty(x1) || icl::is_empty(x2))
Chris@16:         return icl::identity_element<DiffT>::value();
Chris@16:     else if(domain_less<Type>(upper(x1), lower(x2)))
Chris@16:         return lower(x2) - upper(x1);
Chris@16:     else if(domain_less<Type>(upper(x2), lower(x1)))
Chris@16:         return lower(x1) - upper(x2);
Chris@16:     else
Chris@16:         return icl::identity_element<DiffT>::value();
Chris@16: }
Chris@16: 
Chris@16: //==============================================================================
Chris@16: //= Streaming, representation
Chris@16: //==============================================================================
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16:     enable_if< mpl::or_< is_static_left_open<Type>
Chris@16:                        , is_static_open<Type>    >, std::string>::type
Chris@16: left_bracket(const Type&) { return "("; }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16:     enable_if< mpl::or_< is_static_right_open<Type>
Chris@16:                        , is_static_closed<Type>   >, std::string>::type
Chris@16: left_bracket(const Type&) { return "["; }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type
Chris@16: left_bracket(const Type& object) 
Chris@16: { 
Chris@16:     return left_bracket(object.bounds()); 
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16:     enable_if< mpl::or_< is_static_right_open<Type>
Chris@16:                        , is_static_open<Type>     >, std::string>::type
Chris@16: right_bracket(const Type&) { return ")"; }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::
Chris@16:     enable_if< mpl::or_< is_static_left_open<Type>
Chris@16:                        , is_static_closed<Type>    >, std::string>::type
Chris@16: right_bracket(const Type&) { return "]"; }
Chris@16: 
Chris@16: template<class Type>
Chris@16: typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type
Chris@16: right_bracket(const Type& object) 
Chris@16: { 
Chris@16:     return right_bracket(object.bounds()); 
Chris@16: }
Chris@16: 
Chris@16: //------------------------------------------------------------------------------
Chris@16: template<class CharType, class CharTraits, class Type>
Chris@16: typename boost::enable_if<is_interval<Type>, 
Chris@16:                           std::basic_ostream<CharType, CharTraits> >::type&
Chris@16: operator << (std::basic_ostream<CharType, CharTraits> &stream, Type const& object)
Chris@16: {
Chris@16:     if(boost::icl::is_empty(object))
Chris@16:         return stream << left_bracket<Type>(object) << right_bracket<Type>(object); 
Chris@16:     else
Chris@16:         return stream << left_bracket<Type>(object) 
Chris@16:                       << interval_traits<Type>::lower(object) 
Chris@16:                       << "," 
Chris@16:                       << interval_traits<Type>::upper(object) 
Chris@16:                       << right_bracket<Type>(object) ;
Chris@16: }
Chris@16: 
Chris@16: }} // namespace icl boost
Chris@16: 
Chris@16: #endif
Chris@16: