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1473 lines
52 KiB
1473 lines
52 KiB
/*-----------------------------------------------------------------------------+ |
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Copyright (c) 2010-2010: Joachim Faulhaber |
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+------------------------------------------------------------------------------+ |
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Distributed under the Boost Software License, Version 1.0. |
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(See accompanying file LICENCE.txt or copy at |
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http://www.boost.org/LICENSE_1_0.txt) |
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+-----------------------------------------------------------------------------*/ |
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#ifndef BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323 |
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#define BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323 |
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|
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#include <boost/assert.hpp> |
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#include <boost/utility/enable_if.hpp> |
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#include <boost/mpl/and.hpp> |
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#include <boost/mpl/or.hpp> |
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#include <boost/mpl/not.hpp> |
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#include <boost/icl/detail/design_config.hpp> |
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#include <boost/icl/type_traits/unit_element.hpp> |
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#include <boost/icl/type_traits/identity_element.hpp> |
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#include <boost/icl/type_traits/infinity.hpp> |
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#include <boost/icl/type_traits/succ_pred.hpp> |
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#include <boost/icl/type_traits/is_numeric.hpp> |
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#include <boost/icl/type_traits/is_discrete.hpp> |
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#include <boost/icl/type_traits/is_continuous.hpp> |
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#include <boost/icl/type_traits/is_asymmetric_interval.hpp> |
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#include <boost/icl/type_traits/is_discrete_interval.hpp> |
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#include <boost/icl/type_traits/is_continuous_interval.hpp> |
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|
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#include <boost/icl/concept/interval_bounds.hpp> |
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#include <boost/icl/interval_traits.hpp> |
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#include <boost/icl/dynamic_interval_traits.hpp> |
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namespace boost{namespace icl |
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{ |
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|
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//============================================================================== |
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//= Ordering |
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//============================================================================== |
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template<class Type> |
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inline typename enable_if<is_interval<Type>, bool>::type |
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domain_less(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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return typename interval_traits<Type>::domain_compare()(left, right); |
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} |
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template<class Type> |
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inline typename enable_if<is_interval<Type>, bool>::type |
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domain_less_equal(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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return !(typename interval_traits<Type>::domain_compare()(right, left)); |
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} |
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template<class Type> |
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inline typename enable_if<is_interval<Type>, bool>::type |
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domain_equal(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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return !(domain_compare()(left, right)) && !(domain_compare()(right, left)); |
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} |
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template<class Type> |
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inline typename enable_if< is_interval<Type> |
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, typename interval_traits<Type>::domain_type>::type |
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domain_next(const typename interval_traits<Type>::domain_type value) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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return icl::successor<domain_type,domain_compare>::apply(value); |
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} |
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template<class Type> |
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inline typename enable_if< is_interval<Type> |
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, typename interval_traits<Type>::domain_type>::type |
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domain_prior(const typename interval_traits<Type>::domain_type value) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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return icl::predecessor<domain_type,domain_compare>::apply(value); |
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} |
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//============================================================================== |
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//= Construct<Interval> singleton |
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//============================================================================== |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_right_open<Type> |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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singleton(const typename interval_traits<Type>::domain_type& value) |
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{ |
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//ASSERT: This always creates an interval with exactly one element |
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return interval_traits<Type>::construct(value, domain_next<Type>(value)); |
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} |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_left_open<Type> |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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singleton(const typename interval_traits<Type>::domain_type& value) |
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{ |
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//ASSERT: This always creates an interval with exactly one element |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(value) )); |
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return interval_traits<Type>::construct(domain_prior<Type>(value), value); |
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} |
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template<class Type> |
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typename enable_if<is_discrete_static_open<Type>, Type>::type |
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singleton(const typename interval_traits<Type>::domain_type& value) |
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{ |
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//ASSERT: This always creates an interval with exactly one element |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(value))); |
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return interval_traits<Type>::construct( domain_prior<Type>(value) |
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, domain_next<Type>(value)); |
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} |
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template<class Type> |
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typename enable_if<is_discrete_static_closed<Type>, Type>::type |
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singleton(const typename interval_traits<Type>::domain_type& value) |
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{ |
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//ASSERT: This always creates an interval with exactly one element |
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return interval_traits<Type>::construct(value, value); |
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} |
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template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, Type>::type |
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singleton(const typename interval_traits<Type>::domain_type& value) |
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{ |
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return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed()); |
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} |
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namespace detail |
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{ |
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//============================================================================== |
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//= Construct<Interval> unit_trail == generalized singleton |
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// The smallest interval on an incrementable (and decrementable) type that can |
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// be constructed using ++ and -- and such that it contains a given value. |
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// If 'Type' is discrete, 'unit_trail' and 'singleton' are identical. So we |
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// can view 'unit_trail' as a generalized singleton for static intervals of |
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// continuous types. |
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//============================================================================== |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_right_open<Type> |
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, boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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unit_trail(const typename interval_traits<Type>::domain_type& value) |
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{ |
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return interval_traits<Type>::construct(value, domain_next<Type>(value)); |
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} |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_left_open<Type> |
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, boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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unit_trail(const typename interval_traits<Type>::domain_type& value) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(value) )); |
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return interval_traits<Type>::construct(domain_prior<Type>(value), value); |
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} |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_open<Type> |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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unit_trail(const typename interval_traits<Type>::domain_type& value) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(value))); |
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return interval_traits<Type>::construct( domain_prior<Type>(value) |
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, domain_next<Type>(value)); |
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} |
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template<class Type> |
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typename enable_if |
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< |
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mpl::and_< is_static_closed<Type> |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, Type |
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>::type |
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unit_trail(const typename interval_traits<Type>::domain_type& value) |
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{ |
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return interval_traits<Type>::construct(value, value); |
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} |
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//NOTE: statically bounded closed or open intervals of continuous domain types |
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// are NOT supported by ICL. They can not be used with interval containers |
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// consistently. |
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template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, Type>::type |
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unit_trail(const typename interval_traits<Type>::domain_type& value) |
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{ |
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return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed()); |
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} |
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} //namespace detail |
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//============================================================================== |
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//= Construct<Interval> multon |
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//============================================================================== |
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template<class Type> |
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typename enable_if<has_static_bounds<Type>, Type>::type |
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construct(const typename interval_traits<Type>::domain_type& low, |
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const typename interval_traits<Type>::domain_type& up ) |
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{ |
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return interval_traits<Type>::construct(low, up); |
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} |
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template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, Type>::type |
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construct(const typename interval_traits<Type>::domain_type& low, |
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const typename interval_traits<Type>::domain_type& up, |
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interval_bounds bounds = interval_bounds::right_open()) |
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{ |
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return dynamic_interval_traits<Type>::construct(low, up, bounds); |
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} |
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//- construct form bounded values ---------------------------------------------- |
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template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, Type>::type |
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construct(const typename Type::bounded_domain_type& low, |
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const typename Type::bounded_domain_type& up) |
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{ |
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return dynamic_interval_traits<Type>::construct_bounded(low, up); |
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} |
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template<class Type> |
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typename enable_if<is_interval<Type>, Type>::type |
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span(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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return construct<Type>(left, right); |
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else |
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return construct<Type>(right, left); |
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} |
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//============================================================================== |
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template<class Type> |
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typename enable_if<is_static_right_open<Type>, Type>::type |
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hull(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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return construct<Type>(left, domain_next<Type>(right)); |
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else |
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return construct<Type>(right, domain_next<Type>(left)); |
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} |
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template<class Type> |
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typename enable_if<is_static_left_open<Type>, Type>::type |
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hull(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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{ |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(left) )); |
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return construct<Type>(domain_prior<Type>(left), right); |
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} |
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else |
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{ |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(right) )); |
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return construct<Type>(domain_prior<Type>(right), left); |
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} |
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} |
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template<class Type> |
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typename enable_if<is_static_closed<Type>, Type>::type |
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hull(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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return construct<Type>(left, right); |
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else |
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return construct<Type>(right, left); |
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} |
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template<class Type> |
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typename enable_if<is_static_open<Type>, Type>::type |
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hull(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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{ |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(left) )); |
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return construct<Type>( domain_prior<Type>(left) |
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, domain_next<Type>(right)); |
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} |
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else |
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{ |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(right) )); |
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return construct<Type>( domain_prior<Type>(right) |
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, domain_next<Type>(left)); |
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} |
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} |
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template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, Type>::type |
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hull(const typename interval_traits<Type>::domain_type& left, |
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const typename interval_traits<Type>::domain_type& right) |
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{ |
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if(interval_traits<Type>::domain_compare()(left,right)) |
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return construct<Type>(left, right, interval_bounds::closed()); |
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else |
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return construct<Type>(right, left, interval_bounds::closed()); |
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} |
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//============================================================================== |
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//= Selection |
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//============================================================================== |
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template<class Type> |
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inline typename enable_if<is_interval<Type>, |
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typename interval_traits<Type>::domain_type>::type |
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lower(const Type& object) |
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{ |
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return interval_traits<Type>::lower(object); |
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} |
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template<class Type> |
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inline typename enable_if<is_interval<Type>, |
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typename interval_traits<Type>::domain_type>::type |
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upper(const Type& object) |
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{ |
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return interval_traits<Type>::upper(object); |
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} |
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//- first ---------------------------------------------------------------------- |
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template<class Type> |
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inline typename |
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enable_if< mpl::or_<is_static_right_open<Type>, is_static_closed<Type> > |
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, typename interval_traits<Type>::domain_type>::type |
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first(const Type& object) |
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{ |
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return lower(object); |
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} |
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|
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template<class Type> |
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inline typename |
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enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_open<Type> > |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, typename interval_traits<Type>::domain_type>::type |
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first(const Type& object) |
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{ |
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return domain_next<Type>(lower(object)); |
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} |
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|
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template<class Type> |
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inline typename enable_if<is_discrete_interval<Type>, |
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typename interval_traits<Type>::domain_type>::type |
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first(const Type& object) |
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{ |
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return is_left_closed(object.bounds()) ? |
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lower(object) : |
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domain_next<Type>(lower(object)); |
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} |
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|
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//- last ----------------------------------------------------------------------- |
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template<class Type> |
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inline typename |
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enable_if< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> > |
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, typename interval_traits<Type>::domain_type>::type |
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last(const Type& object) |
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{ |
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return upper(object); |
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} |
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|
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template<class Type> |
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inline typename |
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enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> > |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, typename interval_traits<Type>::domain_type>::type |
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last(const Type& object) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than(upper(object)) )); |
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return domain_prior<Type>(upper(object)); |
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} |
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|
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template<class Type> |
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inline typename enable_if<is_discrete_interval<Type>, |
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typename interval_traits<Type>::domain_type>::type |
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last(const Type& object) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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typedef typename interval_traits<Type>::domain_compare domain_compare; |
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BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value> |
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::is_less_than_or(upper(object), is_right_closed(object.bounds())) )); |
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return is_right_closed(object.bounds()) ? |
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upper(object) : |
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domain_prior<Type>(upper(object)); |
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} |
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|
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//- last_next ------------------------------------------------------------------ |
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template<class Type> |
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inline typename |
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enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> > |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, typename interval_traits<Type>::domain_type>::type |
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last_next(const Type& object) |
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{ |
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return domain_next<Type>(upper(object)); |
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} |
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|
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template<class Type> |
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inline typename |
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enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> > |
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, is_discrete<typename interval_traits<Type>::domain_type> > |
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, typename interval_traits<Type>::domain_type>::type |
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last_next(const Type& object) |
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{ |
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typedef typename interval_traits<Type>::domain_type domain_type; |
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return upper(object); // NOTE: last_next is implemented to avoid calling pred(object) |
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} // For unsigned integral types this may cause underflow. |
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|
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template<class Type> |
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inline typename enable_if<is_discrete_interval<Type>, |
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typename interval_traits<Type>::domain_type>::type |
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last_next(const Type& object) |
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{ |
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return is_right_closed(object.bounds()) ? |
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domain_next<Type>(upper(object)): |
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upper(object) ; |
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} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type>::type |
|
bounded_lower(const Type& object) |
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{ |
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return typename |
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Type::bounded_domain_type(lower(object), object.bounds().left()); |
|
} |
|
|
|
template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, |
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typename Type::bounded_domain_type>::type |
|
reverse_bounded_lower(const Type& object) |
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{ |
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return typename |
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Type::bounded_domain_type(lower(object), |
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object.bounds().reverse_left()); |
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} |
|
|
|
template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type>::type |
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bounded_upper(const Type& object) |
|
{ |
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return typename |
|
Type::bounded_domain_type(upper(object), |
|
object.bounds().right()); |
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} |
|
|
|
template<class Type> |
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typename enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type>::type |
|
reverse_bounded_upper(const Type& object) |
|
{ |
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return typename |
|
Type::bounded_domain_type(upper(object), |
|
object.bounds().reverse_right()); |
|
} |
|
|
|
//- bounds --------------------------------------------------------------------- |
|
template<class Type> |
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inline typename enable_if<has_dynamic_bounds<Type>, interval_bounds>::type |
|
bounds(const Type& object) |
|
{ |
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return object.bounds(); |
|
} |
|
|
|
template<class Type> |
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inline typename enable_if<has_static_bounds<Type>, interval_bounds>::type |
|
bounds(const Type&) |
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{ |
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return interval_bounds(interval_bound_type<Type>::value); |
|
} |
|
|
|
|
|
//============================================================================== |
|
//= Emptieness |
|
//============================================================================== |
|
/** Is the interval empty? */ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
is_empty(const Type& object) |
|
{ |
|
return domain_less_equal<Type>(upper(object), lower(object)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_closed<Type>, bool>::type |
|
is_empty(const Type& object) |
|
{ |
|
return domain_less<Type>(upper(object), lower(object)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_open<Type>, bool>::type |
|
is_empty(const Type& object) |
|
{ |
|
return domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object))); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
is_empty(const Type& object) |
|
{ |
|
if(object.bounds() == interval_bounds::closed()) |
|
return domain_less<Type>(upper(object), lower(object)); |
|
else if(object.bounds() == interval_bounds::open()) |
|
return domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object))); |
|
else |
|
return domain_less_equal<Type>(upper(object), lower(object)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
is_empty(const Type& object) |
|
{ |
|
return domain_less<Type>(upper(object), lower(object)) |
|
|| ( domain_equal<Type>(upper(object), lower(object)) |
|
&& object.bounds() != interval_bounds::closed() ); |
|
} |
|
|
|
//============================================================================== |
|
//= Orderings, containedness (non empty) |
|
//============================================================================== |
|
namespace non_empty |
|
{ |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right))); |
|
return domain_less_equal<Type>(upper(left), lower(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right))); |
|
return domain_less<Type>(last(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost:: |
|
enable_if<has_symmetric_bounds<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right))); |
|
return domain_less<Type>(last(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right))); |
|
return domain_less <Type>(left.upper(), right.lower()) |
|
|| ( domain_equal<Type>(left.upper(), right.lower()) |
|
&& inner_bounds(left,right) != interval_bounds::open() ); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_interval<Type>, bool>::type |
|
contains(const Type& super, const Type& sub) |
|
{ |
|
return lower_less_equal(super,sub) && upper_less_equal(sub,super); |
|
} |
|
|
|
|
|
} //namespace non_empty |
|
|
|
|
|
//- contains ------------------------------------------------------------------- |
|
template<class Type> |
|
inline typename boost::enable_if<is_interval<Type>, bool>::type |
|
contains(const Type& super, const Type& sub) |
|
{ |
|
return icl::is_empty(sub) || non_empty::contains(super, sub); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_static<Type>, bool>::type |
|
contains(const Type& super, const typename interval_traits<Type>::domain_type& element) |
|
{ |
|
return domain_less_equal<Type>(icl::first(super), element ) |
|
&& domain_less_equal<Type>( element, icl::last(super)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_left_open<Type>, bool>::type |
|
contains(const Type& super, const typename interval_traits<Type>::domain_type& element) |
|
{ |
|
return domain_less <Type>(icl::lower(super), element ) |
|
&& domain_less_equal<Type>( element, icl::upper(super)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_right_open<Type>, bool>::type |
|
contains(const Type& super, const typename interval_traits<Type>::domain_type& element) |
|
{ |
|
return domain_less_equal<Type>(icl::lower(super), element ) |
|
&& domain_less <Type>( element, icl::upper(super)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, bool>::type |
|
contains(const Type& super, const typename interval_traits<Type>::domain_type& element) |
|
{ |
|
return |
|
(is_left_closed(super.bounds()) |
|
? domain_less_equal<Type>(super.lower(), element) |
|
: domain_less<Type>(super.lower(), element)) |
|
&& |
|
(is_right_closed(super.bounds()) |
|
? domain_less_equal<Type>(element, super.upper()) |
|
: domain_less<Type>(element, super.upper())); |
|
} |
|
|
|
//- within --------------------------------------------------------------------- |
|
template<class Type> |
|
inline typename boost::enable_if<is_interval<Type>, bool>::type |
|
within(const Type& sub, const Type& super) |
|
{ |
|
return contains(super,sub); |
|
} |
|
|
|
|
|
//============================================================================== |
|
//= Equivalences and Orderings |
|
//============================================================================== |
|
//- exclusive_less ------------------------------------------------------------- |
|
/** Maximal element of <tt>left</tt> is less than the minimal element of |
|
<tt>right</tt> */ |
|
template<class Type> |
|
inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
return icl::is_empty(left) || icl::is_empty(right) |
|
|| domain_less_equal<Type>(upper(left), lower(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
return icl::is_empty(left) || icl::is_empty(right) |
|
|| domain_less<Type>(last(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost:: |
|
enable_if<has_symmetric_bounds<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
return icl::is_empty(left) || icl::is_empty(right) |
|
|| domain_less<Type>(last(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
exclusive_less(const Type& left, const Type& right) |
|
{ |
|
return icl::is_empty(left) || icl::is_empty(right) |
|
|| domain_less<Type>(left.upper(), right.lower()) |
|
|| ( domain_equal<Type>(left.upper(), right.lower()) |
|
&& inner_bounds(left,right) != interval_bounds::open() ); |
|
} |
|
|
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_static_bounds<Type>, bool>::type |
|
lower_less(const Type& left, const Type& right) |
|
{ |
|
return domain_less<Type>(left.lower(), right.lower()); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
lower_less(const Type& left, const Type& right) |
|
{ |
|
return domain_less<Type>(first(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
lower_less(const Type& left, const Type& right) |
|
{ |
|
if(left_bounds(left,right) == interval_bounds::right_open()) //'[(' == 10 |
|
return domain_less_equal<Type>(left.lower(), right.lower()); |
|
else |
|
return domain_less<Type>(left.lower(), right.lower()); |
|
} |
|
|
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_static_bounds<Type>, bool>::type |
|
upper_less(const Type& left, const Type& right) |
|
{ |
|
return domain_less<Type>(left.upper(), right.upper()); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
upper_less(const Type& left, const Type& right) |
|
{ |
|
return domain_less<Type>(last(left), last(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
upper_less(const Type& left, const Type& right) |
|
{ |
|
if(right_bounds(left,right) == interval_bounds::left_open()) |
|
return domain_less_equal<Type>(left.upper(), right.upper()); |
|
else |
|
return domain_less<Type>(left.upper(), right.upper()); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type >::type |
|
lower_min(const Type& left, const Type& right) |
|
{ |
|
return lower_less(left, right) ? bounded_lower(left) : bounded_lower(right); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type >::type |
|
lower_max(const Type& left, const Type& right) |
|
{ |
|
return lower_less(left, right) ? bounded_lower(right) : bounded_lower(left); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type >::type |
|
upper_max(const Type& left, const Type& right) |
|
{ |
|
return upper_less(left, right) ? bounded_upper(right) : bounded_upper(left); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, |
|
typename Type::bounded_domain_type >::type |
|
upper_min(const Type& left, const Type& right) |
|
{ |
|
return upper_less(left, right) ? bounded_upper(left) : bounded_upper(right); |
|
} |
|
|
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
lower_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(left.lower(), right.lower()); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type |
|
lower_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(first(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
lower_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(first(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
lower_equal(const Type& left, const Type& right) |
|
{ |
|
return (left.bounds().left()==right.bounds().left()) |
|
&& domain_equal<Type>(left.lower(), right.lower()); |
|
} |
|
|
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
upper_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(left.upper(), right.upper()); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type |
|
upper_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(last(left), last(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
upper_equal(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(last(left), last(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
upper_equal(const Type& left, const Type& right) |
|
{ |
|
return (left.bounds().right()==right.bounds().right()) |
|
&& domain_equal<Type>(left.upper(), right.upper()); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
lower_less_equal(const Type& left, const Type& right) |
|
{ |
|
return lower_less(left,right) || lower_equal(left,right); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
upper_less_equal(const Type& left, const Type& right) |
|
{ |
|
return upper_less(left,right) || upper_equal(left,right); |
|
} |
|
|
|
|
|
//- operator == ---------------------------------------------------------------- |
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
operator == (const Type& left, const Type& right) |
|
{ |
|
return (icl::is_empty(left) && icl::is_empty(right)) |
|
|| (lower_equal(left,right) && upper_equal(left,right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
operator != (const Type& left, const Type& right) |
|
{ |
|
return !(left == right); |
|
} |
|
|
|
//- operator < ----------------------------------------------------------------- |
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
operator < (const Type& left, const Type& right) |
|
{ |
|
if(icl::is_empty(left)) |
|
return !icl::is_empty(right); |
|
else |
|
return lower_less(left,right) |
|
|| (lower_equal(left,right) && upper_less(left,right)); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_interval<Type>, bool>::type |
|
operator > (const Type& left, const Type& right) |
|
{ |
|
return right < left; |
|
} |
|
|
|
|
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type |
|
touches(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(upper(left), lower(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type |
|
touches(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(last_next(left), first(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, bool>::type |
|
touches(const Type& left, const Type& right) |
|
{ |
|
return domain_equal<Type>(domain_next<Type>(last(left)), first(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, bool>::type |
|
touches(const Type& left, const Type& right) |
|
{ |
|
return is_complementary(inner_bounds(left,right)) |
|
&& domain_equal<Type>(left.upper(), right.lower()); |
|
} |
|
|
|
|
|
//============================================================================== |
|
//= Size |
|
//============================================================================== |
|
//- cardinality ---------------------------------------------------------------- |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_interval<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
cardinality(const Type& object) |
|
{ |
|
typedef typename size_type_of<interval_traits<Type> >::type SizeT; |
|
if(icl::is_empty(object)) |
|
return icl::identity_element<SizeT>::value(); |
|
else if( object.bounds() == interval_bounds::closed() |
|
&& domain_equal<Type>(lower(object), upper(object))) |
|
return icl::unit_element<SizeT>::value(); |
|
else |
|
return icl::infinity<SizeT>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_interval<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
cardinality(const Type& object) |
|
{ |
|
typedef typename size_type_of<interval_traits<Type> >::type SizeT; |
|
return icl::is_empty(object) ? identity_element<SizeT>::value() |
|
: static_cast<SizeT>(last_next(object) - first(object)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_asymmetric<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
cardinality(const Type& object) |
|
{ |
|
typedef typename size_type_of<interval_traits<Type> >::type SizeT; |
|
if(icl::is_empty(object)) |
|
return icl::identity_element<SizeT>::value(); |
|
else |
|
return icl::infinity<SizeT>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_asymmetric<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
cardinality(const Type& object) |
|
{ |
|
typedef typename size_type_of<interval_traits<Type> >::type SizeT; |
|
return icl::is_empty(object) ? identity_element<SizeT>::value() |
|
: static_cast<SizeT>(last_next(object) - first(object)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_symmetric_bounds<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
cardinality(const Type& object) |
|
{ |
|
typedef typename size_type_of<interval_traits<Type> >::type SizeT; |
|
return icl::is_empty(object) ? identity_element<SizeT>::value() |
|
: static_cast<SizeT>(last_next(object) - first(object)); |
|
} |
|
|
|
|
|
|
|
//- size ----------------------------------------------------------------------- |
|
template<class Type> |
|
inline typename enable_if<is_interval<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
size(const Type& object) |
|
{ |
|
return cardinality(object); |
|
} |
|
|
|
//- length --------------------------------------------------------------------- |
|
template<class Type> |
|
inline typename boost::enable_if<is_continuous_interval<Type>, |
|
typename difference_type_of<interval_traits<Type> >::type>::type |
|
length(const Type& object) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type DiffT; |
|
return icl::is_empty(object) ? identity_element<DiffT>::value() |
|
: upper(object) - lower(object); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_discrete_interval<Type>, |
|
typename difference_type_of<interval_traits<Type> >::type>::type |
|
length(const Type& object) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type DiffT; |
|
return icl::is_empty(object) ? identity_element<DiffT>::value() |
|
: last_next(object) - first(object); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_continuous_asymmetric<Type>, |
|
typename difference_type_of<interval_traits<Type> >::type>::type |
|
length(const Type& object) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type DiffT; |
|
return icl::is_empty(object) ? identity_element<DiffT>::value() |
|
: upper(object) - lower(object); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_discrete_static<Type>, |
|
typename difference_type_of<interval_traits<Type> >::type>::type |
|
length(const Type& object) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type DiffT; |
|
return icl::is_empty(object) ? identity_element<DiffT>::value() |
|
: last_next(object) - first(object); |
|
} |
|
|
|
//- iterative_size ------------------------------------------------------------- |
|
template<class Type> |
|
inline typename enable_if<is_interval<Type>, |
|
typename size_type_of<interval_traits<Type> >::type>::type |
|
iterative_size(const Type&) |
|
{ |
|
return 2; |
|
} |
|
|
|
|
|
//============================================================================== |
|
//= Addition |
|
//============================================================================== |
|
//- hull ----------------------------------------------------------------------- |
|
/** \c hull returns the smallest interval containing \c left and \c right. */ |
|
template<class Type> |
|
typename boost::enable_if<has_static_bounds<Type>, Type>::type |
|
hull(Type left, const Type& right) |
|
{ |
|
typedef typename interval_traits<Type>::domain_compare domain_compare; |
|
|
|
if(icl::is_empty(right)) |
|
return left; |
|
else if(icl::is_empty(left)) |
|
return right; |
|
|
|
return |
|
construct<Type> |
|
( |
|
(std::min)(lower(left), lower(right), domain_compare()), |
|
(std::max)(upper(left), upper(right), domain_compare()) |
|
); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type |
|
hull(Type left, const Type& right) |
|
{ |
|
if(icl::is_empty(right)) |
|
return left; |
|
else if(icl::is_empty(left)) |
|
return right; |
|
|
|
return dynamic_interval_traits<Type>::construct_bounded |
|
( |
|
lower_min(left, right), |
|
upper_max(left, right) |
|
); |
|
} |
|
|
|
//============================================================================== |
|
//= Subtraction |
|
//============================================================================== |
|
//- left_subtract -------------------------------------------------------------- |
|
/** subtract \c left_minuend from the \c right interval on it's left side. |
|
Return the difference: The part of \c right right of \c left_minuend. |
|
\code |
|
right_over = right - left_minuend; //on the left. |
|
... d) : right |
|
... c) : left_minuend |
|
[c d) : right_over |
|
\endcode |
|
*/ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type |
|
left_subtract(Type right, const Type& left_minuend) |
|
{ |
|
if(exclusive_less(left_minuend, right)) |
|
return right; |
|
|
|
return construct<Type>(upper(left_minuend), upper(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_closed<Type>, Type>::type |
|
left_subtract(Type right, const Type& left_minuend) |
|
{ |
|
if(exclusive_less(left_minuend, right)) |
|
return right; |
|
|
|
return construct<Type>(domain_next<Type>(upper(left_minuend)), upper(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_open<Type>, Type>::type |
|
left_subtract(Type right, const Type& left_minuend) |
|
{ |
|
if(exclusive_less(left_minuend, right)) |
|
return right; |
|
|
|
return construct<Type>(domain_prior<Type>(upper(left_minuend)), upper(right)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type |
|
left_subtract(Type right, const Type& left_minuend) |
|
{ |
|
if(exclusive_less(left_minuend, right)) |
|
return right; |
|
return dynamic_interval_traits<Type>::construct_bounded |
|
( reverse_bounded_upper(left_minuend), bounded_upper(right) ); |
|
} |
|
|
|
|
|
//- right_subtract ------------------------------------------------------------- |
|
/** subtract \c right_minuend from the \c left interval on it's right side. |
|
Return the difference: The part of \c left right of \c right_minuend. |
|
\code |
|
left_over = left - right_minuend; //on the right side. |
|
[a ... : left |
|
[b ... : right_minuend |
|
[a b) : left_over |
|
\endcode |
|
*/ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type |
|
right_subtract(Type left, const Type& right_minuend) |
|
{ |
|
if(exclusive_less(left, right_minuend)) |
|
return left; |
|
return construct<Type>(lower(left), lower(right_minuend)); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_closed<Type>, Type>::type |
|
right_subtract(Type left, const Type& right_minuend) |
|
{ |
|
if(exclusive_less(left, right_minuend)) |
|
return left; |
|
else if(lower_less_equal(right_minuend, left)) |
|
return identity_element<Type>::value(); |
|
|
|
return construct<Type>(lower(left), domain_prior<Type>(lower(right_minuend))); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_static_open<Type>, Type>::type |
|
right_subtract(Type left, const Type& right_minuend) |
|
{ |
|
if(exclusive_less(left, right_minuend)) |
|
return left; |
|
|
|
return construct<Type>(lower(left), domain_next<Type>(lower(right_minuend))); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type |
|
right_subtract(Type left, const Type& right_minuend) |
|
{ |
|
if(exclusive_less(left, right_minuend)) |
|
return left; |
|
|
|
return dynamic_interval_traits<Type>::construct_bounded |
|
( bounded_lower(left), reverse_bounded_lower(right_minuend) ); |
|
} |
|
|
|
//============================================================================== |
|
//= Intersection |
|
//============================================================================== |
|
//- operator & ----------------------------------------------------------------- |
|
/** Returns the intersection of \c left and \c right interval. */ |
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type |
|
operator & (Type left, const Type& right) |
|
{ |
|
typedef typename interval_traits<Type>::domain_compare domain_compare; |
|
|
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else |
|
return |
|
construct<Type> |
|
( |
|
(std::max)(icl::lower(left), icl::lower(right), domain_compare()), |
|
(std::min)(icl::upper(left), icl::upper(right), domain_compare()) |
|
); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_symmetric_bounds<Type>, Type>::type |
|
operator & (Type left, const Type& right) |
|
{ |
|
typedef typename interval_traits<Type>::domain_compare domain_compare; |
|
|
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else |
|
return |
|
construct<Type> |
|
( |
|
(std::max)(icl::lower(left), icl::lower(right), domain_compare()), |
|
(std::min)(icl::upper(left), icl::upper(right), domain_compare()) |
|
); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type |
|
operator & (Type left, const Type& right) |
|
{ |
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else |
|
return dynamic_interval_traits<Type>::construct_bounded |
|
( |
|
lower_max(left, right), |
|
upper_min(left, right) |
|
); |
|
} |
|
|
|
|
|
//- intersects ----------------------------------------------------------------- |
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
intersects(const Type& left, const Type& right) |
|
{ |
|
return !( icl::is_empty(left) || icl::is_empty(right) |
|
|| exclusive_less(left,right) || exclusive_less(right,left)); |
|
} |
|
|
|
//- disjoint ------------------------------------------------------------------- |
|
template<class Type> |
|
typename boost::enable_if<is_interval<Type>, bool>::type |
|
disjoint(const Type& left, const Type& right) |
|
{ |
|
return icl::is_empty(left) || icl::is_empty(right) |
|
|| exclusive_less(left,right) || exclusive_less(right,left); |
|
} |
|
|
|
//============================================================================== |
|
//= Complement |
|
//============================================================================== |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type |
|
inner_complement(const Type& left, const Type& right) |
|
{ |
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else if(exclusive_less(left, right)) |
|
return construct<Type>(upper(left), lower(right)); |
|
else if(exclusive_less(right, left)) |
|
return construct<Type>(upper(right), lower(left)); |
|
else |
|
return identity_element<Type>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_static_closed<Type>, Type>::type |
|
inner_complement(const Type& left, const Type& right) |
|
{ |
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else if(exclusive_less(left, right)) |
|
return construct<Type>(domain_next<Type>(upper(left)), domain_prior<Type>(lower(right))); |
|
else if(exclusive_less(right, left)) |
|
return construct<Type>(domain_next<Type>(upper(right)), domain_prior<Type>(lower(left))); |
|
else |
|
return identity_element<Type>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<is_discrete_static_open<Type>, Type>::type |
|
inner_complement(const Type& left, const Type& right) |
|
{ |
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else if(exclusive_less(left, right)) |
|
return construct<Type>(last(left), first(right)); |
|
else if(exclusive_less(right, left)) |
|
return construct<Type>(last(right), first(left)); |
|
else |
|
return identity_element<Type>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type |
|
inner_complement(const Type& left, const Type& right) |
|
{ |
|
if(icl::is_empty(left) || icl::is_empty(right)) |
|
return identity_element<Type>::value(); |
|
else if(exclusive_less(left, right)) |
|
return right_subtract(left_subtract(hull(left, right), left), right); |
|
else if(exclusive_less(right, left)) |
|
return right_subtract(left_subtract(hull(right, left), right), left); |
|
else |
|
return identity_element<Type>::value(); |
|
} |
|
|
|
template<class Type> |
|
inline typename boost::enable_if<is_interval<Type>, Type>::type |
|
between(const Type& left, const Type& right) |
|
{ |
|
return inner_complement(left, right); |
|
} |
|
|
|
|
|
|
|
//============================================================================== |
|
//= Distance |
|
//============================================================================== |
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::and_< is_interval<Type> |
|
, has_difference<typename interval_traits<Type>::domain_type> |
|
, is_discrete<typename interval_traits<Type>::domain_type> |
|
> |
|
, typename difference_type_of<interval_traits<Type> >::type>::type |
|
distance(const Type& x1, const Type& x2) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type difference_type; |
|
|
|
if(icl::is_empty(x1) || icl::is_empty(x2)) |
|
return icl::identity_element<difference_type>::value(); |
|
else if(domain_less<Type>(last(x1), first(x2))) |
|
return static_cast<difference_type>(icl::pred(first(x2) - last(x1))); |
|
else if(domain_less<Type>(last(x2), first(x1))) |
|
return static_cast<difference_type>(icl::pred(first(x1) - last(x2))); |
|
else |
|
return icl::identity_element<difference_type>::value(); |
|
} |
|
|
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::and_< is_interval<Type> |
|
, has_difference<typename interval_traits<Type>::domain_type> |
|
, is_continuous<typename interval_traits<Type>::domain_type> |
|
> |
|
, typename difference_type_of<interval_traits<Type> >::type>::type |
|
distance(const Type& x1, const Type& x2) |
|
{ |
|
typedef typename difference_type_of<interval_traits<Type> >::type DiffT; |
|
|
|
if(icl::is_empty(x1) || icl::is_empty(x2)) |
|
return icl::identity_element<DiffT>::value(); |
|
else if(domain_less<Type>(upper(x1), lower(x2))) |
|
return x2.lower() - x1.upper(); |
|
else if(domain_less<Type>(upper(x2), lower(x1))) |
|
return lower(x1) - upper(x2); |
|
else |
|
return icl::identity_element<DiffT>::value(); |
|
} |
|
|
|
//============================================================================== |
|
//= Streaming, representation |
|
//============================================================================== |
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::or_< is_static_left_open<Type> |
|
, is_static_open<Type> >, std::string>::type |
|
left_bracket(const Type&) { return "("; } |
|
|
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::or_< is_static_right_open<Type> |
|
, is_static_closed<Type> >, std::string>::type |
|
left_bracket(const Type&) { return "["; } |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type |
|
left_bracket(const Type& object) |
|
{ |
|
return left_bracket(object.bounds()); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::or_< is_static_right_open<Type> |
|
, is_static_open<Type> >, std::string>::type |
|
right_bracket(const Type&) { return ")"; } |
|
|
|
template<class Type> |
|
typename boost:: |
|
enable_if< mpl::or_< is_static_left_open<Type> |
|
, is_static_closed<Type> >, std::string>::type |
|
right_bracket(const Type&) { return "]"; } |
|
|
|
template<class Type> |
|
typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type |
|
right_bracket(const Type& object) |
|
{ |
|
return right_bracket(object.bounds()); |
|
} |
|
|
|
//------------------------------------------------------------------------------ |
|
template<class CharType, class CharTraits, class Type> |
|
typename boost::enable_if<is_interval<Type>, |
|
std::basic_ostream<CharType, CharTraits> >::type& |
|
operator << (std::basic_ostream<CharType, CharTraits> &stream, Type const& object) |
|
{ |
|
if(boost::icl::is_empty(object)) |
|
return stream << left_bracket<Type>(object) << right_bracket<Type>(object); |
|
else |
|
return stream << left_bracket<Type>(object) |
|
<< interval_traits<Type>::lower(object) |
|
<< "," |
|
<< interval_traits<Type>::upper(object) |
|
<< right_bracket<Type>(object) ; |
|
} |
|
|
|
}} // namespace icl boost |
|
|
|
#endif |
|
|
|
|