boost/icl/concept/interval.hpp
/*-----------------------------------------------------------------------------+
Copyright (c) 2010-2010: Joachim Faulhaber
+------------------------------------------------------------------------------+
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENCE.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
+-----------------------------------------------------------------------------*/
#ifndef BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
#define BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
#include <boost/assert.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/mpl/and.hpp>
#include <boost/mpl/or.hpp>
#include <boost/mpl/not.hpp>
#include <boost/icl/detail/design_config.hpp>
#include <boost/icl/type_traits/unit_element.hpp>
#include <boost/icl/type_traits/identity_element.hpp>
#include <boost/icl/type_traits/infinity.hpp>
#include <boost/icl/type_traits/succ_pred.hpp>
#include <boost/icl/type_traits/is_numeric.hpp>
#include <boost/icl/type_traits/is_discrete.hpp>
#include <boost/icl/type_traits/is_continuous.hpp>
#include <boost/icl/type_traits/is_asymmetric_interval.hpp>
#include <boost/icl/type_traits/is_discrete_interval.hpp>
#include <boost/icl/type_traits/is_continuous_interval.hpp>
#include <boost/icl/concept/interval_bounds.hpp>
#include <boost/icl/interval_traits.hpp>
#include <boost/icl/dynamic_interval_traits.hpp>
#include <algorithm>
namespace boost{namespace icl
{
//==============================================================================
//= Ordering
//==============================================================================
template<class Type>
inline typename enable_if<is_interval<Type>, bool>::type
domain_less(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
return typename interval_traits<Type>::domain_compare()(left, right);
}
template<class Type>
inline typename enable_if<is_interval<Type>, bool>::type
domain_less_equal(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
return !(typename interval_traits<Type>::domain_compare()(right, left));
}
template<class Type>
inline typename enable_if<is_interval<Type>, bool>::type
domain_equal(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_compare domain_compare;
return !(domain_compare()(left, right)) && !(domain_compare()(right, left));
}
template<class Type>
inline typename enable_if< is_interval<Type>
, typename interval_traits<Type>::domain_type>::type
domain_next(const typename interval_traits<Type>::domain_type value)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
return icl::successor<domain_type,domain_compare>::apply(value);
}
template<class Type>
inline typename enable_if< is_interval<Type>
, typename interval_traits<Type>::domain_type>::type
domain_prior(const typename interval_traits<Type>::domain_type value)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
return icl::predecessor<domain_type,domain_compare>::apply(value);
}
//==============================================================================
//= Construct<Interval> singleton
//==============================================================================
template<class Type>
typename enable_if
<
mpl::and_< is_static_right_open<Type>
, is_discrete<typename interval_traits<Type>::domain_type> >
, Type
>::type
singleton(const typename interval_traits<Type>::domain_type& value)
{
//ASSERT: This always creates an interval with exactly one element
return interval_traits<Type>::construct(value, domain_next<Type>(value));
}
template<class Type>
typename enable_if
<
mpl::and_< is_static_left_open<Type>
, is_discrete<typename interval_traits<Type>::domain_type> >
, Type
>::type
singleton(const typename interval_traits<Type>::domain_type& value)
{
//ASSERT: This always creates an interval with exactly one element
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(value) ));
return interval_traits<Type>::construct(domain_prior<Type>(value), value);
}
template<class Type>
typename enable_if<is_discrete_static_open<Type>, Type>::type
singleton(const typename interval_traits<Type>::domain_type& value)
{
//ASSERT: This always creates an interval with exactly one element
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(value)));
return interval_traits<Type>::construct( domain_prior<Type>(value)
, domain_next<Type>(value));
}
template<class Type>
typename enable_if<is_discrete_static_closed<Type>, Type>::type
singleton(const typename interval_traits<Type>::domain_type& value)
{
//ASSERT: This always creates an interval with exactly one element
return interval_traits<Type>::construct(value, value);
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>, Type>::type
singleton(const typename interval_traits<Type>::domain_type& value)
{
return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
}
namespace detail
{
//==============================================================================
//= Construct<Interval> unit_trail == generalized singleton
// The smallest interval on an incrementable (and decrementable) type that can
// be constructed using ++ and -- and such that it contains a given value.
// If 'Type' is discrete, 'unit_trail' and 'singleton' are identical. So we
// can view 'unit_trail' as a generalized singleton for static intervals of
// continuous types.
//==============================================================================
template<class Type>
typename enable_if
<
mpl::and_< is_static_right_open<Type>
, boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
, Type
>::type
unit_trail(const typename interval_traits<Type>::domain_type& value)
{
return interval_traits<Type>::construct(value, domain_next<Type>(value));
}
template<class Type>
typename enable_if
<
mpl::and_< is_static_left_open<Type>
, boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
, Type
>::type
unit_trail(const typename interval_traits<Type>::domain_type& value)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(value) ));
return interval_traits<Type>::construct(domain_prior<Type>(value), value);
}
template<class Type>
typename enable_if
<
mpl::and_< is_static_open<Type>
, is_discrete<typename interval_traits<Type>::domain_type> >
, Type
>::type
unit_trail(const typename interval_traits<Type>::domain_type& value)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(value)));
return interval_traits<Type>::construct( domain_prior<Type>(value)
, domain_next<Type>(value));
}
template<class Type>
typename enable_if
<
mpl::and_< is_static_closed<Type>
, is_discrete<typename interval_traits<Type>::domain_type> >
, Type
>::type
unit_trail(const typename interval_traits<Type>::domain_type& value)
{
return interval_traits<Type>::construct(value, value);
}
//NOTE: statically bounded closed or open intervals of continuous domain types
// are NOT supported by ICL. They can not be used with interval containers
// consistently.
template<class Type>
typename enable_if<has_dynamic_bounds<Type>, Type>::type
unit_trail(const typename interval_traits<Type>::domain_type& value)
{
return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
}
} //namespace detail
//==============================================================================
//= Construct<Interval> multon
//==============================================================================
template<class Type>
typename enable_if<has_static_bounds<Type>, Type>::type
construct(const typename interval_traits<Type>::domain_type& low,
const typename interval_traits<Type>::domain_type& up )
{
return interval_traits<Type>::construct(low, up);
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>, Type>::type
construct(const typename interval_traits<Type>::domain_type& low,
const typename interval_traits<Type>::domain_type& up,
interval_bounds bounds = interval_bounds::right_open())
{
return dynamic_interval_traits<Type>::construct(low, up, bounds);
}
//- construct form bounded values ----------------------------------------------
template<class Type>
typename enable_if<has_dynamic_bounds<Type>, Type>::type
construct(const typename Type::bounded_domain_type& low,
const typename Type::bounded_domain_type& up)
{
return dynamic_interval_traits<Type>::construct_bounded(low, up);
}
template<class Type>
typename enable_if<is_interval<Type>, Type>::type
span(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
return construct<Type>(left, right);
else
return construct<Type>(right, left);
}
//==============================================================================
template<class Type>
typename enable_if<is_static_right_open<Type>, Type>::type
hull(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
return construct<Type>(left, domain_next<Type>(right));
else
return construct<Type>(right, domain_next<Type>(left));
}
template<class Type>
typename enable_if<is_static_left_open<Type>, Type>::type
hull(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
{
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(left) ));
return construct<Type>(domain_prior<Type>(left), right);
}
else
{
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(right) ));
return construct<Type>(domain_prior<Type>(right), left);
}
}
template<class Type>
typename enable_if<is_static_closed<Type>, Type>::type
hull(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
return construct<Type>(left, right);
else
return construct<Type>(right, left);
}
template<class Type>
typename enable_if<is_static_open<Type>, Type>::type
hull(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
{
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(left) ));
return construct<Type>( domain_prior<Type>(left)
, domain_next<Type>(right));
}
else
{
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(right) ));
return construct<Type>( domain_prior<Type>(right)
, domain_next<Type>(left));
}
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>, Type>::type
hull(const typename interval_traits<Type>::domain_type& left,
const typename interval_traits<Type>::domain_type& right)
{
typedef typename interval_traits<Type>::domain_compare domain_compare;
if(domain_compare()(left,right))
return construct<Type>(left, right, interval_bounds::closed());
else
return construct<Type>(right, left, interval_bounds::closed());
}
//==============================================================================
//= Selection
//==============================================================================
template<class Type>
inline typename enable_if<is_interval<Type>,
typename interval_traits<Type>::domain_type>::type
lower(const Type& object)
{
return interval_traits<Type>::lower(object);
}
template<class Type>
inline typename enable_if<is_interval<Type>,
typename interval_traits<Type>::domain_type>::type
upper(const Type& object)
{
return interval_traits<Type>::upper(object);
}
//- first ----------------------------------------------------------------------
template<class Type>
inline typename
enable_if< mpl::or_<is_static_right_open<Type>, is_static_closed<Type> >
, typename interval_traits<Type>::domain_type>::type
first(const Type& object)
{
return lower(object);
}
template<class Type>
inline typename
enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_open<Type> >
, is_discrete<typename interval_traits<Type>::domain_type> >
, typename interval_traits<Type>::domain_type>::type
first(const Type& object)
{
return domain_next<Type>(lower(object));
}
template<class Type>
inline typename enable_if<is_discrete_interval<Type>,
typename interval_traits<Type>::domain_type>::type
first(const Type& object)
{
return is_left_closed(object.bounds()) ?
lower(object) :
domain_next<Type>(lower(object));
}
//- last -----------------------------------------------------------------------
template<class Type>
inline typename
enable_if< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
, typename interval_traits<Type>::domain_type>::type
last(const Type& object)
{
return upper(object);
}
template<class Type>
inline typename
enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
, is_discrete<typename interval_traits<Type>::domain_type> >
, typename interval_traits<Type>::domain_type>::type
last(const Type& object)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than(upper(object)) ));
return domain_prior<Type>(upper(object));
}
template<class Type>
inline typename enable_if<is_discrete_interval<Type>,
typename interval_traits<Type>::domain_type>::type
last(const Type& object)
{
typedef typename interval_traits<Type>::domain_type domain_type;
typedef typename interval_traits<Type>::domain_compare domain_compare;
BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
::is_less_than_or(upper(object), is_right_closed(object.bounds())) ));
return is_right_closed(object.bounds()) ?
upper(object) :
domain_prior<Type>(upper(object));
}
//- last_next ------------------------------------------------------------------
template<class Type>
inline typename
enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
, is_discrete<typename interval_traits<Type>::domain_type> >
, typename interval_traits<Type>::domain_type>::type
last_next(const Type& object)
{
return domain_next<Type>(upper(object));
}
template<class Type>
inline typename
enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
, is_discrete<typename interval_traits<Type>::domain_type> >
, typename interval_traits<Type>::domain_type>::type
last_next(const Type& object)
{
//CL typedef typename interval_traits<Type>::domain_type domain_type;
return upper(object); // NOTE: last_next is implemented to avoid calling pred(object)
} // For unsigned integral types this may cause underflow.
template<class Type>
inline typename enable_if<is_discrete_interval<Type>,
typename interval_traits<Type>::domain_type>::type
last_next(const Type& object)
{
return is_right_closed(object.bounds()) ?
domain_next<Type>(upper(object)):
upper(object) ;
}
//------------------------------------------------------------------------------
template<class Type>
typename enable_if<has_dynamic_bounds<Type>,
typename Type::bounded_domain_type>::type
bounded_lower(const Type& object)
{
return typename
Type::bounded_domain_type(lower(object), object.bounds().left());
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>,
typename Type::bounded_domain_type>::type
reverse_bounded_lower(const Type& object)
{
return typename
Type::bounded_domain_type(lower(object),
object.bounds().reverse_left());
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>,
typename Type::bounded_domain_type>::type
bounded_upper(const Type& object)
{
return typename
Type::bounded_domain_type(upper(object),
object.bounds().right());
}
template<class Type>
typename enable_if<has_dynamic_bounds<Type>,
typename Type::bounded_domain_type>::type
reverse_bounded_upper(const Type& object)
{
return typename
Type::bounded_domain_type(upper(object),
object.bounds().reverse_right());
}
//- bounds ---------------------------------------------------------------------
template<class Type>
inline typename enable_if<has_dynamic_bounds<Type>, interval_bounds>::type
bounds(const Type& object)
{
return object.bounds();
}
template<class Type>
inline typename enable_if<has_static_bounds<Type>, interval_bounds>::type
bounds(const Type&)
{
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), lower(object) )
|| 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), lower(object) )
|| 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() );
}
//==============================================================================
//= 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>(upper(left), lower(right))
|| ( domain_equal<Type>(upper(left), lower(right))
&& 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>(lower(left), lower(right));
}
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>(lower(left), lower(right));
else
return domain_less<Type>(lower(left), lower(right));
}
//------------------------------------------------------------------------------
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>(upper(left), upper(right));
}
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>(upper(left), upper(right));
else
return domain_less<Type>(upper(left), upper(right));
}
//------------------------------------------------------------------------------
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>(lower(left), lower(right));
}
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>(lower(left), lower(right));
}
//------------------------------------------------------------------------------
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>(upper(left), upper(right));
}
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>(upper(left), upper(right));
}
//------------------------------------------------------------------------------
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);
}
//==============================================================================
//= 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>(upper(left), lower(right))
|| ( domain_equal<Type>(upper(left), lower(right))
&& 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>(lower(super), element)
: domain_less<Type>(lower(super), element))
&&
(is_right_closed(super.bounds())
? domain_less_equal<Type>(element, upper(super))
: domain_less<Type>(element, upper(super)));
}
//- 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);
}
//- 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>(upper(left), lower(right));
}
//==============================================================================
//= 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;
else if(upper_less_equal(right, left_minuend))
return identity_element<Type>::value();
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 left 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 lower(x2) - upper(x1);
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
