/* Boost interval/utility.hpp template implementation file | |
* | |
* Copyright 2000 Jens Maurer | |
* Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion | |
* | |
* Distributed under the Boost Software License, Version 1.0. | |
* (See accompanying file LICENSE_1_0.txt or | |
* copy at http://www.boost.org/LICENSE_1_0.txt) | |
*/ | |
#ifndef BOOST_NUMERIC_INTERVAL_UTILITY_HPP | |
#define BOOST_NUMERIC_INTERVAL_UTILITY_HPP | |
#include <boost/config.hpp> | |
#include <boost/numeric/interval/detail/interval_prototype.hpp> | |
#include <boost/numeric/interval/detail/test_input.hpp> | |
#include <boost/numeric/interval/detail/bugs.hpp> | |
#include <algorithm> | |
#include <utility> | |
/* | |
* Implementation of simple functions | |
*/ | |
namespace boost { | |
namespace numeric { | |
/* | |
* Utility Functions | |
*/ | |
template<class T, class Policies> inline | |
const T& lower(const interval<T, Policies>& x) | |
{ | |
return x.lower(); | |
} | |
template<class T, class Policies> inline | |
const T& upper(const interval<T, Policies>& x) | |
{ | |
return x.upper(); | |
} | |
template<class T, class Policies> inline | |
T checked_lower(const interval<T, Policies>& x) | |
{ | |
if (empty(x)) { | |
typedef typename Policies::checking checking; | |
return checking::nan(); | |
} | |
return x.lower(); | |
} | |
template<class T, class Policies> inline | |
T checked_upper(const interval<T, Policies>& x) | |
{ | |
if (empty(x)) { | |
typedef typename Policies::checking checking; | |
return checking::nan(); | |
} | |
return x.upper(); | |
} | |
template<class T, class Policies> inline | |
T width(const interval<T, Policies>& x) | |
{ | |
if (interval_lib::detail::test_input(x)) return static_cast<T>(0); | |
typename Policies::rounding rnd; | |
return rnd.sub_up(x.upper(), x.lower()); | |
} | |
template<class T, class Policies> inline | |
T median(const interval<T, Policies>& x) | |
{ | |
if (interval_lib::detail::test_input(x)) { | |
typedef typename Policies::checking checking; | |
return checking::nan(); | |
} | |
typename Policies::rounding rnd; | |
return rnd.median(x.lower(), x.upper()); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> widen(const interval<T, Policies>& x, const T& v) | |
{ | |
if (interval_lib::detail::test_input(x)) | |
return interval<T, Policies>::empty(); | |
typename Policies::rounding rnd; | |
return interval<T, Policies>(rnd.sub_down(x.lower(), v), | |
rnd.add_up (x.upper(), v), true); | |
} | |
/* | |
* Set-like operations | |
*/ | |
template<class T, class Policies> inline | |
bool empty(const interval<T, Policies>& x) | |
{ | |
return interval_lib::detail::test_input(x); | |
} | |
template<class T, class Policies> inline | |
bool zero_in(const interval<T, Policies>& x) | |
{ | |
if (interval_lib::detail::test_input(x)) return false; | |
return (!interval_lib::user::is_pos(x.lower())) && | |
(!interval_lib::user::is_neg(x.upper())); | |
} | |
template<class T, class Policies> inline | |
bool in_zero(const interval<T, Policies>& x) // DEPRECATED | |
{ | |
return zero_in<T, Policies>(x); | |
} | |
template<class T, class Policies> inline | |
bool in(const T& x, const interval<T, Policies>& y) | |
{ | |
if (interval_lib::detail::test_input(x, y)) return false; | |
return y.lower() <= x && x <= y.upper(); | |
} | |
template<class T, class Policies> inline | |
bool subset(const interval<T, Policies>& x, | |
const interval<T, Policies>& y) | |
{ | |
if (empty(x)) return true; | |
return !empty(y) && y.lower() <= x.lower() && x.upper() <= y.upper(); | |
} | |
template<class T, class Policies1, class Policies2> inline | |
bool proper_subset(const interval<T, Policies1>& x, | |
const interval<T, Policies2>& y) | |
{ | |
if (empty(y)) return false; | |
if (empty(x)) return true; | |
return y.lower() <= x.lower() && x.upper() <= y.upper() && | |
(y.lower() != x.lower() || x.upper() != y.upper()); | |
} | |
template<class T, class Policies1, class Policies2> inline | |
bool overlap(const interval<T, Policies1>& x, | |
const interval<T, Policies2>& y) | |
{ | |
if (interval_lib::detail::test_input(x, y)) return false; | |
return (x.lower() <= y.lower() && y.lower() <= x.upper()) || | |
(y.lower() <= x.lower() && x.lower() <= y.upper()); | |
} | |
template<class T, class Policies> inline | |
bool singleton(const interval<T, Policies>& x) | |
{ | |
return !empty(x) && x.lower() == x.upper(); | |
} | |
template<class T, class Policies1, class Policies2> inline | |
bool equal(const interval<T, Policies1>& x, const interval<T, Policies2>& y) | |
{ | |
if (empty(x)) return empty(y); | |
return !empty(y) && x.lower() == y.lower() && x.upper() == y.upper(); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> intersect(const interval<T, Policies>& x, | |
const interval<T, Policies>& y) | |
{ | |
BOOST_USING_STD_MIN(); | |
BOOST_USING_STD_MAX(); | |
if (interval_lib::detail::test_input(x, y)) | |
return interval<T, Policies>::empty(); | |
const T& l = max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()); | |
const T& u = min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()); | |
if (l <= u) return interval<T, Policies>(l, u, true); | |
else return interval<T, Policies>::empty(); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> hull(const interval<T, Policies>& x, | |
const interval<T, Policies>& y) | |
{ | |
BOOST_USING_STD_MIN(); | |
BOOST_USING_STD_MAX(); | |
bool bad_x = interval_lib::detail::test_input(x); | |
bool bad_y = interval_lib::detail::test_input(y); | |
if (bad_x) | |
if (bad_y) return interval<T, Policies>::empty(); | |
else return y; | |
else | |
if (bad_y) return x; | |
return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), | |
max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> hull(const interval<T, Policies>& x, const T& y) | |
{ | |
BOOST_USING_STD_MIN(); | |
BOOST_USING_STD_MAX(); | |
bool bad_x = interval_lib::detail::test_input(x); | |
bool bad_y = interval_lib::detail::test_input<T, Policies>(y); | |
if (bad_y) | |
if (bad_x) return interval<T, Policies>::empty(); | |
else return x; | |
else | |
if (bad_x) return interval<T, Policies>(y, y, true); | |
return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), | |
max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> hull(const T& x, const interval<T, Policies>& y) | |
{ | |
BOOST_USING_STD_MIN(); | |
BOOST_USING_STD_MAX(); | |
bool bad_x = interval_lib::detail::test_input<T, Policies>(x); | |
bool bad_y = interval_lib::detail::test_input(y); | |
if (bad_x) | |
if (bad_y) return interval<T, Policies>::empty(); | |
else return y; | |
else | |
if (bad_y) return interval<T, Policies>(x, x, true); | |
return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), | |
max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); | |
} | |
template<class T> inline | |
interval<T> hull(const T& x, const T& y) | |
{ | |
return interval<T>::hull(x, y); | |
} | |
template<class T, class Policies> inline | |
std::pair<interval<T, Policies>, interval<T, Policies> > | |
bisect(const interval<T, Policies>& x) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x)) | |
return std::pair<I,I>(I::empty(), I::empty()); | |
const T m = median(x); | |
return std::pair<I,I>(I(x.lower(), m, true), I(m, x.upper(), true)); | |
} | |
/* | |
* Elementary functions | |
*/ | |
template<class T, class Policies> inline | |
T norm(const interval<T, Policies>& x) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x)) { | |
typedef typename Policies::checking checking; | |
return checking::nan(); | |
} | |
BOOST_USING_STD_MAX(); | |
return max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> abs(const interval<T, Policies>& x) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x)) | |
return I::empty(); | |
if (!interval_lib::user::is_neg(x.lower())) return x; | |
if (!interval_lib::user::is_pos(x.upper())) return -x; | |
BOOST_USING_STD_MAX(); | |
return I(static_cast<T>(0), max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, | |
const interval<T, Policies>& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MAX(); | |
return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MAX(); | |
return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MAX(); | |
return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, | |
const interval<T, Policies>& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MIN(); | |
return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MIN(); | |
return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); | |
} | |
template<class T, class Policies> inline | |
interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y) | |
{ | |
typedef interval<T, Policies> I; | |
if (interval_lib::detail::test_input(x, y)) | |
return I::empty(); | |
BOOST_USING_STD_MIN(); | |
return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); | |
} | |
} // namespace numeric | |
} // namespace boost | |
#endif // BOOST_NUMERIC_INTERVAL_UTILITY_HPP |