338 lines
11 KiB
Plaintext
338 lines
11 KiB
Plaintext
/* 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
|