| /* 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 |