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