[1022] | 1 | /* Boost interval/utility.hpp template implementation file |
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| 2 | * |
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| 3 | * Copyright 2000 Jens Maurer |
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| 4 | * Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion |
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| 5 | * |
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| 6 | * Distributed under the Boost Software License, Version 1.0. |
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| 7 | * (See accompanying file LICENSE_1_0.txt or |
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| 8 | * copy at http://www.boost.org/LICENSE_1_0.txt) |
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| 9 | */ |
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| 10 | |
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| 11 | #ifndef BOOST_NUMERIC_INTERVAL_UTILITY_HPP |
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| 12 | #define BOOST_NUMERIC_INTERVAL_UTILITY_HPP |
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| 13 | |
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| 14 | #include <boost/config.hpp> |
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| 15 | #include <boost/numeric/interval/detail/interval_prototype.hpp> |
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| 16 | #include <boost/numeric/interval/detail/test_input.hpp> |
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| 17 | #include <boost/numeric/interval/detail/bugs.hpp> |
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| 18 | #include <algorithm> |
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| 19 | #include <utility> |
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| 20 | |
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| 21 | /* |
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| 22 | * Implementation of simple functions |
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| 23 | */ |
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| 24 | |
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| 25 | namespace boost { |
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| 26 | namespace numeric { |
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| 27 | |
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| 28 | /* |
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| 29 | * Utility Functions |
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| 30 | */ |
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| 31 | |
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| 32 | template<class T, class Policies> inline |
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| 33 | const T& lower(const interval<T, Policies>& x) |
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| 34 | { |
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| 35 | return x.lower(); |
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| 36 | } |
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| 37 | |
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| 38 | template<class T, class Policies> inline |
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| 39 | const T& upper(const interval<T, Policies>& x) |
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| 40 | { |
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| 41 | return x.upper(); |
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| 42 | } |
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| 43 | |
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| 44 | template<class T, class Policies> inline |
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| 45 | T checked_lower(const interval<T, Policies>& x) |
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| 46 | { |
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| 47 | if (empty(x)) { |
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| 48 | typedef typename Policies::checking checking; |
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| 49 | return checking::nan(); |
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| 50 | } |
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| 51 | return x.lower(); |
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| 52 | } |
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| 53 | |
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| 54 | template<class T, class Policies> inline |
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| 55 | T checked_upper(const interval<T, Policies>& x) |
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| 56 | { |
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| 57 | if (empty(x)) { |
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| 58 | typedef typename Policies::checking checking; |
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| 59 | return checking::nan(); |
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| 60 | } |
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| 61 | return x.upper(); |
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| 62 | } |
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| 63 | |
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| 64 | template<class T, class Policies> inline |
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| 65 | T width(const interval<T, Policies>& x) |
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| 66 | { |
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| 67 | if (interval_lib::detail::test_input(x)) return static_cast<T>(0); |
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| 68 | typename Policies::rounding rnd; |
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| 69 | return rnd.sub_up(x.upper(), x.lower()); |
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| 70 | } |
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| 71 | |
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| 72 | template<class T, class Policies> inline |
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| 73 | T median(const interval<T, Policies>& x) |
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| 74 | { |
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| 75 | if (interval_lib::detail::test_input(x)) { |
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| 76 | typedef typename Policies::checking checking; |
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| 77 | return checking::nan(); |
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| 78 | } |
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| 79 | typename Policies::rounding rnd; |
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| 80 | return rnd.median(x.lower(), x.upper()); |
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| 81 | } |
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| 82 | |
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| 83 | template<class T, class Policies> inline |
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| 84 | interval<T, Policies> widen(const interval<T, Policies>& x, const T& v) |
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| 85 | { |
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| 86 | if (interval_lib::detail::test_input(x)) |
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| 87 | return interval<T, Policies>::empty(); |
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| 88 | typename Policies::rounding rnd; |
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| 89 | return interval<T, Policies>(rnd.sub_down(x.lower(), v), |
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| 90 | rnd.add_up (x.upper(), v), true); |
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| 91 | } |
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| 92 | |
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| 93 | /* |
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| 94 | * Set-like operations |
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| 95 | */ |
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| 96 | |
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| 97 | template<class T, class Policies> inline |
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| 98 | bool empty(const interval<T, Policies>& x) |
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| 99 | { |
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| 100 | return interval_lib::detail::test_input(x); |
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| 101 | } |
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| 102 | |
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| 103 | template<class T, class Policies> inline |
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| 104 | bool zero_in(const interval<T, Policies>& x) |
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| 105 | { |
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| 106 | if (interval_lib::detail::test_input(x)) return false; |
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| 107 | return (!interval_lib::user::is_pos(x.lower())) && |
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| 108 | (!interval_lib::user::is_neg(x.upper())); |
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| 109 | } |
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| 110 | |
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| 111 | template<class T, class Policies> inline |
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| 112 | bool in_zero(const interval<T, Policies>& x) // DEPRECATED |
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| 113 | { |
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| 114 | return zero_in<T, Policies>(x); |
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| 115 | } |
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| 116 | |
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| 117 | template<class T, class Policies> inline |
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| 118 | bool in(const T& x, const interval<T, Policies>& y) |
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| 119 | { |
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| 120 | if (interval_lib::detail::test_input(x, y)) return false; |
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| 121 | return y.lower() <= x && x <= y.upper(); |
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| 122 | } |
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| 123 | |
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| 124 | template<class T, class Policies> inline |
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| 125 | bool subset(const interval<T, Policies>& x, |
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| 126 | const interval<T, Policies>& y) |
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| 127 | { |
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| 128 | if (empty(x)) return true; |
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| 129 | return !empty(y) && y.lower() <= x.lower() && x.upper() <= y.upper(); |
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| 130 | } |
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| 131 | |
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| 132 | template<class T, class Policies1, class Policies2> inline |
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| 133 | bool proper_subset(const interval<T, Policies1>& x, |
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| 134 | const interval<T, Policies2>& y) |
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| 135 | { |
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| 136 | if (empty(y)) return false; |
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| 137 | if (empty(x)) return true; |
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| 138 | return y.lower() <= x.lower() && x.upper() <= y.upper() && |
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| 139 | (y.lower() != x.lower() || x.upper() != y.upper()); |
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| 140 | } |
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| 141 | |
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| 142 | template<class T, class Policies1, class Policies2> inline |
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| 143 | bool overlap(const interval<T, Policies1>& x, |
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| 144 | const interval<T, Policies2>& y) |
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| 145 | { |
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| 146 | if (interval_lib::detail::test_input(x, y)) return false; |
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| 147 | return x.lower() <= y.lower() && y.lower() <= x.upper() || |
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| 148 | y.lower() <= x.lower() && x.lower() <= y.upper(); |
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| 149 | } |
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| 150 | |
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| 151 | template<class T, class Policies> inline |
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| 152 | bool singleton(const interval<T, Policies>& x) |
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| 153 | { |
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| 154 | return !empty(x) && x.lower() == x.upper(); |
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| 155 | } |
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| 156 | |
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| 157 | template<class T, class Policies1, class Policies2> inline |
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| 158 | bool equal(const interval<T, Policies1>& x, const interval<T, Policies2>& y) |
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| 159 | { |
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| 160 | if (empty(x)) return empty(y); |
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| 161 | return !empty(y) && x.lower() == y.lower() && x.upper() == y.upper(); |
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| 162 | } |
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| 163 | |
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| 164 | template<class T, class Policies> inline |
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| 165 | interval<T, Policies> intersect(const interval<T, Policies>& x, |
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| 166 | const interval<T, Policies>& y) |
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| 167 | { |
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| 168 | BOOST_USING_STD_MIN(); |
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| 169 | BOOST_USING_STD_MAX(); |
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| 170 | if (interval_lib::detail::test_input(x, y)) |
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| 171 | return interval<T, Policies>::empty(); |
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| 172 | const T& l = max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()); |
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| 173 | const T& u = min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()); |
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| 174 | if (l <= u) return interval<T, Policies>(l, u, true); |
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| 175 | else return interval<T, Policies>::empty(); |
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| 176 | } |
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| 177 | |
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| 178 | template<class T, class Policies> inline |
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| 179 | interval<T, Policies> hull(const interval<T, Policies>& x, |
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| 180 | const interval<T, Policies>& y) |
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| 181 | { |
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| 182 | BOOST_USING_STD_MIN(); |
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| 183 | BOOST_USING_STD_MAX(); |
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| 184 | bool bad_x = interval_lib::detail::test_input(x); |
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| 185 | bool bad_y = interval_lib::detail::test_input(y); |
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| 186 | if (bad_x) |
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| 187 | if (bad_y) return interval<T, Policies>::empty(); |
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| 188 | else return y; |
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| 189 | else |
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| 190 | if (bad_y) return x; |
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| 191 | return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), |
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| 192 | max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true); |
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| 193 | } |
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| 194 | |
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| 195 | template<class T, class Policies> inline |
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| 196 | interval<T, Policies> hull(const interval<T, Policies>& x, const T& y) |
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| 197 | { |
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| 198 | BOOST_USING_STD_MIN(); |
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| 199 | BOOST_USING_STD_MAX(); |
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| 200 | bool bad_x = interval_lib::detail::test_input(x); |
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| 201 | bool bad_y = interval_lib::detail::test_input<T, Policies>(y); |
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| 202 | if (bad_y) |
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| 203 | if (bad_x) return interval<T, Policies>::empty(); |
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| 204 | else return x; |
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| 205 | else |
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| 206 | if (bad_x) return interval<T, Policies>(y, y, true); |
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| 207 | return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), |
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| 208 | max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); |
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| 209 | } |
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| 210 | |
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| 211 | template<class T, class Policies> inline |
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| 212 | interval<T, Policies> hull(const T& x, const interval<T, Policies>& y) |
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| 213 | { |
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| 214 | BOOST_USING_STD_MIN(); |
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| 215 | BOOST_USING_STD_MAX(); |
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| 216 | bool bad_x = interval_lib::detail::test_input<T, Policies>(x); |
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| 217 | bool bad_y = interval_lib::detail::test_input(y); |
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| 218 | if (bad_x) |
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| 219 | if (bad_y) return interval<T, Policies>::empty(); |
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| 220 | else return y; |
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| 221 | else |
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| 222 | if (bad_y) return interval<T, Policies>(x, x, true); |
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| 223 | return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), |
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| 224 | max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); |
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| 225 | } |
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| 226 | |
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| 227 | template<class T> inline |
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| 228 | interval<T> hull(const T& x, const T& y) |
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| 229 | { |
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| 230 | return interval<T>::hull(x, y); |
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| 231 | } |
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| 232 | |
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| 233 | template<class T, class Policies> inline |
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| 234 | std::pair<interval<T, Policies>, interval<T, Policies> > |
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| 235 | bisect(const interval<T, Policies>& x) |
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| 236 | { |
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| 237 | typedef interval<T, Policies> I; |
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| 238 | if (interval_lib::detail::test_input(x)) |
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| 239 | return std::pair<I,I>(I::empty(), I::empty()); |
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| 240 | const T m = median(x); |
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| 241 | return std::pair<I,I>(I(x.lower(), m, true), I(m, x.upper(), true)); |
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| 242 | } |
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| 243 | |
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| 244 | /* |
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| 245 | * Elementary functions |
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| 246 | */ |
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| 247 | |
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| 248 | template<class T, class Policies> inline |
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| 249 | T norm(const interval<T, Policies>& x) |
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| 250 | { |
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| 251 | typedef interval<T, Policies> I; |
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| 252 | if (interval_lib::detail::test_input(x)) { |
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| 253 | typedef typename Policies::checking checking; |
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| 254 | return checking::nan(); |
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| 255 | } |
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| 256 | BOOST_USING_STD_MAX(); |
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| 257 | return max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()); |
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| 258 | } |
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| 259 | |
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| 260 | template<class T, class Policies> inline |
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| 261 | interval<T, Policies> abs(const interval<T, Policies>& x) |
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| 262 | { |
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| 263 | typedef interval<T, Policies> I; |
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| 264 | if (interval_lib::detail::test_input(x)) |
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| 265 | return I::empty(); |
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| 266 | if (!interval_lib::user::is_neg(x.lower())) return x; |
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| 267 | if (!interval_lib::user::is_pos(x.upper())) return -x; |
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| 268 | BOOST_USING_STD_MAX(); |
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| 269 | return I(static_cast<T>(0), max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()), true); |
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| 270 | } |
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| 271 | |
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| 272 | template<class T, class Policies> inline |
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| 273 | interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, |
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| 274 | const interval<T, Policies>& y) |
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| 275 | { |
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| 276 | typedef interval<T, Policies> I; |
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| 277 | if (interval_lib::detail::test_input(x, y)) |
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| 278 | return I::empty(); |
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| 279 | BOOST_USING_STD_MAX(); |
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| 280 | 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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| 281 | } |
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| 282 | |
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| 283 | template<class T, class Policies> inline |
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| 284 | interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y) |
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| 285 | { |
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| 286 | typedef interval<T, Policies> I; |
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| 287 | if (interval_lib::detail::test_input(x, y)) |
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| 288 | return I::empty(); |
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| 289 | BOOST_USING_STD_MAX(); |
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| 290 | return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); |
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| 291 | } |
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| 292 | |
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| 293 | template<class T, class Policies> inline |
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| 294 | interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y) |
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| 295 | { |
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| 296 | typedef interval<T, Policies> I; |
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| 297 | if (interval_lib::detail::test_input(x, y)) |
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| 298 | return I::empty(); |
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| 299 | BOOST_USING_STD_MAX(); |
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| 300 | return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); |
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| 301 | } |
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| 302 | |
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| 303 | template<class T, class Policies> inline |
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| 304 | interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, |
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| 305 | const interval<T, Policies>& y) |
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| 306 | { |
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| 307 | typedef interval<T, Policies> I; |
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| 308 | if (interval_lib::detail::test_input(x, y)) |
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| 309 | return I::empty(); |
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| 310 | BOOST_USING_STD_MIN(); |
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| 311 | 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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| 312 | } |
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| 313 | |
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| 314 | template<class T, class Policies> inline |
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| 315 | interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y) |
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| 316 | { |
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| 317 | typedef interval<T, Policies> I; |
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| 318 | if (interval_lib::detail::test_input(x, y)) |
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| 319 | return I::empty(); |
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| 320 | BOOST_USING_STD_MIN(); |
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| 321 | return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true); |
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| 322 | } |
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| 323 | |
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| 324 | template<class T, class Policies> inline |
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| 325 | interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y) |
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| 326 | { |
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| 327 | typedef interval<T, Policies> I; |
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| 328 | if (interval_lib::detail::test_input(x, y)) |
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| 329 | return I::empty(); |
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| 330 | BOOST_USING_STD_MIN(); |
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| 331 | return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true); |
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| 332 | } |
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| 333 | |
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| 334 | } // namespace numeric |
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| 335 | } // namespace boost |
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| 336 | |
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| 337 | #endif // BOOST_NUMERIC_INTERVAL_UTILITY_HPP |
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