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1/* Boost interval/arith.hpp template implementation file
2 *
3 * Copyright 2000 Jens Maurer
4 * Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion
5 *
6 * Distributed under the Boost Software License, Version 1.0.
7 * (See accompanying file LICENSE_1_0.txt or
8 * copy at http://www.boost.org/LICENSE_1_0.txt)
9 */
10
11#ifndef GECODE_BOOST_NUMERIC_INTERVAL_ARITH_HPP
12#define GECODE_BOOST_NUMERIC_INTERVAL_ARITH_HPP
13
14#include <gecode/third-party/boost/config.hpp>
15#include <gecode/third-party/boost/numeric/interval/interval.hpp>
16#include <gecode/third-party/boost/numeric/interval/detail/bugs.hpp>
17#include <gecode/third-party/boost/numeric/interval/detail/test_input.hpp>
18#include <gecode/third-party/boost/numeric/interval/detail/division.hpp>
19#include <algorithm>
20
21namespace gecode_boost {
22namespace numeric {
23
24/*
25 * Basic arithmetic operators
26 */
27
28template<class T, class Policies> inline
29const interval<T, Policies>& operator+(const interval<T, Policies>& x)
30{
31 return x;
32}
33
34template<class T, class Policies> inline
35interval<T, Policies> operator-(const interval<T, Policies>& x)
36{
37 if (interval_lib::detail::test_input(x))
38 return interval<T, Policies>::empty();
39 return interval<T, Policies>(-x.upper(), -x.lower(), true);
40}
41
42template<class T, class Policies> inline
43interval<T, Policies>& interval<T, Policies>::operator+=(const interval<T, Policies>& r)
44{
45 if (interval_lib::detail::test_input(*this, r))
46 set_empty();
47 else {
48 typename Policies::rounding rnd;
49 set(rnd.add_down(low, r.low), rnd.add_up(up, r.up));
50 }
51 return *this;
52}
53
54template<class T, class Policies> inline
55interval<T, Policies>& interval<T, Policies>::operator+=(const T& r)
56{
57 if (interval_lib::detail::test_input(*this, r))
58 set_empty();
59 else {
60 typename Policies::rounding rnd;
61 set(rnd.add_down(low, r), rnd.add_up(up, r));
62 }
63 return *this;
64}
65
66template<class T, class Policies> inline
67interval<T, Policies>& interval<T, Policies>::operator-=(const interval<T, Policies>& r)
68{
69 if (interval_lib::detail::test_input(*this, r))
70 set_empty();
71 else {
72 typename Policies::rounding rnd;
73 set(rnd.sub_down(low, r.up), rnd.sub_up(up, r.low));
74 }
75 return *this;
76}
77
78template<class T, class Policies> inline
79interval<T, Policies>& interval<T, Policies>::operator-=(const T& r)
80{
81 if (interval_lib::detail::test_input(*this, r))
82 set_empty();
83 else {
84 typename Policies::rounding rnd;
85 set(rnd.sub_down(low, r), rnd.sub_up(up, r));
86 }
87 return *this;
88}
89
90template<class T, class Policies> inline
91interval<T, Policies>& interval<T, Policies>::operator*=(const interval<T, Policies>& r)
92{
93 return *this = *this * r;
94}
95
96template<class T, class Policies> inline
97interval<T, Policies>& interval<T, Policies>::operator*=(const T& r)
98{
99 return *this = r * *this;
100}
101
102template<class T, class Policies> inline
103interval<T, Policies>& interval<T, Policies>::operator/=(const interval<T, Policies>& r)
104{
105 return *this = *this / r;
106}
107
108template<class T, class Policies> inline
109interval<T, Policies>& interval<T, Policies>::operator/=(const T& r)
110{
111 return *this = *this / r;
112}
113
114template<class T, class Policies> inline
115interval<T, Policies> operator+(const interval<T, Policies>& x,
116 const interval<T, Policies>& y)
117{
118 if (interval_lib::detail::test_input(x, y))
119 return interval<T, Policies>::empty();
120 typename Policies::rounding rnd;
121 return interval<T,Policies>(rnd.add_down(x.lower(), y.lower()),
122 rnd.add_up (x.upper(), y.upper()), true);
123}
124
125template<class T, class Policies> inline
126interval<T, Policies> operator+(const T& x, const interval<T, Policies>& y)
127{
128 if (interval_lib::detail::test_input(x, y))
129 return interval<T, Policies>::empty();
130 typename Policies::rounding rnd;
131 return interval<T,Policies>(rnd.add_down(x, y.lower()),
132 rnd.add_up (x, y.upper()), true);
133}
134
135template<class T, class Policies> inline
136interval<T, Policies> operator+(const interval<T, Policies>& x, const T& y)
137{ return y + x; }
138
139template<class T, class Policies> inline
140interval<T, Policies> operator-(const interval<T, Policies>& x,
141 const interval<T, Policies>& y)
142{
143 if (interval_lib::detail::test_input(x, y))
144 return interval<T, Policies>::empty();
145 typename Policies::rounding rnd;
146 return interval<T,Policies>(rnd.sub_down(x.lower(), y.upper()),
147 rnd.sub_up (x.upper(), y.lower()), true);
148}
149
150template<class T, class Policies> inline
151interval<T, Policies> operator-(const T& x, const interval<T, Policies>& y)
152{
153 if (interval_lib::detail::test_input(x, y))
154 return interval<T, Policies>::empty();
155 typename Policies::rounding rnd;
156 return interval<T,Policies>(rnd.sub_down(x, y.upper()),
157 rnd.sub_up (x, y.lower()), true);
158}
159
160template<class T, class Policies> inline
161interval<T, Policies> operator-(const interval<T, Policies>& x, const T& y)
162{
163 if (interval_lib::detail::test_input(x, y))
164 return interval<T, Policies>::empty();
165 typename Policies::rounding rnd;
166 return interval<T,Policies>(rnd.sub_down(x.lower(), y),
167 rnd.sub_up (x.upper(), y), true);
168}
169
170template<class T, class Policies> inline
171interval<T, Policies> operator*(const interval<T, Policies>& x,
172 const interval<T, Policies>& y)
173{
174 GECODE_BOOST_USING_STD_MIN();
175 GECODE_BOOST_USING_STD_MAX();
176 typedef interval<T, Policies> I;
177 if (interval_lib::detail::test_input(x, y))
178 return I::empty();
179 typename Policies::rounding rnd;
180 const T& xl = x.lower();
181 const T& xu = x.upper();
182 const T& yl = y.lower();
183 const T& yu = y.upper();
184
185 if (interval_lib::user::is_neg(xl))
186 if (interval_lib::user::is_pos(xu))
187 if (interval_lib::user::is_neg(yl))
188 if (interval_lib::user::is_pos(yu)) // M * M
189 return I(min GECODE_BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)),
190 max GECODE_BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_up (xl, yl), rnd.mul_up (xu, yu)), true);
191 else // M * N
192 return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true);
193 else
194 if (interval_lib::user::is_pos(yu)) // M * P
195 return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true);
196 else // M * Z
197 return I(static_cast<T>(0), static_cast<T>(0), true);
198 else
199 if (interval_lib::user::is_neg(yl))
200 if (interval_lib::user::is_pos(yu)) // N * M
201 return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true);
202 else // N * N
203 return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true);
204 else
205 if (interval_lib::user::is_pos(yu)) // N * P
206 return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true);
207 else // N * Z
208 return I(static_cast<T>(0), static_cast<T>(0), true);
209 else
210 if (interval_lib::user::is_pos(xu))
211 if (interval_lib::user::is_neg(yl))
212 if (interval_lib::user::is_pos(yu)) // P * M
213 return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true);
214 else // P * N
215 return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true);
216 else
217 if (interval_lib::user::is_pos(yu)) // P * P
218 return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true);
219 else // P * Z
220 return I(static_cast<T>(0), static_cast<T>(0), true);
221 else // Z * ?
222 return I(static_cast<T>(0), static_cast<T>(0), true);
223}
224
225template<class T, class Policies> inline
226interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y)
227{
228 typedef interval<T, Policies> I;
229 if (interval_lib::detail::test_input(x, y))
230 return I::empty();
231 typename Policies::rounding rnd;
232 const T& yl = y.lower();
233 const T& yu = y.upper();
234 // x is supposed not to be infinite
235 if (interval_lib::user::is_neg(x))
236 return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true);
237 else if (interval_lib::user::is_zero(x))
238 return I(static_cast<T>(0), static_cast<T>(0), true);
239 else
240 return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true);
241}
242
243template<class T, class Policies> inline
244interval<T, Policies> operator*(const interval<T, Policies>& x, const T& y)
245{ return y * x; }
246
247template<class T, class Policies> inline
248interval<T, Policies> operator/(const interval<T, Policies>& x,
249 const interval<T, Policies>& y)
250{
251 if (interval_lib::detail::test_input(x, y))
252 return interval<T, Policies>::empty();
253 if (zero_in(y))
254 if (!interval_lib::user::is_zero(y.lower()))
255 if (!interval_lib::user::is_zero(y.upper()))
256 return interval_lib::detail::div_zero(x);
257 else
258 return interval_lib::detail::div_negative(x, y.lower());
259 else
260 if (!interval_lib::user::is_zero(y.upper()))
261 return interval_lib::detail::div_positive(x, y.upper());
262 else
263 return interval<T, Policies>::empty();
264 else
265 return interval_lib::detail::div_non_zero(x, y);
266}
267
268template<class T, class Policies> inline
269interval<T, Policies> operator/(const T& x, const interval<T, Policies>& y)
270{
271 if (interval_lib::detail::test_input(x, y))
272 return interval<T, Policies>::empty();
273 if (zero_in(y))
274 if (!interval_lib::user::is_zero(y.lower()))
275 if (!interval_lib::user::is_zero(y.upper()))
276 return interval_lib::detail::div_zero<T, Policies>(x);
277 else
278 return interval_lib::detail::div_negative<T, Policies>(x, y.lower());
279 else
280 if (!interval_lib::user::is_zero(y.upper()))
281 return interval_lib::detail::div_positive<T, Policies>(x, y.upper());
282 else
283 return interval<T, Policies>::empty();
284 else
285 return interval_lib::detail::div_non_zero(x, y);
286}
287
288template<class T, class Policies> inline
289interval<T, Policies> operator/(const interval<T, Policies>& x, const T& y)
290{
291 if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y))
292 return interval<T, Policies>::empty();
293 typename Policies::rounding rnd;
294 const T& xl = x.lower();
295 const T& xu = x.upper();
296 if (interval_lib::user::is_neg(y))
297 return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true);
298 else
299 return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true);
300}
301
302} // namespace numeric
303} // namespace gecode_boost
304
305#endif // GECODE_BOOST_NUMERIC_INTERVAL_ARITH_HPP