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