1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_TOLERANCE_H |
---|
20 | #define LEMON_TOLERANCE_H |
---|
21 | |
---|
22 | ///\ingroup misc |
---|
23 | ///\file |
---|
24 | ///\brief A basic tool to handle the anomalies of calculation with |
---|
25 | ///floating point numbers. |
---|
26 | /// |
---|
27 | ///\todo It should be in a module like "Basic tools" |
---|
28 | |
---|
29 | |
---|
30 | namespace lemon { |
---|
31 | |
---|
32 | /// \addtogroup misc |
---|
33 | /// @{ |
---|
34 | |
---|
35 | ///\brief A class to provide a basic way to |
---|
36 | ///handle the comparison of numbers that are obtained |
---|
37 | ///as a result of a probably inexact computation. |
---|
38 | /// |
---|
39 | ///Tolerance is a class to provide a basic way to |
---|
40 | ///handle the comparison of numbers that are obtained |
---|
41 | ///as a result of a probably inexact computation. |
---|
42 | /// |
---|
43 | ///This is an abstract class, it should be specialized for all numerical |
---|
44 | ///data types. These specialized classes like \ref Tolerance\<double\> |
---|
45 | ///may offer additional tuning parameters. |
---|
46 | /// |
---|
47 | ///\sa Tolerance<float> |
---|
48 | ///\sa Tolerance<double> |
---|
49 | ///\sa Tolerance<long double> |
---|
50 | ///\sa Tolerance<int> |
---|
51 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
---|
52 | ///\sa Tolerance<long long int> |
---|
53 | #endif |
---|
54 | ///\sa Tolerance<unsigned int> |
---|
55 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
---|
56 | ///\sa Tolerance<unsigned long long int> |
---|
57 | #endif |
---|
58 | |
---|
59 | template<class T> |
---|
60 | class Tolerance |
---|
61 | { |
---|
62 | public: |
---|
63 | typedef T Value; |
---|
64 | |
---|
65 | ///\name Comparisons |
---|
66 | ///The concept is that these bool functions return with \c true only if |
---|
67 | ///the related comparisons hold even if some numerical error appeared |
---|
68 | ///during the computations. |
---|
69 | |
---|
70 | ///@{ |
---|
71 | |
---|
72 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
73 | static bool less(Value a,Value b) {return false;} |
---|
74 | ///Returns \c true if \c a is \e surely different from \c b |
---|
75 | static bool different(Value a,Value b) {return false;} |
---|
76 | ///Returns \c true if \c a is \e surely positive |
---|
77 | static bool positive(Value a) {return false;} |
---|
78 | ///Returns \c true if \c a is \e surely negative |
---|
79 | static bool negative(Value a) {return false;} |
---|
80 | ///Returns \c true if \c a is \e surely non-zero |
---|
81 | static bool nonZero(Value a) {return false;} |
---|
82 | |
---|
83 | ///@} |
---|
84 | |
---|
85 | ///Returns the zero value. |
---|
86 | static Value zero() {return T();} |
---|
87 | |
---|
88 | // static bool finite(Value a) {} |
---|
89 | // static Value big() {} |
---|
90 | // static Value negativeBig() {} |
---|
91 | }; |
---|
92 | |
---|
93 | |
---|
94 | ///Float specialization of \ref Tolerance. |
---|
95 | |
---|
96 | ///Float specialization of \ref Tolerance. |
---|
97 | ///\sa Tolerance |
---|
98 | ///\relates Tolerance |
---|
99 | template<> |
---|
100 | class Tolerance<float> |
---|
101 | { |
---|
102 | static float def_epsilon; |
---|
103 | float _epsilon; |
---|
104 | public: |
---|
105 | ///\e |
---|
106 | typedef float Value; |
---|
107 | |
---|
108 | ///Constructor setting the epsilon tolerance to the default value. |
---|
109 | Tolerance() : _epsilon(def_epsilon) {} |
---|
110 | ///Constructor setting the epsilon tolerance. |
---|
111 | Tolerance(float e) : _epsilon(e) {} |
---|
112 | |
---|
113 | ///Return the epsilon value. |
---|
114 | Value epsilon() const {return _epsilon;} |
---|
115 | ///Set the epsilon value. |
---|
116 | void epsilon(Value e) {_epsilon=e;} |
---|
117 | |
---|
118 | ///Return the default epsilon value. |
---|
119 | static Value defaultEpsilon() {return def_epsilon;} |
---|
120 | ///Set the default epsilon value. |
---|
121 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
---|
122 | |
---|
123 | ///\name Comparisons |
---|
124 | ///See class Tolerance for more details. |
---|
125 | |
---|
126 | ///@{ |
---|
127 | |
---|
128 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
129 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
---|
130 | ///Returns \c true if \c a is \e surely different from \c b |
---|
131 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
---|
132 | ///Returns \c true if \c a is \e surely positive |
---|
133 | bool positive(Value a) const { return _epsilon<a; } |
---|
134 | ///Returns \c true if \c a is \e surely negative |
---|
135 | bool negative(Value a) const { return -_epsilon>a; } |
---|
136 | ///Returns \c true if \c a is \e surely non-zero |
---|
137 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
---|
138 | |
---|
139 | ///@} |
---|
140 | |
---|
141 | ///Returns zero |
---|
142 | static Value zero() {return 0;} |
---|
143 | }; |
---|
144 | |
---|
145 | ///Double specialization of \ref Tolerance. |
---|
146 | |
---|
147 | ///Double specialization of \ref Tolerance. |
---|
148 | ///\sa Tolerance |
---|
149 | ///\relates Tolerance |
---|
150 | template<> |
---|
151 | class Tolerance<double> |
---|
152 | { |
---|
153 | static double def_epsilon; |
---|
154 | double _epsilon; |
---|
155 | public: |
---|
156 | ///\e |
---|
157 | typedef double Value; |
---|
158 | |
---|
159 | ///Constructor setting the epsilon tolerance to the default value. |
---|
160 | Tolerance() : _epsilon(def_epsilon) {} |
---|
161 | ///Constructor setting the epsilon tolerance. |
---|
162 | Tolerance(double e) : _epsilon(e) {} |
---|
163 | |
---|
164 | ///Return the epsilon value. |
---|
165 | Value epsilon() const {return _epsilon;} |
---|
166 | ///Set the epsilon value. |
---|
167 | void epsilon(Value e) {_epsilon=e;} |
---|
168 | |
---|
169 | ///Return the default epsilon value. |
---|
170 | static Value defaultEpsilon() {return def_epsilon;} |
---|
171 | ///Set the default epsilon value. |
---|
172 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
---|
173 | |
---|
174 | ///\name Comparisons |
---|
175 | ///See class Tolerance for more details. |
---|
176 | |
---|
177 | ///@{ |
---|
178 | |
---|
179 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
180 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
---|
181 | ///Returns \c true if \c a is \e surely different from \c b |
---|
182 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
---|
183 | ///Returns \c true if \c a is \e surely positive |
---|
184 | bool positive(Value a) const { return _epsilon<a; } |
---|
185 | ///Returns \c true if \c a is \e surely negative |
---|
186 | bool negative(Value a) const { return -_epsilon>a; } |
---|
187 | ///Returns \c true if \c a is \e surely non-zero |
---|
188 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
---|
189 | |
---|
190 | ///@} |
---|
191 | |
---|
192 | ///Returns zero |
---|
193 | static Value zero() {return 0;} |
---|
194 | }; |
---|
195 | |
---|
196 | ///Long double specialization of \ref Tolerance. |
---|
197 | |
---|
198 | ///Long double specialization of \ref Tolerance. |
---|
199 | ///\sa Tolerance |
---|
200 | ///\relates Tolerance |
---|
201 | template<> |
---|
202 | class Tolerance<long double> |
---|
203 | { |
---|
204 | static long double def_epsilon; |
---|
205 | long double _epsilon; |
---|
206 | public: |
---|
207 | ///\e |
---|
208 | typedef long double Value; |
---|
209 | |
---|
210 | ///Constructor setting the epsilon tolerance to the default value. |
---|
211 | Tolerance() : _epsilon(def_epsilon) {} |
---|
212 | ///Constructor setting the epsilon tolerance. |
---|
213 | Tolerance(long double e) : _epsilon(e) {} |
---|
214 | |
---|
215 | ///Return the epsilon value. |
---|
216 | Value epsilon() const {return _epsilon;} |
---|
217 | ///Set the epsilon value. |
---|
218 | void epsilon(Value e) {_epsilon=e;} |
---|
219 | |
---|
220 | ///Return the default epsilon value. |
---|
221 | static Value defaultEpsilon() {return def_epsilon;} |
---|
222 | ///Set the default epsilon value. |
---|
223 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
---|
224 | |
---|
225 | ///\name Comparisons |
---|
226 | ///See class Tolerance for more details. |
---|
227 | |
---|
228 | ///@{ |
---|
229 | |
---|
230 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
231 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
---|
232 | ///Returns \c true if \c a is \e surely different from \c b |
---|
233 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
---|
234 | ///Returns \c true if \c a is \e surely positive |
---|
235 | bool positive(Value a) const { return _epsilon<a; } |
---|
236 | ///Returns \c true if \c a is \e surely negative |
---|
237 | bool negative(Value a) const { return -_epsilon>a; } |
---|
238 | ///Returns \c true if \c a is \e surely non-zero |
---|
239 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
---|
240 | |
---|
241 | ///@} |
---|
242 | |
---|
243 | ///Returns zero |
---|
244 | static Value zero() {return 0;} |
---|
245 | }; |
---|
246 | |
---|
247 | ///Integer specialization of \ref Tolerance. |
---|
248 | |
---|
249 | ///Integer specialization of \ref Tolerance. |
---|
250 | ///\sa Tolerance |
---|
251 | template<> |
---|
252 | class Tolerance<int> |
---|
253 | { |
---|
254 | public: |
---|
255 | ///\e |
---|
256 | typedef int Value; |
---|
257 | |
---|
258 | ///\name Comparisons |
---|
259 | ///See \ref Tolerance for more details. |
---|
260 | |
---|
261 | ///@{ |
---|
262 | |
---|
263 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
264 | static bool less(Value a,Value b) { return a<b;} |
---|
265 | ///Returns \c true if \c a is \e surely different from \c b |
---|
266 | static bool different(Value a,Value b) { return a!=b; } |
---|
267 | ///Returns \c true if \c a is \e surely positive |
---|
268 | static bool positive(Value a) { return 0<a; } |
---|
269 | ///Returns \c true if \c a is \e surely negative |
---|
270 | static bool negative(Value a) { return 0>a; } |
---|
271 | ///Returns \c true if \c a is \e surely non-zero |
---|
272 | static bool nonZero(Value a) { return a!=0; } |
---|
273 | |
---|
274 | ///@} |
---|
275 | |
---|
276 | ///Returns zero |
---|
277 | static Value zero() {return 0;} |
---|
278 | }; |
---|
279 | |
---|
280 | ///Unsigned integer specialization of \ref Tolerance. |
---|
281 | |
---|
282 | ///Unsigned integer specialization of \ref Tolerance. |
---|
283 | ///\sa Tolerance |
---|
284 | template<> |
---|
285 | class Tolerance<unsigned int> |
---|
286 | { |
---|
287 | public: |
---|
288 | ///\e |
---|
289 | typedef unsigned int Value; |
---|
290 | |
---|
291 | ///\name Comparisons |
---|
292 | ///See \ref Tolerance for more details. |
---|
293 | |
---|
294 | ///@{ |
---|
295 | |
---|
296 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
297 | static bool less(Value a,Value b) { return a<b;} |
---|
298 | ///Returns \c true if \c a is \e surely different from \c b |
---|
299 | static bool different(Value a,Value b) { return a!=b; } |
---|
300 | ///Returns \c true if \c a is \e surely positive |
---|
301 | static bool positive(Value a) { return 0<a; } |
---|
302 | ///Returns \c true if \c a is \e surely negative |
---|
303 | static bool negative(Value) { return false; } |
---|
304 | ///Returns \c true if \c a is \e surely non-zero |
---|
305 | static bool nonZero(Value a) { return a!=0; } |
---|
306 | |
---|
307 | ///@} |
---|
308 | |
---|
309 | ///Returns zero |
---|
310 | static Value zero() {return 0;} |
---|
311 | }; |
---|
312 | |
---|
313 | |
---|
314 | ///Long integer specialization of \ref Tolerance. |
---|
315 | |
---|
316 | ///Long integer specialization of \ref Tolerance. |
---|
317 | ///\sa Tolerance |
---|
318 | template<> |
---|
319 | class Tolerance<long int> |
---|
320 | { |
---|
321 | public: |
---|
322 | ///\e |
---|
323 | typedef long int Value; |
---|
324 | |
---|
325 | ///\name Comparisons |
---|
326 | ///See \ref Tolerance for more details. |
---|
327 | |
---|
328 | ///@{ |
---|
329 | |
---|
330 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
331 | static bool less(Value a,Value b) { return a<b;} |
---|
332 | ///Returns \c true if \c a is \e surely different from \c b |
---|
333 | static bool different(Value a,Value b) { return a!=b; } |
---|
334 | ///Returns \c true if \c a is \e surely positive |
---|
335 | static bool positive(Value a) { return 0<a; } |
---|
336 | ///Returns \c true if \c a is \e surely negative |
---|
337 | static bool negative(Value a) { return 0>a; } |
---|
338 | ///Returns \c true if \c a is \e surely non-zero |
---|
339 | static bool nonZero(Value a) { return a!=0;} |
---|
340 | |
---|
341 | ///@} |
---|
342 | |
---|
343 | ///Returns zero |
---|
344 | static Value zero() {return 0;} |
---|
345 | }; |
---|
346 | |
---|
347 | ///Unsigned long integer specialization of \ref Tolerance. |
---|
348 | |
---|
349 | ///Unsigned long integer specialization of \ref Tolerance. |
---|
350 | ///\sa Tolerance |
---|
351 | template<> |
---|
352 | class Tolerance<unsigned long int> |
---|
353 | { |
---|
354 | public: |
---|
355 | ///\e |
---|
356 | typedef unsigned long int Value; |
---|
357 | |
---|
358 | ///\name Comparisons |
---|
359 | ///See \ref Tolerance for more details. |
---|
360 | |
---|
361 | ///@{ |
---|
362 | |
---|
363 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
364 | static bool less(Value a,Value b) { return a<b;} |
---|
365 | ///Returns \c true if \c a is \e surely different from \c b |
---|
366 | static bool different(Value a,Value b) { return a!=b; } |
---|
367 | ///Returns \c true if \c a is \e surely positive |
---|
368 | static bool positive(Value a) { return 0<a; } |
---|
369 | ///Returns \c true if \c a is \e surely negative |
---|
370 | static bool negative(Value) { return false; } |
---|
371 | ///Returns \c true if \c a is \e surely non-zero |
---|
372 | static bool nonZero(Value a) { return a!=0;} |
---|
373 | |
---|
374 | ///@} |
---|
375 | |
---|
376 | ///Returns zero |
---|
377 | static Value zero() {return 0;} |
---|
378 | }; |
---|
379 | |
---|
380 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
---|
381 | |
---|
382 | ///Long long integer specialization of \ref Tolerance. |
---|
383 | |
---|
384 | ///Long long integer specialization of \ref Tolerance. |
---|
385 | ///\warning This class (more exactly, type <tt>long long</tt>) |
---|
386 | ///is not ansi compatible. |
---|
387 | ///\sa Tolerance |
---|
388 | template<> |
---|
389 | class Tolerance<long long int> |
---|
390 | { |
---|
391 | public: |
---|
392 | ///\e |
---|
393 | typedef long long int Value; |
---|
394 | |
---|
395 | ///\name Comparisons |
---|
396 | ///See \ref Tolerance for more details. |
---|
397 | |
---|
398 | ///@{ |
---|
399 | |
---|
400 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
401 | static bool less(Value a,Value b) { return a<b;} |
---|
402 | ///Returns \c true if \c a is \e surely different from \c b |
---|
403 | static bool different(Value a,Value b) { return a!=b; } |
---|
404 | ///Returns \c true if \c a is \e surely positive |
---|
405 | static bool positive(Value a) { return 0<a; } |
---|
406 | ///Returns \c true if \c a is \e surely negative |
---|
407 | static bool negative(Value a) { return 0>a; } |
---|
408 | ///Returns \c true if \c a is \e surely non-zero |
---|
409 | static bool nonZero(Value a) { return a!=0;} |
---|
410 | |
---|
411 | ///@} |
---|
412 | |
---|
413 | ///Returns zero |
---|
414 | static Value zero() {return 0;} |
---|
415 | }; |
---|
416 | |
---|
417 | ///Unsigned long long integer specialization of \ref Tolerance. |
---|
418 | |
---|
419 | ///Unsigned long long integer specialization of \ref Tolerance. |
---|
420 | ///\warning This class (more exactly, type <tt>unsigned long long</tt>) |
---|
421 | ///is not ansi compatible. |
---|
422 | ///\sa Tolerance |
---|
423 | template<> |
---|
424 | class Tolerance<unsigned long long int> |
---|
425 | { |
---|
426 | public: |
---|
427 | ///\e |
---|
428 | typedef unsigned long long int Value; |
---|
429 | |
---|
430 | ///\name Comparisons |
---|
431 | ///See \ref Tolerance for more details. |
---|
432 | |
---|
433 | ///@{ |
---|
434 | |
---|
435 | ///Returns \c true if \c a is \e surely strictly less than \c b |
---|
436 | static bool less(Value a,Value b) { return a<b;} |
---|
437 | ///Returns \c true if \c a is \e surely different from \c b |
---|
438 | static bool different(Value a,Value b) { return a!=b; } |
---|
439 | ///Returns \c true if \c a is \e surely positive |
---|
440 | static bool positive(Value a) { return 0<a; } |
---|
441 | ///Returns \c true if \c a is \e surely negative |
---|
442 | static bool negative(Value) { return false; } |
---|
443 | ///Returns \c true if \c a is \e surely non-zero |
---|
444 | static bool nonZero(Value a) { return a!=0;} |
---|
445 | |
---|
446 | ///@} |
---|
447 | |
---|
448 | ///Returns zero |
---|
449 | static Value zero() {return 0;} |
---|
450 | }; |
---|
451 | |
---|
452 | #endif |
---|
453 | |
---|
454 | /// @} |
---|
455 | |
---|
456 | } //namespace lemon |
---|
457 | |
---|
458 | #endif //LEMON_TOLERANCE_H |
---|