Unionfind changes induced some bugs here. Also some augmentations made.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
19 #ifndef LEMON_TOLERANCE_H
20 #define LEMON_TOLERANCE_H
24 ///\brief A basic tool to handle the anomalies of calculation with
25 ///floating point numbers.
27 ///\todo It should be in a module like "Basic tools"
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.
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.
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.
47 ///\sa Tolerance<float>
48 ///\sa Tolerance<double>
49 ///\sa Tolerance<long double>
51 ///\sa Tolerance<long long int>
60 ///The concept is that these bool functions return with \c true only if
61 ///the related comparisons hold even if some numerical error appeared
62 ///during the computations.
66 ///Returns \c true if \c a is \e surely strictly less than \c b
67 static bool less(Value a,Value b) {return false;}
68 ///Returns \c true if \c a is \e surely different from \c b
69 static bool different(Value a,Value b) {return false;}
70 ///Returns \c true if \c a is \e surely positive
71 static bool positive(Value a) {return false;}
72 ///Returns \c true if \c a is \e surely negative
73 static bool negative(Value a) {return false;}
74 ///Returns \c true if \c a is \e surely non-zero
75 static bool nonZero(Value a) {return false;}
79 ///Returns the zero value.
80 static Value zero() {return T();}
82 // static bool finite(Value a) {}
83 // static Value big() {}
84 // static Value negativeBig() {}
88 ///Float specialization of \ref Tolerance.
90 ///Float specialization of \ref Tolerance.
94 class Tolerance<float>
96 static float def_epsilon;
102 ///Constructor setting the epsilon tolerance to the default value.
103 Tolerance() : _epsilon(def_epsilon) {}
104 ///Constructor setting the epsilon tolerance.
105 Tolerance(float e) : _epsilon(e) {}
107 ///Return the epsilon value.
108 Value epsilon() {return _epsilon;}
109 ///Set the epsilon value.
110 void epsilon(Value e) {_epsilon=e;}
112 ///Return the default epsilon value.
113 static Value defaultEpsilon() {return def_epsilon;}
114 ///Set the default epsilon value.
115 static void defaultEpsilon(Value e) {def_epsilon=e;}
118 ///See class Tolerance for more details.
122 ///Returns \c true if \c a is \e surely strictly less than \c b
123 bool less(Value a,Value b) {return a+_epsilon<b;}
124 ///Returns \c true if \c a is \e surely different from \c b
125 bool different(Value a,Value b) { return less(a,b)||less(b,a); }
126 ///Returns \c true if \c a is \e surely positive
127 bool positive(Value a) { return _epsilon<a; }
128 ///Returns \c true if \c a is \e surely negative
129 bool negative(Value a) { return -_epsilon>a; }
130 ///Returns \c true if \c a is \e surely non-zero
131 Value nonZero(Value a) { return positive(a)||negative(a); };
136 static Value zero() {return 0;}
139 ///Double specialization of \ref Tolerance.
141 ///Double specialization of \ref Tolerance.
143 ///\relates Tolerance
145 class Tolerance<double>
147 static double def_epsilon;
151 typedef double Value;
153 ///Constructor setting the epsilon tolerance to the default value.
154 Tolerance() : _epsilon(def_epsilon) {}
155 ///Constructor setting the epsilon tolerance.
156 Tolerance(double e) : _epsilon(e) {}
158 ///Return the epsilon value.
159 Value epsilon() {return _epsilon;}
160 ///Set the epsilon value.
161 void epsilon(Value e) {_epsilon=e;}
163 ///Return the default epsilon value.
164 static Value defaultEpsilon() {return def_epsilon;}
165 ///Set the default epsilon value.
166 static void defaultEpsilon(Value e) {def_epsilon=e;}
169 ///See class Tolerance for more details.
173 ///Returns \c true if \c a is \e surely strictly less than \c b
174 bool less(Value a,Value b) {return a+_epsilon<b;}
175 ///Returns \c true if \c a is \e surely different from \c b
176 bool different(Value a,Value b) { return less(a,b)||less(b,a); }
177 ///Returns \c true if \c a is \e surely positive
178 bool positive(Value a) { return _epsilon<a; }
179 ///Returns \c true if \c a is \e surely negative
180 bool negative(Value a) { return -_epsilon>a; }
181 ///Returns \c true if \c a is \e surely non-zero
182 Value nonZero(Value a) { return positive(a)||negative(a); };
187 static Value zero() {return 0;}
190 ///Long double specialization of \ref Tolerance.
192 ///Long double specialization of \ref Tolerance.
194 ///\relates Tolerance
196 class Tolerance<long double>
198 static long double def_epsilon;
199 long double _epsilon;
202 typedef long double Value;
204 ///Constructor setting the epsilon tolerance to the default value.
205 Tolerance() : _epsilon(def_epsilon) {}
206 ///Constructor setting the epsilon tolerance.
207 Tolerance(long double e) : _epsilon(e) {}
209 ///Return the epsilon value.
210 Value epsilon() {return _epsilon;}
211 ///Set the epsilon value.
212 void epsilon(Value e) {_epsilon=e;}
214 ///Return the default epsilon value.
215 static Value defaultEpsilon() {return def_epsilon;}
216 ///Set the default epsilon value.
217 static void defaultEpsilon(Value e) {def_epsilon=e;}
220 ///See class Tolerance for more details.
224 ///Returns \c true if \c a is \e surely strictly less than \c b
225 bool less(Value a,Value b) {return a+_epsilon<b;}
226 ///Returns \c true if \c a is \e surely different from \c b
227 bool different(Value a,Value b) { return less(a,b)||less(b,a); }
228 ///Returns \c true if \c a is \e surely positive
229 bool positive(Value a) { return _epsilon<a; }
230 ///Returns \c true if \c a is \e surely negative
231 bool negative(Value a) { return -_epsilon>a; }
232 ///Returns \c true if \c a is \e surely non-zero
233 Value nonZero(Value a) { return positive(a)||negative(a); };
238 static Value zero() {return 0;}
241 ///Integer specialization of \ref Tolerance.
243 ///Integer specialization of \ref Tolerance.
253 ///See \ref Tolerance for more details.
257 ///Returns \c true if \c a is \e surely strictly less than \c b
258 static bool less(Value a,Value b) { return a<b;}
259 ///Returns \c true if \c a is \e surely different from \c b
260 static bool different(Value a,Value b) { return a!=b; }
261 ///Returns \c true if \c a is \e surely positive
262 static bool positive(Value a) { return 0<a; }
263 ///Returns \c true if \c a is \e surely negative
264 static bool negative(Value a) { return 0>a; }
265 ///Returns \c true if \c a is \e surely non-zero
266 static Value nonZero(Value a) { return a!=0;};
271 static Value zero() {return 0;}
274 #ifndef __STRICT_ANSI__
276 ///Long long integer specialization of \ref Tolerance.
278 ///Long long integer specialization of \ref Tolerance.
279 ///\warning This class is not ansi compatible.
282 class Tolerance<long long int>
286 typedef long long int Value;
289 ///See \ref Tolerance for more details.
293 ///Returns \c true if \c a is \e surely strictly less than \c b
294 static bool less(Value a,Value b) { return a<b;}
295 ///Returns \c true if \c a is \e surely different from \c b
296 static bool different(Value a,Value b) { return a!=b; }
297 ///Returns \c true if \c a is \e surely positive
298 static bool positive(Value a) { return 0<a; }
299 ///Returns \c true if \c a is \e surely negative
300 static bool negative(Value a) { return 0>a; }
301 ///Returns \c true if \c a is \e surely non-zero
302 static Value nonZero(Value a) { return a!=0;};
307 static Value zero() {return 0;}
316 #endif //LEMON_TOLERANCE_H