lemon/tolerance.h
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     1 /* -*- C++ -*-
       
     2  *
       
     3  * This file is a part of LEMON, a generic C++ optimization library
       
     4  *
       
     5  * Copyright (C) 2003-2007
       
     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   ///\sa Tolerance<long long int>
       
    52   ///\sa Tolerance<unsigned int>
       
    53   ///\sa Tolerance<unsigned long long int>
       
    54 
       
    55   template<class T>
       
    56   class Tolerance
       
    57   {
       
    58   public:
       
    59     typedef T Value;
       
    60 
       
    61     ///\name Comparisons
       
    62     ///The concept is that these bool functions return with \c true only if
       
    63     ///the related comparisons hold even if some numerical error appeared
       
    64     ///during the computations.
       
    65 
       
    66     ///@{
       
    67 
       
    68     ///Returns \c true if \c a is \e surely strictly less than \c b
       
    69     static bool less(Value a,Value b) {return false;}
       
    70     ///Returns \c true if \c a is \e surely different from \c b
       
    71     static bool different(Value a,Value b) {return false;}
       
    72     ///Returns \c true if \c a is \e surely positive
       
    73     static bool positive(Value a) {return false;}
       
    74     ///Returns \c true if \c a is \e surely negative
       
    75     static bool negative(Value a) {return false;}
       
    76     ///Returns \c true if \c a is \e surely non-zero
       
    77     static bool nonZero(Value a) {return false;}
       
    78 
       
    79     ///@}
       
    80 
       
    81     ///Returns the zero value.
       
    82     static Value zero() {return T();}
       
    83 
       
    84     //   static bool finite(Value a) {}
       
    85     //   static Value big() {}
       
    86     //   static Value negativeBig() {}
       
    87   };
       
    88 
       
    89 
       
    90   ///Float specialization of \ref Tolerance.
       
    91 
       
    92   ///Float specialization of \ref Tolerance.
       
    93   ///\sa Tolerance
       
    94   ///\relates Tolerance
       
    95   template<>
       
    96   class Tolerance<float>
       
    97   {
       
    98     static float def_epsilon;
       
    99     float _epsilon;
       
   100   public:
       
   101     ///\e
       
   102     typedef float Value;
       
   103 
       
   104     ///Constructor setting the epsilon tolerance to the default value.
       
   105     Tolerance() : _epsilon(def_epsilon) {}
       
   106     ///Constructor setting the epsilon tolerance.
       
   107     Tolerance(float e) : _epsilon(e) {}
       
   108 
       
   109     ///Return the epsilon value.
       
   110     Value epsilon() const {return _epsilon;}
       
   111     ///Set the epsilon value.
       
   112     void epsilon(Value e) {_epsilon=e;}
       
   113 
       
   114     ///Return the default epsilon value.
       
   115     static Value defaultEpsilon() {return def_epsilon;}
       
   116     ///Set the default epsilon value.
       
   117     static void defaultEpsilon(Value e) {def_epsilon=e;}
       
   118 
       
   119     ///\name Comparisons
       
   120     ///See class Tolerance for more details.
       
   121 
       
   122     ///@{
       
   123 
       
   124     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   125     bool less(Value a,Value b) const {return a+_epsilon<b;}
       
   126     ///Returns \c true if \c a is \e surely different from \c b
       
   127     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
       
   128     ///Returns \c true if \c a is \e surely positive
       
   129     bool positive(Value a) const { return _epsilon<a; }
       
   130     ///Returns \c true if \c a is \e surely negative
       
   131     bool negative(Value a) const { return -_epsilon>a; }
       
   132     ///Returns \c true if \c a is \e surely non-zero
       
   133     bool nonZero(Value a) const { return positive(a)||negative(a); };
       
   134 
       
   135     ///@}
       
   136 
       
   137     ///Returns zero
       
   138     static Value zero() {return 0;}
       
   139   };
       
   140 
       
   141   ///Double specialization of \ref Tolerance.
       
   142 
       
   143   ///Double specialization of \ref Tolerance.
       
   144   ///\sa Tolerance
       
   145   ///\relates Tolerance
       
   146   template<>
       
   147   class Tolerance<double>
       
   148   {
       
   149     static double def_epsilon;
       
   150     double _epsilon;
       
   151   public:
       
   152     ///\e
       
   153     typedef double Value;
       
   154 
       
   155     ///Constructor setting the epsilon tolerance to the default value.
       
   156     Tolerance() : _epsilon(def_epsilon) {}
       
   157     ///Constructor setting the epsilon tolerance.
       
   158     Tolerance(double e) : _epsilon(e) {}
       
   159 
       
   160     ///Return the epsilon value.
       
   161     Value epsilon() const {return _epsilon;}
       
   162     ///Set the epsilon value.
       
   163     void epsilon(Value e) {_epsilon=e;}
       
   164 
       
   165     ///Return the default epsilon value.
       
   166     static Value defaultEpsilon() {return def_epsilon;}
       
   167     ///Set the default epsilon value.
       
   168     static void defaultEpsilon(Value e) {def_epsilon=e;}
       
   169 
       
   170     ///\name Comparisons
       
   171     ///See class Tolerance for more details.
       
   172 
       
   173     ///@{
       
   174 
       
   175     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   176     bool less(Value a,Value b) const {return a+_epsilon<b;}
       
   177     ///Returns \c true if \c a is \e surely different from \c b
       
   178     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
       
   179     ///Returns \c true if \c a is \e surely positive
       
   180     bool positive(Value a) const { return _epsilon<a; }
       
   181     ///Returns \c true if \c a is \e surely negative
       
   182     bool negative(Value a) const { return -_epsilon>a; }
       
   183     ///Returns \c true if \c a is \e surely non-zero
       
   184     bool nonZero(Value a) const { return positive(a)||negative(a); };
       
   185 
       
   186     ///@}
       
   187 
       
   188     ///Returns zero
       
   189     static Value zero() {return 0;}
       
   190   };
       
   191 
       
   192   ///Long double specialization of \ref Tolerance.
       
   193 
       
   194   ///Long double specialization of \ref Tolerance.
       
   195   ///\sa Tolerance
       
   196   ///\relates Tolerance
       
   197   template<>
       
   198   class Tolerance<long double>
       
   199   {
       
   200     static long double def_epsilon;
       
   201     long double _epsilon;
       
   202   public:
       
   203     ///\e
       
   204     typedef long double Value;
       
   205 
       
   206     ///Constructor setting the epsilon tolerance to the default value.
       
   207     Tolerance() : _epsilon(def_epsilon) {}
       
   208     ///Constructor setting the epsilon tolerance.
       
   209     Tolerance(long double e) : _epsilon(e) {}
       
   210 
       
   211     ///Return the epsilon value.
       
   212     Value epsilon() const {return _epsilon;}
       
   213     ///Set the epsilon value.
       
   214     void epsilon(Value e) {_epsilon=e;}
       
   215 
       
   216     ///Return the default epsilon value.
       
   217     static Value defaultEpsilon() {return def_epsilon;}
       
   218     ///Set the default epsilon value.
       
   219     static void defaultEpsilon(Value e) {def_epsilon=e;}
       
   220 
       
   221     ///\name Comparisons
       
   222     ///See class Tolerance for more details.
       
   223 
       
   224     ///@{
       
   225 
       
   226     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   227     bool less(Value a,Value b) const {return a+_epsilon<b;}
       
   228     ///Returns \c true if \c a is \e surely different from \c b
       
   229     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
       
   230     ///Returns \c true if \c a is \e surely positive
       
   231     bool positive(Value a) const { return _epsilon<a; }
       
   232     ///Returns \c true if \c a is \e surely negative
       
   233     bool negative(Value a) const { return -_epsilon>a; }
       
   234     ///Returns \c true if \c a is \e surely non-zero
       
   235     bool nonZero(Value a) const { return positive(a)||negative(a); };
       
   236 
       
   237     ///@}
       
   238 
       
   239     ///Returns zero
       
   240     static Value zero() {return 0;}
       
   241   };
       
   242 
       
   243   ///Integer specialization of \ref Tolerance.
       
   244 
       
   245   ///Integer specialization of \ref Tolerance.
       
   246   ///\sa Tolerance
       
   247   template<>
       
   248   class Tolerance<int>
       
   249   {
       
   250   public:
       
   251     ///\e
       
   252     typedef int Value;
       
   253 
       
   254     ///\name Comparisons
       
   255     ///See \ref Tolerance for more details.
       
   256 
       
   257     ///@{
       
   258 
       
   259     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   260     static bool less(Value a,Value b) { return a<b;}
       
   261     ///Returns \c true if \c a is \e surely different from \c b
       
   262     static bool different(Value a,Value b) { return a!=b; }
       
   263     ///Returns \c true if \c a is \e surely positive
       
   264     static bool positive(Value a) { return 0<a; }
       
   265     ///Returns \c true if \c a is \e surely negative
       
   266     static bool negative(Value a) { return 0>a; }
       
   267     ///Returns \c true if \c a is \e surely non-zero
       
   268     static bool nonZero(Value a) { return a!=0; };
       
   269 
       
   270     ///@}
       
   271 
       
   272     ///Returns zero
       
   273     static Value zero() {return 0;}
       
   274   };
       
   275 
       
   276   ///Unsigned integer specialization of \ref Tolerance.
       
   277 
       
   278   ///Unsigned integer specialization of \ref Tolerance.
       
   279   ///\sa Tolerance
       
   280   template<>
       
   281   class Tolerance<unsigned int>
       
   282   {
       
   283   public:
       
   284     ///\e
       
   285     typedef unsigned int Value;
       
   286 
       
   287     ///\name Comparisons
       
   288     ///See \ref Tolerance for more details.
       
   289 
       
   290     ///@{
       
   291 
       
   292     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   293     static bool less(Value a,Value b) { return a<b;}
       
   294     ///Returns \c true if \c a is \e surely different from \c b
       
   295     static bool different(Value a,Value b) { return a!=b; }
       
   296     ///Returns \c true if \c a is \e surely positive
       
   297     static bool positive(Value a) { return 0<a; }
       
   298     ///Returns \c true if \c a is \e surely negative
       
   299     static bool negative(Value) { return false; }
       
   300     ///Returns \c true if \c a is \e surely non-zero
       
   301     static bool nonZero(Value a) { return a!=0; };
       
   302 
       
   303     ///@}
       
   304 
       
   305     ///Returns zero
       
   306     static Value zero() {return 0;}
       
   307   };
       
   308   
       
   309 
       
   310   ///Long integer specialization of \ref Tolerance.
       
   311 
       
   312   ///Long integer specialization of \ref Tolerance.
       
   313   ///\sa Tolerance
       
   314   template<>
       
   315   class Tolerance<long int>
       
   316   {
       
   317   public:
       
   318     ///\e
       
   319     typedef long int Value;
       
   320 
       
   321     ///\name Comparisons
       
   322     ///See \ref Tolerance for more details.
       
   323 
       
   324     ///@{
       
   325 
       
   326     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   327     static bool less(Value a,Value b) { return a<b;}
       
   328     ///Returns \c true if \c a is \e surely different from \c b
       
   329     static bool different(Value a,Value b) { return a!=b; }
       
   330     ///Returns \c true if \c a is \e surely positive
       
   331     static bool positive(Value a) { return 0<a; }
       
   332     ///Returns \c true if \c a is \e surely negative
       
   333     static bool negative(Value a) { return 0>a; }
       
   334     ///Returns \c true if \c a is \e surely non-zero
       
   335     static bool nonZero(Value a) { return a!=0;};
       
   336 
       
   337     ///@}
       
   338 
       
   339     ///Returns zero
       
   340     static Value zero() {return 0;}
       
   341   };
       
   342 
       
   343   ///Unsigned long integer specialization of \ref Tolerance.
       
   344 
       
   345   ///Unsigned long integer specialization of \ref Tolerance.
       
   346   ///\sa Tolerance
       
   347   template<>
       
   348   class Tolerance<unsigned long int>
       
   349   {
       
   350   public:
       
   351     ///\e
       
   352     typedef unsigned long int Value;
       
   353 
       
   354     ///\name Comparisons
       
   355     ///See \ref Tolerance for more details.
       
   356 
       
   357     ///@{
       
   358 
       
   359     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   360     static bool less(Value a,Value b) { return a<b;}
       
   361     ///Returns \c true if \c a is \e surely different from \c b
       
   362     static bool different(Value a,Value b) { return a!=b; }
       
   363     ///Returns \c true if \c a is \e surely positive
       
   364     static bool positive(Value a) { return 0<a; }
       
   365     ///Returns \c true if \c a is \e surely negative
       
   366     static bool negative(Value) { return false; }
       
   367     ///Returns \c true if \c a is \e surely non-zero
       
   368     static bool nonZero(Value a) { return a!=0;};
       
   369 
       
   370     ///@}
       
   371 
       
   372     ///Returns zero
       
   373     static Value zero() {return 0;}
       
   374   };
       
   375 
       
   376 #if defined __GNUC__ && !defined __STRICT_ANSI__
       
   377 
       
   378   ///Long long integer specialization of \ref Tolerance.
       
   379 
       
   380   ///Long long integer specialization of \ref Tolerance.
       
   381   ///\warning This class (more exactly, type <tt>long long</tt>)
       
   382   ///is not ansi compatible.
       
   383   ///\sa Tolerance
       
   384   template<>
       
   385   class Tolerance<long long int>
       
   386   {
       
   387   public:
       
   388     ///\e
       
   389     typedef long long int Value;
       
   390 
       
   391     ///\name Comparisons
       
   392     ///See \ref Tolerance for more details.
       
   393 
       
   394     ///@{
       
   395 
       
   396     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   397     static bool less(Value a,Value b) { return a<b;}
       
   398     ///Returns \c true if \c a is \e surely different from \c b
       
   399     static bool different(Value a,Value b) { return a!=b; }
       
   400     ///Returns \c true if \c a is \e surely positive
       
   401     static bool positive(Value a) { return 0<a; }
       
   402     ///Returns \c true if \c a is \e surely negative
       
   403     static bool negative(Value a) { return 0>a; }
       
   404     ///Returns \c true if \c a is \e surely non-zero
       
   405     static bool nonZero(Value a) { return a!=0;};
       
   406 
       
   407     ///@}
       
   408 
       
   409     ///Returns zero
       
   410     static Value zero() {return 0;}
       
   411   };
       
   412 
       
   413   ///Unsigned long long integer specialization of \ref Tolerance.
       
   414 
       
   415   ///Unsigned long long integer specialization of \ref Tolerance.
       
   416   ///\warning This class (more exactly, type <tt>unsigned long long</tt>)
       
   417   ///is not ansi compatible.
       
   418   ///\sa Tolerance
       
   419   template<>
       
   420   class Tolerance<unsigned long long int>
       
   421   {
       
   422   public:
       
   423     ///\e
       
   424     typedef unsigned long long int Value;
       
   425 
       
   426     ///\name Comparisons
       
   427     ///See \ref Tolerance for more details.
       
   428 
       
   429     ///@{
       
   430 
       
   431     ///Returns \c true if \c a is \e surely strictly less than \c b
       
   432     static bool less(Value a,Value b) { return a<b;}
       
   433     ///Returns \c true if \c a is \e surely different from \c b
       
   434     static bool different(Value a,Value b) { return a!=b; }
       
   435     ///Returns \c true if \c a is \e surely positive
       
   436     static bool positive(Value a) { return 0<a; }
       
   437     ///Returns \c true if \c a is \e surely negative
       
   438     static bool negative(Value) { return false; }
       
   439     ///Returns \c true if \c a is \e surely non-zero
       
   440     static bool nonZero(Value a) { return a!=0;};
       
   441 
       
   442     ///@}
       
   443 
       
   444     ///Returns zero
       
   445     static Value zero() {return 0;}
       
   446   };
       
   447 
       
   448 #endif
       
   449 
       
   450   /// @}
       
   451 
       
   452 } //namespace lemon
       
   453 
       
   454 #endif //LEMON_TOLERANCE_H