/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_TOLERANCE_H

 #define LEMON_TOLERANCE_H

 ///\ingroup misc

 ///\file

 ///\brief A basic tool to handle the anomalies of calculation with

 ///floating point numbers.

 ///

 ///\todo It should be in a module like "Basic tools"

 namespace lemon {

   /// \addtogroup misc

   /// @{

   ///\brief A class to provide a basic way to

   ///handle the comparison of numbers that are obtained

   ///as a result of a probably inexact computation.

   ///

   ///\ref Tolerance is a class to provide a basic way to

   ///handle the comparison of numbers that are obtained

   ///as a result of a probably inexact computation.

   ///

   ///This is an abstract class, it should be specialized for all numerical

   ///data types. These specialized classes like \ref Tolerance<double>

   ///may offer additional tuning parameters.

   ///

   ///\sa Tolerance<float>

   ///\sa Tolerance<double>

   ///\sa Tolerance<long double>

   ///\sa Tolerance<int>

   ///\sa Tolerance<long long int>

   ///\sa Tolerance<unsigned int>

   ///\sa Tolerance<unsigned long long int>

   template<class T>

   class Tolerance

   {

   public:

     typedef T Value;

     ///\name Comparisons

     ///The concept is that these bool functions return \c true only if

     ///the related comparisons hold even if some numerical error appeared

     ///during the computations.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) {return false;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) {return false;}

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) {return false;}

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value a) {return false;}

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) {return false;}

     ///@}

     ///Returns the zero value.

     static Value zero() {return T();}

     //   static bool finite(Value a) {}

     //   static Value big() {}

     //   static Value negativeBig() {}

   };

   ///Float specialization of Tolerance.

   ///Float specialization of Tolerance.

   ///\sa Tolerance

   ///\relates Tolerance

   template<>

   class Tolerance<float>

   {

     static float def_epsilon;

     float _epsilon;

   public:

     ///\e

     typedef float Value;

     ///Constructor setting the epsilon tolerance to the default value.

     Tolerance() : _epsilon(def_epsilon) {}

     ///Constructor setting the epsilon tolerance to the given value.

     Tolerance(float e) : _epsilon(e) {}

     ///Returns the epsilon value.

     Value epsilon() const {return _epsilon;}

     ///Sets the epsilon value.

     void epsilon(Value e) {_epsilon=e;}

     ///Returns the default epsilon value.

     static Value defaultEpsilon() {return def_epsilon;}

     ///Sets the default epsilon value.

     static void defaultEpsilon(Value e) {def_epsilon=e;}

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     bool less(Value a,Value b) const {return a+_epsilon<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }

     ///Returns \c true if \c a is \e surely positive

     bool positive(Value a) const { return _epsilon<a; }

     ///Returns \c true if \c a is \e surely negative

     bool negative(Value a) const { return -_epsilon>a; }

     ///Returns \c true if \c a is \e surely non-zero

     bool nonZero(Value a) const { return positive(a)||negative(a); }

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Double specialization of Tolerance.

   ///Double specialization of Tolerance.

   ///\sa Tolerance

   ///\relates Tolerance

   template<>

   class Tolerance<double>

   {

     static double def_epsilon;

     double _epsilon;

   public:

     ///\e

     typedef double Value;

     ///Constructor setting the epsilon tolerance to the default value.

     Tolerance() : _epsilon(def_epsilon) {}

     ///Constructor setting the epsilon tolerance to the given value.

     Tolerance(double e) : _epsilon(e) {}

     ///Returns the epsilon value.

     Value epsilon() const {return _epsilon;}

     ///Sets the epsilon value.

     void epsilon(Value e) {_epsilon=e;}

     ///Returns the default epsilon value.

     static Value defaultEpsilon() {return def_epsilon;}

     ///Sets the default epsilon value.

     static void defaultEpsilon(Value e) {def_epsilon=e;}

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     bool less(Value a,Value b) const {return a+_epsilon<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }

     ///Returns \c true if \c a is \e surely positive

     bool positive(Value a) const { return _epsilon<a; }

     ///Returns \c true if \c a is \e surely negative

     bool negative(Value a) const { return -_epsilon>a; }

     ///Returns \c true if \c a is \e surely non-zero

     bool nonZero(Value a) const { return positive(a)||negative(a); }

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Long double specialization of Tolerance.

   ///Long double specialization of Tolerance.

   ///\sa Tolerance

   ///\relates Tolerance

   template<>

   class Tolerance<long double>

   {

     static long double def_epsilon;

     long double _epsilon;

   public:

     ///\e

     typedef long double Value;

     ///Constructor setting the epsilon tolerance to the default value.

     Tolerance() : _epsilon(def_epsilon) {}

     ///Constructor setting the epsilon tolerance to the given value.

     Tolerance(long double e) : _epsilon(e) {}

     ///Returns the epsilon value.

     Value epsilon() const {return _epsilon;}

     ///Sets the epsilon value.

     void epsilon(Value e) {_epsilon=e;}

     ///Returns the default epsilon value.

     static Value defaultEpsilon() {return def_epsilon;}

     ///Sets the default epsilon value.

     static void defaultEpsilon(Value e) {def_epsilon=e;}

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     bool less(Value a,Value b) const {return a+_epsilon<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     bool different(Value a,Value b) const { return less(a,b)||less(b,a); }

     ///Returns \c true if \c a is \e surely positive

     bool positive(Value a) const { return _epsilon<a; }

     ///Returns \c true if \c a is \e surely negative

     bool negative(Value a) const { return -_epsilon>a; }

     ///Returns \c true if \c a is \e surely non-zero

     bool nonZero(Value a) const { return positive(a)||negative(a); }

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Integer specialization of Tolerance.

   ///Integer specialization of Tolerance.

   ///\sa Tolerance

   template<>

   class Tolerance<int>

   {

   public:

     ///\e

     typedef int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value a) { return 0>a; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0; }

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Unsigned integer specialization of Tolerance.

   ///Unsigned integer specialization of \ref Tolerance.

   ///\sa Tolerance

   template<>

   class Tolerance<unsigned int>

   {

   public:

     ///\e

     typedef unsigned int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value) { return false; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0; }

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Long integer specialization of Tolerance.

   ///Long integer specialization of Tolerance.

   ///\sa Tolerance

   template<>

   class Tolerance<long int>

   {

   public:

     ///\e

     typedef long int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value a) { return 0>a; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0;}

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Unsigned long integer specialization of Tolerance.

   ///Unsigned long integer specialization of \ref Tolerance.

   ///\sa Tolerance

   template<>

   class Tolerance<unsigned long int>

   {

   public:

     ///\e

     typedef unsigned long int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value) { return false; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0;}

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

 #if defined __GNUC__ && !defined __STRICT_ANSI__

   ///Long long integer specialization of Tolerance.

   ///Long long integer specialization of \ref Tolerance.

   ///\warning This class (more exactly, type <tt>long long</tt>)

   ///is not ansi compatible.

   ///\sa Tolerance

   template<>

   class Tolerance<long long int>

   {

   public:

     ///\e

     typedef long long int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value a) { return 0>a; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0;}

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

   ///Unsigned long long integer specialization of Tolerance.

   ///Unsigned long long integer specialization of \ref Tolerance.

   ///\warning This class (more exactly, type <tt>unsigned long long</tt>)

   ///is not ansi compatible.

   ///\sa Tolerance

   template<>

   class Tolerance<unsigned long long int>

   {

   public:

     ///\e

     typedef unsigned long long int Value;

     ///\name Comparisons

     ///See \ref Tolerance for more details.

     ///@{

     ///Returns \c true if \c a is \e surely strictly less than \c b

     static bool less(Value a,Value b) { return a<b;}

     ///Returns \c true if \c a is \e surely different from \c b

     static bool different(Value a,Value b) { return a!=b; }

     ///Returns \c true if \c a is \e surely positive

     static bool positive(Value a) { return 0<a; }

     ///Returns \c true if \c a is \e surely negative

     static bool negative(Value) { return false; }

     ///Returns \c true if \c a is \e surely non-zero

     static bool nonZero(Value a) { return a!=0;}

     ///@}

     ///Returns zero

     static Value zero() {return 0;}

   };

 #endif

   /// @}

 } //namespace lemon

 #endif //LEMON_TOLERANCE_H