/* -*- 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.

  ///

  ///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 with \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 \ref Tolerance.

  ///Float specialization of \ref 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.

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

    ///Return the epsilon value.

    Value epsilon() const {return _epsilon;}

    ///Set the epsilon value.

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

    ///Return the default epsilon value.

    static Value defaultEpsilon() {return def_epsilon;}

    ///Set the default epsilon value.

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

    ///\name Comparisons

    ///See class 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 \ref Tolerance.

  ///Double specialization of \ref 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.

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

    ///Return the epsilon value.

    Value epsilon() const {return _epsilon;}

    ///Set the epsilon value.

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

    ///Return the default epsilon value.

    static Value defaultEpsilon() {return def_epsilon;}

    ///Set the default epsilon value.

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

    ///\name Comparisons

    ///See class 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 \ref Tolerance.

  ///Long double specialization of \ref 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.

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

    ///Return the epsilon value.

    Value epsilon() const {return _epsilon;}

    ///Set the epsilon value.

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

    ///Return the default epsilon value.

    static Value defaultEpsilon() {return def_epsilon;}

    ///Set the default epsilon value.

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

    ///\name Comparisons

    ///See class 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 \ref Tolerance.

  ///Integer specialization of \ref 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 \ref 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 \ref Tolerance.

  ///Long integer specialization of \ref 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 \ref 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 \ref 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 \ref 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