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/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2009
* 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.
///
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.
///
///The general implementation is suitable only if the data type is exact,
///like the integer types, otherwise a specialized version must be
///implemented. These specialized classes like
///Tolerance<double> may offer additional tuning parameters.
///
///\sa Tolerance<float>
///\sa Tolerance<double>
///\sa Tolerance<long double>
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 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 static_cast<Value>(0) < a;}
///Returns \c true if \c a is \e surely negative
static bool negative(Value a) {return a < static_cast<Value>(0);}
///Returns \c true if \c a is \e surely non-zero
static bool nonZero(Value a) {return a != static_cast<Value>(0);}
///@}
///Returns the zero value.
static Value zero() {return static_cast<Value>(0);}
// 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 lemon::Tolerance "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 lemon::Tolerance "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 lemon::Tolerance "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;}
};
/// @}
} //namespace lemon
#endif //LEMON_TOLERANCE_H
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