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/* -*- C++ -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library
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*
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* Copyright (C) 2003-2007
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_TOLERANCE_H
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#define LEMON_TOLERANCE_H
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///\ingroup misc
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///\file
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///\brief A basic tool to handle the anomalies of calculation with
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///floating point numbers.
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///
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///\todo It should be in a module like "Basic tools"
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namespace lemon {
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/// \addtogroup misc
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/// @{
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///\brief A class to provide a basic way to
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///handle the comparison of numbers that are obtained
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///as a result of a probably inexact computation.
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///
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///Tolerance is a class to provide a basic way to
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///handle the comparison of numbers that are obtained
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///as a result of a probably inexact computation.
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///
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///This is an abstract class, it should be specialized for all numerical
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///data types. These specialized classes like \ref Tolerance\<double\>
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///may offer additional tuning parameters.
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///
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///\sa Tolerance<float>
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///\sa Tolerance<double>
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///\sa Tolerance<long double>
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///\sa Tolerance<int>
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///\sa Tolerance<long long int>
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///\sa Tolerance<unsigned int>
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///\sa Tolerance<unsigned long long int>
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template<class T>
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class Tolerance
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{
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public:
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typedef T Value;
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///\name Comparisons
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///The concept is that these bool functions return with \c true only if
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///the related comparisons hold even if some numerical error appeared
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///during the computations.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) {return false;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) {return false;}
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) {return false;}
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value a) {return false;}
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) {return false;}
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///@}
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///Returns the zero value.
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static Value zero() {return T();}
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// static bool finite(Value a) {}
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// static Value big() {}
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// static Value negativeBig() {}
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};
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///Float specialization of \ref Tolerance.
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///Float specialization of \ref Tolerance.
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///\sa Tolerance
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///\relates Tolerance
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template<>
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class Tolerance<float>
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{
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static float def_epsilon;
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float _epsilon;
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public:
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///\e
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typedef float Value;
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///Constructor setting the epsilon tolerance to the default value.
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Tolerance() : _epsilon(def_epsilon) {}
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///Constructor setting the epsilon tolerance.
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Tolerance(float e) : _epsilon(e) {}
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///Return the epsilon value.
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Value epsilon() const {return _epsilon;}
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///Set the epsilon value.
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void epsilon(Value e) {_epsilon=e;}
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///Return the default epsilon value.
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static Value defaultEpsilon() {return def_epsilon;}
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///Set the default epsilon value.
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static void defaultEpsilon(Value e) {def_epsilon=e;}
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///\name Comparisons
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///See class Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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bool less(Value a,Value b) const {return a+_epsilon<b;}
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///Returns \c true if \c a is \e surely different from \c b
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bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
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///Returns \c true if \c a is \e surely positive
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bool positive(Value a) const { return _epsilon<a; }
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///Returns \c true if \c a is \e surely negative
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bool negative(Value a) const { return -_epsilon>a; }
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///Returns \c true if \c a is \e surely non-zero
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bool nonZero(Value a) const { return positive(a)||negative(a); };
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Double specialization of \ref Tolerance.
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///Double specialization of \ref Tolerance.
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///\sa Tolerance
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///\relates Tolerance
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template<>
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class Tolerance<double>
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{
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static double def_epsilon;
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double _epsilon;
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public:
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///\e
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typedef double Value;
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///Constructor setting the epsilon tolerance to the default value.
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Tolerance() : _epsilon(def_epsilon) {}
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///Constructor setting the epsilon tolerance.
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Tolerance(double e) : _epsilon(e) {}
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///Return the epsilon value.
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Value epsilon() const {return _epsilon;}
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///Set the epsilon value.
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void epsilon(Value e) {_epsilon=e;}
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///Return the default epsilon value.
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static Value defaultEpsilon() {return def_epsilon;}
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///Set the default epsilon value.
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static void defaultEpsilon(Value e) {def_epsilon=e;}
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///\name Comparisons
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///See class Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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bool less(Value a,Value b) const {return a+_epsilon<b;}
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///Returns \c true if \c a is \e surely different from \c b
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bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
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///Returns \c true if \c a is \e surely positive
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bool positive(Value a) const { return _epsilon<a; }
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///Returns \c true if \c a is \e surely negative
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bool negative(Value a) const { return -_epsilon>a; }
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///Returns \c true if \c a is \e surely non-zero
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bool nonZero(Value a) const { return positive(a)||negative(a); };
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Long double specialization of \ref Tolerance.
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///Long double specialization of \ref Tolerance.
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///\sa Tolerance
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///\relates Tolerance
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template<>
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class Tolerance<long double>
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{
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static long double def_epsilon;
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long double _epsilon;
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public:
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///\e
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typedef long double Value;
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///Constructor setting the epsilon tolerance to the default value.
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Tolerance() : _epsilon(def_epsilon) {}
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///Constructor setting the epsilon tolerance.
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Tolerance(long double e) : _epsilon(e) {}
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///Return the epsilon value.
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Value epsilon() const {return _epsilon;}
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///Set the epsilon value.
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void epsilon(Value e) {_epsilon=e;}
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///Return the default epsilon value.
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static Value defaultEpsilon() {return def_epsilon;}
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///Set the default epsilon value.
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static void defaultEpsilon(Value e) {def_epsilon=e;}
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///\name Comparisons
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///See class Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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bool less(Value a,Value b) const {return a+_epsilon<b;}
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///Returns \c true if \c a is \e surely different from \c b
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bool different(Value a,Value b) const { return less(a,b)||less(b,a); }
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///Returns \c true if \c a is \e surely positive
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bool positive(Value a) const { return _epsilon<a; }
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///Returns \c true if \c a is \e surely negative
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bool negative(Value a) const { return -_epsilon>a; }
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///Returns \c true if \c a is \e surely non-zero
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bool nonZero(Value a) const { return positive(a)||negative(a); };
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Integer specialization of \ref Tolerance.
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///Integer specialization of \ref Tolerance.
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///\sa Tolerance
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template<>
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class Tolerance<int>
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{
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public:
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///\e
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typedef int Value;
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///\name Comparisons
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///See \ref Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) { return a<b;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) { return a!=b; }
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) { return 0<a; }
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value a) { return 0>a; }
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) { return a!=0; };
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Unsigned integer specialization of \ref Tolerance.
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///Unsigned integer specialization of \ref Tolerance.
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///\sa Tolerance
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template<>
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class Tolerance<unsigned int>
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{
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public:
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///\e
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typedef unsigned int Value;
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///\name Comparisons
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///See \ref Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) { return a<b;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) { return a!=b; }
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) { return 0<a; }
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value) { return false; }
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) { return a!=0; };
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Long integer specialization of \ref Tolerance.
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///Long integer specialization of \ref Tolerance.
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///\sa Tolerance
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template<>
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class Tolerance<long int>
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{
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public:
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///\e
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typedef long int Value;
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///\name Comparisons
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///See \ref Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) { return a<b;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) { return a!=b; }
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) { return 0<a; }
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value a) { return 0>a; }
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) { return a!=0;};
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Unsigned long integer specialization of \ref Tolerance.
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///Unsigned long integer specialization of \ref Tolerance.
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///\sa Tolerance
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template<>
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class Tolerance<unsigned long int>
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{
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public:
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///\e
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typedef unsigned long int Value;
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///\name Comparisons
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///See \ref Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) { return a<b;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) { return a!=b; }
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) { return 0<a; }
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value) { return false; }
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) { return a!=0;};
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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#if defined __GNUC__ && !defined __STRICT_ANSI__
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///Long long integer specialization of \ref Tolerance.
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///Long long integer specialization of \ref Tolerance.
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///\warning This class (more exactly, type <tt>long long</tt>)
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///is not ansi compatible.
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///\sa Tolerance
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template<>
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class Tolerance<long long int>
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{
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public:
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///\e
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typedef long long int Value;
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///\name Comparisons
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///See \ref Tolerance for more details.
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///@{
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///Returns \c true if \c a is \e surely strictly less than \c b
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static bool less(Value a,Value b) { return a<b;}
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///Returns \c true if \c a is \e surely different from \c b
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static bool different(Value a,Value b) { return a!=b; }
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///Returns \c true if \c a is \e surely positive
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static bool positive(Value a) { return 0<a; }
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///Returns \c true if \c a is \e surely negative
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static bool negative(Value a) { return 0>a; }
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///Returns \c true if \c a is \e surely non-zero
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static bool nonZero(Value a) { return a!=0;};
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///@}
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///Returns zero
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static Value zero() {return 0;}
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};
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///Unsigned long long integer specialization of \ref Tolerance.
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///Unsigned long long integer specialization of \ref Tolerance.
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///\warning This class (more exactly, type <tt>unsigned long long</tt>)
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417 |
///is not ansi compatible.
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418 |
///\sa Tolerance
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419 |
template<>
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420 |
class Tolerance<unsigned long long int>
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421 |
{
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public:
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423 |
///\e
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424 |
typedef unsigned long long int Value;
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425 |
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426 |
///\name Comparisons
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427 |
///See \ref Tolerance for more details.
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428 |
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///@{
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430 |
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431 |
///Returns \c true if \c a is \e surely strictly less than \c b
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432 |
static bool less(Value a,Value b) { return a<b;}
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433 |
///Returns \c true if \c a is \e surely different from \c b
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434 |
static bool different(Value a,Value b) { return a!=b; }
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435 |
///Returns \c true if \c a is \e surely positive
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436 |
static bool positive(Value a) { return 0<a; }
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437 |
///Returns \c true if \c a is \e surely negative
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438 |
static bool negative(Value) { return false; }
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439 |
///Returns \c true if \c a is \e surely non-zero
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|
440 |
static bool nonZero(Value a) { return a!=0;};
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441 |
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442 |
///@}
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443 |
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|
444 |
///Returns zero
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|
445 |
static Value zero() {return 0;}
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|
446 |
};
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447 |
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|
448 |
#endif
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449 |
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|
450 |
/// @}
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451 |
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|
452 |
} //namespace lemon
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453 |
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|
454 |
#endif //LEMON_TOLERANCE_H
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