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@@ -20,49 +20,49 @@
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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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///data types. These specialized classes like 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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#if defined __GNUC__ && !defined __STRICT_ANSI__
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///\sa Tolerance<long long int>
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#endif
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///\sa Tolerance<unsigned int>
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#if defined __GNUC__ && !defined __STRICT_ANSI__
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///\sa Tolerance<unsigned long long int>
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#endif
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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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@@ -70,372 +70,372 @@
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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 Tolerance.
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///Float specialization of \ref Tolerance.
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///Float specialization of 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 Tolerance.
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///Double specialization of \ref Tolerance.
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///Double specialization of 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 Tolerance.
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///Long double specialization of \ref Tolerance.
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///Long double specialization of 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 Tolerance.
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///Integer specialization of \ref Tolerance.
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///Integer specialization of 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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| 259 |
|
///See \ref Tolerance for more details.
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///See Tolerance for more details.
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| 260 |
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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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| 271 |
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///Returns \c true if \c a is \e surely non-zero
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| 272 |
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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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277 |
static Value zero() {return 0;}
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| 278 |
278 |
};
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| 279 |
279 |
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| 280 |
|
///Unsigned integer specialization of \ref Tolerance.
|
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280 |
///Unsigned integer specialization of Tolerance.
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| 281 |
281 |
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| 282 |
282 |
///Unsigned integer specialization of \ref Tolerance.
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| 283 |
283 |
///\sa Tolerance
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| 284 |
284 |
template<>
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| 285 |
285 |
class Tolerance<unsigned int>
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| 286 |
286 |
{
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| 287 |
287 |
public:
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| 288 |
288 |
///\e
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| 289 |
289 |
typedef unsigned int Value;
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| 290 |
290 |
|
| 291 |
291 |
///\name Comparisons
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| 292 |
|
///See \ref Tolerance for more details.
|
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292 |
///See Tolerance for more details.
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| 293 |
293 |
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| 294 |
294 |
///@{
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| 295 |
295 |
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296 |
///Returns \c true if \c a is \e surely strictly less than \c b
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297 |
static bool less(Value a,Value b) { return a<b;}
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| 298 |
298 |
///Returns \c true if \c a is \e surely different from \c b
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299 |
static bool different(Value a,Value b) { return a!=b; }
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| 300 |
300 |
///Returns \c true if \c a is \e surely positive
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| 301 |
301 |
static bool positive(Value a) { return 0<a; }
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| 302 |
302 |
///Returns \c true if \c a is \e surely negative
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| 303 |
303 |
static bool negative(Value) { return false; }
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| 304 |
304 |
///Returns \c true if \c a is \e surely non-zero
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| 305 |
305 |
static bool nonZero(Value a) { return a!=0; }
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| 306 |
306 |
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307 |
///@}
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| 308 |
308 |
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309 |
///Returns zero
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| 310 |
310 |
static Value zero() {return 0;}
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| 311 |
311 |
};
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| 312 |
312 |
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| 313 |
313 |
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| 314 |
|
///Long integer specialization of \ref Tolerance.
|
|
314 |
///Long integer specialization of Tolerance.
|
| 315 |
315 |
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| 316 |
|
///Long integer specialization of \ref Tolerance.
|
|
316 |
///Long integer specialization of Tolerance.
|
| 317 |
317 |
///\sa Tolerance
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| 318 |
318 |
template<>
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| 319 |
319 |
class Tolerance<long int>
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| 320 |
320 |
{
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| 321 |
321 |
public:
|
| 322 |
322 |
///\e
|
| 323 |
323 |
typedef long int Value;
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| 324 |
324 |
|
| 325 |
325 |
///\name Comparisons
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| 326 |
|
///See \ref Tolerance for more details.
|
|
326 |
///See Tolerance for more details.
|
| 327 |
327 |
|
| 328 |
328 |
///@{
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| 329 |
329 |
|
| 330 |
330 |
///Returns \c true if \c a is \e surely strictly less than \c b
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| 331 |
331 |
static bool less(Value a,Value b) { return a<b;}
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| 332 |
332 |
///Returns \c true if \c a is \e surely different from \c b
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| 333 |
333 |
static bool different(Value a,Value b) { return a!=b; }
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| 334 |
334 |
///Returns \c true if \c a is \e surely positive
|
| 335 |
335 |
static bool positive(Value a) { return 0<a; }
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| 336 |
336 |
///Returns \c true if \c a is \e surely negative
|
| 337 |
337 |
static bool negative(Value a) { return 0>a; }
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| 338 |
338 |
///Returns \c true if \c a is \e surely non-zero
|
| 339 |
339 |
static bool nonZero(Value a) { return a!=0;}
|
| 340 |
340 |
|
| 341 |
341 |
///@}
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| 342 |
342 |
|
| 343 |
343 |
///Returns zero
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| 344 |
344 |
static Value zero() {return 0;}
|
| 345 |
345 |
};
|
| 346 |
346 |
|
| 347 |
|
///Unsigned long integer specialization of \ref Tolerance.
|
|
347 |
///Unsigned long integer specialization of Tolerance.
|
| 348 |
348 |
|
| 349 |
349 |
///Unsigned long integer specialization of \ref Tolerance.
|
| 350 |
350 |
///\sa Tolerance
|
| 351 |
351 |
template<>
|
| 352 |
352 |
class Tolerance<unsigned long int>
|
| 353 |
353 |
{
|
| 354 |
354 |
public:
|
| 355 |
355 |
///\e
|
| 356 |
356 |
typedef unsigned long int Value;
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| 357 |
357 |
|
| 358 |
358 |
///\name Comparisons
|
| 359 |
|
///See \ref Tolerance for more details.
|
|
359 |
///See Tolerance for more details.
|
| 360 |
360 |
|
| 361 |
361 |
///@{
|
| 362 |
362 |
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| 363 |
363 |
///Returns \c true if \c a is \e surely strictly less than \c b
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| 364 |
364 |
static bool less(Value a,Value b) { return a<b;}
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| 365 |
365 |
///Returns \c true if \c a is \e surely different from \c b
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| 366 |
366 |
static bool different(Value a,Value b) { return a!=b; }
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| 367 |
367 |
///Returns \c true if \c a is \e surely positive
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| 368 |
368 |
static bool positive(Value a) { return 0<a; }
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| 369 |
369 |
///Returns \c true if \c a is \e surely negative
|
| 370 |
370 |
static bool negative(Value) { return false; }
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| 371 |
371 |
///Returns \c true if \c a is \e surely non-zero
|
| 372 |
372 |
static bool nonZero(Value a) { return a!=0;}
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| 373 |
373 |
|
| 374 |
374 |
///@}
|
| 375 |
375 |
|
| 376 |
376 |
///Returns zero
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| 377 |
377 |
static Value zero() {return 0;}
|
| 378 |
378 |
};
|
| 379 |
379 |
|
| 380 |
380 |
#if defined __GNUC__ && !defined __STRICT_ANSI__
|
| 381 |
381 |
|
| 382 |
|
///Long long integer specialization of \ref Tolerance.
|
|
382 |
///Long long integer specialization of Tolerance.
|
| 383 |
383 |
|
| 384 |
384 |
///Long long integer specialization of \ref Tolerance.
|
| 385 |
385 |
///\warning This class (more exactly, type <tt>long long</tt>)
|
| 386 |
386 |
///is not ansi compatible.
|
| 387 |
387 |
///\sa Tolerance
|
| 388 |
388 |
template<>
|
| 389 |
389 |
class Tolerance<long long int>
|
| 390 |
390 |
{
|
| 391 |
391 |
public:
|
| 392 |
392 |
///\e
|
| 393 |
393 |
typedef long long int Value;
|
| 394 |
394 |
|
| 395 |
395 |
///\name Comparisons
|
| 396 |
396 |
///See \ref Tolerance for more details.
|
| 397 |
397 |
|
| 398 |
398 |
///@{
|
| 399 |
399 |
|
| 400 |
400 |
///Returns \c true if \c a is \e surely strictly less than \c b
|
| 401 |
401 |
static bool less(Value a,Value b) { return a<b;}
|
| 402 |
402 |
///Returns \c true if \c a is \e surely different from \c b
|
| 403 |
403 |
static bool different(Value a,Value b) { return a!=b; }
|
| 404 |
404 |
///Returns \c true if \c a is \e surely positive
|
| 405 |
405 |
static bool positive(Value a) { return 0<a; }
|
| 406 |
406 |
///Returns \c true if \c a is \e surely negative
|
| 407 |
407 |
static bool negative(Value a) { return 0>a; }
|
| 408 |
408 |
///Returns \c true if \c a is \e surely non-zero
|
| 409 |
409 |
static bool nonZero(Value a) { return a!=0;}
|
| 410 |
410 |
|
| 411 |
411 |
///@}
|
| 412 |
412 |
|
| 413 |
413 |
///Returns zero
|
| 414 |
414 |
static Value zero() {return 0;}
|
| 415 |
415 |
};
|
| 416 |
416 |
|
| 417 |
|
///Unsigned long long integer specialization of \ref Tolerance.
|
|
417 |
///Unsigned long long integer specialization of Tolerance.
|
| 418 |
418 |
|
| 419 |
419 |
///Unsigned long long integer specialization of \ref Tolerance.
|
| 420 |
420 |
///\warning This class (more exactly, type <tt>unsigned long long</tt>)
|
| 421 |
421 |
///is not ansi compatible.
|
| 422 |
422 |
///\sa Tolerance
|
| 423 |
423 |
template<>
|
| 424 |
424 |
class Tolerance<unsigned long long int>
|
| 425 |
425 |
{
|
| 426 |
426 |
public:
|
| 427 |
427 |
///\e
|
| 428 |
428 |
typedef unsigned long long int Value;
|
| 429 |
429 |
|
| 430 |
430 |
///\name Comparisons
|
| 431 |
431 |
///See \ref Tolerance for more details.
|
| 432 |
432 |
|
| 433 |
433 |
///@{
|
| 434 |
434 |
|
| 435 |
435 |
///Returns \c true if \c a is \e surely strictly less than \c b
|
| 436 |
436 |
static bool less(Value a,Value b) { return a<b;}
|
| 437 |
437 |
///Returns \c true if \c a is \e surely different from \c b
|
| 438 |
438 |
static bool different(Value a,Value b) { return a!=b; }
|
| 439 |
439 |
///Returns \c true if \c a is \e surely positive
|
| 440 |
440 |
static bool positive(Value a) { return 0<a; }
|
| 441 |
441 |
///Returns \c true if \c a is \e surely negative
|