[7] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_TOLERANCE_H |
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| 20 | #define LEMON_TOLERANCE_H |
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| 21 | |
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| 22 | ///\ingroup misc |
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| 23 | ///\file |
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| 24 | ///\brief A basic tool to handle the anomalies of calculation with |
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| 25 | ///floating point numbers. |
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| 26 | /// |
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| 27 | ///\todo It should be in a module like "Basic tools" |
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| 28 | |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \addtogroup misc |
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| 33 | /// @{ |
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| 34 | |
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| 35 | ///\brief A class to provide a basic way to |
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| 36 | ///handle the comparison of numbers that are obtained |
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| 37 | ///as a result of a probably inexact computation. |
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| 38 | /// |
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| 39 | ///Tolerance is a class to provide a basic way to |
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| 40 | ///handle the comparison of numbers that are obtained |
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| 41 | ///as a result of a probably inexact computation. |
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| 42 | /// |
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| 43 | ///This is an abstract class, it should be specialized for all numerical |
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| 44 | ///data types. These specialized classes like \ref Tolerance\<double\> |
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| 45 | ///may offer additional tuning parameters. |
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| 46 | /// |
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| 47 | ///\sa Tolerance<float> |
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| 48 | ///\sa Tolerance<double> |
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| 49 | ///\sa Tolerance<long double> |
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| 50 | ///\sa Tolerance<int> |
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| 51 | ///\sa Tolerance<long long int> |
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| 52 | ///\sa Tolerance<unsigned int> |
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| 53 | ///\sa Tolerance<unsigned long long int> |
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| 54 | |
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| 55 | template<class T> |
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| 56 | class Tolerance |
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| 57 | { |
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| 58 | public: |
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| 59 | typedef T Value; |
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| 60 | |
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| 61 | ///\name Comparisons |
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| 62 | ///The concept is that these bool functions return with \c true only if |
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| 63 | ///the related comparisons hold even if some numerical error appeared |
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| 64 | ///during the computations. |
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| 65 | |
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| 66 | ///@{ |
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| 67 | |
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| 68 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 69 | static bool less(Value a,Value b) {return false;} |
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| 70 | ///Returns \c true if \c a is \e surely different from \c b |
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| 71 | static bool different(Value a,Value b) {return false;} |
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| 72 | ///Returns \c true if \c a is \e surely positive |
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| 73 | static bool positive(Value a) {return false;} |
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| 74 | ///Returns \c true if \c a is \e surely negative |
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| 75 | static bool negative(Value a) {return false;} |
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| 76 | ///Returns \c true if \c a is \e surely non-zero |
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| 77 | static bool nonZero(Value a) {return false;} |
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| 78 | |
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| 79 | ///@} |
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| 80 | |
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| 81 | ///Returns the zero value. |
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| 82 | static Value zero() {return T();} |
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| 83 | |
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| 84 | // static bool finite(Value a) {} |
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| 85 | // static Value big() {} |
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| 86 | // static Value negativeBig() {} |
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| 87 | }; |
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| 88 | |
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| 89 | |
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| 90 | ///Float specialization of \ref Tolerance. |
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| 91 | |
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| 92 | ///Float specialization of \ref Tolerance. |
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| 93 | ///\sa Tolerance |
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| 94 | ///\relates Tolerance |
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| 95 | template<> |
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| 96 | class Tolerance<float> |
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| 97 | { |
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| 98 | static float def_epsilon; |
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| 99 | float _epsilon; |
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| 100 | public: |
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| 101 | ///\e |
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| 102 | typedef float Value; |
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| 103 | |
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| 104 | ///Constructor setting the epsilon tolerance to the default value. |
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| 105 | Tolerance() : _epsilon(def_epsilon) {} |
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| 106 | ///Constructor setting the epsilon tolerance. |
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| 107 | Tolerance(float e) : _epsilon(e) {} |
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| 108 | |
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| 109 | ///Return the epsilon value. |
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| 110 | Value epsilon() const {return _epsilon;} |
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| 111 | ///Set the epsilon value. |
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| 112 | void epsilon(Value e) {_epsilon=e;} |
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| 113 | |
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| 114 | ///Return the default epsilon value. |
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| 115 | static Value defaultEpsilon() {return def_epsilon;} |
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| 116 | ///Set the default epsilon value. |
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| 117 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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| 118 | |
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| 119 | ///\name Comparisons |
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| 120 | ///See class Tolerance for more details. |
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| 121 | |
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| 122 | ///@{ |
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| 123 | |
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| 124 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 125 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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| 126 | ///Returns \c true if \c a is \e surely different from \c b |
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| 127 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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| 128 | ///Returns \c true if \c a is \e surely positive |
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| 129 | bool positive(Value a) const { return _epsilon<a; } |
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| 130 | ///Returns \c true if \c a is \e surely negative |
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| 131 | bool negative(Value a) const { return -_epsilon>a; } |
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| 132 | ///Returns \c true if \c a is \e surely non-zero |
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| 133 | bool nonZero(Value a) const { return positive(a)||negative(a); }; |
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| 134 | |
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| 135 | ///@} |
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| 136 | |
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| 137 | ///Returns zero |
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| 138 | static Value zero() {return 0;} |
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| 139 | }; |
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| 140 | |
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| 141 | ///Double specialization of \ref Tolerance. |
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| 142 | |
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| 143 | ///Double specialization of \ref Tolerance. |
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| 144 | ///\sa Tolerance |
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| 145 | ///\relates Tolerance |
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| 146 | template<> |
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| 147 | class Tolerance<double> |
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| 148 | { |
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| 149 | static double def_epsilon; |
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| 150 | double _epsilon; |
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| 151 | public: |
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| 152 | ///\e |
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| 153 | typedef double Value; |
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| 154 | |
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| 155 | ///Constructor setting the epsilon tolerance to the default value. |
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| 156 | Tolerance() : _epsilon(def_epsilon) {} |
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| 157 | ///Constructor setting the epsilon tolerance. |
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| 158 | Tolerance(double e) : _epsilon(e) {} |
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| 159 | |
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| 160 | ///Return the epsilon value. |
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| 161 | Value epsilon() const {return _epsilon;} |
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| 162 | ///Set the epsilon value. |
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| 163 | void epsilon(Value e) {_epsilon=e;} |
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| 164 | |
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| 165 | ///Return the default epsilon value. |
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| 166 | static Value defaultEpsilon() {return def_epsilon;} |
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| 167 | ///Set the default epsilon value. |
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| 168 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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| 169 | |
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| 170 | ///\name Comparisons |
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| 171 | ///See class Tolerance for more details. |
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| 172 | |
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| 173 | ///@{ |
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| 174 | |
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| 175 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 176 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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| 177 | ///Returns \c true if \c a is \e surely different from \c b |
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| 178 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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| 179 | ///Returns \c true if \c a is \e surely positive |
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| 180 | bool positive(Value a) const { return _epsilon<a; } |
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| 181 | ///Returns \c true if \c a is \e surely negative |
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| 182 | bool negative(Value a) const { return -_epsilon>a; } |
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| 183 | ///Returns \c true if \c a is \e surely non-zero |
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| 184 | bool nonZero(Value a) const { return positive(a)||negative(a); }; |
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| 185 | |
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| 186 | ///@} |
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| 187 | |
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| 188 | ///Returns zero |
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| 189 | static Value zero() {return 0;} |
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| 190 | }; |
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| 191 | |
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| 192 | ///Long double specialization of \ref Tolerance. |
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| 193 | |
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| 194 | ///Long double specialization of \ref Tolerance. |
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| 195 | ///\sa Tolerance |
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| 196 | ///\relates Tolerance |
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| 197 | template<> |
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| 198 | class Tolerance<long double> |
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| 199 | { |
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| 200 | static long double def_epsilon; |
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| 201 | long double _epsilon; |
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| 202 | public: |
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| 203 | ///\e |
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| 204 | typedef long double Value; |
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| 205 | |
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| 206 | ///Constructor setting the epsilon tolerance to the default value. |
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| 207 | Tolerance() : _epsilon(def_epsilon) {} |
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| 208 | ///Constructor setting the epsilon tolerance. |
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| 209 | Tolerance(long double e) : _epsilon(e) {} |
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| 210 | |
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| 211 | ///Return the epsilon value. |
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| 212 | Value epsilon() const {return _epsilon;} |
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| 213 | ///Set the epsilon value. |
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| 214 | void epsilon(Value e) {_epsilon=e;} |
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| 215 | |
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| 216 | ///Return the default epsilon value. |
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| 217 | static Value defaultEpsilon() {return def_epsilon;} |
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| 218 | ///Set the default epsilon value. |
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| 219 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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| 220 | |
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| 221 | ///\name Comparisons |
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| 222 | ///See class Tolerance for more details. |
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| 223 | |
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| 224 | ///@{ |
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| 225 | |
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| 226 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 227 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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| 228 | ///Returns \c true if \c a is \e surely different from \c b |
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| 229 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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| 230 | ///Returns \c true if \c a is \e surely positive |
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| 231 | bool positive(Value a) const { return _epsilon<a; } |
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| 232 | ///Returns \c true if \c a is \e surely negative |
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| 233 | bool negative(Value a) const { return -_epsilon>a; } |
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| 234 | ///Returns \c true if \c a is \e surely non-zero |
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| 235 | bool nonZero(Value a) const { return positive(a)||negative(a); }; |
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| 236 | |
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| 237 | ///@} |
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| 238 | |
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| 239 | ///Returns zero |
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| 240 | static Value zero() {return 0;} |
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| 241 | }; |
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| 242 | |
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| 243 | ///Integer specialization of \ref Tolerance. |
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| 244 | |
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| 245 | ///Integer specialization of \ref Tolerance. |
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| 246 | ///\sa Tolerance |
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| 247 | template<> |
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| 248 | class Tolerance<int> |
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| 249 | { |
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| 250 | public: |
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| 251 | ///\e |
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| 252 | typedef int Value; |
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| 253 | |
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| 254 | ///\name Comparisons |
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| 255 | ///See \ref Tolerance for more details. |
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| 256 | |
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| 257 | ///@{ |
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| 258 | |
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| 259 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 260 | static bool less(Value a,Value b) { return a<b;} |
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| 261 | ///Returns \c true if \c a is \e surely different from \c b |
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| 262 | static bool different(Value a,Value b) { return a!=b; } |
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| 263 | ///Returns \c true if \c a is \e surely positive |
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| 264 | static bool positive(Value a) { return 0<a; } |
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| 265 | ///Returns \c true if \c a is \e surely negative |
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| 266 | static bool negative(Value a) { return 0>a; } |
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| 267 | ///Returns \c true if \c a is \e surely non-zero |
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| 268 | static bool nonZero(Value a) { return a!=0; }; |
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| 269 | |
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| 270 | ///@} |
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| 271 | |
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| 272 | ///Returns zero |
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| 273 | static Value zero() {return 0;} |
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| 274 | }; |
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| 275 | |
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| 276 | ///Unsigned integer specialization of \ref Tolerance. |
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| 277 | |
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| 278 | ///Unsigned integer specialization of \ref Tolerance. |
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| 279 | ///\sa Tolerance |
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| 280 | template<> |
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| 281 | class Tolerance<unsigned int> |
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| 282 | { |
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| 283 | public: |
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| 284 | ///\e |
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| 285 | typedef unsigned int Value; |
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| 286 | |
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| 287 | ///\name Comparisons |
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| 288 | ///See \ref Tolerance for more details. |
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| 289 | |
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| 290 | ///@{ |
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| 291 | |
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| 292 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 293 | static bool less(Value a,Value b) { return a<b;} |
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| 294 | ///Returns \c true if \c a is \e surely different from \c b |
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| 295 | static bool different(Value a,Value b) { return a!=b; } |
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| 296 | ///Returns \c true if \c a is \e surely positive |
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| 297 | static bool positive(Value a) { return 0<a; } |
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| 298 | ///Returns \c true if \c a is \e surely negative |
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| 299 | static bool negative(Value) { return false; } |
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| 300 | ///Returns \c true if \c a is \e surely non-zero |
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| 301 | static bool nonZero(Value a) { return a!=0; }; |
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| 302 | |
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| 303 | ///@} |
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| 304 | |
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| 305 | ///Returns zero |
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| 306 | static Value zero() {return 0;} |
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| 307 | }; |
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| 308 | |
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| 309 | |
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| 310 | ///Long integer specialization of \ref Tolerance. |
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| 311 | |
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| 312 | ///Long integer specialization of \ref Tolerance. |
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| 313 | ///\sa Tolerance |
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| 314 | template<> |
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| 315 | class Tolerance<long int> |
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| 316 | { |
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| 317 | public: |
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| 318 | ///\e |
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| 319 | typedef long int Value; |
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| 320 | |
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| 321 | ///\name Comparisons |
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| 322 | ///See \ref Tolerance for more details. |
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| 323 | |
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| 324 | ///@{ |
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| 325 | |
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| 326 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 327 | static bool less(Value a,Value b) { return a<b;} |
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| 328 | ///Returns \c true if \c a is \e surely different from \c b |
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| 329 | static bool different(Value a,Value b) { return a!=b; } |
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| 330 | ///Returns \c true if \c a is \e surely positive |
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| 331 | static bool positive(Value a) { return 0<a; } |
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| 332 | ///Returns \c true if \c a is \e surely negative |
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| 333 | static bool negative(Value a) { return 0>a; } |
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| 334 | ///Returns \c true if \c a is \e surely non-zero |
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| 335 | static bool nonZero(Value a) { return a!=0;}; |
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| 336 | |
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| 337 | ///@} |
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| 338 | |
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| 339 | ///Returns zero |
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| 340 | static Value zero() {return 0;} |
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| 341 | }; |
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| 342 | |
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| 343 | ///Unsigned long integer specialization of \ref Tolerance. |
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| 344 | |
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| 345 | ///Unsigned long integer specialization of \ref Tolerance. |
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| 346 | ///\sa Tolerance |
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| 347 | template<> |
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| 348 | class Tolerance<unsigned long int> |
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| 349 | { |
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| 350 | public: |
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| 351 | ///\e |
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| 352 | typedef unsigned long int Value; |
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| 353 | |
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| 354 | ///\name Comparisons |
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| 355 | ///See \ref Tolerance for more details. |
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| 356 | |
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| 357 | ///@{ |
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| 358 | |
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| 359 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 360 | static bool less(Value a,Value b) { return a<b;} |
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| 361 | ///Returns \c true if \c a is \e surely different from \c b |
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| 362 | static bool different(Value a,Value b) { return a!=b; } |
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| 363 | ///Returns \c true if \c a is \e surely positive |
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| 364 | static bool positive(Value a) { return 0<a; } |
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| 365 | ///Returns \c true if \c a is \e surely negative |
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| 366 | static bool negative(Value) { return false; } |
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| 367 | ///Returns \c true if \c a is \e surely non-zero |
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| 368 | static bool nonZero(Value a) { return a!=0;}; |
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| 369 | |
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| 370 | ///@} |
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| 371 | |
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| 372 | ///Returns zero |
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| 373 | static Value zero() {return 0;} |
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| 374 | }; |
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| 375 | |
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| 376 | #if defined __GNUC__ && !defined __STRICT_ANSI__ |
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| 377 | |
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| 378 | ///Long long integer specialization of \ref Tolerance. |
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| 379 | |
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| 380 | ///Long long integer specialization of \ref Tolerance. |
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| 381 | ///\warning This class (more exactly, type <tt>long long</tt>) |
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| 382 | ///is not ansi compatible. |
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| 383 | ///\sa Tolerance |
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| 384 | template<> |
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| 385 | class Tolerance<long long int> |
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| 386 | { |
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| 387 | public: |
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| 388 | ///\e |
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| 389 | typedef long long int Value; |
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| 390 | |
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| 391 | ///\name Comparisons |
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| 392 | ///See \ref Tolerance for more details. |
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| 393 | |
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| 394 | ///@{ |
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| 395 | |
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| 396 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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| 397 | static bool less(Value a,Value b) { return a<b;} |
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| 398 | ///Returns \c true if \c a is \e surely different from \c b |
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| 399 | static bool different(Value a,Value b) { return a!=b; } |
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| 400 | ///Returns \c true if \c a is \e surely positive |
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| 401 | static bool positive(Value a) { return 0<a; } |
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| 402 | ///Returns \c true if \c a is \e surely negative |
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| 403 | static bool negative(Value a) { return 0>a; } |
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| 404 | ///Returns \c true if \c a is \e surely non-zero |
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| 405 | static bool nonZero(Value a) { return a!=0;}; |
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| 406 | |
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| 407 | ///@} |
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| 408 | |
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| 409 | ///Returns zero |
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| 410 | static Value zero() {return 0;} |
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| 411 | }; |
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| 412 | |
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| 413 | ///Unsigned long long integer specialization of \ref Tolerance. |
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| 414 | |
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| 415 | ///Unsigned long long integer specialization of \ref Tolerance. |
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| 416 | ///\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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| 422 | 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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| 429 | ///@{ |
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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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