1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2008 |
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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 | ///\ref 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 |
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44 | ///numerical data types. These specialized classes like |
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45 | ///Tolerance<double> 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 \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 Tolerance. |
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91 | |
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92 | ///Float specialization of 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 to the given value. |
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107 | Tolerance(float e) : _epsilon(e) {} |
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108 | |
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109 | ///Returns the epsilon value. |
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110 | Value epsilon() const {return _epsilon;} |
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111 | ///Sets the epsilon value. |
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112 | void epsilon(Value e) {_epsilon=e;} |
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113 | |
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114 | ///Returns the default epsilon value. |
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115 | static Value defaultEpsilon() {return def_epsilon;} |
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116 | ///Sets 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 \ref lemon::Tolerance "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 Tolerance. |
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142 | |
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143 | ///Double specialization of 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 to the given value. |
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158 | Tolerance(double e) : _epsilon(e) {} |
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159 | |
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160 | ///Returns the epsilon value. |
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161 | Value epsilon() const {return _epsilon;} |
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162 | ///Sets the epsilon value. |
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163 | void epsilon(Value e) {_epsilon=e;} |
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164 | |
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165 | ///Returns the default epsilon value. |
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166 | static Value defaultEpsilon() {return def_epsilon;} |
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167 | ///Sets 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 \ref lemon::Tolerance "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 Tolerance. |
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193 | |
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194 | ///Long double specialization of 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 to the given value. |
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209 | Tolerance(long double e) : _epsilon(e) {} |
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210 | |
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211 | ///Returns the epsilon value. |
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212 | Value epsilon() const {return _epsilon;} |
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213 | ///Sets the epsilon value. |
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214 | void epsilon(Value e) {_epsilon=e;} |
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215 | |
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216 | ///Returns the default epsilon value. |
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217 | static Value defaultEpsilon() {return def_epsilon;} |
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218 | ///Sets 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 \ref lemon::Tolerance "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 Tolerance. |
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244 | |
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245 | ///Integer specialization of 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 lemon::Tolerance "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 Tolerance. |
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277 | |
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278 | ///Unsigned integer specialization of 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 lemon::Tolerance "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 Tolerance. |
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311 | |
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312 | ///Long integer specialization of 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 lemon::Tolerance "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 Tolerance. |
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344 | |
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345 | ///Unsigned long integer specialization of 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 lemon::Tolerance "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 Tolerance. |
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379 | |
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380 | ///Long long integer specialization of 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 lemon::Tolerance "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 Tolerance. |
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414 | |
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415 | ///Unsigned long long integer specialization of 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 lemon::Tolerance "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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