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 | |
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28 | namespace lemon { |
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29 | |
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30 | /// \addtogroup misc |
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31 | /// @{ |
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32 | |
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33 | ///\brief A class to provide a basic way to |
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34 | ///handle the comparison of numbers that are obtained |
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35 | ///as a result of a probably inexact computation. |
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36 | /// |
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37 | ///\ref Tolerance is a class to provide a basic way to |
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38 | ///handle the comparison of numbers that are obtained |
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39 | ///as a result of a probably inexact computation. |
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40 | /// |
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41 | ///The general implementation is suitable only if the data type is exact, |
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42 | ///like the integer types, otherwise a specialized version must be |
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43 | ///implemented. These specialized classes like |
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44 | ///Tolerance<double> may offer additional tuning parameters. |
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45 | /// |
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46 | ///\sa Tolerance<float> |
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47 | ///\sa Tolerance<double> |
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48 | ///\sa Tolerance<long double> |
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49 | |
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50 | template<class T> |
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51 | class Tolerance |
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52 | { |
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53 | public: |
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54 | typedef T Value; |
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55 | |
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56 | ///\name Comparisons |
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57 | ///The concept is that these bool functions return \c true only if |
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58 | ///the related comparisons hold even if some numerical error appeared |
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59 | ///during the computations. |
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60 | |
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61 | ///@{ |
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62 | |
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63 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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64 | static bool less(Value a,Value b) {return a<b;} |
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65 | ///Returns \c true if \c a is \e surely different from \c b |
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66 | static bool different(Value a,Value b) {return a!=b;} |
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67 | ///Returns \c true if \c a is \e surely positive |
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68 | static bool positive(Value a) {return static_cast<Value>(0) < a;} |
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69 | ///Returns \c true if \c a is \e surely negative |
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70 | static bool negative(Value a) {return a < static_cast<Value>(0);} |
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71 | ///Returns \c true if \c a is \e surely non-zero |
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72 | static bool nonZero(Value a) {return a != static_cast<Value>(0);} |
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73 | |
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74 | ///@} |
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75 | |
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76 | ///Returns the zero value. |
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77 | static Value zero() {return static_cast<Value>(0);} |
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78 | |
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79 | // static bool finite(Value a) {} |
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80 | // static Value big() {} |
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81 | // static Value negativeBig() {} |
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82 | }; |
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83 | |
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84 | |
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85 | ///Float specialization of Tolerance. |
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86 | |
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87 | ///Float specialization of Tolerance. |
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88 | ///\sa Tolerance |
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89 | ///\relates Tolerance |
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90 | template<> |
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91 | class Tolerance<float> |
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92 | { |
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93 | static float def_epsilon; |
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94 | float _epsilon; |
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95 | public: |
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96 | ///\e |
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97 | typedef float Value; |
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98 | |
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99 | ///Constructor setting the epsilon tolerance to the default value. |
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100 | Tolerance() : _epsilon(def_epsilon) {} |
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101 | ///Constructor setting the epsilon tolerance to the given value. |
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102 | Tolerance(float e) : _epsilon(e) {} |
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103 | |
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104 | ///Returns the epsilon value. |
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105 | Value epsilon() const {return _epsilon;} |
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106 | ///Sets the epsilon value. |
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107 | void epsilon(Value e) {_epsilon=e;} |
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108 | |
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109 | ///Returns the default epsilon value. |
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110 | static Value defaultEpsilon() {return def_epsilon;} |
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111 | ///Sets the default epsilon value. |
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112 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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113 | |
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114 | ///\name Comparisons |
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115 | ///See \ref lemon::Tolerance "Tolerance" for more details. |
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116 | |
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117 | ///@{ |
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118 | |
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119 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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120 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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121 | ///Returns \c true if \c a is \e surely different from \c b |
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122 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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123 | ///Returns \c true if \c a is \e surely positive |
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124 | bool positive(Value a) const { return _epsilon<a; } |
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125 | ///Returns \c true if \c a is \e surely negative |
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126 | bool negative(Value a) const { return -_epsilon>a; } |
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127 | ///Returns \c true if \c a is \e surely non-zero |
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128 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
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129 | |
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130 | ///@} |
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131 | |
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132 | ///Returns zero |
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133 | static Value zero() {return 0;} |
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134 | }; |
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135 | |
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136 | ///Double specialization of Tolerance. |
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137 | |
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138 | ///Double specialization of Tolerance. |
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139 | ///\sa Tolerance |
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140 | ///\relates Tolerance |
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141 | template<> |
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142 | class Tolerance<double> |
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143 | { |
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144 | static double def_epsilon; |
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145 | double _epsilon; |
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146 | public: |
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147 | ///\e |
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148 | typedef double Value; |
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149 | |
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150 | ///Constructor setting the epsilon tolerance to the default value. |
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151 | Tolerance() : _epsilon(def_epsilon) {} |
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152 | ///Constructor setting the epsilon tolerance to the given value. |
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153 | Tolerance(double e) : _epsilon(e) {} |
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154 | |
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155 | ///Returns the epsilon value. |
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156 | Value epsilon() const {return _epsilon;} |
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157 | ///Sets the epsilon value. |
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158 | void epsilon(Value e) {_epsilon=e;} |
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159 | |
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160 | ///Returns the default epsilon value. |
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161 | static Value defaultEpsilon() {return def_epsilon;} |
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162 | ///Sets the default epsilon value. |
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163 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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164 | |
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165 | ///\name Comparisons |
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166 | ///See \ref lemon::Tolerance "Tolerance" for more details. |
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167 | |
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168 | ///@{ |
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169 | |
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170 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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171 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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172 | ///Returns \c true if \c a is \e surely different from \c b |
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173 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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174 | ///Returns \c true if \c a is \e surely positive |
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175 | bool positive(Value a) const { return _epsilon<a; } |
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176 | ///Returns \c true if \c a is \e surely negative |
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177 | bool negative(Value a) const { return -_epsilon>a; } |
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178 | ///Returns \c true if \c a is \e surely non-zero |
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179 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
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180 | |
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181 | ///@} |
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182 | |
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183 | ///Returns zero |
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184 | static Value zero() {return 0;} |
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185 | }; |
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186 | |
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187 | ///Long double specialization of Tolerance. |
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188 | |
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189 | ///Long double specialization of Tolerance. |
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190 | ///\sa Tolerance |
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191 | ///\relates Tolerance |
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192 | template<> |
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193 | class Tolerance<long double> |
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194 | { |
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195 | static long double def_epsilon; |
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196 | long double _epsilon; |
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197 | public: |
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198 | ///\e |
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199 | typedef long double Value; |
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200 | |
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201 | ///Constructor setting the epsilon tolerance to the default value. |
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202 | Tolerance() : _epsilon(def_epsilon) {} |
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203 | ///Constructor setting the epsilon tolerance to the given value. |
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204 | Tolerance(long double e) : _epsilon(e) {} |
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205 | |
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206 | ///Returns the epsilon value. |
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207 | Value epsilon() const {return _epsilon;} |
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208 | ///Sets the epsilon value. |
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209 | void epsilon(Value e) {_epsilon=e;} |
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210 | |
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211 | ///Returns the default epsilon value. |
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212 | static Value defaultEpsilon() {return def_epsilon;} |
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213 | ///Sets the default epsilon value. |
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214 | static void defaultEpsilon(Value e) {def_epsilon=e;} |
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215 | |
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216 | ///\name Comparisons |
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217 | ///See \ref lemon::Tolerance "Tolerance" for more details. |
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218 | |
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219 | ///@{ |
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220 | |
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221 | ///Returns \c true if \c a is \e surely strictly less than \c b |
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222 | bool less(Value a,Value b) const {return a+_epsilon<b;} |
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223 | ///Returns \c true if \c a is \e surely different from \c b |
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224 | bool different(Value a,Value b) const { return less(a,b)||less(b,a); } |
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225 | ///Returns \c true if \c a is \e surely positive |
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226 | bool positive(Value a) const { return _epsilon<a; } |
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227 | ///Returns \c true if \c a is \e surely negative |
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228 | bool negative(Value a) const { return -_epsilon>a; } |
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229 | ///Returns \c true if \c a is \e surely non-zero |
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230 | bool nonZero(Value a) const { return positive(a)||negative(a); } |
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231 | |
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232 | ///@} |
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233 | |
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234 | ///Returns zero |
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235 | static Value zero() {return 0;} |
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236 | }; |
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237 | |
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238 | /// @} |
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239 | |
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240 | } //namespace lemon |
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241 | |
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242 | #endif //LEMON_TOLERANCE_H |
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