1 | // |
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2 | // Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo |
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3 | // |
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4 | // The contents of this file are covered under the licence agreement in the |
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5 | // file "LICENCE" distributed with Cforall. |
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6 | // |
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7 | // rational.c -- |
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8 | // |
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9 | // Author : Peter A. Buhr |
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10 | // Created On : Wed Apr 6 17:54:28 2016 |
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11 | // Last Modified By : Peter A. Buhr |
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12 | // Last Modified On : Sat Feb 8 17:56:36 2020 |
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13 | // Update Count : 187 |
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14 | // |
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15 | |
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16 | #include "rational.hfa" |
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17 | #include "fstream.hfa" |
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18 | #include "stdlib.hfa" |
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19 | |
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20 | forall( RationalImpl | arithmetic( RationalImpl ) ) { |
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21 | // helper routines |
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22 | |
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23 | // Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce |
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24 | // rationals. alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm |
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25 | static RationalImpl gcd( RationalImpl a, RationalImpl b ) { |
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26 | for ( ;; ) { // Euclid's algorithm |
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27 | RationalImpl r = a % b; |
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28 | if ( r == (RationalImpl){0} ) break; |
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29 | a = b; |
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30 | b = r; |
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31 | } // for |
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32 | return b; |
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33 | } // gcd |
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34 | |
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35 | static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) { |
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36 | if ( d == (RationalImpl){0} ) { |
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37 | abort | "Invalid rational number construction: denominator cannot be equal to 0."; |
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38 | } // exit |
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39 | if ( d < (RationalImpl){0} ) { d = -d; n = -n; } // move sign to numerator |
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40 | return gcd( abs( n ), d ); // simplify |
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41 | } // Rationalnumber::simplify |
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42 | |
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43 | // constructors |
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44 | |
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45 | void ?{}( Rational(RationalImpl) & r ) { |
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46 | r{ (RationalImpl){0}, (RationalImpl){1} }; |
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47 | } // rational |
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48 | |
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49 | void ?{}( Rational(RationalImpl) & r, RationalImpl n ) { |
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50 | r{ n, (RationalImpl){1} }; |
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51 | } // rational |
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52 | |
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53 | void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) { |
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54 | RationalImpl t = simplify( n, d ); // simplify |
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55 | r.[numerator, denominator] = [n / t, d / t]; |
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56 | } // rational |
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57 | |
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58 | void ?{}( Rational(RationalImpl) & r, zero_t ) { |
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59 | r{ (RationalImpl){0}, (RationalImpl){1} }; |
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60 | } // rational |
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61 | |
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62 | void ?{}( Rational(RationalImpl) & r, one_t ) { |
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63 | r{ (RationalImpl){1}, (RationalImpl){1} }; |
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64 | } // rational |
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65 | |
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66 | // getter for numerator/denominator |
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67 | |
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68 | RationalImpl numerator( Rational(RationalImpl) r ) { |
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69 | return r.numerator; |
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70 | } // numerator |
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71 | |
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72 | RationalImpl denominator( Rational(RationalImpl) r ) { |
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73 | return r.denominator; |
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74 | } // denominator |
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75 | |
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76 | [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) { |
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77 | return dest = src.[ numerator, denominator ]; |
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78 | } // ?=? |
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79 | |
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80 | // setter for numerator/denominator |
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81 | |
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82 | RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) { |
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83 | RationalImpl prev = r.numerator; |
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84 | RationalImpl t = gcd( abs( n ), r.denominator ); // simplify |
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85 | r.[numerator, denominator] = [n / t, r.denominator / t]; |
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86 | return prev; |
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87 | } // numerator |
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88 | |
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89 | RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) { |
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90 | RationalImpl prev = r.denominator; |
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91 | RationalImpl t = simplify( r.numerator, d ); // simplify |
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92 | r.[numerator, denominator] = [r.numerator / t, d / t]; |
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93 | return prev; |
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94 | } // denominator |
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95 | |
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96 | // comparison |
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97 | |
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98 | int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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99 | return l.numerator * r.denominator == l.denominator * r.numerator; |
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100 | } // ?==? |
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101 | |
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102 | int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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103 | return ! ( l == r ); |
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104 | } // ?!=? |
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105 | |
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106 | int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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107 | return l.numerator * r.denominator < l.denominator * r.numerator; |
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108 | } // ?<? |
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109 | |
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110 | int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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111 | return l.numerator * r.denominator <= l.denominator * r.numerator; |
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112 | } // ?<=? |
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113 | |
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114 | int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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115 | return ! ( l <= r ); |
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116 | } // ?>? |
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117 | |
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118 | int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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119 | return ! ( l < r ); |
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120 | } // ?>=? |
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121 | |
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122 | // arithmetic |
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123 | |
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124 | Rational(RationalImpl) +?( Rational(RationalImpl) r ) { |
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125 | return (Rational(RationalImpl)){ r.numerator, r.denominator }; |
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126 | } // +? |
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127 | |
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128 | Rational(RationalImpl) -?( Rational(RationalImpl) r ) { |
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129 | return (Rational(RationalImpl)){ -r.numerator, r.denominator }; |
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130 | } // -? |
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131 | |
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132 | Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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133 | if ( l.denominator == r.denominator ) { // special case |
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134 | return (Rational(RationalImpl)){ l.numerator + r.numerator, l.denominator }; |
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135 | } else { |
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136 | return (Rational(RationalImpl)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator }; |
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137 | } // if |
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138 | } // ?+? |
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139 | |
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140 | Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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141 | if ( l.denominator == r.denominator ) { // special case |
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142 | return (Rational(RationalImpl)){ l.numerator - r.numerator, l.denominator }; |
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143 | } else { |
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144 | return (Rational(RationalImpl)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator }; |
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145 | } // if |
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146 | } // ?-? |
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147 | |
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148 | Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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149 | return (Rational(RationalImpl)){ l.numerator * r.numerator, l.denominator * r.denominator }; |
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150 | } // ?*? |
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151 | |
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152 | Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { |
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153 | if ( r.numerator < (RationalImpl){0} ) { |
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154 | r.[numerator, denominator] = [-r.numerator, -r.denominator]; |
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155 | } // if |
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156 | return (Rational(RationalImpl)){ l.numerator * r.denominator, l.denominator * r.numerator }; |
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157 | } // ?/? |
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158 | |
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159 | // I/O |
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160 | |
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161 | forall( istype & | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } ) |
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162 | istype & ?|?( istype & is, Rational(RationalImpl) & r ) { |
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163 | is | r.numerator | r.denominator; |
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164 | RationalImpl t = simplify( r.numerator, r.denominator ); |
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165 | r.numerator /= t; |
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166 | r.denominator /= t; |
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167 | return is; |
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168 | } // ?|? |
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169 | |
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170 | forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) { |
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171 | ostype & ?|?( ostype & os, Rational(RationalImpl) r ) { |
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172 | return os | r.numerator | '/' | r.denominator; |
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173 | } // ?|? |
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174 | |
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175 | void ?|?( ostype & os, Rational(RationalImpl) r ) { |
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176 | (ostype &)(os | r); ends( os ); |
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177 | } // ?|? |
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178 | } // distribution |
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179 | } // distribution |
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180 | |
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181 | forall( RationalImpl | arithmetic( RationalImpl ) | { RationalImpl ?\?( RationalImpl, unsigned long ); } ) |
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182 | Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y ) { |
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183 | if ( y < 0 ) { |
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184 | return (Rational(RationalImpl)){ x.denominator \ -y, x.numerator \ -y }; |
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185 | } else { |
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186 | return (Rational(RationalImpl)){ x.numerator \ y, x.denominator \ y }; |
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187 | } // if |
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188 | } |
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189 | |
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190 | // conversion |
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191 | |
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192 | forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) |
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193 | double widen( Rational(RationalImpl) r ) { |
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194 | return convert( r.numerator ) / convert( r.denominator ); |
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195 | } // widen |
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196 | |
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197 | forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } ) |
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198 | Rational(RationalImpl) narrow( double f, RationalImpl md ) { |
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199 | // http://www.ics.uci.edu/~eppstein/numth/frap.c |
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200 | if ( md <= (RationalImpl){1} ) { // maximum fractional digits too small? |
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201 | return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction |
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202 | } // if |
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203 | |
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204 | // continued fraction coefficients |
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205 | RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 }; |
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206 | RationalImpl ai, t; |
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207 | |
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208 | // find terms until denom gets too big |
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209 | for ( ;; ) { |
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210 | ai = convert( f ); |
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211 | if ( ! (m10 * ai + m11 <= md) ) break; |
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212 | t = m00 * ai + m01; |
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213 | m01 = m00; |
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214 | m00 = t; |
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215 | t = m10 * ai + m11; |
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216 | m11 = m10; |
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217 | m10 = t; |
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218 | double temp = convert( ai ); |
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219 | if ( f == temp ) break; // prevent division by zero |
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220 | f = 1 / (f - temp); |
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221 | if ( f > (double)0x7FFFFFFF ) break; // representation failure |
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222 | } // for |
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223 | return (Rational(RationalImpl)){ m00, m10 }; |
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224 | } // narrow |
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225 | |
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226 | // Local Variables: // |
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227 | // tab-width: 4 // |
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228 | // End: // |
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