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 -- Rational numbers are numbers written as a ratio, i.e., as a fraction, where the numerator (top number) |
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8 | // and the denominator (bottom number) are whole numbers. When creating and computing with rational numbers, results |
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9 | // are constantly reduced to keep the numerator and denominator as small as possible. |
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10 | // |
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11 | // Author : Peter A. Buhr |
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12 | // Created On : Wed Apr 6 17:56:25 2016 |
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13 | // Last Modified By : Peter A. Buhr |
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14 | // Last Modified On : Fri Jul 7 09:34:33 2017 |
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15 | // Update Count : 93 |
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16 | // |
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17 | |
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18 | #pragma once |
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19 | |
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20 | #include "iostream" |
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21 | |
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22 | trait scalar( otype T ) { |
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23 | }; |
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24 | |
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25 | trait arithmetic( otype T | scalar( T ) ) { |
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26 | int !?( T ); |
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27 | int ?==?( T, T ); |
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28 | int ?!=?( T, T ); |
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29 | int ?<?( T, T ); |
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30 | int ?<=?( T, T ); |
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31 | int ?>?( T, T ); |
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32 | int ?>=?( T, T ); |
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33 | void ?{}( T &, zero_t ); |
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34 | void ?{}( T &, one_t ); |
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35 | T +?( T ); |
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36 | T -?( T ); |
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37 | T ?+?( T, T ); |
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38 | T ?-?( T, T ); |
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39 | T ?*?( T, T ); |
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40 | T ?/?( T, T ); |
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41 | T ?%?( T, T ); |
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42 | T ?/=?( T *, T ); |
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43 | T abs( T ); |
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44 | }; |
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45 | |
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46 | // implementation |
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47 | |
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48 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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49 | struct Rational { |
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50 | RationalImpl numerator, denominator; // invariant: denominator > 0 |
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51 | }; // Rational |
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52 | |
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53 | // constructors |
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54 | |
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55 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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56 | void ?{}( Rational(RationalImpl) & r ); |
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57 | |
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58 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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59 | void ?{}( Rational(RationalImpl) & r, RationalImpl n ); |
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60 | |
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61 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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62 | void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ); |
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63 | |
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64 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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65 | void ?{}( Rational(RationalImpl) & r, zero_t ); |
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66 | |
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67 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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68 | void ?{}( Rational(RationalImpl) & r, one_t ); |
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69 | |
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70 | // numerator/denominator getter |
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71 | |
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72 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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73 | RationalImpl numerator( Rational(RationalImpl) r ); |
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74 | |
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75 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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76 | RationalImpl denominator( Rational(RationalImpl) r ); |
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77 | |
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78 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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79 | [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ); |
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80 | |
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81 | // numerator/denominator setter |
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82 | |
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83 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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84 | RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ); |
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85 | |
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86 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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87 | RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ); |
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88 | |
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89 | // comparison |
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90 | |
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91 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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92 | int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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93 | |
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94 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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95 | int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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96 | |
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97 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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98 | int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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99 | |
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100 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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101 | int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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102 | |
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103 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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104 | int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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105 | |
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106 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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107 | int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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108 | |
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109 | // arithmetic |
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110 | |
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111 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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112 | Rational(RationalImpl) +?( Rational(RationalImpl) r ); |
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113 | |
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114 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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115 | Rational(RationalImpl) -?( Rational(RationalImpl) r ); |
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116 | |
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117 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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118 | Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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119 | |
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120 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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121 | Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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122 | |
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123 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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124 | Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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125 | |
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126 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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127 | Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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128 | |
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129 | // conversion |
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130 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) |
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131 | double widen( Rational(RationalImpl) r ); |
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132 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double );} ) |
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133 | Rational(RationalImpl) narrow( double f, RationalImpl md ); |
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134 | |
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135 | // I/O |
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136 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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137 | forall( dtype istype | istream( istype ) | { istype * ?|?( istype *, RationalImpl * ); } ) |
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138 | istype * ?|?( istype *, Rational(RationalImpl) * ); |
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139 | |
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140 | forall( otype RationalImpl | arithmetic( RationalImpl ) ) |
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141 | forall( dtype ostype | ostream( ostype ) | { ostype * ?|?( ostype *, RationalImpl ); } ) |
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142 | ostype * ?|?( ostype *, Rational(RationalImpl ) ); |
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143 | |
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144 | // Local Variables: // |
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145 | // mode: c // |
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146 | // tab-width: 4 // |
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147 | // End: // |
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