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 : Tue Dec 4 23:07:46 2018 |
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15 | // Update Count : 106 |
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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.hfa" |
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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 | void ?{}( Rational(RationalImpl) & r ); |
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56 | void ?{}( Rational(RationalImpl) & r, RationalImpl n ); |
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57 | void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ); |
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58 | void ?{}( Rational(RationalImpl) & r, zero_t ); |
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59 | void ?{}( Rational(RationalImpl) & r, one_t ); |
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60 | |
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61 | // numerator/denominator getter |
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62 | |
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63 | RationalImpl numerator( Rational(RationalImpl) r ); |
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64 | RationalImpl denominator( Rational(RationalImpl) r ); |
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65 | [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ); |
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66 | |
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67 | // numerator/denominator setter |
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68 | |
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69 | RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ); |
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70 | RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ); |
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71 | |
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72 | // comparison |
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73 | |
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74 | int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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75 | int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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76 | int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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77 | int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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78 | int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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79 | int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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80 | |
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81 | // arithmetic |
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82 | |
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83 | Rational(RationalImpl) +?( Rational(RationalImpl) r ); |
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84 | Rational(RationalImpl) -?( Rational(RationalImpl) r ); |
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85 | Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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86 | Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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87 | Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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88 | Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ); |
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89 | |
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90 | // I/O |
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91 | forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } ) |
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92 | istype & ?|?( istype &, Rational(RationalImpl) & ); |
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93 | |
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94 | forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) { |
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95 | ostype & ?|?( ostype &, Rational(RationalImpl) ); |
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96 | void ?|?( ostype &, Rational(RationalImpl) ); |
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97 | } // distribution |
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98 | } // distribution |
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99 | |
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100 | // conversion |
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101 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) |
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102 | double widen( Rational(RationalImpl) r ); |
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103 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double );} ) |
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104 | Rational(RationalImpl) narrow( double f, RationalImpl md ); |
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105 | |
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106 | // Local Variables: // |
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107 | // mode: c // |
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108 | // tab-width: 4 // |
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109 | // End: // |
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