| 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 Mar 26 23:16:10 2019 |
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| 15 | // Update Count : 109 |
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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 | forall( otype RationalImpl | arithmetic( RationalImpl ) |{RationalImpl ?\?( RationalImpl, unsigned long );} ) |
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| 101 | Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y ); |
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| 102 | |
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| 103 | // conversion |
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| 104 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) |
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| 105 | double widen( Rational(RationalImpl) r ); |
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| 106 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double );} ) |
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| 107 | Rational(RationalImpl) narrow( double f, RationalImpl md ); |
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| 108 | |
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| 109 | // Local Variables: // |
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| 110 | // mode: c // |
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| 111 | // tab-width: 4 // |
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| 112 | // End: // |
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