| 1 | //
 | 
|---|
| 2 | // Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
 | 
|---|
| 3 | //
 | 
|---|
| 4 | // The contents of this file are covered under the licence agreement in the
 | 
|---|
| 5 | // file "LICENCE" distributed with Cforall.
 | 
|---|
| 6 | //
 | 
|---|
| 7 | // rational -- Rational numbers are numbers written as a ratio, i.e., as a fraction, where the numerator (top number)
 | 
|---|
| 8 | //     and the denominator (bottom number) are whole numbers. When creating and computing with rational numbers, results
 | 
|---|
| 9 | //     are constantly reduced to keep the numerator and denominator as small as possible.
 | 
|---|
| 10 | //
 | 
|---|
| 11 | // Author           : Peter A. Buhr
 | 
|---|
| 12 | // Created On       : Wed Apr  6 17:56:25 2016
 | 
|---|
| 13 | // Last Modified By : Peter A. Buhr
 | 
|---|
| 14 | // Last Modified On : Tue Mar 26 23:16:10 2019
 | 
|---|
| 15 | // Update Count     : 109
 | 
|---|
| 16 | //
 | 
|---|
| 17 | 
 | 
|---|
| 18 | #pragma once
 | 
|---|
| 19 | 
 | 
|---|
| 20 | #include "iostream.hfa"
 | 
|---|
| 21 | 
 | 
|---|
| 22 | trait scalar( T ) {
 | 
|---|
| 23 | };
 | 
|---|
| 24 | 
 | 
|---|
| 25 | trait arithmetic( T | scalar( T ) ) {
 | 
|---|
| 26 |         int !?( T );
 | 
|---|
| 27 |         int ?==?( T, T );
 | 
|---|
| 28 |         int ?!=?( T, T );
 | 
|---|
| 29 |         int ?<?( T, T );
 | 
|---|
| 30 |         int ?<=?( T, T );
 | 
|---|
| 31 |         int ?>?( T, T );
 | 
|---|
| 32 |         int ?>=?( T, T );
 | 
|---|
| 33 |         void ?{}( T &, zero_t );
 | 
|---|
| 34 |         void ?{}( T &, one_t );
 | 
|---|
| 35 |         T +?( T );
 | 
|---|
| 36 |         T -?( T );
 | 
|---|
| 37 |         T ?+?( T, T );
 | 
|---|
| 38 |         T ?-?( T, T );
 | 
|---|
| 39 |         T ?*?( T, T );
 | 
|---|
| 40 |         T ?/?( T, T );
 | 
|---|
| 41 |         T ?%?( T, T );
 | 
|---|
| 42 |         T ?/=?( T &, T );
 | 
|---|
| 43 |         T abs( T );
 | 
|---|
| 44 | };
 | 
|---|
| 45 | 
 | 
|---|
| 46 | // implementation
 | 
|---|
| 47 | 
 | 
|---|
| 48 | forall( RationalImpl | arithmetic( RationalImpl ) ) {
 | 
|---|
| 49 |         struct Rational {
 | 
|---|
| 50 |                 RationalImpl numerator, denominator;                    // invariant: denominator > 0
 | 
|---|
| 51 |         }; // Rational
 | 
|---|
| 52 | 
 | 
|---|
| 53 |         // constructors
 | 
|---|
| 54 | 
 | 
|---|
| 55 |         void ?{}( Rational(RationalImpl) & r );
 | 
|---|
| 56 |         void ?{}( Rational(RationalImpl) & r, RationalImpl n );
 | 
|---|
| 57 |         void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d );
 | 
|---|
| 58 |         void ?{}( Rational(RationalImpl) & r, zero_t );
 | 
|---|
| 59 |         void ?{}( Rational(RationalImpl) & r, one_t );
 | 
|---|
| 60 | 
 | 
|---|
| 61 |         // numerator/denominator getter
 | 
|---|
| 62 | 
 | 
|---|
| 63 |         RationalImpl numerator( Rational(RationalImpl) r );
 | 
|---|
| 64 |         RationalImpl denominator( Rational(RationalImpl) r );
 | 
|---|
| 65 |         [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src );
 | 
|---|
| 66 | 
 | 
|---|
| 67 |         // numerator/denominator setter
 | 
|---|
| 68 | 
 | 
|---|
| 69 |         RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n );
 | 
|---|
| 70 |         RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d );
 | 
|---|
| 71 | 
 | 
|---|
| 72 |         // comparison
 | 
|---|
| 73 | 
 | 
|---|
| 74 |         int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 75 |         int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 76 |         int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 77 |         int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 78 |         int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 79 |         int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 80 | 
 | 
|---|
| 81 |         // arithmetic
 | 
|---|
| 82 | 
 | 
|---|
| 83 |         Rational(RationalImpl) +?( Rational(RationalImpl) r );
 | 
|---|
| 84 |         Rational(RationalImpl) -?( Rational(RationalImpl) r );
 | 
|---|
| 85 |         Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 86 |         Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 87 |         Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 88 |         Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 | 
|---|
| 89 | 
 | 
|---|
| 90 |         // I/O
 | 
|---|
| 91 |         forall( istype & | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
 | 
|---|
| 92 |         istype & ?|?( istype &, Rational(RationalImpl) & );
 | 
|---|
| 93 | 
 | 
|---|
| 94 |         forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) {
 | 
|---|
| 95 |                 ostype & ?|?( ostype &, Rational(RationalImpl) );
 | 
|---|
| 96 |                 void ?|?( ostype &, Rational(RationalImpl) );
 | 
|---|
| 97 |         } // distribution
 | 
|---|
| 98 | } // distribution
 | 
|---|
| 99 | 
 | 
|---|
| 100 | forall( RationalImpl | arithmetic( RationalImpl ) |{RationalImpl ?\?( RationalImpl, unsigned long );} )
 | 
|---|
| 101 | Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y );
 | 
|---|
| 102 | 
 | 
|---|
| 103 | // conversion
 | 
|---|
| 104 | forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
 | 
|---|
| 105 | double widen( Rational(RationalImpl) r );
 | 
|---|
| 106 | forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl );  RationalImpl convert( double );} )
 | 
|---|
| 107 | Rational(RationalImpl) narrow( double f, RationalImpl md );
 | 
|---|
| 108 | 
 | 
|---|
| 109 | // Local Variables: //
 | 
|---|
| 110 | // mode: c //
 | 
|---|
| 111 | // tab-width: 4 //
 | 
|---|
| 112 | // End: //
 | 
|---|