| 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 : Sat Jun 2 09:10:01 2018
|
|---|
| 15 | // Update Count : 105
|
|---|
| 16 | //
|
|---|
| 17 |
|
|---|
| 18 | #pragma once
|
|---|
| 19 |
|
|---|
| 20 | #include "iostream"
|
|---|
| 21 |
|
|---|
| 22 | trait scalar( otype T ) {
|
|---|
| 23 | };
|
|---|
| 24 |
|
|---|
| 25 | trait arithmetic( otype 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( otype 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( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
|
|---|
| 92 | istype & ?|?( istype &, Rational(RationalImpl) & );
|
|---|
| 93 |
|
|---|
| 94 | forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } )
|
|---|
| 95 | ostype & ?|?( ostype &, Rational(RationalImpl ) );
|
|---|
| 96 | } // distribution
|
|---|
| 97 |
|
|---|
| 98 | // conversion
|
|---|
| 99 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
|
|---|
| 100 | double widen( Rational(RationalImpl) r );
|
|---|
| 101 | forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double );} )
|
|---|
| 102 | Rational(RationalImpl) narrow( double f, RationalImpl md );
|
|---|
| 103 |
|
|---|
| 104 | // Local Variables: //
|
|---|
| 105 | // mode: c //
|
|---|
| 106 | // tab-width: 4 //
|
|---|
| 107 | // End: //
|
|---|
