| 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 Jul 20 17:45:29 2021
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| 15 | // Update Count : 118
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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 | #include "math.trait.hfa" // Arithmetic
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| 22 |
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| 23 | // implementation
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| 24 |
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| 25 | forall( T | Arithmetic( T ) ) {
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| 26 | struct Rational {
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| 27 | T numerator, denominator; // invariant: denominator > 0
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| 28 | }; // Rational
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| 29 |
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| 30 | // constructors
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| 31 |
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| 32 | void ?{}( Rational(T) & r );
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| 33 | void ?{}( Rational(T) & r, zero_t );
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| 34 | void ?{}( Rational(T) & r, one_t );
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| 35 | void ?{}( Rational(T) & r, T n );
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| 36 | void ?{}( Rational(T) & r, T n, T d );
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| 37 |
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| 38 | // numerator/denominator getter
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| 39 |
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| 40 | T numerator( Rational(T) r );
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| 41 | T denominator( Rational(T) r );
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| 42 | [ T, T ] ?=?( & [ T, T ] dest, Rational(T) src );
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| 43 |
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| 44 | // numerator/denominator setter
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| 45 |
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| 46 | T numerator( Rational(T) r, T n );
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| 47 | T denominator( Rational(T) r, T d );
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| 48 |
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| 49 | // comparison
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| 50 |
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| 51 | int ?==?( Rational(T) l, Rational(T) r );
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| 52 | int ?!=?( Rational(T) l, Rational(T) r );
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| 53 | int ?!=?( Rational(T) l, zero_t ); // => !
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| 54 | int ?<?( Rational(T) l, Rational(T) r );
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| 55 | int ?<=?( Rational(T) l, Rational(T) r );
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| 56 | int ?>?( Rational(T) l, Rational(T) r );
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| 57 | int ?>=?( Rational(T) l, Rational(T) r );
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| 58 |
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| 59 | // arithmetic
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| 60 |
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| 61 | Rational(T) +?( Rational(T) r );
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| 62 | Rational(T) -?( Rational(T) r );
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| 63 | Rational(T) ?+?( Rational(T) l, Rational(T) r );
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| 64 | Rational(T) ?+=?( Rational(T) & l, Rational(T) r );
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| 65 | Rational(T) ?+=?( Rational(T) & l, one_t ); // => ++?, ?++
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| 66 | Rational(T) ?-?( Rational(T) l, Rational(T) r );
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| 67 | Rational(T) ?-=?( Rational(T) & l, Rational(T) r );
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| 68 | Rational(T) ?-=?( Rational(T) & l, one_t ); // => --?, ?--
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| 69 | Rational(T) ?*?( Rational(T) l, Rational(T) r );
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| 70 | Rational(T) ?*=?( Rational(T) & l, Rational(T) r );
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| 71 | Rational(T) ?/?( Rational(T) l, Rational(T) r );
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| 72 | Rational(T) ?/=?( Rational(T) & l, Rational(T) r );
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| 73 |
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| 74 | // I/O
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| 75 | forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } )
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| 76 | istype & ?|?( istype &, Rational(T) & );
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| 77 |
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| 78 | forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
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| 79 | ostype & ?|?( ostype &, Rational(T) );
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| 80 | void ?|?( ostype &, Rational(T) );
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| 81 | } // distribution
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| 82 | } // distribution
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| 83 |
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| 84 | forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
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| 85 | Rational(T) ?\?( Rational(T) x, long int y );
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| 86 | Rational(T) ?\=?( Rational(T) & x, long int y );
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| 87 | } // distribution
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| 88 |
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| 89 | // conversion
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| 90 | forall( T | Arithmetic( T ) | { double convert( T ); } )
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| 91 | double widen( Rational(T) r );
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| 92 | forall( T | Arithmetic( T ) | { double convert( T ); T convert( double );} )
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| 93 | Rational(T) narrow( double f, T md );
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| 94 |
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| 95 | // Local Variables: //
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| 96 | // mode: c //
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| 97 | // tab-width: 4 //
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| 98 | // End: //
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