source: libcfa/src/rational.hfa@ 13fece5

//
// Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
//
// The contents of this file are covered under the licence agreement in the
// file "LICENCE" distributed with Cforall.
//
// rational -- Rational numbers are numbers written as a ratio, i.e., as a fraction, where the numerator (top number)
//     and the denominator (bottom number) are whole numbers. When creating and computing with rational numbers, results
//     are constantly reduced to keep the numerator and denominator as small as possible.
//
// Author           : Peter A. Buhr
// Created On       : Wed Apr  6 17:56:25 2016
// Last Modified By : Peter A. Buhr
// Last Modified On : Tue Mar 26 23:16:10 2019
// Update Count     : 109
//

#pragma once

#include "iostream.hfa"

trait scalar( otype T ) {
};

trait arithmetic( otype T | scalar( T ) ) {
        int !?( T );
        int ?==?( T, T );
        int ?!=?( T, T );
        int ?<?( T, T );
        int ?<=?( T, T );
        int ?>?( T, T );
        int ?>=?( T, T );
        void ?{}( T &, zero_t );
        void ?{}( T &, one_t );
        T +?( T );
        T -?( T );
        T ?+?( T, T );
        T ?-?( T, T );
        T ?*?( T, T );
        T ?/?( T, T );
        T ?%?( T, T );
        T ?/=?( T &, T );
        T abs( T );
};

// implementation

forall( otype RationalImpl | arithmetic( RationalImpl ) ) {
        struct Rational {
                RationalImpl numerator, denominator;                    // invariant: denominator > 0
        }; // Rational

        // constructors

        void ?{}( Rational(RationalImpl) & r );
        void ?{}( Rational(RationalImpl) & r, RationalImpl n );
        void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d );
        void ?{}( Rational(RationalImpl) & r, zero_t );
        void ?{}( Rational(RationalImpl) & r, one_t );

        // numerator/denominator getter

        RationalImpl numerator( Rational(RationalImpl) r );
        RationalImpl denominator( Rational(RationalImpl) r );
        [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src );

        // numerator/denominator setter

        RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n );
        RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d );

        // comparison

        int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r );

        // arithmetic

        Rational(RationalImpl) +?( Rational(RationalImpl) r );
        Rational(RationalImpl) -?( Rational(RationalImpl) r );
        Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r );
        Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r );

        // I/O
        forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
        istype & ?|?( istype &, Rational(RationalImpl) & );

        forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) {
                ostype & ?|?( ostype &, Rational(RationalImpl) );
                void ?|?( ostype &, Rational(RationalImpl) );
        } // distribution
} // distribution

forall( otype RationalImpl | arithmetic( RationalImpl ) |{RationalImpl ?\?( RationalImpl, unsigned long );} )
Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y );

// conversion
forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
double widen( Rational(RationalImpl) r );
forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl );  RationalImpl convert( double );} )
Rational(RationalImpl) narrow( double f, RationalImpl md );

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