source: libcfa/src/rational.hfa @ 866cad3

//
// 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 Jul 20 17:45:29 2021
// Update Count     : 118
//

#pragma once

#include "iostream.hfa"
#include "math.trait.hfa"                                                               // Arithmetic

// implementation

forall( T | Arithmetic( T ) ) {
        struct Rational {
                T numerator, denominator;                                               // invariant: denominator > 0
        }; // Rational

        // constructors

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

        // numerator/denominator getter

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

        // numerator/denominator setter

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

        // comparison

        int ?==?( Rational(T) l, Rational(T) r );
        int ?!=?( Rational(T) l, Rational(T) r );
        int ?!=?( Rational(T) l, zero_t );                                      // => !
        int ?<?( Rational(T) l, Rational(T) r );
        int ?<=?( Rational(T) l, Rational(T) r );
        int ?>?( Rational(T) l, Rational(T) r );
        int ?>=?( Rational(T) l, Rational(T) r );

        // arithmetic

        Rational(T) +?( Rational(T) r );
        Rational(T) -?( Rational(T) r );
        Rational(T) ?+?( Rational(T) l, Rational(T) r );
        Rational(T) ?+=?( Rational(T) & l, Rational(T) r );
        Rational(T) ?+=?( Rational(T) & l, one_t );                     // => ++?, ?++
        Rational(T) ?-?( Rational(T) l, Rational(T) r );
        Rational(T) ?-=?( Rational(T) & l, Rational(T) r );
        Rational(T) ?-=?( Rational(T) & l, one_t );                     // => --?, ?--
        Rational(T) ?*?( Rational(T) l, Rational(T) r );
        Rational(T) ?*=?( Rational(T) & l, Rational(T) r );
        Rational(T) ?/?( Rational(T) l, Rational(T) r );
        Rational(T) ?/=?( Rational(T) & l, Rational(T) r );

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

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

forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
        Rational(T) ?\?( Rational(T) x, long int y );
        Rational(T) ?\=?( Rational(T) & x, long int y );
} // distribution

// conversion
forall( T | Arithmetic( T ) | { double convert( T ); } )
double widen( Rational(T) r );
forall( T | Arithmetic( T ) | { double convert( T );  T convert( double );} )
Rational(T) narrow( double f, T md );

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