//
// 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 );

// Local Variables: //
// mode: c //
// tab-width: 4 //
// End: //