//
// 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 18 11:08:24 2023
// Update Count     : 121
//

#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) );
		OSTYPE_VOID( 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: //