//
// 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.c --
//
// Author           : Peter A. Buhr
// Created On       : Wed Apr  6 17:54:28 2016
// Last Modified By : Peter A. Buhr
// Last Modified On : Sat Jun  2 09:24:33 2018
// Update Count     : 162
//

#include "rational"
#include "fstream"
#include "stdlib"

forall( otype RationalImpl | arithmetic( RationalImpl ) ) {
	// helper routines

	// Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce
	// rationals.  alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
	static RationalImpl gcd( RationalImpl a, RationalImpl b ) {
		for ( ;; ) {									// Euclid's algorithm
			RationalImpl r = a % b;
		  if ( r == (RationalImpl){0} ) break;
			a = b;
			b = r;
		} // for
		return b;
	} // gcd

	static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) {
		if ( d == (RationalImpl){0} ) {
			serr | "Invalid rational number construction: denominator cannot be equal to 0." | endl;
			exit( EXIT_FAILURE );
		} // exit
		if ( d < (RationalImpl){0} ) { d = -d; n = -n; } // move sign to numerator
		return gcd( abs( n ), d );						// simplify
	} // Rationalnumber::simplify

	// constructors

	void ?{}( Rational(RationalImpl) & r ) {
		r{ (RationalImpl){0}, (RationalImpl){1} };
	} // rational

	void ?{}( Rational(RationalImpl) & r, RationalImpl n ) {
		r{ n, (RationalImpl){1} };
	} // rational

	void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
		RationalImpl t = simplify( n, d );				// simplify
		r.numerator = n / t;
		r.denominator = d / t;
	} // rational


	// getter for numerator/denominator

	RationalImpl numerator( Rational(RationalImpl) r ) {
		return r.numerator;
	} // numerator

	RationalImpl denominator( Rational(RationalImpl) r ) {
		return r.denominator;
	} // denominator

	[ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
		return dest = src.[ numerator, denominator ];
	} // ?=?

	// setter for numerator/denominator

	RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
		RationalImpl prev = r.numerator;
		RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
		r.numerator = n / t;
		r.denominator = r.denominator / t;
		return prev;
	} // numerator

	RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
		RationalImpl prev = r.denominator;
		RationalImpl t = simplify( r.numerator, d );	// simplify
		r.numerator = r.numerator / t;
		r.denominator = d / t;
		return prev;
	} // denominator

	// comparison

	int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return l.numerator * r.denominator == l.denominator * r.numerator;
	} // ?==?

	int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return ! ( l == r );
	} // ?!=?

	int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return l.numerator * r.denominator < l.denominator * r.numerator;
	} // ?<?

	int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return l.numerator * r.denominator <= l.denominator * r.numerator;
	} // ?<=?

	int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return ! ( l <= r );
	} // ?>?

	int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		return ! ( l < r );
	} // ?>=?

	// arithmetic

	Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
		Rational(RationalImpl) t = { r.numerator, r.denominator };
		return t;
	} // +?

	Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
		Rational(RationalImpl) t = { -r.numerator, r.denominator };
		return t;
	} // -?

	Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		if ( l.denominator == r.denominator ) {			// special case
			Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
			return t;
		} else {
			Rational(RationalImpl) t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
			return t;
		} // if
	} // ?+?

	Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		if ( l.denominator == r.denominator ) {			// special case
			Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
			return t;
		} else {
			Rational(RationalImpl) t = { l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
			return t;
		} // if
	} // ?-?

	Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		Rational(RationalImpl) t = { l.numerator * r.numerator, l.denominator * r.denominator };
		return t;
	} // ?*?

	Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
		if ( r.numerator < (RationalImpl){0} ) {
			r.numerator = -r.numerator;
			r.denominator = -r.denominator;
		} // if
		Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
		return t;
	} // ?/?

	// I/O

	forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
	istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
		RationalImpl t;
		is | r.numerator | r.denominator;
		t = simplify( r.numerator, r.denominator );
		r.numerator /= t;
		r.denominator /= t;
		return is;
	} // ?|?

	forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } )
	ostype & ?|?( ostype & os, Rational(RationalImpl ) r ) {
		return os | r.numerator | '/' | r.denominator;
	} // ?|?
} // distribution

// conversion

forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
double widen( Rational(RationalImpl) r ) {
 	return convert( r.numerator ) / convert( r.denominator );
} // widen

forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
Rational(RationalImpl) narrow( double f, RationalImpl md ) {
	// http://www.ics.uci.edu/~eppstein/numth/frap.c
	if ( md <= (RationalImpl){1} ) {					// maximum fractional digits too small?
		return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction
	} // if

	// continued fraction coefficients
	RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
	RationalImpl ai, t;

	// find terms until denom gets too big
	for ( ;; ) {
		ai = convert( f );
	  if ( ! (m10 * ai + m11 <= md) ) break;
		t = m00 * ai + m01;
		m01 = m00;
		m00 = t;
		t = m10 * ai + m11;
		m11 = m10;
		m10 = t;
		double temp = convert( ai );
	  if ( f == temp ) break;							// prevent division by zero
		f = 1 / (f - temp);
	  if ( f > (double)0x7FFFFFFF ) break;				// representation failure
	} // for
	return (Rational(RationalImpl)){ m00, m10 };
} // narrow

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