//
// 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 : Tue Jul 20 16:30:06 2021
// Update Count     : 193
//

#include "rational.hfa"
#include "fstream.hfa"
#include "stdlib.hfa"

forall( T | Arithmetic( T ) ) {
	// 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 T gcd( T a, T b ) {
		for ( ;; ) {									// Euclid's algorithm
			T r = a % b;
		  if ( r == (T){0} ) break;
			a = b;
			b = r;
		} // for
		return b;
	} // gcd

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

	// constructors

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

	void ?{}( Rational(T) & r, one_t ) {
		r{ (T){1}, (T){1} };
	} // rational

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

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

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

	// getter for numerator/denominator

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

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

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

	// setter for numerator/denominator

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

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

	// comparison

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

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

	int ?!=?( Rational(T) l, zero_t ) {
		return ! ( l == (Rational(T)){ 0 } );
	} // ?!=?

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

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

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

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

	// arithmetic

	Rational(T) +?( Rational(T) r ) {
		return (Rational(T)){ r.numerator, r.denominator };
	} // +?

	Rational(T) -?( Rational(T) r ) {
		return (Rational(T)){ -r.numerator, r.denominator };
	} // -?

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

	Rational(T) ?+=?( Rational(T) & l, Rational(T) r ) {
		l = l + r;
		return l;
	} // ?+?

	Rational(T) ?+=?( Rational(T) & l, one_t ) {
		l = l + (Rational(T)){ 1 };
		return l;
	} // ?+?

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

	Rational(T) ?-=?( Rational(T) & l, Rational(T) r ) {
		l = l - r;
		return l;
	} // ?-?

	Rational(T) ?-=?( Rational(T) & l, one_t ) {
		l = l - (Rational(T)){ 1 };
		return l;
	} // ?-?

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

	Rational(T) ?*=?( Rational(T) & l, Rational(T) r ) {
		return l = l * r;
	} // ?*?

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

	Rational(T) ?/=?( Rational(T) & l, Rational(T) r ) {
		return l = l / r;
	} // ?/?

	// I/O

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

	forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) {
		ostype & ?|?( ostype & os, Rational(T) r ) {
			return os | r.numerator | '/' | r.denominator;
		} // ?|?

		void ?|?( ostype & os, Rational(T) r ) {
			(ostype &)(os | r); ends( os );
		} // ?|?
	} // distribution
} // distribution

forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) {
	Rational(T) ?\?( Rational(T) x, long int y ) {
		if ( y < 0 ) {
			return (Rational(T)){ x.denominator \ -y, x.numerator \ -y };
		} else {
			return (Rational(T)){ x.numerator \ y, x.denominator \ y };
		} // if
	} // ?\?

	Rational(T) ?\=?( Rational(T) & x, long int y ) {
		return x = x \ y;
	} // ?\?
} // distribution

// conversion

forall( T | Arithmetic( T ) | { double convert( T ); } )
double widen( Rational(T) r ) {
 	return convert( r.numerator ) / convert( r.denominator );
} // widen

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

	// continued fraction coefficients
	T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
	T 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(T)){ m00, m10 };
} // narrow

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