unitfrac.cal

Calc Software Package for Number Calc

/*
 * unixfrac - represent a fraction as a sum of distince unit fractions
 *
 * Copyright (C) 1999  David I. Bell
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 *
 * @(#) $Revision: 29.2 $
 * @(#) $Id: unitfrac.cal,v 29.2 2000/06/07 14:02:25 chongo Exp $
 * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/unitfrac.cal,v $
 *
 * Under source code control:	1990/02/15 01:50:38
 * File existed as early as:	before 1990
 *
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */

/*
 * Represent a fraction as sum of distinct unit fractions.
 * The output is the unit fractions themselves, and in square brackets,
 * the number of digits in the numerator and denominator of the value left
 * to be found.	 Numbers larger than 3.5 become very difficult to calculate.
 */


define unitfrac(x)
{
	local	d, di, n;

	if (x <= 0)
		quit "Non-positive argument";
	d = 2;
	do {
		n = int(1 / x) + 1;
		if (n > d)
			d = n;
		di = 1/d;
		print '	 [': digits(num(x)): '/': digits(den(x)): ']',, di;
		x -= di;
		d++;
	} while ((num(x) > 1) || (x == di) || (x == 1));
	print '	 [1/1]',, x;
}