1/*
2 * unixfrac - represent a fraction as a sum of distance unit fractions
3 *
4 * Copyright (C) 1999,2021  David I. Bell
5 *
6 * Calc is open software; you can redistribute it and/or modify it under
7 * the terms of the version 2.1 of the GNU Lesser General Public License
8 * as published by the Free Software Foundation.
9 *
10 * Calc is distributed in the hope that it will be useful, but WITHOUT
11 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
12 * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
13 * Public License for more details.
14 *
15 * A copy of version 2.1 of the GNU Lesser General Public License is
16 * distributed with calc under the filename COPYING-LGPL.  You should have
17 * received a copy with calc; if not, write to Free Software Foundation, Inc.
18 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
19 *
20 * Under source code control:	1990/02/15 01:50:38
21 * File existed as early as:	before 1990
22 *
23 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
24 */
25
26/*
27 * Represent a fraction as sum of distinct unit fractions.
28 * The output is the unit fractions themselves, and in square brackets,
29 * the number of digits in the numerator and denominator of the value left
30 * to be found.	 Numbers larger than 3.5 become very difficult to calculate.
31 */
32
33
34define unitfrac(x)
35{
36	local	d, di, n;
37
38	if (x <= 0)
39		quit "Non-positive argument";
40	d = 2;
41	do {
42		n = int(1 / x) + 1;
43		if (n > d)
44			d = n;
45		di = 1/d;
46		print '	 [': digits(num(x)): '/': digits(den(x)): ']',, di;
47		x -= di;
48		d++;
49	} while ((num(x) > 1) || (x == di) || (x == 1));
50	print '	 [1/1]',, x;
51}
52