1// SPDX-License-Identifier: GPL-2.0
 2/*
 3 * rational fractions
 4 *
 5 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
 6 *
 7 * helper functions when coping with rational numbers
 8 */
 9
10#include <linux/rational.h>
11#include <linux/compiler.h>
12#include <linux/export.h>
13
14/*
15 * calculate best rational approximation for a given fraction
16 * taking into account restricted register size, e.g. to find
17 * appropriate values for a pll with 5 bit denominator and
18 * 8 bit numerator register fields, trying to set up with a
19 * frequency ratio of 3.1415, one would say:
20 *
21 * rational_best_approximation(31415, 10000,
22 *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
23 *
24 * you may look at given_numerator as a fixed point number,
25 * with the fractional part size described in given_denominator.
26 *
27 * for theoretical background, see:
28 * http://en.wikipedia.org/wiki/Continued_fraction
29 */
30
31void rational_best_approximation(
32	unsigned long given_numerator, unsigned long given_denominator,
33	unsigned long max_numerator, unsigned long max_denominator,
34	unsigned long *best_numerator, unsigned long *best_denominator)
35{
36	unsigned long n, d, n0, d0, n1, d1;
37	n = given_numerator;
38	d = given_denominator;
39	n0 = d1 = 0;
40	n1 = d0 = 1;
41	for (;;) {
42		unsigned long t, a;
43		if ((n1 > max_numerator) || (d1 > max_denominator)) {
44			n1 = n0;
45			d1 = d0;
46			break;
47		}
48		if (d == 0)
49			break;
50		t = d;
51		a = n / d;
52		d = n % d;
53		n = t;
54		t = n0 + a * n1;
55		n0 = n1;
56		n1 = t;
57		t = d0 + a * d1;
58		d0 = d1;
59		d1 = t;
60	}
61	*best_numerator = n1;
62	*best_denominator = d1;
63}
64
65EXPORT_SYMBOL(rational_best_approximation);