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
31 void 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
65 EXPORT_SYMBOL(rational_best_approximation);