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