Root/lib/rational.c

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

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