Root/lib/rational.c

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

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