```   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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