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 
rational_best_approximation(unsigned long given_numerator,unsigned long given_denominator,unsigned long max_numerator,unsigned long max_denominator,unsigned long * best_numerator,unsigned long * best_denominator)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);
66