1// SPDX-License-Identifier: GPL-2.0
2/*
3 * rational fractions
4 *
5 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
6 * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
7 *
8 * helper functions when coping with rational numbers
9 */
10
11#include <linux/rational.h>
12#include <linux/compiler.h>
13#include <linux/kernel.h>
14
15/*
16 * calculate best rational approximation for a given fraction
17 * taking into account restricted register size, e.g. to find
18 * appropriate values for a pll with 5 bit denominator and
19 * 8 bit numerator register fields, trying to set up with a
20 * frequency ratio of 3.1415, one would say:
21 *
22 * rational_best_approximation(31415, 10000,
23 *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
24 *
25 * you may look at given_numerator as a fixed point number,
26 * with the fractional part size described in given_denominator.
27 *
28 * for theoretical background, see:
29 * http://en.wikipedia.org/wiki/Continued_fraction
30 */
31
32void rational_best_approximation(
33	unsigned long given_numerator, unsigned long given_denominator,
34	unsigned long max_numerator, unsigned long max_denominator,
35	unsigned long *best_numerator, unsigned long *best_denominator)
36{
37	/* n/d is the starting rational, which is continually
38	 * decreased each iteration using the Euclidean algorithm.
39	 *
40	 * dp is the value of d from the prior iteration.
41	 *
42	 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
43	 * approximations of the rational.  They are, respectively,
44	 * the current, previous, and two prior iterations of it.
45	 *
46	 * a is current term of the continued fraction.
47	 */
48	unsigned long n, d, n0, d0, n1, d1, n2, d2;
49	n = given_numerator;
50	d = given_denominator;
51	n0 = d1 = 0;
52	n1 = d0 = 1;
53
54	for (;;) {
55		unsigned long dp, a;
56
57		if (d == 0)
58			break;
59		/* Find next term in continued fraction, 'a', via
60		 * Euclidean algorithm.
61		 */
62		dp = d;
63		a = n / d;
64		d = n % d;
65		n = dp;
66
67		/* Calculate the current rational approximation (aka
68		 * convergent), n2/d2, using the term just found and
69		 * the two prior approximations.
70		 */
71		n2 = n0 + a * n1;
72		d2 = d0 + a * d1;
73
74		/* If the current convergent exceeds the maxes, then
75		 * return either the previous convergent or the
76		 * largest semi-convergent, the final term of which is
77		 * found below as 't'.
78		 */
79		if ((n2 > max_numerator) || (d2 > max_denominator)) {
80			unsigned long t = min((max_numerator - n0) / n1,
81					      (max_denominator - d0) / d1);
82
83			/* This tests if the semi-convergent is closer
84			 * than the previous convergent.
85			 */
86			if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
87				n1 = n0 + t * n1;
88				d1 = d0 + t * d1;
89			}
90			break;
91		}
92		n0 = n1;
93		n1 = n2;
94		d0 = d1;
95		d1 = d2;
96	}
97	*best_numerator = n1;
98	*best_denominator = d1;
99}
100