xref: /kernel/linux/linux-5.10/lib/math/rational.c (revision 8c2ecf20) 
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/export.h>
14#include <linux/minmax.h>
15#include <linux/limits.h>
16
17/*
18 * calculate best rational approximation for a given fraction
19 * taking into account restricted register size, e.g. to find
20 * appropriate values for a pll with 5 bit denominator and
21 * 8 bit numerator register fields, trying to set up with a
22 * frequency ratio of 3.1415, one would say:
23 *
24 * rational_best_approximation(31415, 10000,
25 *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
26 *
27 * you may look at given_numerator as a fixed point number,
28 * with the fractional part size described in given_denominator.
29 *
30 * for theoretical background, see:
31 * https://en.wikipedia.org/wiki/Continued_fraction
32 */
33
34void rational_best_approximation(
35	unsigned long given_numerator, unsigned long given_denominator,
36	unsigned long max_numerator, unsigned long max_denominator,
37	unsigned long *best_numerator, unsigned long *best_denominator)
38{
39	/* n/d is the starting rational, which is continually
40	 * decreased each iteration using the Euclidean algorithm.
41	 *
42	 * dp is the value of d from the prior iteration.
43	 *
44	 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
45	 * approximations of the rational.  They are, respectively,
46	 * the current, previous, and two prior iterations of it.
47	 *
48	 * a is current term of the continued fraction.
49	 */
50	unsigned long n, d, n0, d0, n1, d1, n2, d2;
51	n = given_numerator;
52	d = given_denominator;
53	n0 = d1 = 0;
54	n1 = d0 = 1;
55
56	for (;;) {
57		unsigned long dp, a;
58
59		if (d == 0)
60			break;
61		/* Find next term in continued fraction, 'a', via
62		 * Euclidean algorithm.
63		 */
64		dp = d;
65		a = n / d;
66		d = n % d;
67		n = dp;
68
69		/* Calculate the current rational approximation (aka
70		 * convergent), n2/d2, using the term just found and
71		 * the two prior approximations.
72		 */
73		n2 = n0 + a * n1;
74		d2 = d0 + a * d1;
75
76		/* If the current convergent exceeds the maxes, then
77		 * return either the previous convergent or the
78		 * largest semi-convergent, the final term of which is
79		 * found below as 't'.
80		 */
81		if ((n2 > max_numerator) || (d2 > max_denominator)) {
82			unsigned long t = ULONG_MAX;
83
84			if (d1)
85				t = (max_denominator - d0) / d1;
86			if (n1)
87				t = min(t, (max_numerator - n0) / n1);
88
89			/* This tests if the semi-convergent is closer than the previous
90			 * convergent.  If d1 is zero there is no previous convergent as this
91			 * is the 1st iteration, so always choose the semi-convergent.
92			 */
93			if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
94				n1 = n0 + t * n1;
95				d1 = d0 + t * d1;
96			}
97			break;
98		}
99		n0 = n1;
100		n1 = n2;
101		d0 = d1;
102		d1 = d2;
103	}
104	*best_numerator = n1;
105	*best_denominator = d1;
106}
107
108EXPORT_SYMBOL(rational_best_approximation);
109