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
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)32 void 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