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
16 /*
17 * calculate best rational approximation for a given fraction
18 * taking into account restricted register size, e.g. to find
19 * appropriate values for a pll with 5 bit denominator and
20 * 8 bit numerator register fields, trying to set up with a
21 * frequency ratio of 3.1415, one would say:
22 *
23 * rational_best_approximation(31415, 10000,
24 * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
25 *
26 * you may look at given_numerator as a fixed point number,
27 * with the fractional part size described in given_denominator.
28 *
29 * for theoretical background, see:
30 * https://en.wikipedia.org/wiki/Continued_fraction
31 */
32
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)33 void rational_best_approximation(
34 unsigned long given_numerator, unsigned long given_denominator,
35 unsigned long max_numerator, unsigned long max_denominator,
36 unsigned long *best_numerator, unsigned long *best_denominator)
37 {
38 /* n/d is the starting rational, which is continually
39 * decreased each iteration using the Euclidean algorithm.
40 *
41 * dp is the value of d from the prior iteration.
42 *
43 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
44 * approximations of the rational. They are, respectively,
45 * the current, previous, and two prior iterations of it.
46 *
47 * a is current term of the continued fraction.
48 */
49 unsigned long n, d, n0, d0, n1, d1, n2, d2;
50 n = given_numerator;
51 d = given_denominator;
52 n0 = d1 = 0;
53 n1 = d0 = 1;
54
55 for (;;) {
56 unsigned long dp, a;
57
58 if (d == 0)
59 break;
60 /* Find next term in continued fraction, 'a', via
61 * Euclidean algorithm.
62 */
63 dp = d;
64 a = n / d;
65 d = n % d;
66 n = dp;
67
68 /* Calculate the current rational approximation (aka
69 * convergent), n2/d2, using the term just found and
70 * the two prior approximations.
71 */
72 n2 = n0 + a * n1;
73 d2 = d0 + a * d1;
74
75 /* If the current convergent exceeds the maxes, then
76 * return either the previous convergent or the
77 * largest semi-convergent, the final term of which is
78 * found below as 't'.
79 */
80 if ((n2 > max_numerator) || (d2 > max_denominator)) {
81 unsigned long t = min((max_numerator - n0) / n1,
82 (max_denominator - d0) / d1);
83
84 /* This tests if the semi-convergent is closer
85 * than the previous convergent.
86 */
87 if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
88 n1 = n0 + t * n1;
89 d1 = d0 + t * d1;
90 }
91 break;
92 }
93 n0 = n1;
94 n1 = n2;
95 d0 = d1;
96 d1 = d2;
97 }
98 *best_numerator = n1;
99 *best_denominator = d1;
100 }
101
102 EXPORT_SYMBOL(rational_best_approximation);
103
