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 | #include <linux/module.h> |
17 | |
18 | /* |
19 | * calculate best rational approximation for a given fraction |
20 | * taking into account restricted register size, e.g. to find |
21 | * appropriate values for a pll with 5 bit denominator and |
22 | * 8 bit numerator register fields, trying to set up with a |
23 | * frequency ratio of 3.1415, one would say: |
24 | * |
25 | * rational_best_approximation(31415, 10000, |
26 | * (1 << 8) - 1, (1 << 5) - 1, &n, &d); |
27 | * |
28 | * you may look at given_numerator as a fixed point number, |
29 | * with the fractional part size described in given_denominator. |
30 | * |
31 | * for theoretical background, see: |
32 | * https://en.wikipedia.org/wiki/Continued_fraction |
33 | */ |
34 | |
35 | void rational_best_approximation( |
36 | unsigned long given_numerator, unsigned long given_denominator, |
37 | unsigned long max_numerator, unsigned long max_denominator, |
38 | unsigned long *best_numerator, unsigned long *best_denominator) |
39 | { |
40 | /* n/d is the starting rational, which is continually |
41 | * decreased each iteration using the Euclidean algorithm. |
42 | * |
43 | * dp is the value of d from the prior iteration. |
44 | * |
45 | * n2/d2, n1/d1, and n0/d0 are our successively more accurate |
46 | * approximations of the rational. They are, respectively, |
47 | * the current, previous, and two prior iterations of it. |
48 | * |
49 | * a is current term of the continued fraction. |
50 | */ |
51 | unsigned long n, d, n0, d0, n1, d1, n2, d2; |
52 | n = given_numerator; |
53 | d = given_denominator; |
54 | n0 = d1 = 0; |
55 | n1 = d0 = 1; |
56 | |
57 | for (;;) { |
58 | unsigned long dp, a; |
59 | |
60 | if (d == 0) |
61 | break; |
62 | /* Find next term in continued fraction, 'a', via |
63 | * Euclidean algorithm. |
64 | */ |
65 | dp = d; |
66 | a = n / d; |
67 | d = n % d; |
68 | n = dp; |
69 | |
70 | /* Calculate the current rational approximation (aka |
71 | * convergent), n2/d2, using the term just found and |
72 | * the two prior approximations. |
73 | */ |
74 | n2 = n0 + a * n1; |
75 | d2 = d0 + a * d1; |
76 | |
77 | /* If the current convergent exceeds the maxes, then |
78 | * return either the previous convergent or the |
79 | * largest semi-convergent, the final term of which is |
80 | * found below as 't'. |
81 | */ |
82 | if ((n2 > max_numerator) || (d2 > max_denominator)) { |
83 | unsigned long t = ULONG_MAX; |
84 | |
85 | if (d1) |
86 | t = (max_denominator - d0) / d1; |
87 | if (n1) |
88 | t = min(t, (max_numerator - n0) / n1); |
89 | |
90 | /* This tests if the semi-convergent is closer than the previous |
91 | * convergent. If d1 is zero there is no previous convergent as this |
92 | * is the 1st iteration, so always choose the semi-convergent. |
93 | */ |
94 | if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) { |
95 | n1 = n0 + t * n1; |
96 | d1 = d0 + t * d1; |
97 | } |
98 | break; |
99 | } |
100 | n0 = n1; |
101 | n1 = n2; |
102 | d0 = d1; |
103 | d1 = d2; |
104 | } |
105 | *best_numerator = n1; |
106 | *best_denominator = d1; |
107 | } |
108 | |
109 | EXPORT_SYMBOL(rational_best_approximation); |
110 | |
111 | MODULE_LICENSE("GPL v2" ); |
112 | |