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b2441318 | 1 | // SPDX-License-Identifier: GPL-2.0 |
8759ef32 OS |
2 | /* |
3 | * rational fractions | |
4 | * | |
6684b572 | 5 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com> |
323dd2c3 | 6 | * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com> |
8759ef32 OS |
7 | * |
8 | * helper functions when coping with rational numbers | |
9 | */ | |
10 | ||
11 | #include <linux/rational.h> | |
8bc3bcc9 PG |
12 | #include <linux/compiler.h> |
13 | #include <linux/export.h> | |
b296a6d5 | 14 | #include <linux/minmax.h> |
65a0d3c1 | 15 | #include <linux/limits.h> |
bcda5fd3 | 16 | #include <linux/module.h> |
8759ef32 OS |
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: | |
d89775fc | 32 | * https://en.wikipedia.org/wiki/Continued_fraction |
8759ef32 OS |
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 | { | |
323dd2c3 TP |
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; | |
8759ef32 OS |
52 | n = given_numerator; |
53 | d = given_denominator; | |
54 | n0 = d1 = 0; | |
55 | n1 = d0 = 1; | |
323dd2c3 | 56 | |
8759ef32 | 57 | for (;;) { |
323dd2c3 TP |
58 | unsigned long dp, a; |
59 | ||
8759ef32 OS |
60 | if (d == 0) |
61 | break; | |
323dd2c3 TP |
62 | /* Find next term in continued fraction, 'a', via |
63 | * Euclidean algorithm. | |
64 | */ | |
65 | dp = d; | |
8759ef32 OS |
66 | a = n / d; |
67 | d = n % d; | |
323dd2c3 TP |
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)) { | |
65a0d3c1 | 83 | unsigned long t = ULONG_MAX; |
323dd2c3 | 84 | |
65a0d3c1 TP |
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. | |
323dd2c3 | 93 | */ |
65a0d3c1 | 94 | if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) { |
323dd2c3 TP |
95 | n1 = n0 + t * n1; |
96 | d1 = d0 + t * d1; | |
97 | } | |
98 | break; | |
99 | } | |
8759ef32 | 100 | n0 = n1; |
323dd2c3 | 101 | n1 = n2; |
8759ef32 | 102 | d0 = d1; |
323dd2c3 | 103 | d1 = d2; |
8759ef32 OS |
104 | } |
105 | *best_numerator = n1; | |
106 | *best_denominator = d1; | |
107 | } | |
108 | ||
109 | EXPORT_SYMBOL(rational_best_approximation); | |
bcda5fd3 GU |
110 | |
111 | MODULE_LICENSE("GPL v2"); |