1 // SPDX-License-Identifier: GPL-2.0 1
2 /*
3 * rational fractions
4 *
5 * Copyright (C) 2009 emlix GmbH, Oskar Schirm
6 * Copyright (C) 2019 Trent Piepho <tpiepho@gm
7 *
8 * helper functions when coping with rational
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
20 * taking into account restricted register siz
21 * appropriate values for a pll with 5 bit den
22 * 8 bit numerator register fields, trying to
23 * frequency ratio of 3.1415, one would say:
24 *
25 * rational_best_approximation(31415, 10000,
26 * (1 << 8) - 1, (1 << 5) - 1, &n
27 *
28 * you may look at given_numerator as a fixed
29 * with the fractional part size described in
30 *
31 * for theoretical background, see:
32 * https://en.wikipedia.org/wiki/Continued_fra
33 */
34
35 void rational_best_approximation(
36 unsigned long given_numerator, unsigne
37 unsigned long max_numerator, unsigned
38 unsigned long *best_numerator, unsigne
39 {
40 /* n/d is the starting rational, which
41 * decreased each iteration using the
42 *
43 * dp is the value of d from the prior
44 *
45 * n2/d2, n1/d1, and n0/d0 are our suc
46 * approximations of the rational. Th
47 * the current, previous, and two prio
48 *
49 * a is current term of the continued
50 */
51 unsigned long n, d, n0, d0, n1, d1, n2
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
63 * Euclidean algorithm.
64 */
65 dp = d;
66 a = n / d;
67 d = n % d;
68 n = dp;
69
70 /* Calculate the current ratio
71 * convergent), n2/d2, using t
72 * the two prior approximation
73 */
74 n2 = n0 + a * n1;
75 d2 = d0 + a * d1;
76
77 /* If the current convergent e
78 * return either the previous
79 * largest semi-convergent, th
80 * found below as 't'.
81 */
82 if ((n2 > max_numerator) || (d
83 unsigned long t = ULON
84
85 if (d1)
86 t = (max_denom
87 if (n1)
88 t = min(t, (ma
89
90 /* This tests if the s
91 * convergent. If d1
92 * is the 1st iteratio
93 */
94 if (!d1 || 2u * t > a
95 n1 = n0 + t *
96 d1 = d0 + t *
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_DESCRIPTION("Rational fraction support
112 MODULE_LICENSE("GPL v2");
113
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