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