1 // SPDX-License-Identifier: GPL-2.0 1 // SPDX-License-Identifier: GPL-2.0
2 /* 2 /*
3 * rational fractions 3 * rational fractions
4 * 4 *
5 * Copyright (C) 2009 emlix GmbH, Oskar Schirm 5 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
6 * Copyright (C) 2019 Trent Piepho <tpiepho@gm 6 * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
7 * 7 *
8 * helper functions when coping with rational 8 * helper functions when coping with rational numbers
9 */ 9 */
10 10
11 #include <linux/rational.h> 11 #include <linux/rational.h>
12 #include <linux/compiler.h> 12 #include <linux/compiler.h>
13 #include <linux/export.h> 13 #include <linux/export.h>
14 #include <linux/minmax.h> 14 #include <linux/minmax.h>
15 #include <linux/limits.h> 15 #include <linux/limits.h>
16 #include <linux/module.h> 16 #include <linux/module.h>
17 17
18 /* 18 /*
19 * calculate best rational approximation for a 19 * calculate best rational approximation for a given fraction
20 * taking into account restricted register siz 20 * taking into account restricted register size, e.g. to find
21 * appropriate values for a pll with 5 bit den 21 * appropriate values for a pll with 5 bit denominator and
22 * 8 bit numerator register fields, trying to 22 * 8 bit numerator register fields, trying to set up with a
23 * frequency ratio of 3.1415, one would say: 23 * frequency ratio of 3.1415, one would say:
24 * 24 *
25 * rational_best_approximation(31415, 10000, 25 * rational_best_approximation(31415, 10000,
26 * (1 << 8) - 1, (1 << 5) - 1, &n 26 * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
27 * 27 *
28 * you may look at given_numerator as a fixed 28 * you may look at given_numerator as a fixed point number,
29 * with the fractional part size described in 29 * with the fractional part size described in given_denominator.
30 * 30 *
31 * for theoretical background, see: 31 * for theoretical background, see:
32 * https://en.wikipedia.org/wiki/Continued_fra 32 * https://en.wikipedia.org/wiki/Continued_fraction
33 */ 33 */
34 34
35 void rational_best_approximation( 35 void rational_best_approximation(
36 unsigned long given_numerator, unsigne 36 unsigned long given_numerator, unsigned long given_denominator,
37 unsigned long max_numerator, unsigned 37 unsigned long max_numerator, unsigned long max_denominator,
38 unsigned long *best_numerator, unsigne 38 unsigned long *best_numerator, unsigned long *best_denominator)
39 { 39 {
40 /* n/d is the starting rational, which 40 /* n/d is the starting rational, which is continually
41 * decreased each iteration using the 41 * decreased each iteration using the Euclidean algorithm.
42 * 42 *
43 * dp is the value of d from the prior 43 * dp is the value of d from the prior iteration.
44 * 44 *
45 * n2/d2, n1/d1, and n0/d0 are our suc 45 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
46 * approximations of the rational. Th 46 * approximations of the rational. They are, respectively,
47 * the current, previous, and two prio 47 * the current, previous, and two prior iterations of it.
48 * 48 *
49 * a is current term of the continued 49 * a is current term of the continued fraction.
50 */ 50 */
51 unsigned long n, d, n0, d0, n1, d1, n2 51 unsigned long n, d, n0, d0, n1, d1, n2, d2;
52 n = given_numerator; 52 n = given_numerator;
53 d = given_denominator; 53 d = given_denominator;
54 n0 = d1 = 0; 54 n0 = d1 = 0;
55 n1 = d0 = 1; 55 n1 = d0 = 1;
56 56
57 for (;;) { 57 for (;;) {
58 unsigned long dp, a; 58 unsigned long dp, a;
59 59
60 if (d == 0) 60 if (d == 0)
61 break; 61 break;
62 /* Find next term in continued 62 /* Find next term in continued fraction, 'a', via
63 * Euclidean algorithm. 63 * Euclidean algorithm.
64 */ 64 */
65 dp = d; 65 dp = d;
66 a = n / d; 66 a = n / d;
67 d = n % d; 67 d = n % d;
68 n = dp; 68 n = dp;
69 69
70 /* Calculate the current ratio 70 /* Calculate the current rational approximation (aka
71 * convergent), n2/d2, using t 71 * convergent), n2/d2, using the term just found and
72 * the two prior approximation 72 * the two prior approximations.
73 */ 73 */
74 n2 = n0 + a * n1; 74 n2 = n0 + a * n1;
75 d2 = d0 + a * d1; 75 d2 = d0 + a * d1;
76 76
77 /* If the current convergent e 77 /* If the current convergent exceeds the maxes, then
78 * return either the previous 78 * return either the previous convergent or the
79 * largest semi-convergent, th 79 * largest semi-convergent, the final term of which is
80 * found below as 't'. 80 * found below as 't'.
81 */ 81 */
82 if ((n2 > max_numerator) || (d 82 if ((n2 > max_numerator) || (d2 > max_denominator)) {
83 unsigned long t = ULON 83 unsigned long t = ULONG_MAX;
84 84
85 if (d1) 85 if (d1)
86 t = (max_denom 86 t = (max_denominator - d0) / d1;
87 if (n1) 87 if (n1)
88 t = min(t, (ma 88 t = min(t, (max_numerator - n0) / n1);
89 89
90 /* This tests if the s 90 /* This tests if the semi-convergent is closer than the previous
91 * convergent. If d1 91 * convergent. If d1 is zero there is no previous convergent as this
92 * is the 1st iteratio 92 * is the 1st iteration, so always choose the semi-convergent.
93 */ 93 */
94 if (!d1 || 2u * t > a 94 if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
95 n1 = n0 + t * 95 n1 = n0 + t * n1;
96 d1 = d0 + t * 96 d1 = d0 + t * d1;
97 } 97 }
98 break; 98 break;
99 } 99 }
100 n0 = n1; 100 n0 = n1;
101 n1 = n2; 101 n1 = n2;
102 d0 = d1; 102 d0 = d1;
103 d1 = d2; 103 d1 = d2;
104 } 104 }
105 *best_numerator = n1; 105 *best_numerator = n1;
106 *best_denominator = d1; 106 *best_denominator = d1;
107 } 107 }
108 108
109 EXPORT_SYMBOL(rational_best_approximation); 109 EXPORT_SYMBOL(rational_best_approximation);
110 110
111 MODULE_DESCRIPTION("Rational fraction support <<
112 MODULE_LICENSE("GPL v2"); 111 MODULE_LICENSE("GPL v2");
113 112
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