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> <<
16 #include <linux/module.h> <<
17 15
18 /* 16 /*
19 * calculate best rational approximation for a 17 * calculate best rational approximation for a given fraction
20 * taking into account restricted register siz 18 * taking into account restricted register size, e.g. to find
21 * appropriate values for a pll with 5 bit den 19 * appropriate values for a pll with 5 bit denominator and
22 * 8 bit numerator register fields, trying to 20 * 8 bit numerator register fields, trying to set up with a
23 * frequency ratio of 3.1415, one would say: 21 * frequency ratio of 3.1415, one would say:
24 * 22 *
25 * rational_best_approximation(31415, 10000, 23 * rational_best_approximation(31415, 10000,
26 * (1 << 8) - 1, (1 << 5) - 1, &n 24 * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
27 * 25 *
28 * you may look at given_numerator as a fixed 26 * you may look at given_numerator as a fixed point number,
29 * with the fractional part size described in 27 * with the fractional part size described in given_denominator.
30 * 28 *
31 * for theoretical background, see: 29 * for theoretical background, see:
32 * https://en.wikipedia.org/wiki/Continued_fra 30 * https://en.wikipedia.org/wiki/Continued_fraction
33 */ 31 */
34 32
35 void rational_best_approximation( 33 void rational_best_approximation(
36 unsigned long given_numerator, unsigne 34 unsigned long given_numerator, unsigned long given_denominator,
37 unsigned long max_numerator, unsigned 35 unsigned long max_numerator, unsigned long max_denominator,
38 unsigned long *best_numerator, unsigne 36 unsigned long *best_numerator, unsigned long *best_denominator)
39 { 37 {
40 /* n/d is the starting rational, which 38 /* n/d is the starting rational, which is continually
41 * decreased each iteration using the 39 * decreased each iteration using the Euclidean algorithm.
42 * 40 *
43 * dp is the value of d from the prior 41 * dp is the value of d from the prior iteration.
44 * 42 *
45 * n2/d2, n1/d1, and n0/d0 are our suc 43 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
46 * approximations of the rational. Th 44 * approximations of the rational. They are, respectively,
47 * the current, previous, and two prio 45 * the current, previous, and two prior iterations of it.
48 * 46 *
49 * a is current term of the continued 47 * a is current term of the continued fraction.
50 */ 48 */
51 unsigned long n, d, n0, d0, n1, d1, n2 49 unsigned long n, d, n0, d0, n1, d1, n2, d2;
52 n = given_numerator; 50 n = given_numerator;
53 d = given_denominator; 51 d = given_denominator;
54 n0 = d1 = 0; 52 n0 = d1 = 0;
55 n1 = d0 = 1; 53 n1 = d0 = 1;
56 54
57 for (;;) { 55 for (;;) {
58 unsigned long dp, a; 56 unsigned long dp, a;
59 57
60 if (d == 0) 58 if (d == 0)
61 break; 59 break;
62 /* Find next term in continued 60 /* Find next term in continued fraction, 'a', via
63 * Euclidean algorithm. 61 * Euclidean algorithm.
64 */ 62 */
65 dp = d; 63 dp = d;
66 a = n / d; 64 a = n / d;
67 d = n % d; 65 d = n % d;
68 n = dp; 66 n = dp;
69 67
70 /* Calculate the current ratio 68 /* Calculate the current rational approximation (aka
71 * convergent), n2/d2, using t 69 * convergent), n2/d2, using the term just found and
72 * the two prior approximation 70 * the two prior approximations.
73 */ 71 */
74 n2 = n0 + a * n1; 72 n2 = n0 + a * n1;
75 d2 = d0 + a * d1; 73 d2 = d0 + a * d1;
76 74
77 /* If the current convergent e 75 /* If the current convergent exceeds the maxes, then
78 * return either the previous 76 * return either the previous convergent or the
79 * largest semi-convergent, th 77 * largest semi-convergent, the final term of which is
80 * found below as 't'. 78 * found below as 't'.
81 */ 79 */
82 if ((n2 > max_numerator) || (d 80 if ((n2 > max_numerator) || (d2 > max_denominator)) {
83 unsigned long t = ULON !! 81 unsigned long t = min((max_numerator - n0) / n1,
>> 82 (max_denominator - d0) / d1);
84 83
85 if (d1) !! 84 /* This tests if the semi-convergent is closer
86 t = (max_denom !! 85 * than the previous convergent.
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 */ 86 */
94 if (!d1 || 2u * t > a !! 87 if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
95 n1 = n0 + t * 88 n1 = n0 + t * n1;
96 d1 = d0 + t * 89 d1 = d0 + t * d1;
97 } 90 }
98 break; 91 break;
99 } 92 }
100 n0 = n1; 93 n0 = n1;
101 n1 = n2; 94 n1 = n2;
102 d0 = d1; 95 d0 = d1;
103 d1 = d2; 96 d1 = d2;
104 } 97 }
105 *best_numerator = n1; 98 *best_numerator = n1;
106 *best_denominator = d1; 99 *best_denominator = d1;
107 } 100 }
108 101
109 EXPORT_SYMBOL(rational_best_approximation); 102 EXPORT_SYMBOL(rational_best_approximation);
110 <<
111 MODULE_DESCRIPTION("Rational fraction support <<
112 MODULE_LICENSE("GPL v2"); <<
113 103
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