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 <<
7 * 6 *
8 * helper functions when coping with rational 7 * helper functions when coping with rational numbers
9 */ 8 */
10 9
11 #include <linux/rational.h> 10 #include <linux/rational.h>
12 #include <linux/compiler.h> 11 #include <linux/compiler.h>
13 #include <linux/export.h> 12 #include <linux/export.h>
14 #include <linux/minmax.h> <<
15 #include <linux/limits.h> <<
16 #include <linux/module.h> <<
17 13
18 /* 14 /*
19 * calculate best rational approximation for a 15 * calculate best rational approximation for a given fraction
20 * taking into account restricted register siz 16 * taking into account restricted register size, e.g. to find
21 * appropriate values for a pll with 5 bit den 17 * appropriate values for a pll with 5 bit denominator and
22 * 8 bit numerator register fields, trying to 18 * 8 bit numerator register fields, trying to set up with a
23 * frequency ratio of 3.1415, one would say: 19 * frequency ratio of 3.1415, one would say:
24 * 20 *
25 * rational_best_approximation(31415, 10000, 21 * rational_best_approximation(31415, 10000,
26 * (1 << 8) - 1, (1 << 5) - 1, &n 22 * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
27 * 23 *
28 * you may look at given_numerator as a fixed 24 * you may look at given_numerator as a fixed point number,
29 * with the fractional part size described in 25 * with the fractional part size described in given_denominator.
30 * 26 *
31 * for theoretical background, see: 27 * for theoretical background, see:
32 * https://en.wikipedia.org/wiki/Continued_fra !! 28 * http://en.wikipedia.org/wiki/Continued_fraction
33 */ 29 */
34 30
35 void rational_best_approximation( 31 void rational_best_approximation(
36 unsigned long given_numerator, unsigne 32 unsigned long given_numerator, unsigned long given_denominator,
37 unsigned long max_numerator, unsigned 33 unsigned long max_numerator, unsigned long max_denominator,
38 unsigned long *best_numerator, unsigne 34 unsigned long *best_numerator, unsigned long *best_denominator)
39 { 35 {
40 /* n/d is the starting rational, which !! 36 unsigned long n, d, n0, d0, n1, d1;
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; 37 n = given_numerator;
53 d = given_denominator; 38 d = given_denominator;
54 n0 = d1 = 0; 39 n0 = d1 = 0;
55 n1 = d0 = 1; 40 n1 = d0 = 1;
56 <<
57 for (;;) { 41 for (;;) {
58 unsigned long dp, a; !! 42 unsigned long t, a;
59 !! 43 if ((n1 > max_numerator) || (d1 > max_denominator)) {
>> 44 n1 = n0;
>> 45 d1 = d0;
>> 46 break;
>> 47 }
60 if (d == 0) 48 if (d == 0)
61 break; 49 break;
62 /* Find next term in continued !! 50 t = d;
63 * Euclidean algorithm. <<
64 */ <<
65 dp = d; <<
66 a = n / d; 51 a = n / d;
67 d = n % d; 52 d = n % d;
68 n = dp; !! 53 n = t;
69 !! 54 t = n0 + a * n1;
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; 55 n0 = n1;
101 n1 = n2; !! 56 n1 = t;
>> 57 t = d0 + a * d1;
102 d0 = d1; 58 d0 = d1;
103 d1 = d2; !! 59 d1 = t;
104 } 60 }
105 *best_numerator = n1; 61 *best_numerator = n1;
106 *best_denominator = d1; 62 *best_denominator = d1;
107 } 63 }
108 64
109 EXPORT_SYMBOL(rational_best_approximation); 65 EXPORT_SYMBOL(rational_best_approximation);
110 <<
111 MODULE_DESCRIPTION("Rational fraction support <<
112 MODULE_LICENSE("GPL v2"); <<
113 66
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