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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 
rational_best_approximation(unsigned long given_numerator,unsigned long given_denominator,unsigned long max_numerator,unsigned long max_denominator,unsigned long * best_numerator,unsigned long * best_denominator)35 void 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 
109 EXPORT_SYMBOL(rational_best_approximation);
110 
111 MODULE_LICENSE("GPL v2");
112