1// SPDX-License-Identifier: GPL-2.0
 2/*
 3 * rational fractions
 4 *
 5 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
 
 6 *
 7 * helper functions when coping with rational numbers
 8 */
 9
10#include <linux/rational.h>
11#include <linux/compiler.h>
12#include <linux/export.h>
 
 
13
14/*
15 * calculate best rational approximation for a given fraction
16 * taking into account restricted register size, e.g. to find
17 * appropriate values for a pll with 5 bit denominator and
18 * 8 bit numerator register fields, trying to set up with a
19 * frequency ratio of 3.1415, one would say:
20 *
21 * rational_best_approximation(31415, 10000,
22 *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
23 *
24 * you may look at given_numerator as a fixed point number,
25 * with the fractional part size described in given_denominator.
26 *
27 * for theoretical background, see:
28 * http://en.wikipedia.org/wiki/Continued_fraction
29 */
30
31void rational_best_approximation(
32	unsigned long given_numerator, unsigned long given_denominator,
33	unsigned long max_numerator, unsigned long max_denominator,
34	unsigned long *best_numerator, unsigned long *best_denominator)
35{
36	unsigned long n, d, n0, d0, n1, d1;
 
 
 
 
 
 
 
 
 
 
 
37	n = given_numerator;
38	d = given_denominator;
39	n0 = d1 = 0;
40	n1 = d0 = 1;
 
41	for (;;) {
42		unsigned long t, a;
43		if ((n1 > max_numerator) || (d1 > max_denominator)) {
44			n1 = n0;
45			d1 = d0;
46			break;
47		}
48		if (d == 0)
49			break;
50		t = d;
 
 
 
51		a = n / d;
52		d = n % d;
53		n = t;
54		t = n0 + a * n1;
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
55		n0 = n1;
56		n1 = t;
57		t = d0 + a * d1;
58		d0 = d1;
59		d1 = t;
60	}
61	*best_numerator = n1;
62	*best_denominator = d1;
63}
64
65EXPORT_SYMBOL(rational_best_approximation);

  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);