103 lines
2.7 KiB
C
103 lines
2.7 KiB
C
// SPDX-License-Identifier: GPL-2.0
|
|
/*
|
|
* rational fractions
|
|
*
|
|
* Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
|
|
* Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
|
|
*
|
|
* helper functions when coping with rational numbers
|
|
*/
|
|
|
|
#include <linux/rational.h>
|
|
#include <linux/compiler.h>
|
|
#include <linux/export.h>
|
|
#include <linux/minmax.h>
|
|
|
|
/*
|
|
* calculate best rational approximation for a given fraction
|
|
* taking into account restricted register size, e.g. to find
|
|
* appropriate values for a pll with 5 bit denominator and
|
|
* 8 bit numerator register fields, trying to set up with a
|
|
* frequency ratio of 3.1415, one would say:
|
|
*
|
|
* rational_best_approximation(31415, 10000,
|
|
* (1 << 8) - 1, (1 << 5) - 1, &n, &d);
|
|
*
|
|
* you may look at given_numerator as a fixed point number,
|
|
* with the fractional part size described in given_denominator.
|
|
*
|
|
* for theoretical background, see:
|
|
* https://en.wikipedia.org/wiki/Continued_fraction
|
|
*/
|
|
|
|
void 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)
|
|
{
|
|
/* n/d is the starting rational, which is continually
|
|
* decreased each iteration using the Euclidean algorithm.
|
|
*
|
|
* dp is the value of d from the prior iteration.
|
|
*
|
|
* n2/d2, n1/d1, and n0/d0 are our successively more accurate
|
|
* approximations of the rational. They are, respectively,
|
|
* the current, previous, and two prior iterations of it.
|
|
*
|
|
* a is current term of the continued fraction.
|
|
*/
|
|
unsigned long n, d, n0, d0, n1, d1, n2, d2;
|
|
n = given_numerator;
|
|
d = given_denominator;
|
|
n0 = d1 = 0;
|
|
n1 = d0 = 1;
|
|
|
|
for (;;) {
|
|
unsigned long dp, a;
|
|
|
|
if (d == 0)
|
|
break;
|
|
/* Find next term in continued fraction, 'a', via
|
|
* Euclidean algorithm.
|
|
*/
|
|
dp = d;
|
|
a = n / d;
|
|
d = n % d;
|
|
n = dp;
|
|
|
|
/* Calculate the current rational approximation (aka
|
|
* convergent), n2/d2, using the term just found and
|
|
* the two prior approximations.
|
|
*/
|
|
n2 = n0 + a * n1;
|
|
d2 = d0 + a * d1;
|
|
|
|
/* If the current convergent exceeds the maxes, then
|
|
* return either the previous convergent or the
|
|
* largest semi-convergent, the final term of which is
|
|
* found below as 't'.
|
|
*/
|
|
if ((n2 > max_numerator) || (d2 > max_denominator)) {
|
|
unsigned long t = min((max_numerator - n0) / n1,
|
|
(max_denominator - d0) / d1);
|
|
|
|
/* This tests if the semi-convergent is closer
|
|
* than the previous convergent.
|
|
*/
|
|
if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
|
|
n1 = n0 + t * n1;
|
|
d1 = d0 + t * d1;
|
|
}
|
|
break;
|
|
}
|
|
n0 = n1;
|
|
n1 = n2;
|
|
d0 = d1;
|
|
d1 = d2;
|
|
}
|
|
*best_numerator = n1;
|
|
*best_denominator = d1;
|
|
}
|
|
|
|
EXPORT_SYMBOL(rational_best_approximation);
|