```// 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>
#include <linux/limits.h>
#include <linux/module.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 = ULONG_MAX;

if (d1)
t = (max_denominator - d0) / d1;
if (n1)
t = min(t, (max_numerator - n0) / n1);

/* This tests if the semi-convergent is closer than the previous
* convergent.  If d1 is zero there is no previous convergent as this
* is the 1st iteration, so always choose the semi-convergent.
*/
if (!d1 || 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);