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/*
* rational fractions
*
* Copyright (C) 2009 emlix GmbH, Oskar Schirmer <os@emlix.com>
*
* helper functions when coping with rational numbers
*/
#include <linux/rational.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:
* http://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)
{
unsigned long n, d, n0, d0, n1, d1;
n = given_numerator;
d = given_denominator;
n0 = d1 = 0;
n1 = d0 = 1;
for (;;) {
unsigned long t, a;
if ((n1 > max_numerator) || (d1 > max_denominator)) {
n1 = n0;
d1 = d0;
break;
}
if (d == 0)
break;
t = d;
a = n / d;
d = n % d;
n = t;
t = n0 + a * n1;
n0 = n1;
n1 = t;
t = d0 + a * d1;
d0 = d1;
d1 = t;
}
*best_numerator = n1;
*best_denominator = d1;
}
EXPORT_SYMBOL(rational_best_approximation);
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