linux/lib/rational.c

/*
 * 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);