// 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);