// 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); MODULE_LICENSE("GPL v2"