// SPDX-License-Identifier: GPL-2.0
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/*
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* rational fractions
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*
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* Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
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* Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
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*
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* helper functions when coping with rational numbers
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*/
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#include <linux/rational.h>
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#include <linux/compiler.h>
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#include <linux/export.h>
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#include <linux/minmax.h>
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#include <linux/limits.h>
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/*
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* calculate best rational approximation for a given fraction
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* taking into account restricted register size, e.g. to find
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* appropriate values for a pll with 5 bit denominator and
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* 8 bit numerator register fields, trying to set up with a
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* frequency ratio of 3.1415, one would say:
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*
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* rational_best_approximation(31415, 10000,
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* (1 << 8) - 1, (1 << 5) - 1, &n, &d);
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*
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* you may look at given_numerator as a fixed point number,
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* with the fractional part size described in given_denominator.
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*
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* for theoretical background, see:
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* https://en.wikipedia.org/wiki/Continued_fraction
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*/
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void rational_best_approximation(
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unsigned long given_numerator, unsigned long given_denominator,
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unsigned long max_numerator, unsigned long max_denominator,
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unsigned long *best_numerator, unsigned long *best_denominator)
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{
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/* n/d is the starting rational, which is continually
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* decreased each iteration using the Euclidean algorithm.
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*
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* dp is the value of d from the prior iteration.
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*
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* n2/d2, n1/d1, and n0/d0 are our successively more accurate
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* approximations of the rational. They are, respectively,
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* the current, previous, and two prior iterations of it.
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*
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* a is current term of the continued fraction.
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*/
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unsigned long n, d, n0, d0, n1, d1, n2, d2;
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n = given_numerator;
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d = given_denominator;
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n0 = d1 = 0;
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n1 = d0 = 1;
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for (;;) {
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unsigned long dp, a;
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if (d == 0)
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break;
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/* Find next term in continued fraction, 'a', via
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* Euclidean algorithm.
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*/
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dp = d;
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a = n / d;
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d = n % d;
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n = dp;
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/* Calculate the current rational approximation (aka
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* convergent), n2/d2, using the term just found and
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* the two prior approximations.
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*/
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n2 = n0 + a * n1;
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d2 = d0 + a * d1;
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/* If the current convergent exceeds the maxes, then
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* return either the previous convergent or the
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* largest semi-convergent, the final term of which is
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* found below as 't'.
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*/
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if ((n2 > max_numerator) || (d2 > max_denominator)) {
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unsigned long t = ULONG_MAX;
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if (d1)
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t = (max_denominator - d0) / d1;
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if (n1)
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t = min(t, (max_numerator - n0) / n1);
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/* This tests if the semi-convergent is closer than the previous
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* convergent. If d1 is zero there is no previous convergent as this
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* is the 1st iteration, so always choose the semi-convergent.
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*/
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if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
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n1 = n0 + t * n1;
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d1 = d0 + t * d1;
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}
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break;
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}
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n0 = n1;
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n1 = n2;
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d0 = d1;
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d1 = d2;
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}
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*best_numerator = n1;
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*best_denominator = d1;
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}
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EXPORT_SYMBOL(rational_best_approximation);
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