// 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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*
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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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/*
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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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* http://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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unsigned long n, d, n0, d0, n1, d1;
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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 t, a;
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if ((n1 > max_numerator) || (d1 > max_denominator)) {
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n1 = n0;
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d1 = d0;
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break;
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}
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if (d == 0)
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break;
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t = d;
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a = n / d;
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d = n % d;
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n = t;
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t = n0 + a * n1;
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n0 = n1;
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n1 = t;
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t = d0 + a * d1;
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d0 = d1;
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d1 = t;
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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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