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bcda5fd344
Patch series "math: RATIONAL and RATIONAL_KUNIT_TEST improvements". This series makes the RATIONAL symbol tristate, so it is not forced builtin if all users are modular, and makes the RATIONAL_KUNIT_TEST depend on RATIONAL, to avoid enabling RATIONAL if there are no real users. This patch (of 2): All but one symbols that select RATIONAL are tristate, but RATIONAL itself is bool. Change it to tristate, so the rational fractions support code can be modular if no builtin code relies on it. Link: https://lkml.kernel.org/r/20210706100945.3803694-1-geert@linux-m68k.org Link: https://lkml.kernel.org/r/20210706100945.3803694-2-geert@linux-m68k.org Signed-off-by: Geert Uytterhoeven <geert@linux-m68k.org> Reviewed-by: Andy Shevchenko <andriy.shevchenko@linux.intel.com> Cc: Trent Piepho <tpiepho@gmail.com> Cc: Colin Ian King <colin.king@canonical.com> Cc: Brendan Higgins <brendanhiggins@google.com> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
111 lines
3 KiB
C
111 lines
3 KiB
C
// 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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#include <linux/module.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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MODULE_LICENSE("GPL v2");
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