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111 lines
3.0 KiB
111 lines
3.0 KiB
// 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 <[email protected]> |
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* Copyright (C) 2019 Trent Piepho <[email protected]> |
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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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