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@@ -0,0 +1,99 @@
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+// 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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+
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+#include <linux/rational.h>
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+#include <linux/compiler.h>
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+#include <linux/kernel.h>
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+
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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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+
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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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+
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+ for (;;) {
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+ unsigned long dp, a;
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+
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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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+
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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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+
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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 = min((max_numerator - n0) / n1,
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+ (max_denominator - d0) / d1);
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+
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+ /* This tests if the semi-convergent is closer
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+ * than the previous convergent.
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+ */
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+ if (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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