// SPDX-License-Identifier: GPL-2.0
/*
 * rational fractions
 *
 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
 * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
 *
 * helper functions when coping with rational numbers
 */

#include <linux/rational.h>
#include <linux/compiler.h>
#include <linux/export.h>
#include <linux/minmax.h>
#include <linux/limits.h>
#include <linux/module.h>

/*
 * calculate best rational approximation for a given fraction
 * taking into account restricted register size, e.g. to find
 * appropriate values for a pll with 5 bit denominator and
 * 8 bit numerator register fields, trying to set up with a
 * frequency ratio of 3.1415, one would say:
 *
 * rational_best_approximation(31415, 10000,
 *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
 *
 * you may look at given_numerator as a fixed point number,
 * with the fractional part size described in given_denominator.
 *
 * for theoretical background, see:
 * https://en.wikipedia.org/wiki/Continued_fraction
 */

void rational_best_approximation(
        unsigned long given_numerator, unsigned long given_denominator,
        unsigned long max_numerator, unsigned long max_denominator,
        unsigned long *best_numerator, unsigned long *best_denominator)
{
        /* n/d is the starting rational, which is continually
         * decreased each iteration using the Euclidean algorithm.
         *
         * dp is the value of d from the prior iteration.
         *
         * n2/d2, n1/d1, and n0/d0 are our successively more accurate
         * approximations of the rational.  They are, respectively,
         * the current, previous, and two prior iterations of it.
         *
         * a is current term of the continued fraction.
         */
        unsigned long n, d, n0, d0, n1, d1, n2, d2;
        n = given_numerator;
        d = given_denominator;
        n0 = d1 = 0;
        n1 = d0 = 1;

        for (;;) {
                unsigned long dp, a;

                if (d == 0)
                        break;
                /* Find next term in continued fraction, 'a', via
                 * Euclidean algorithm.
                 */
                dp = d;
                a = n / d;
                d = n % d;
                n = dp;

                /* Calculate the current rational approximation (aka
                 * convergent), n2/d2, using the term just found and
                 * the two prior approximations.
                 */
                n2 = n0 + a * n1;
                d2 = d0 + a * d1;

                /* If the current convergent exceeds the maxes, then
                 * return either the previous convergent or the
                 * largest semi-convergent, the final term of which is
                 * found below as 't'.
                 */
                if ((n2 > max_numerator) || (d2 > max_denominator)) {
                        unsigned long t = ULONG_MAX;

                        if (d1)
                                t = (max_denominator - d0) / d1;
                        if (n1)
                                t = min(t, (max_numerator - n0) / n1);

                        /* This tests if the semi-convergent is closer than the previous
                         * convergent.  If d1 is zero there is no previous convergent as this
                         * is the 1st iteration, so always choose the semi-convergent.
                         */
                        if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
                                n1 = n0 + t * n1;
                                d1 = d0 + t * d1;
                        }
                        break;
                }
                n0 = n1;
                n1 = n2;
                d0 = d1;
                d1 = d2;
        }
        *best_numerator = n1;
        *best_denominator = d1;
}

EXPORT_SYMBOL(rational_best_approximation);

MODULE_DESCRIPTION("Rational fraction support library");
MODULE_LICENSE("GPL v2");