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1// SPDX-License-Identifier: GPL-2.02/*3 * rational fractions4 *5 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>6 * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>7 *8 * helper functions when coping with rational numbers9 */10 11#include <linux/rational.h>12#include <linux/compiler.h>13#include <linux/export.h>14#include <linux/minmax.h>15#include <linux/limits.h>16#include <linux/module.h>17 18/*19 * calculate best rational approximation for a given fraction20 * taking into account restricted register size, e.g. to find21 * appropriate values for a pll with 5 bit denominator and22 * 8 bit numerator register fields, trying to set up with a23 * frequency ratio of 3.1415, one would say:24 *25 * rational_best_approximation(31415, 10000,26 * (1 << 8) - 1, (1 << 5) - 1, &n, &d);27 *28 * you may look at given_numerator as a fixed point number,29 * with the fractional part size described in given_denominator.30 *31 * for theoretical background, see:32 * https://en.wikipedia.org/wiki/Continued_fraction33 */34 35void rational_best_approximation(36 unsigned long given_numerator, unsigned long given_denominator,37 unsigned long max_numerator, unsigned long max_denominator,38 unsigned long *best_numerator, unsigned long *best_denominator)39{40 /* n/d is the starting rational, which is continually41 * decreased each iteration using the Euclidean algorithm.42 *43 * dp is the value of d from the prior iteration.44 *45 * n2/d2, n1/d1, and n0/d0 are our successively more accurate46 * approximations of the rational. They are, respectively,47 * the current, previous, and two prior iterations of it.48 *49 * a is current term of the continued fraction.50 */51 unsigned long n, d, n0, d0, n1, d1, n2, d2;52 n = given_numerator;53 d = given_denominator;54 n0 = d1 = 0;55 n1 = d0 = 1;56 57 for (;;) {58 unsigned long dp, a;59 60 if (d == 0)61 break;62 /* Find next term in continued fraction, 'a', via63 * Euclidean algorithm.64 */65 dp = d;66 a = n / d;67 d = n % d;68 n = dp;69 70 /* Calculate the current rational approximation (aka71 * convergent), n2/d2, using the term just found and72 * the two prior approximations.73 */74 n2 = n0 + a * n1;75 d2 = d0 + a * d1;76 77 /* If the current convergent exceeds the maxes, then78 * return either the previous convergent or the79 * largest semi-convergent, the final term of which is80 * found below as 't'.81 */82 if ((n2 > max_numerator) || (d2 > max_denominator)) {83 unsigned long t = ULONG_MAX;84 85 if (d1)86 t = (max_denominator - d0) / d1;87 if (n1)88 t = min(t, (max_numerator - n0) / n1);89 90 /* This tests if the semi-convergent is closer than the previous91 * convergent. If d1 is zero there is no previous convergent as this92 * is the 1st iteration, so always choose the semi-convergent.93 */94 if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {95 n1 = n0 + t * n1;96 d1 = d0 + t * d1;97 }98 break;99 }100 n0 = n1;101 n1 = n2;102 d0 = d1;103 d1 = d2;104 }105 *best_numerator = n1;106 *best_denominator = d1;107}108 109EXPORT_SYMBOL(rational_best_approximation);110 111MODULE_DESCRIPTION("Rational fraction support library");112MODULE_LICENSE("GPL v2");113