cachepc-linux

Fork of AMDESE/linux with modifications for CachePC side-channel attack
git clone https://git.sinitax.com/sinitax/cachepc-linux
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rational.c (3054B)

      1// SPDX-License-Identifier: GPL-2.0
      2/*
      3 * rational fractions
      4 *
      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 numbers
      9 */
     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 fraction
     20 * taking into account restricted register size, e.g. to find
     21 * appropriate values for a pll with 5 bit denominator and
     22 * 8 bit numerator register fields, trying to set up with a
     23 * 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_fraction
     33 */
     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 continually
     41	 * 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 accurate
     46	 * 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', via
     63		 * Euclidean algorithm.
     64		 */
     65		dp = d;
     66		a = n / d;
     67		d = n % d;
     68		n = dp;
     69
     70		/* Calculate the current rational approximation (aka
     71		 * convergent), n2/d2, using the term just found and
     72		 * the two prior approximations.
     73		 */
     74		n2 = n0 + a * n1;
     75		d2 = d0 + a * d1;
     76
     77		/* If the current convergent exceeds the maxes, then
     78		 * return either the previous convergent or the
     79		 * largest semi-convergent, the final term of which is
     80		 * 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 previous
     91			 * convergent.  If d1 is zero there is no previous convergent as this
     92			 * 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_LICENSE("GPL v2");