LXR uboot/lib/rational.c

   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/kernel.h>
  14
  15/*
  16 * calculate best rational approximation for a given fraction
  17 * taking into account restricted register size, e.g. to find
  18 * appropriate values for a pll with 5 bit denominator and
  19 * 8 bit numerator register fields, trying to set up with a
  20 * frequency ratio of 3.1415, one would say:
  21 *
  22 * rational_best_approximation(31415, 10000,
  23 *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  24 *
  25 * you may look at given_numerator as a fixed point number,
  26 * with the fractional part size described in given_denominator.
  27 *
  28 * for theoretical background, see:
  29 * http://en.wikipedia.org/wiki/Continued_fraction
  30 */
  31
  32void rational_best_approximation(
  33        unsigned long given_numerator, unsigned long given_denominator,
  34        unsigned long max_numerator, unsigned long max_denominator,
  35        unsigned long *best_numerator, unsigned long *best_denominator)
  36{
  37        /* n/d is the starting rational, which is continually
  38         * decreased each iteration using the Euclidean algorithm.
  39         *
  40         * dp is the value of d from the prior iteration.
  41         *
  42         * n2/d2, n1/d1, and n0/d0 are our successively more accurate
  43         * approximations of the rational.  They are, respectively,
  44         * the current, previous, and two prior iterations of it.
  45         *
  46         * a is current term of the continued fraction.
  47         */
  48        unsigned long n, d, n0, d0, n1, d1, n2, d2;
  49        n = given_numerator;
  50        d = given_denominator;
  51        n0 = d1 = 0;
  52        n1 = d0 = 1;
  53
  54        for (;;) {
  55                unsigned long dp, a;
  56
  57                if (d == 0)
  58                        break;
  59                /* Find next term in continued fraction, 'a', via
  60                 * Euclidean algorithm.
  61                 */
  62                dp = d;
  63                a = n / d;
  64                d = n % d;
  65                n = dp;
  66
  67                /* Calculate the current rational approximation (aka
  68                 * convergent), n2/d2, using the term just found and
  69                 * the two prior approximations.
  70                 */
  71                n2 = n0 + a * n1;
  72                d2 = d0 + a * d1;
  73
  74                /* If the current convergent exceeds the maxes, then
  75                 * return either the previous convergent or the
  76                 * largest semi-convergent, the final term of which is
  77                 * found below as 't'.
  78                 */
  79                if ((n2 > max_numerator) || (d2 > max_denominator)) {
  80                        unsigned long t = min((max_numerator - n0) / n1,
  81                                              (max_denominator - d0) / d1);
  82
  83                        /* This tests if the semi-convergent is closer
  84                         * than the previous convergent.
  85                         */
  86                        if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
  87                                n1 = n0 + t * n1;
  88                                d1 = d0 + t * d1;
  89                        }
  90                        break;
  91                }
  92                n0 = n1;
  93                n1 = n2;
  94                d0 = d1;
  95                d1 = d2;
  96        }
  97        *best_numerator = n1;
  98        *best_denominator = d1;
  99}
 100