LXR linux/lib/math/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/export.h>
  14#include <linux/minmax.h>
  15
  16/*
  17 * calculate best rational approximation for a given fraction
  18 * taking into account restricted register size, e.g. to find
  19 * appropriate values for a pll with 5 bit denominator and
  20 * 8 bit numerator register fields, trying to set up with a
  21 * frequency ratio of 3.1415, one would say:
  22 *
  23 * rational_best_approximation(31415, 10000,
  24 *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  25 *
  26 * you may look at given_numerator as a fixed point number,
  27 * with the fractional part size described in given_denominator.
  28 *
  29 * for theoretical background, see:
  30 * https://en.wikipedia.org/wiki/Continued_fraction
  31 */
  32
  33void rational_best_approximation(
  34        unsigned long given_numerator, unsigned long given_denominator,
  35        unsigned long max_numerator, unsigned long max_denominator,
  36        unsigned long *best_numerator, unsigned long *best_denominator)
  37{
  38        /* n/d is the starting rational, which is continually
  39         * decreased each iteration using the Euclidean algorithm.
  40         *
  41         * dp is the value of d from the prior iteration.
  42         *
  43         * n2/d2, n1/d1, and n0/d0 are our successively more accurate
  44         * approximations of the rational.  They are, respectively,
  45         * the current, previous, and two prior iterations of it.
  46         *
  47         * a is current term of the continued fraction.
  48         */
  49        unsigned long n, d, n0, d0, n1, d1, n2, d2;
  50        n = given_numerator;
  51        d = given_denominator;
  52        n0 = d1 = 0;
  53        n1 = d0 = 1;
  54
  55        for (;;) {
  56                unsigned long dp, a;
  57
  58                if (d == 0)
  59                        break;
  60                /* Find next term in continued fraction, 'a', via
  61                 * Euclidean algorithm.
  62                 */
  63                dp = d;
  64                a = n / d;
  65                d = n % d;
  66                n = dp;
  67
  68                /* Calculate the current rational approximation (aka
  69                 * convergent), n2/d2, using the term just found and
  70                 * the two prior approximations.
  71                 */
  72                n2 = n0 + a * n1;
  73                d2 = d0 + a * d1;
  74
  75                /* If the current convergent exceeds the maxes, then
  76                 * return either the previous convergent or the
  77                 * largest semi-convergent, the final term of which is
  78                 * found below as 't'.
  79                 */
  80                if ((n2 > max_numerator) || (d2 > max_denominator)) {
  81                        unsigned long t = min((max_numerator - n0) / n1,
  82                                              (max_denominator - d0) / d1);
  83
  84                        /* This tests if the semi-convergent is closer
  85                         * than the previous convergent.
  86                         */
  87                        if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
  88                                n1 = n0 + t * n1;
  89                                d1 = d0 + t * d1;
  90                        }
  91                        break;
  92                }
  93                n0 = n1;
  94                n1 = n2;
  95                d0 = d1;
  96                d1 = d2;
  97        }
  98        *best_numerator = n1;
  99        *best_denominator = d1;
 100}
 101
 102EXPORT_SYMBOL(rational_best_approximation);
 103