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#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");
 112