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 *
   7 * helper functions when coping with rational numbers
   8 */
   9
  10#include <linux/rational.h>
  11#include <linux/compiler.h>
  12#include <linux/export.h>
  13
  14/*
  15 * calculate best rational approximation for a given fraction
  16 * taking into account restricted register size, e.g. to find
  17 * appropriate values for a pll with 5 bit denominator and
  18 * 8 bit numerator register fields, trying to set up with a
  19 * frequency ratio of 3.1415, one would say:
  20 *
  21 * rational_best_approximation(31415, 10000,
  22 *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  23 *
  24 * you may look at given_numerator as a fixed point number,
  25 * with the fractional part size described in given_denominator.
  26 *
  27 * for theoretical background, see:
  28 * http://en.wikipedia.org/wiki/Continued_fraction
  29 */
  30
  31void rational_best_approximation(
  32        unsigned long given_numerator, unsigned long given_denominator,
  33        unsigned long max_numerator, unsigned long max_denominator,
  34        unsigned long *best_numerator, unsigned long *best_denominator)
  35{
  36        unsigned long n, d, n0, d0, n1, d1;
  37        n = given_numerator;
  38        d = given_denominator;
  39        n0 = d1 = 0;
  40        n1 = d0 = 1;
  41        for (;;) {
  42                unsigned long t, a;
  43                if ((n1 > max_numerator) || (d1 > max_denominator)) {
  44                        n1 = n0;
  45                        d1 = d0;
  46                        break;
  47                }
  48                if (d == 0)
  49                        break;
  50                t = d;
  51                a = n / d;
  52                d = n % d;
  53                n = t;
  54                t = n0 + a * n1;
  55                n0 = n1;
  56                n1 = t;
  57                t = d0 + a * d1;
  58                d0 = d1;
  59                d1 = t;
  60        }
  61        *best_numerator = n1;
  62        *best_denominator = d1;
  63}
  64
  65EXPORT_SYMBOL(rational_best_approximation);
  66