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  *
   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
  31 void 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
  65 EXPORT_SYMBOL(rational_best_approximation);