lib/rational.c

   1 /*
   2  * rational fractions
   3  *
   4  * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <os@emlix.com>
   5  *
   6  * helper functions when coping with rational numbers
   7  */
   8
   9 #include <linux/rational.h>
  10
  11 /*
  12  * calculate best rational approximation for a given fraction
  13  * taking into account restricted register size, e.g. to find
  14  * appropriate values for a pll with 5 bit denominator and
  15  * 8 bit numerator register fields, trying to set up with a
  16  * frequency ratio of 3.1415, one would say:
  17  *
  18  * rational_best_approximation(31415, 10000,
  19  *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  20  *
  21  * you may look at given_numerator as a fixed point number,
  22  * with the fractional part size described in given_denominator.
  23  *
  24  * for theoretical background, see:
  25  * http://en.wikipedia.org/wiki/Continued_fraction
  26  */
  27
  28 void rational_best_approximation(
  29         unsigned long given_numerator, unsigned long given_denominator,
  30         unsigned long max_numerator, unsigned long max_denominator,
  31         unsigned long *best_numerator, unsigned long *best_denominator)
  32 {
  33         unsigned long n, d, n0, d0, n1, d1;
  34         n = given_numerator;
  35         d = given_denominator;
  36         n0 = d1 = 0;
  37         n1 = d0 = 1;
  38         for (;;) {
  39                 unsigned long t, a;
  40                 if ((n1 > max_numerator) || (d1 > max_denominator)) {
  41                         n1 = n0;
  42                         d1 = d0;
  43                         break;
  44                 }
  45                 if (d == 0)
  46                         break;
  47                 t = d;
  48                 a = n / d;
  49                 d = n % d;
  50                 n = t;
  51                 t = n0 + a * n1;
  52                 n0 = n1;
  53                 n1 = t;
  54                 t = d0 + a * d1;
  55                 d0 = d1;
  56                 d1 = t;
  57         }
  58         *best_numerator = n1;
  59         *best_denominator = d1;
  60 }
  61
  62 EXPORT_SYMBOL(rational_best_approximation);