LXR linux/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
  28void 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
  62EXPORT_SYMBOL(rational_best_approximation);
  63