linux/lib/rational.c
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   1/*
   2 * rational fractions
   3 *
   4 * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
   5 *
   6 * helper functions when coping with rational numbers
   7 */
   8
   9#include <linux/rational.h>
  10#include <linux/compiler.h>
  11#include <linux/export.h>
  12
  13/*
  14 * calculate best rational approximation for a given fraction
  15 * taking into account restricted register size, e.g. to find
  16 * appropriate values for a pll with 5 bit denominator and
  17 * 8 bit numerator register fields, trying to set up with a
  18 * frequency ratio of 3.1415, one would say:
  19 *
  20 * rational_best_approximation(31415, 10000,
  21 *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  22 *
  23 * you may look at given_numerator as a fixed point number,
  24 * with the fractional part size described in given_denominator.
  25 *
  26 * for theoretical background, see:
  27 * http://en.wikipedia.org/wiki/Continued_fraction
  28 */
  29
  30void rational_best_approximation(
  31        unsigned long given_numerator, unsigned long given_denominator,
  32        unsigned long max_numerator, unsigned long max_denominator,
  33        unsigned long *best_numerator, unsigned long *best_denominator)
  34{
  35        unsigned long n, d, n0, d0, n1, d1;
  36        n = given_numerator;
  37        d = given_denominator;
  38        n0 = d1 = 0;
  39        n1 = d0 = 1;
  40        for (;;) {
  41                unsigned long t, a;
  42                if ((n1 > max_numerator) || (d1 > max_denominator)) {
  43                        n1 = n0;
  44                        d1 = d0;
  45                        break;
  46                }
  47                if (d == 0)
  48                        break;
  49                t = d;
  50                a = n / d;
  51                d = n % d;
  52                n = t;
  53                t = n0 + a * n1;
  54                n0 = n1;
  55                n1 = t;
  56                t = d0 + a * d1;
  57                d0 = d1;
  58                d1 = t;
  59        }
  60        *best_numerator = n1;
  61        *best_denominator = d1;
  62}
  63
  64EXPORT_SYMBOL(rational_best_approximation);
  65
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