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Linux/lib/rational.c

  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 
 30 void 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 
 64 EXPORT_SYMBOL(rational_best_approximation);
 65 

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