Branch data     Line data    Source code

       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                 :          0 : 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         [ #  # ]:          0 :                 if ((n1 > max_numerator) || (d1 > max_denominator)) {
      44                 :          0 :                         n1 = n0;
      45                 :          0 :                         d1 = d0;
      46                 :          0 :                         break;
      47                 :            :                 }
      48         [ #  # ]:          0 :                 if (d == 0)
      49                 :            :                         break;
      50                 :            :                 t = d;
      51                 :          0 :                 a = n / d;
      52                 :          0 :                 d = n % d;
      53                 :            :                 n = t;
      54                 :          0 :                 t = n0 + a * n1;
      55                 :            :                 n0 = n1;
      56                 :            :                 n1 = t;
      57                 :          0 :                 t = d0 + a * d1;
      58                 :            :                 d0 = d1;
      59                 :            :                 d1 = t;
      60                 :          0 :         }
      61                 :          0 :         *best_numerator = n1;
      62                 :          0 :         *best_denominator = d1;
      63                 :          0 : }
      64                 :            : 
      65                 :            : EXPORT_SYMBOL(rational_best_approximation);