lib/rational.c

   1 // SPDX-License-Identifier: GPL-2.0
   2 /*
   3  * rational fractions
   4  *
   5  * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
   6  * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
   7  *
   8  * helper functions when coping with rational numbers
   9  */
  10
  11 #include <linux/rational.h>
  12 #include <linux/compiler.h>
  13 #include <linux/kernel.h>
  14
  15 /*
  16  * calculate best rational approximation for a given fraction
  17  * taking into account restricted register size, e.g. to find
  18  * appropriate values for a pll with 5 bit denominator and
  19  * 8 bit numerator register fields, trying to set up with a
  20  * frequency ratio of 3.1415, one would say:
  21  *
  22  * rational_best_approximation(31415, 10000,
  23  *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  24  *
  25  * you may look at given_numerator as a fixed point number,
  26  * with the fractional part size described in given_denominator.
  27  *
  28  * for theoretical background, see:
  29  * http://en.wikipedia.org/wiki/Continued_fraction
  30  */
  31
  32 void rational_best_approximation(
  33         unsigned long given_numerator, unsigned long given_denominator,
  34         unsigned long max_numerator, unsigned long max_denominator,
  35         unsigned long *best_numerator, unsigned long *best_denominator)
  36 {
  37         /* n/d is the starting rational, which is continually
  38          * decreased each iteration using the Euclidean algorithm.
  39          *
  40          * dp is the value of d from the prior iteration.
  41          *
  42          * n2/d2, n1/d1, and n0/d0 are our successively more accurate
  43          * approximations of the rational.  They are, respectively,
  44          * the current, previous, and two prior iterations of it.
  45          *
  46          * a is current term of the continued fraction.
  47          */
  48         unsigned long n, d, n0, d0, n1, d1, n2, d2;
  49         n = given_numerator;
  50         d = given_denominator;
  51         n0 = d1 = 0;
  52         n1 = d0 = 1;
  53
  54         for (;;) {
  55                 unsigned long dp, a;
  56
  57                 if (d == 0)
  58                         break;
  59                 /* Find next term in continued fraction, 'a', via
  60                  * Euclidean algorithm.
  61                  */
  62                 dp = d;
  63                 a = n / d;
  64                 d = n % d;
  65                 n = dp;
  66
  67                 /* Calculate the current rational approximation (aka
  68                  * convergent), n2/d2, using the term just found and
  69                  * the two prior approximations.
  70                  */
  71                 n2 = n0 + a * n1;
  72                 d2 = d0 + a * d1;
  73
  74                 /* If the current convergent exceeds the maxes, then
  75                  * return either the previous convergent or the
  76                  * largest semi-convergent, the final term of which is
  77                  * found below as 't'.
  78                  */
  79                 if ((n2 > max_numerator) || (d2 > max_denominator)) {
  80                         unsigned long t = min((max_numerator - n0) / n1,
  81                                               (max_denominator - d0) / d1);
  82
  83                         /* This tests if the semi-convergent is closer
  84                          * than the previous convergent.
  85                          */
  86                         if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
  87                                 n1 = n0 + t * n1;
  88                                 d1 = d0 + t * d1;
  89                         }
  90                         break;
  91                 }
  92                 n0 = n1;
  93                 n1 = n2;
  94                 d0 = d1;
  95                 d1 = d2;
  96         }
  97         *best_numerator = n1;
  98         *best_denominator = d1;
  99 }