lib/math/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/export.h>
  14 #include <linux/minmax.h>
  15
  16 /*
  17  * calculate best rational approximation for a given fraction
  18  * taking into account restricted register size, e.g. to find
  19  * appropriate values for a pll with 5 bit denominator and
  20  * 8 bit numerator register fields, trying to set up with a
  21  * frequency ratio of 3.1415, one would say:
  22  *
  23  * rational_best_approximation(31415, 10000,
  24  *              (1 << 8) - 1, (1 << 5) - 1, &n, &d);
  25  *
  26  * you may look at given_numerator as a fixed point number,
  27  * with the fractional part size described in given_denominator.
  28  *
  29  * for theoretical background, see:
  30  * https://en.wikipedia.org/wiki/Continued_fraction
  31  */
  32
  33 void rational_best_approximation(
  34         unsigned long given_numerator, unsigned long given_denominator,
  35         unsigned long max_numerator, unsigned long max_denominator,
  36         unsigned long *best_numerator, unsigned long *best_denominator)
  37 {
  38         /* n/d is the starting rational, which is continually
  39          * decreased each iteration using the Euclidean algorithm.
  40          *
  41          * dp is the value of d from the prior iteration.
  42          *
  43          * n2/d2, n1/d1, and n0/d0 are our successively more accurate
  44          * approximations of the rational.  They are, respectively,
  45          * the current, previous, and two prior iterations of it.
  46          *
  47          * a is current term of the continued fraction.
  48          */
  49         unsigned long n, d, n0, d0, n1, d1, n2, d2;
  50         n = given_numerator;
  51         d = given_denominator;
  52         n0 = d1 = 0;
  53         n1 = d0 = 1;
  54
  55         for (;;) {
  56                 unsigned long dp, a;
  57
  58                 if (d == 0)
  59                         break;
  60                 /* Find next term in continued fraction, 'a', via
  61                  * Euclidean algorithm.
  62                  */
  63                 dp = d;
  64                 a = n / d;
  65                 d = n % d;
  66                 n = dp;
  67
  68                 /* Calculate the current rational approximation (aka
  69                  * convergent), n2/d2, using the term just found and
  70                  * the two prior approximations.
  71                  */
  72                 n2 = n0 + a * n1;
  73                 d2 = d0 + a * d1;
  74
  75                 /* If the current convergent exceeds the maxes, then
  76                  * return either the previous convergent or the
  77                  * largest semi-convergent, the final term of which is
  78                  * found below as 't'.
  79                  */
  80                 if ((n2 > max_numerator) || (d2 > max_denominator)) {
  81                         unsigned long t = min((max_numerator - n0) / n1,
  82                                               (max_denominator - d0) / d1);
  83
  84                         /* This tests if the semi-convergent is closer
  85                          * than the previous convergent.
  86                          */
  87                         if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
  88                                 n1 = n0 + t * n1;
  89                                 d1 = d0 + t * d1;
  90                         }
  91                         break;
  92                 }
  93                 n0 = n1;
  94                 n1 = n2;
  95                 d0 = d1;
  96                 d1 = d2;
  97         }
  98         *best_numerator = n1;
  99         *best_denominator = d1;
 100 }
 101
 102 EXPORT_SYMBOL(rational_best_approximation);