src/commonlib/rational.c

   1 /* SPDX-License-Identifier: GPL-2.0-only */
   2 /*
   3  * Helper functions for rational numbers.
   4  *
   5  * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
   6  * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
   7  */
   8
   9 #include <commonlib/helpers.h>
  10 #include <commonlib/rational.h>
  11 #include <limits.h>
  12
  13 /*
  14  * For theoretical background, see:
  15  * https://en.wikipedia.org/wiki/Continued_fraction
  16  */
  17 void rational_best_approximation(
  18         unsigned long numerator, unsigned long denominator,
  19         unsigned long max_numerator, unsigned long max_denominator,
  20         unsigned long *best_numerator, unsigned long *best_denominator)
  21 {
  22         /*
  23          * n/d is the starting rational, where both n and d will
  24          * decrease in each iteration using the Euclidean algorithm.
  25          *
  26          * dp is the value of d from the prior iteration.
  27          *
  28          * n2/d2, n1/d1, and n0/d0 are our successively more accurate
  29          * approximations of the rational.  They are, respectively,
  30          * the current, previous, and two prior iterations of it.
  31          *
  32          * a is current term of the continued fraction.
  33          */
  34         unsigned long n, d, n0, d0, n1, d1, n2, d2;
  35         n = numerator;
  36         d = denominator;
  37         n0 = d1 = 0;
  38         n1 = d0 = 1;
  39
  40         for (;;) {
  41                 unsigned long dp, a;
  42
  43                 if (d == 0)
  44                         break;
  45                 /*
  46                  * Find next term in continued fraction, 'a', via
  47                  * Euclidean algorithm.
  48                  */
  49                 dp = d;
  50                 a = n / d;
  51                 d = n % d;
  52                 n = dp;
  53
  54                 /*
  55                  * Calculate the current rational approximation (aka
  56                  * convergent), n2/d2, using the term just found and
  57                  * the two prior approximations.
  58                  */
  59                 n2 = n0 + a * n1;
  60                 d2 = d0 + a * d1;
  61
  62                 /*
  63                  * If the current convergent exceeds the maximum, then
  64                  * return either the previous convergent or the
  65                  * largest semi-convergent, the final term of which is
  66                  * found below as 't'.
  67                  */
  68                 if ((n2 > max_numerator) || (d2 > max_denominator)) {
  69                         unsigned long t = ULONG_MAX;
  70
  71                         if (d1)
  72                                 t = (max_denominator - d0) / d1;
  73                         if (n1)
  74                                 t = MIN(t, (max_numerator - n0) / n1);
  75
  76                         /*
  77                          * This tests if the semi-convergent is closer than the previous
  78                          * convergent.  If d1 is zero there is no previous convergent as
  79                          * this is the 1st iteration, so always choose the semi-convergent.
  80                          */
  81                         if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
  82                                 n1 = n0 + t * n1;
  83                                 d1 = d0 + t * d1;
  84                         }
  85                         break;
  86                 }
  87                 n0 = n1;
  88                 n1 = n2;
  89                 d0 = d1;
  90                 d1 = d2;
  91         }
  92
  93         *best_numerator = n1;
  94         *best_denominator = d1;
  95 }