gnu/dist/gettext/gettext-tools/lib/gcd.c

   1 /* Arithmetic.
   2    Copyright (C) 2001-2002 Free Software Foundation, Inc.
   3    Written by Bruno Haible <bruno@clisp.org>, 2001.
   4
   5    This program is free software; you can redistribute it and/or modify
   6    it under the terms of the GNU General Public License as published by
   7    the Free Software Foundation; either version 2, or (at your option)
   8    any later version.
   9
  10    This program is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13    GNU General Public License for more details.
  14
  15    You should have received a copy of the GNU General Public License
  16    along with this program; if not, write to the Free Software Foundation,
  17    Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
  18
  19 /* Specification.  */
  20 #include "gcd.h"
  21
  22 #include <stdlib.h>
  23
  24 /* Return the greatest common divisor of a > 0 and b > 0.  */
  25 unsigned long
  26 gcd (unsigned long a, unsigned long b)
  27 {
  28   /* Why no division, as in Euclid's algorithm? Because in Euclid's algorithm
  29      the division result floor(a/b) or floor(b/a) is very often = 1 or = 2,
  30      and nearly always < 8.  A sequence of a few subtractions and tests is
  31      faster than a division.  */
  32   /* Why not Euclid's algorithm? Because the two integers can be shifted by 1
  33      bit in a single instruction, and the algorithm uses fewer variables than
  34      Euclid's algorithm.  */
  35
  36   unsigned long c = a | b;
  37   c = c ^ (c - 1);
  38   /* c = largest power of 2 that divides a and b.  */
  39
  40   if (a & c)
  41     {
  42       if (b & c)
  43         goto odd_odd;
  44       else
  45         goto odd_even;
  46     }
  47   else
  48     {
  49       if (b & c)
  50         goto even_odd;
  51       else
  52         abort ();
  53     }
  54
  55   for (;;)
  56     {
  57     odd_odd: /* a/c and b/c both odd */
  58       if (a == b)
  59         break;
  60       if (a > b)
  61         {
  62           a = a - b;
  63         even_odd: /* a/c even, b/c odd */
  64           do
  65             a = a >> 1;
  66           while ((a & c) == 0);
  67         }
  68       else
  69         {
  70           b = b - a;
  71         odd_even: /* a/c odd, b/c even */
  72           do
  73             b = b >> 1;
  74           while ((b & c) == 0);
  75         }
  76     }
  77
  78   /* a = b */
  79   return a;
  80 }