gcd.c   [plain text]

/* Arithmetic.
   Copyright (C) 2001-2002 Free Software Foundation, Inc.
   Written by Bruno Haible <bruno@clisp.org>, 2001.

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2, or (at your option)
   any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software Foundation,
   Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */

/* Specification.  */
#include "gcd.h"

#include <stdlib.h>

/* Return the greatest common divisor of a > 0 and b > 0.  */
unsigned long
gcd (unsigned long a, unsigned long b)
{
  /* Why no division, as in Euclid's algorithm? Because in Euclid's algorithm
     the division result floor(a/b) or floor(b/a) is very often = 1 or = 2,
     and nearly always < 8.  A sequence of a few subtractions and tests is
     faster than a division.  */
  /* Why not Euclid's algorithm? Because the two integers can be shifted by 1
     bit in a single instruction, and the algorithm uses fewer variables than
     Euclid's algorithm.  */

  unsigned long c = a | b;
  c = c ^ (c - 1);
  /* c = largest power of 2 that divides a and b.  */

  if (a & c)
    {
      if (b & c)
	goto odd_odd;
      else
	goto odd_even;
    }
  else
    {
      if (b & c)
	goto even_odd;
      else
	abort ();
    }

  for (;;)
    {
    odd_odd: /* a/c and b/c both odd */
      if (a == b)
	break;
      if (a > b)
	{
	  a = a - b;
	even_odd: /* a/c even, b/c odd */
	  do
	    a = a >> 1;
	  while ((a & c) == 0);
	}
      else
	{
	  b = b - a;
	odd_even: /* a/c odd, b/c even */
	  do
	    b = b >> 1;
	  while ((b & c) == 0);
	}
    }

  /* a = b */
  return a;
}