/*
 * pix - iterative method of finding the number of primes less than x
 *
 * Copyright (C) 1999  Landon Curt Noll
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc 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 Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * Under source code control:	1996/07/09 03:14:14
 * File existed as early as:	1996
 *
 * chongo <was here> /\oo/\	http://www.isthe.com/chongo/
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */

/*
 * Here is an iterative method of finding the number of primes less than
 * or equal to a given number.	This method is from "Computer Recreations"
 * June 1996 issue of Scientific American.
 *
 * NOTE: For reasonable values of x, the builtin function pix(x) is
 *	 much faster.  This code is provided because the method
 *	 is interesting.
 */


define pi_of_x(x)
{
	local An;	/* A(n) */
	local An1;	/* A(n-1) */
	local An2;	/* A(n-2) */
	local An3;	/* A(n-3) */
	local primes;	/* number of primes found */
	local n;	/* loop counter */

	/*
	 * setup
	 */
	An1 = 2;
	An2 = 0;
	An3 = 3;
	primes = 1;

	/*
	 * main A(n+1)=A(n-1)+A(n-2) sequence loop
	 */
	for (n = 3; n < x; ++n) {
		An = An2 + An3;
		An3 = An2;
		An2 = An1;
		An1 = An;
		if (An % n == 0)
			++primes;
	}
	return primes;
}
