/*
 * 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;
}