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/*
* 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;
}