Release calc version 2.11.1t1

cal/pix.cal

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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.
+ * 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
+ *
+ * @(#) $Revision: 29.1 $
+ * @(#) $Id: pix.cal,v 29.1 1999/12/14 09:15:31 chongo Exp $
+ * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pix.cal,v $
+ *
+ * Under source code control:	1996/07/09 03:14:14
+ * File existed as early as:	1996
+ *
+ * chongo <was here> /\oo/\	http://reality.sgi.com/chongo/
+ * Share and enjoy!  :-)	http://reality.sgi.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;
+}