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//******************************************************************************
//
// File: Mathe.java
// Package: edu.rit.util
// Unit: Class edu.rit.util.Mathe
//
// This Java source file is copyright (C) 2010 by Alan Kaminsky. All rights
// reserved. For further information, contact the author, Alan Kaminsky, at
// ark@cs.rit.edu.
//
// This Java source file is part of the Parallel Java Library ("PJ"). PJ 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 3 of the License, or (at your option) any later version.
//
// PJ 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.
//
// Linking this library statically or dynamically with other modules is making a
// combined work based on this library. Thus, the terms and conditions of the
// GNU General Public License cover the whole combination.
//
// As a special exception, the copyright holders of this library give you
// permission to link this library with independent modules to produce an
// executable, regardless of the license terms of these independent modules, and
// to copy and distribute the resulting executable under terms of your choice,
// provided that you also meet, for each linked independent module, the terms
// and conditions of the license of that module. An independent module is a
// module which is not derived from or based on this library. If you modify this
// library, you may extend this exception to your version of the library, but
// you are not obligated to do so. If you do not wish to do so, delete this
// exception statement from your version.
//
// A copy of the GNU General Public License is provided in the file gpl.txt. You
// may also obtain a copy of the GNU General Public License on the World Wide
// Web at http://www.gnu.org/licenses/gpl.html.
//
//******************************************************************************
package edu.rit.util;
/**
* Class Mathe provides useful mathematical operations. The class is named
* "Mathe" so the compiler won't confuse it with class java.lang.Math.
*
* @author Alan Kaminsky
* @version 11-Feb-2010
*/
public class Mathe
{
// Prevent construction.
private Mathe()
{
}
// Exported operations.
/**
* Compute the integer square root of the integer <TT>x</TT>. The value
* floor(<TT>x</TT><SUP>1/2</SUP>) is returned. The answer is calculated
* using an exact integer algorithm taken from:
* <UL>
* <LI>
* J. Crenshaw. Integer square roots.
* <A HREF="http://www.embedded.com/98/9802fe2.htm" TARGET="_top">http://www.embedded.com/98/9802fe2.htm</A>
* </UL>
*
* @param x Input.
*
* @return Floor(<TT>x</TT><SUP>1/2</SUP>).
*
* @exception ArithmeticException
* (unchecked exception) Thrown if <TT>x</TT> < 0.
*/
public static int sqrt
(int x)
{
if (x < 0)
{
throw new ArithmeticException ("Mathe.sqrt(): x < 0");
}
int rem = 0;
int root = 0;
for (int i = 0; i < 16; ++ i)
{
root <<= 1;
rem = (rem << 2) | (x >>> 30);
x <<= 2;
++ root;
if (root <= rem)
{
rem -= root;
++ root;
}
else
{
-- root;
}
}
return root >>> 1;
}
// Unit test main program.
// /**
// * Unit test main program.
// */
// public static void main
// (String[] args)
// {
// for (int x = 0; x <= 100000000; ++ x)
// {
// if ((x % 10000000) == 0) System.out.printf ("%d%n", x);
// int y = Mathe.sqrt(x);
// if (y*y > x || x >= (y + 1)*(y + 1))
// {
// System.out.printf ("x = %d, sqrt(x) = %d, fail%n", x, y);
// }
// }
// }
}
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