Java gcd gcd(final int p, final int q)

Description

Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations.

License

Open Source License

Parameter

Parameter	Description
p	any number
q	any number

Exception

Parameter	Description
ArithmeticException	if the result cannot be represented as a nonnegative intvalue

Return

the greatest common divisor, never negative

Declaration

public static int gcd(final int p, final int q)

Method Source Code

//package com.java2s;
/*//from w w w.j  a  v  a 2 s.  com
 * Copyright (c) 2006-2011 Karsten Schmidt
 * 
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 * 
 * http://creativecommons.org/licenses/LGPL/2.1/
 * 
 * This library 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.
 * 
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
 */

public class Main {
    /**
     * <p>
     * Gets the greatest common divisor of the absolute value of two numbers,
     * using the "binary gcd" method which avoids division and modulo
     * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef
     * Stein (1961).
     * </p>
     * Special cases:
     * <ul>
     * <li>The invocations
     * <code>gcd(Integer.MIN_VALUE, Integer.MIN_VALUE)</code>,
     * <code>gcd(Integer.MIN_VALUE, 0)</code> and
     * <code>gcd(0, Integer.MIN_VALUE)</code> throw an
     * <code>ArithmeticException</code>, because the result would be 2^31, which
     * is too large for an int value.</li>
     * <li>The result of <code>gcd(x, x)</code>, <code>gcd(0, x)</code> and
     * <code>gcd(x, 0)</code> is the absolute value of <code>x</code>, except
     * for the special cases above.
     * <li>The invocation <code>gcd(0, 0)</code> is the only one which returns
     * <code>0</code>.</li>
     * </ul>
     * 
     * @param p any number
     * @param q any number
     * @return the greatest common divisor, never negative
     * @throws ArithmeticException
     *             if the result cannot be represented as a nonnegative int
     *             value
     * @since 1.1
     */
    public static int gcd(final int p, final int q) {
        int u = p;
        int v = q;
        if ((u == 0) || (v == 0)) {
            if ((u == Integer.MIN_VALUE) || (v == Integer.MIN_VALUE)) {
                return 0;
            }
            return (Math.abs(u) + Math.abs(v));
        }
        // keep u and v negative, as negative integers range down to
        // -2^31, while positive numbers can only be as large as 2^31-1
        // (i.e. we can't necessarily negate a negative number without
        // overflow)
        /* assert u!=0 && v!=0; */
        if (u > 0) {
            u = -u;
        } // make u negative
        if (v > 0) {
            v = -v;
        } // make v negative
          // B1. [Find power of 2]
        int k = 0;
        while ((u & 1) == 0 && (v & 1) == 0 && k < 31) { // while u and v are
            // both even...
            u /= 2;
            v /= 2;
            k++; // cast out twos.
        }
        if (k == 31) {
            return 0;
        }
        // B2. Initialize: u and v have been divided by 2^k and at least
        // one is odd.
        int t = ((u & 1) == 1) ? v : -(u / 2)/* B3 */;
        // t negative: u was odd, v may be even (t replaces v)
        // t positive: u was even, v is odd (t replaces u)
        do {
            /* assert u<0 && v<0; */
            // B4/B3: cast out twos from t.
            while ((t & 1) == 0) { // while t is even..
                t /= 2; // cast out twos
            }
            // B5 [reset max(u,v)]
            if (t > 0) {
                u = -t;
            } else {
                v = t;
            }
            // B6/B3. at this point both u and v should be odd.
            t = (v - u) / 2;
            // |u| larger: t positive (replace u)
            // |v| larger: t negative (replace v)
        } while (t != 0);
        return -u * (1 << k); // gcd is u*2^k
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final double abs(double x) {
        return x < 0 ? -x : x;
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final float abs(float x) {
        return x < 0 ? -x : x;
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final int abs(int x) {
        int y = x >> 31;
        return (x ^ y) - y;
    }
}