Java gcd gcdPositive(int a, int b)

Description

Computes the greatest common divisor of two positive numbers (this precondition is not checked and the result is undefined if not fulfilled) using the "binary gcd" method which avoids division and modulo operations.

License

Apache License

Parameter

Parameter	Description
a	Positive number.
b	Positive number.

Return

the greatest common divisor.

Declaration

private static int gcdPositive(int a, int b)

Method Source Code

//package com.java2s;
/*//from   w  ww  .jav a2 s.  c  om
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

public class Main {
    /**
     * Computes the greatest common divisor of two <em>positive</em> numbers
     * (this precondition is <em>not</em> checked and the result is undefined
     * if not fulfilled) using the "binary gcd" method which avoids division
     * and modulo operations.
     * See Knuth 4.5.2 algorithm B.
     * The algorithm is due to Josef Stein (1961).
     * <br/>
     * Special cases:
     * <ul>
     *  <li>The result of {@code gcd(x, x)}, {@code gcd(0, x)} and
     *   {@code gcd(x, 0)} is the value of {@code x}.</li>
     *  <li>The invocation {@code gcd(0, 0)} is the only one which returns
     *   {@code 0}.</li>
     * </ul>
     *
     * @param a Positive number.
     * @param b Positive number.
     * @return the greatest common divisor.
     */
    private static int gcdPositive(int a, int b) {
        if (a == 0) {
            return b;
        } else if (b == 0) {
            return a;
        }

        // Make "a" and "b" odd, keeping track of common power of 2.
        final int aTwos = Integer.numberOfTrailingZeros(a);
        a >>= aTwos;
        final int bTwos = Integer.numberOfTrailingZeros(b);
        b >>= bTwos;
        final int shift = Math.min(aTwos, bTwos);

        // "a" and "b" are positive.
        // If a > b then "gdc(a, b)" is equal to "gcd(a - b, b)".
        // If a < b then "gcd(a, b)" is equal to "gcd(b - a, a)".
        // Hence, in the successive iterations:
        //  "a" becomes the absolute difference of the current values,
        //  "b" becomes the minimum of the current values.
        while (a != b) {
            final int delta = a - b;
            b = Math.min(a, b);
            a = Math.abs(delta);

            // Remove any power of 2 in "a" ("b" is guaranteed to be odd).
            a >>= Integer.numberOfTrailingZeros(a);
        }

        // Recover the common power of 2.
        return a << shift;
    }
}