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Java example source code file (PollardRho.java)

This example Java source code file (PollardRho.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, list, pollardrho, util

The PollardRho.java Java example source code

/*
 * 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.
 */
package org.apache.commons.math3.primes;

import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math3.util.FastMath;

/**
 * Implementation of the Pollard's rho factorization algorithm.
 * @since 3.2
 */
class PollardRho {

    /**
     * Hide utility class.
     */
    private PollardRho() {
    }

    /**
     * Factorization using Pollard's rho algorithm.
     * @param n number to factors, must be > 0
     * @return the list of prime factors of n.
     */
    public static List<Integer> primeFactors(int n) {
        final List<Integer> factors = new ArrayList();

        n = SmallPrimes.smallTrialDivision(n, factors);
        if (1 == n) {
            return factors;
        }

        if (SmallPrimes.millerRabinPrimeTest(n)) {
            factors.add(n);
            return factors;
        }

        int divisor = rhoBrent(n);
        factors.add(divisor);
        factors.add(n / divisor);
        return factors;
    }

    /**
     * Implementation of the Pollard's rho factorization algorithm.
     * <p>
     * This implementation follows the paper "An improved Monte Carlo factorization algorithm"
     * by Richard P. Brent. This avoids the triple computation of f(x) typically found in Pollard's
     * rho implementations. It also batches several gcd computation into 1.
     * <p>
     * The backtracking is not implemented as we deal only with semi-primes.
     *
     * @param n number to factor, must be semi-prime.
     * @return a prime factor of n.
     */
    static int rhoBrent(final int n) {
        final int x0 = 2;
        final int m = 25;
        int cst = SmallPrimes.PRIMES_LAST;
        int y = x0;
        int r = 1;
        do {
            int x = y;
            for (int i = 0; i < r; i++) {
                final long y2 = ((long) y) * y;
                y = (int) ((y2 + cst) % n);
            }
            int k = 0;
            do {
                final int bound = FastMath.min(m, r - k);
                int q = 1;
                for (int i = -3; i < bound; i++) { //start at -3 to ensure we enter this loop at least 3 times
                    final long y2 = ((long) y) * y;
                    y = (int) ((y2 + cst) % n);
                    final long divisor = FastMath.abs(x - y);
                    if (0 == divisor) {
                        cst += SmallPrimes.PRIMES_LAST;
                        k = -m;
                        y = x0;
                        r = 1;
                        break;
                    }
                    final long prod = divisor * q;
                    q = (int) (prod % n);
                    if (0 == q) {
                        return gcdPositive(FastMath.abs((int) divisor), n);
                    }
                }
                final int out = gcdPositive(FastMath.abs(q), n);
                if (1 != out) {
                    return out;
                }
                k += m;
            } while (k < r);
            r = 2 * r;
        } while (true);
    }

    /**
     * Gcd between two positive numbers.
     * <p>
     * Gets the greatest common divisor 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 result of {@code gcd(x, x)}, {@code gcd(0, x)} and {@code gcd(x, 0)} is the value of {@code x}.
     * <li>The invocation {@code gcd(0, 0)} is the only one which returns {@code 0}.
     * </ul>
     *
     * @param a first number, must be ≥ 0
     * @param b second number, must be ≥ 0
     * @return gcd(a,b)
     */
    static int gcdPositive(int a, int b){
        // both a and b must be positive, it is not checked here
        // gdc(a,0) = a
        if (a == 0) {
            return b;
        } else if (b == 0) {
            return a;
        }

        // make a and b odd, keep in mind the common power of twos
        final int aTwos = Integer.numberOfTrailingZeros(a);
        a >>= aTwos;
        final int bTwos = Integer.numberOfTrailingZeros(b);
        b >>= bTwos;
        final int shift = FastMath.min(aTwos, bTwos);

        // a and b >0
        // if a > b then gdc(a,b) = gcd(a-b,b)
        // if a < b then gcd(a,b) = gcd(b-a,a)
        // so next a is the absolute difference and next b is the minimum of current values
        while (a != b) {
            final int delta = a - b;
            b = FastMath.min(a, b);
            a = FastMath.abs(delta);
            // for speed optimization:
            // remove any power of two in a as b is guaranteed to be odd throughout all iterations
            a >>= Integer.numberOfTrailingZeros(a);
        }

        // gcd(a,a) = a, just "add" the common power of twos
        return a << shift;
    }
}

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