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/*
 * 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.jmeter.timers;

import java.io.Serializable;
import java.util.concurrent.ThreadLocalRandom;

import org.apache.jmeter.util.JMeterUtils;

/**
 * This class implements those methods needed by RandomTimer to be instantiable
 * and implements a random delay with an average value and a Poisson
 * distributed variation.
 *
 */
public class PoissonRandomTimer extends RandomTimer implements Serializable {
    /**
     *
     */
    private static final long serialVersionUID = 3514708226113231004L;
    /**
     *
     */
    @SuppressWarnings("FloatingPointLiteralPrecision")
    private static final double[] LOG_FACTORIAL =
        {
            0.000000000000000,
            0.000000000000000,
            0.693147180559945,
            1.791759469228055,
            3.178053830347946,
            4.787491742782046,
            6.579251212010101,
            8.525161361065415,
            10.604602902745251,
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            15.104412573075516,
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            19.987214495661885,
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            25.191221182738683,
            27.899271383840894,
            30.671860106080675,
            33.505073450136891,
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            39.339884187199495,
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            168.327445448427650,
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            1156.170837573242400,
        };


    /**
     * {@inheritDoc}
     */
    @Override
    public long delay() {
        return Math.abs(randomPoisson((int)Math.round(getRange())) + super.delay());
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public String toString() {
        return JMeterUtils.getResString("poisson_timer_memo"); //$NON-NLS-1$
    }

    /**
     * Generate Poisson random based using
     * @param lambda Lambda in Poisson
     * @return random
     */
    private static int randomPoisson(int lambda) {
        if(lambda <= 30) {
            return poissonRandomNumberLowEq30(lambda);
        } else {
            return poissonRandomNumberSup30(lambda);
        }
    }
    /**
     * see http://en.wikipedia.org/wiki/Poisson_distribution
     * @param lambda Lambda in Poisson
     * @return random
     */
    private static int poissonRandomNumberLowEq30(int lambda) {
        double L = Math.exp(-lambda);
        int k = 0;
        double p = 1;
        do {
            k = k + 1;
            double u = ThreadLocalRandom.current().nextDouble();
            p = p * u;
        } while (p > L);
        return k - 1;
    }

    /**
     * http://www.johndcook.com/blog/2010/06/14/generating-poisson-random-values/
     * @param lambda Lambda in Poisson
     * @return random
     */
    private static int poissonRandomNumberSup30(int lambda) {
        double c = 0.767 - 3.36/lambda;
        double beta = Math.PI/Math.sqrt(3.0*lambda);
        double alpha = beta*lambda;
        double k = Math.log(c) - lambda - Math.log(beta);
        while(true) {
            double u = Math.random();
            double x = (alpha - Math.log((1.0 - u)/u))/beta;
            int n = (int)Math.floor(x + 0.5);
            if (n < 0){
                continue;
            }
            double v = ThreadLocalRandom.current().nextDouble();
            double y = alpha - beta*x;
            double lhs = y + Math.log(v/Math.pow(1.0 + Math.exp(y),2));
            double rhs = k + n*Math.log(lambda) -logFactorial(n);
            if (lhs <= rhs) {
                return n;
            }
        }
    }

    /**
     * Compute log factorial
     * http://www.johndcook.com/blog/2010/08/16/how-to-compute-log-factorial/
     * @param n Number for which we want log(n!)
     * @return Log factorial
     */
    private static double logFactorial(int n)
    {
        if (n < 0) {
            throw new IllegalArgumentException();
        }
        else if (n > 254) {
            double x = n + 1d;
            return (x - 0.5)*Math.log(x) - x + 0.5*Math.log(2*Math.PI) + 1.0/(12.0*x);
        }
        else {
            return LOG_FACTORIAL[n];
        }
    }
}




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