/*
 * 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 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;
    /**
     *
     */
    private static final double[] LOG_FACTORIAL =
        {
            0.000000000000000,
            0.000000000000000,
            0.693147180559945,
            1.791759469228055,
            3.178053830347946,
            4.787491742782046,
            6.579251212010101,
            8.525161361065415,
            10.604602902745251,
            12.801827480081469,
            15.104412573075516,
            17.502307845873887,
            19.987214495661885,
            22.552163853123421,
            25.191221182738683,
            27.899271383840894,
            30.671860106080675,
            33.505073450136891,
            36.395445208033053,
            39.339884187199495,
            42.335616460753485,
            45.380138898476908,
            48.471181351835227,
            51.606675567764377,
            54.784729398112319,
            58.003605222980518,
            61.261701761002001,
            64.557538627006323,
            67.889743137181526,
            71.257038967168000,
            74.658236348830158,
            78.092223553315307,
            81.557959456115029,
            85.054467017581516,
            88.580827542197682,
            92.136175603687079,
            95.719694542143202,
            99.330612454787428,
            102.968198614513810,
            106.631760260643450,
            110.320639714757390,
            114.034211781461690,
            117.771881399745060,
            121.533081515438640,
            125.317271149356880,
            129.123933639127240,
            132.952575035616290,
            136.802722637326350,
            140.673923648234250,
            144.565743946344900,
            148.477766951773020,
            152.409592584497350,
            156.360836303078800,
            160.331128216630930,
            164.320112263195170,
            168.327445448427650,
            172.352797139162820,
            176.395848406997370,
            180.456291417543780,
            184.533828861449510,
            188.628173423671600,
            192.739047287844900,
            196.866181672889980,
            201.009316399281570,
            205.168199482641200,
            209.342586752536820,
            213.532241494563270,
            217.736934113954250,
            221.956441819130360,
            226.190548323727570,
            230.439043565776930,
            234.701723442818260,
            238.978389561834350,
            243.268849002982730,
            247.572914096186910,
            251.890402209723190,
            256.221135550009480,
            260.564940971863220,
            264.921649798552780,
            269.291097651019810,
            273.673124285693690,
            278.067573440366120,
            282.474292687630400,
            286.893133295426990,
            291.323950094270290,
            295.766601350760600,
            300.220948647014100,
            304.686856765668720,
            309.164193580146900,
            313.652829949878990,
            318.152639620209300,
            322.663499126726210,
            327.185287703775200,
            331.717887196928470,
            336.261181979198450,
            340.815058870798960,
            345.379407062266860,
            349.954118040770250,
            354.539085519440790,
            359.134205369575340,
            363.739375555563470,
            368.354496072404690,
            372.979468885689020,
            377.614197873918670,
            382.258588773060010,
            386.912549123217560,
            391.575988217329610,
            396.248817051791490,
            400.930948278915760,
            405.622296161144900,
            410.322776526937280,
            415.032306728249580,
            419.750805599544780,
            424.478193418257090,
            429.214391866651570,
            433.959323995014870,
            438.712914186121170,
            443.475088120918940,
            448.245772745384610,
            453.024896238496130,
            457.812387981278110,
            462.608178526874890,
            467.412199571608080,
            472.224383926980520,
            477.044665492585580,
            481.872979229887900,
            486.709261136839360,
            491.553448223298010,
            496.405478487217580,
            501.265290891579240,
            506.132825342034830,
            511.008022665236070,
            515.890824587822520,
            520.781173716044240,
            525.679013515995050,
            530.584288294433580,
            535.496943180169520,
            540.416924105997740,
            545.344177791154950,
            550.278651724285620,
            555.220294146894960,
            560.169054037273100,
            565.124881094874350,
            570.087725725134190,
            575.057539024710200,
            580.034272767130800,
            585.017879388839220,
            590.008311975617860,
            595.005524249382010,
            600.009470555327430,
            605.020105849423770,
            610.037385686238740,
            615.061266207084940,
            620.091704128477430,
            625.128656730891070,
            630.172081847810200,
            635.221937855059760,
            640.278183660408100,
            645.340778693435030,
            650.409682895655240,
            655.484856710889060,
            660.566261075873510,
            665.653857411105950,
            670.747607611912710,
            675.847474039736880,
            680.953419513637530,
            686.065407301994010,
            691.183401114410800,
            696.307365093814040,
            701.437263808737160,
            706.573062245787470,
            711.714725802289990,
            716.862220279103440,
            722.015511873601330,
            727.174567172815840,
            732.339353146739310,
            737.509837141777440,
            742.685986874351220,
            747.867770424643370,
            753.055156230484160,
            758.248113081374300,
            763.446610112640200,
            768.650616799717000,
            773.860102952558460,
            779.075038710167410,
            784.295394535245690,
            789.521141208958970,
            794.752249825813460,
            799.988691788643450,
            805.230438803703120,
            810.477462875863580,
            815.729736303910160,
            820.987231675937890,
            826.249921864842800,
            831.517780023906310,
            836.790779582469900,
            842.068894241700490,
            847.352097970438420,
            852.640365001133090,
            857.933669825857460,
            863.231987192405430,
            868.535292100464630,
            873.843559797865740,
            879.156765776907600,
            884.474885770751830,
            889.797895749890240,
            895.125771918679900,
            900.458490711945270,
            905.796028791646340,
            911.138363043611210,
            916.485470574328820,
            921.837328707804890,
            927.193914982476710,
            932.555207148186240,
            937.921183163208070,
            943.291821191335660,
            948.667099599019820,
            954.046996952560450,
            959.431492015349480,
            964.820563745165940,
            970.214191291518320,
            975.612353993036210,
            981.015031374908400,
            986.422203146368590,
            991.833849198223450,
            997.249949600427840,
            1002.670484599700300,
            1008.095434617181700,
            1013.524780246136200,
            1018.958502249690200,
            1024.396581558613400,
            1029.838999269135500,
            1035.285736640801600,
            1040.736775094367400,
            1046.192096209724900,
            1051.651681723869200,
            1057.115513528895000,
            1062.583573670030100,
            1068.055844343701400,
            1073.532307895632800,
            1079.012946818975000,
            1084.497743752465600,
            1089.986681478622400,
            1095.479742921962700,
            1100.976911147256000,
            1106.478169357800900,
            1111.983500893733000,
            1117.492889230361000,
            1123.006317976526100,
            1128.523770872990800,
            1134.045231790853000,
            1139.570684729984800,
            1145.100113817496100,
            1150.633503306223700,
            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 final int poissonRandomNumberLowEq30(int lambda) {
        double L = Math.exp(-lambda);
        int k = 0;
        double p = 1;
        do {
            k = k + 1;
            double u = Math.random();
            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 final 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 = Math.random();
            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 final double logFactorial(int n)
    {
        if (n < 0) {
            throw new IllegalArgumentException();
        }
        else if (n > 254) {
            double x = n + 1;
            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];
        }
    }
}
