/*
 * Copyright (c) 2009-12 University of Washington
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License version 2 as
 * published by the Free Software Foundation;
 *
 * This program 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 * This file is based on rng-test-suite.cc.
 *
 * Modified by Mitch Watrous <watrous@u.washington.edu>
 *
 */

#include "ns3/boolean.h"
#include "ns3/double.h"
#include "ns3/integer.h"
#include "ns3/log.h"
#include "ns3/random-variable-stream.h"
#include "ns3/rng-seed-manager.h"
#include "ns3/string.h"
#include "ns3/test.h"

#include <cmath>
#include <ctime>
#include <fstream>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_histogram.h>
#include <gsl/gsl_sf_zeta.h>

using namespace ns3;

NS_LOG_COMPONENT_DEFINE("RandomVariableStreamGenerators");

namespace ns3
{

namespace test
{

namespace RandomVariable
{

/**
 * \file
 * \ingroup rng-tests
 * Random number generator streams tests.
 */

/**
 * \ingroup rng-tests
 * Base class for RandomVariableStream test suites.
 */
class TestCaseBase : public TestCase
{
  public:
    /** Number of bins for sampling the distributions. */
    static const uint32_t N_BINS{50};
    /** Number of samples to draw when populating the distributions. */
    static const uint32_t N_MEASUREMENTS{1000000};
    /** Number of retry attempts to pass a chi-square test. */
    static const uint32_t N_RUNS{5};

    /**
     * Constructor
     * \param [in] name The test case name.
     */
    TestCaseBase(std::string name)
        : TestCase(name)
    {
    }

    /**
     * Configure a GSL histogram with uniform bins, with optional
     * under/over-flow bins.
     * \param [in,out] h The GSL histogram to configure.
     * \param [in] start The minimum value of the lowest bin.
     * \param [in] end The maximum value of the last bin.
     * \param [in] underflow If \c true the lowest bin should contain the underflow,
     * \param [in] overflow If \c true the highest bin should contain the overflow.
     * \returns A vector of the bin edges, including the top of the highest bin.
     * This vector has one more entry than the number of bins in the histogram.
     */
    std::vector<double> UniformHistogramBins(gsl_histogram* h,
                                             double start,
                                             double end,
                                             bool underflow = true,
                                             bool overflow = true) const
    {
        NS_LOG_FUNCTION(this << h << start << end);
        std::size_t nBins = gsl_histogram_bins(h);
        double increment = (end - start) / (nBins - 1.);
        double d = start;

        std::vector<double> range(nBins + 1);

        for (auto& r : range)
        {
            r = d;
            d += increment;
        }
        if (underflow)
        {
            range[0] = -std::numeric_limits<double>::max();
        }
        if (overflow)
        {
            range[nBins] = std::numeric_limits<double>::max();
        }

        gsl_histogram_set_ranges(h, range.data(), nBins + 1);
        return range;
    }

    /**
     * Compute the average of a random variable.
     * \param [in] rng The random variable to sample.
     * \returns The average of \c N_MEASUREMENTS samples.
     */
    double Average(Ptr<RandomVariableStream> rng) const
    {
        NS_LOG_FUNCTION(this << rng);
        double sum = 0.0;
        for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
        {
            double value = rng->GetValue();
            sum += value;
        }
        double valueMean = sum / N_MEASUREMENTS;
        return valueMean;
    }

    /** A factory base class to create new instances of a random variable. */
    class RngGeneratorBase
    {
      public:
        /**
         * Create a new instance of a random variable stream
         * \returns The new random variable stream instance.
         */
        virtual Ptr<RandomVariableStream> Create() const = 0;
    };

    /**
     * Factory class to create new instances of a particular random variable stream.
     *
     * \tparam RNG The type of random variable generator to create.
     */
    template <typename RNG>
    class RngGenerator : public RngGeneratorBase
    {
      public:
        /**
         * Constructor.
         * \param [in] anti Create antithetic streams if \c true.
         */
        RngGenerator(bool anti = false)
            : m_anti(anti)
        {
        }

        // Inherited
        Ptr<RandomVariableStream> Create() const override
        {
            auto rng = CreateObject<RNG>();
            rng->SetAttribute("Antithetic", BooleanValue(m_anti));
            return rng;
        }

      private:
        /** Whether to create antithetic random variable streams. */
        bool m_anti;
    };

    /**
     * Compute the chi squared value of a sampled distribution
     * compared to the expected distribution.
     *
     * This function captures the actual computation of the chi square,
     * given an expected distribution.
     *
     * The random variable is sampled \c N_MEASUREMENTS times, filling
     * a histogram. The chi square value is formed by comparing to the
     * expected distribution.
     * \param [in,out] h The histogram, which defines the binning for sampling.
     * \param [in] expected The expected distribution.
     * \param [in] rng The random variable to sample.
     * \returns The chi square value.
     */
    double ChiSquared(gsl_histogram* h,
                      const std::vector<double>& expected,
                      Ptr<RandomVariableStream> rng) const
    {
        NS_LOG_FUNCTION(this << h << expected.size() << rng);
        NS_ASSERT_MSG(gsl_histogram_bins(h) == expected.size(),
                      "Histogram and expected vector have different sizes.");

        // Sample the rng into the histogram
        for (std::size_t i = 0; i < N_MEASUREMENTS; ++i)
        {
            double value = rng->GetValue();
            gsl_histogram_increment(h, value);
        }

        // Compute the chi square value
        double chiSquared = 0;
        std::size_t nBins = gsl_histogram_bins(h);
        for (std::size_t i = 0; i < nBins; ++i)
        {
            double hbin = gsl_histogram_get(h, i);
            double tmp = hbin - expected[i];
            tmp *= tmp;
            tmp /= expected[i];
            chiSquared += tmp;
        }

        return chiSquared;
    }

    /**
     * Compute the chi square value from a random variable.
     *
     * This function sets up the binning and expected distribution
     * needed to actually compute the chi squared value, which
     * should be done by a call to ChiSquared.
     *
     * This is the point of customization expected to be implemented
     * in derived classes with the appropriate histogram binning and
     * expected distribution.  For example
     *
     *    SomeRngTestCase::ChiSquaredTest (Ptr<RandomVariableStream> rng) const
     *    {
     *      gsl_histogram * h = gsl_histogram_alloc (N_BINS);
     *      auto range = UniformHistogramBins (h, -4., 4.);
     *      std::vector<double> expected (N_BINS);
     *      // Populated expected
     *      for (std::size_t i = 0; i < N_BINS; ++i)
     *        {
     *          expected[i] = ...;
     *          expected[i] *= N_MEASUREMENTS;
     *        }
     *      double chiSquared = ChiSquared (h, expected, rng);
     *      gsl_histogram_free (h);
     *      return chiSquared;
     *    }
     *
     * \param [in] rng The random number generator to test.
     * \returns The chi squared value.
     */
    virtual double ChiSquaredTest(Ptr<RandomVariableStream> rng) const
    {
        return 0;
    }

    /**
     * Average the chi squared value over some number of runs,
     * each run with a new instance of the random number generator.
     * \param [in] generator The factory to create instances of the
     *             random number generator.
     * \param [in] nRuns The number of runs to average over.
     * \returns The average chi square over the number of runs.
     */
    double ChiSquaredsAverage(const RngGeneratorBase* generator, std::size_t nRuns) const
    {
        NS_LOG_FUNCTION(this << generator << nRuns);

        double sum = 0.;
        for (std::size_t i = 0; i < nRuns; ++i)
        {
            auto rng = generator->Create();
            double result = ChiSquaredTest(rng);
            sum += result;
        }
        sum /= (double)nRuns;
        return sum;
    }

    /**
     * Set the seed used for this test suite.
     *
     * This test suite is designed to be run with both deterministic and
     * random seed and run number values.  Deterministic values can be used
     * for basic regression testing; random values can be used to more
     * exhaustively test the generated streams, with the side effect of
     * occasional test failures.
     *
     * By default, this test suite will use the default values of RngSeed = 1
     * and RngRun = 1.  Users can configure any other seed and run number
     * in the usual way, but the special value of RngRun = 0 results in
     * selecting a RngSeed value that corresponds to the seconds since epoch
     * (\c time (0) from \c ctime).  Note: this is not a recommended practice for
     * seeding normal simulations, as described in the ns-3 manual, but
     * allows the test to be exposed to a wider range of seeds.
     *
     * In either case, the values produced will be checked with a chi-squared
     * test.
     *
     * For example, this command will cause this test suite to use the
     * deterministic value of seed=3 and default run number=1 every time:
     *   NS_GLOBAL_VALUE="RngSeed=3" ./test.py -s random-variable-stream-generators
     * or equivalently (to see log output):
     *   NS_LOG="RandomVariableStreamGenerators" NS_GLOBAL_VALUE="RngSeed=3" ./ns3 run "test-runner
     * --suite=random-variable-stream-generators"
     *
     * Conversely, this command will cause this test suite to use a seed
     * based on time-of-day, and run number=0:
     *   NS_GLOBAL_VALUE="RngRun=0" ./test.py -s random-variable-stream-generators
     */
    void SetTestSuiteSeed()
    {
        if (!m_seedSet)
        {
            uint32_t seed;
            if (RngSeedManager::GetRun() == 0)
            {
                seed = static_cast<uint32_t>(time(nullptr));
                m_seedSet = true;
                NS_LOG_DEBUG(
                    "Special run number value of zero; seeding with time of day: " << seed);
            }
            else
            {
                seed = RngSeedManager::GetSeed();
                m_seedSet = true;
                NS_LOG_DEBUG("Using the values seed: " << seed
                                                       << " and run: " << RngSeedManager::GetRun());
            }
            SeedManager::SetSeed(seed);
        }
    }

  private:
    /** \c true if we've already set the seed the correctly. */
    bool m_seedSet = false;

}; // class TestCaseBase

/**
 * \ingroup rng-tests
 * Test case for uniform distribution random variable stream generator.
 */
class UniformTestCase : public TestCaseBase
{
  public:
    // Constructor
    UniformTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;
};

UniformTestCase::UniformTestCase()
    : TestCaseBase("Uniform Random Variable Stream Generator")
{
}

double
UniformTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);

    // Note that this assumes that the range for u is [0,1], which is
    // the default range for this distribution.
    gsl_histogram_set_ranges_uniform(h, 0., 1.);

    std::vector<double> expected(N_BINS, ((double)N_MEASUREMENTS / (double)N_BINS));

    double chiSquared = ChiSquared(h, expected, rng);
    gsl_histogram_free(h);
    return chiSquared;
}

void
UniformTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    double confidence = 0.99;
    double maxStatistic = gsl_cdf_chisq_Pinv(confidence, (N_BINS - 1));
    NS_LOG_DEBUG("Chi square required at " << confidence << " confidence for " << N_BINS
                                           << " bins is " << maxStatistic);

    double result = maxStatistic;
    // If chi-squared test fails, re-try it up to N_RUNS times
    for (uint32_t i = 0; i < N_RUNS; ++i)
    {
        Ptr<UniformRandomVariable> rng = CreateObject<UniformRandomVariable>();
        result = ChiSquaredTest(rng);
        NS_LOG_DEBUG("Chi square result is " << result);
        if (result < maxStatistic)
        {
            break;
        }
    }

    NS_TEST_ASSERT_MSG_LT(result, maxStatistic, "Chi-squared statistic out of range");

    double min = 0.0;
    double max = 10.0;
    double value;

    // Create the RNG with the specified range.
    Ptr<UniformRandomVariable> x = CreateObject<UniformRandomVariable>();

    x->SetAttribute("Min", DoubleValue(min));
    x->SetAttribute("Max", DoubleValue(max));

    // Test that values are always within the range:
    //
    //     [min, max)
    //
    for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
    {
        value = x->GetValue();
        NS_TEST_ASSERT_MSG_EQ((value >= min), true, "Value less than minimum.");
        NS_TEST_ASSERT_MSG_LT(value, max, "Value greater than or equal to maximum.");
    }

    // Boundary checking on GetInteger; should be [min,max]; from bug 1964
    static const uint32_t UNIFORM_INTEGER_MIN{0};
    static const uint32_t UNIFORM_INTEGER_MAX{4294967295U};
    // [0,0] should return 0
    uint32_t intValue;
    intValue = x->GetInteger(UNIFORM_INTEGER_MIN, UNIFORM_INTEGER_MIN);
    NS_TEST_ASSERT_MSG_EQ(intValue, UNIFORM_INTEGER_MIN, "Uniform RV GetInteger boundary testing");
    // [UNIFORM_INTEGER_MAX, UNIFORM_INTEGER_MAX] should return UNIFORM_INTEGER_MAX
    intValue = x->GetInteger(UNIFORM_INTEGER_MAX, UNIFORM_INTEGER_MAX);
    NS_TEST_ASSERT_MSG_EQ(intValue, UNIFORM_INTEGER_MAX, "Uniform RV GetInteger boundary testing");
    // [0,1] should return mix of 0 or 1
    intValue = 0;
    for (int i = 0; i < 20; i++)
    {
        intValue += x->GetInteger(UNIFORM_INTEGER_MIN, UNIFORM_INTEGER_MIN + 1);
    }
    NS_TEST_ASSERT_MSG_GT(intValue, 0, "Uniform RV GetInteger boundary testing");
    NS_TEST_ASSERT_MSG_LT(intValue, 20, "Uniform RV GetInteger boundary testing");
    // [MAX-1,MAX] should return mix of MAX-1 or MAX
    uint32_t count = 0;
    for (int i = 0; i < 20; i++)
    {
        intValue = x->GetInteger(UNIFORM_INTEGER_MAX - 1, UNIFORM_INTEGER_MAX);
        if (intValue == UNIFORM_INTEGER_MAX)
        {
            count++;
        }
    }
    NS_TEST_ASSERT_MSG_GT(count, 0, "Uniform RV GetInteger boundary testing");
    NS_TEST_ASSERT_MSG_LT(count, 20, "Uniform RV GetInteger boundary testing");
    // multiple [0,UNIFORM_INTEGER_MAX] should return non-zero
    intValue = x->GetInteger(UNIFORM_INTEGER_MIN, UNIFORM_INTEGER_MAX);
    uint32_t intValue2 = x->GetInteger(UNIFORM_INTEGER_MIN, UNIFORM_INTEGER_MAX);
    NS_TEST_ASSERT_MSG_GT(intValue + intValue2, 0, "Uniform RV GetInteger boundary testing");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic uniform distribution random variable stream generator
 */
class UniformAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    UniformAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;
};

UniformAntitheticTestCase::UniformAntitheticTestCase()
    : TestCaseBase("Antithetic Uniform Random Variable Stream Generator")
{
}

double
UniformAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);

    // Note that this assumes that the range for u is [0,1], which is
    // the default range for this distribution.
    gsl_histogram_set_ranges_uniform(h, 0., 1.);

    std::vector<double> expected(N_BINS, ((double)N_MEASUREMENTS / (double)N_BINS));

    double chiSquared = ChiSquared(h, expected, rng);
    gsl_histogram_free(h);
    return chiSquared;
}

void
UniformAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<UniformRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double min = 0.0;
    double max = 10.0;
    double value;

    // Create the RNG with the specified range.
    Ptr<UniformRandomVariable> x = CreateObject<UniformRandomVariable>();

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    x->SetAttribute("Min", DoubleValue(min));
    x->SetAttribute("Max", DoubleValue(max));

    // Test that values are always within the range:
    //
    //     [min, max)
    //
    for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
    {
        value = x->GetValue();
        NS_TEST_ASSERT_MSG_EQ((value >= min), true, "Value less than minimum.");
        NS_TEST_ASSERT_MSG_LT(value, max, "Value greater than or equal to maximum.");
    }
}

/**
 * \ingroup rng-tests
 * Test case for constant random variable stream generator
 */
class ConstantTestCase : public TestCaseBase
{
  public:
    // Constructor
    ConstantTestCase();

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation. */
    static constexpr double TOLERANCE{1e-8};
};

ConstantTestCase::ConstantTestCase()
    : TestCaseBase("Constant Random Variable Stream Generator")
{
}

void
ConstantTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    Ptr<ConstantRandomVariable> c = CreateObject<ConstantRandomVariable>();

    double constant;

    // Test that the constant value can be changed using its attribute.
    constant = 10.0;
    c->SetAttribute("Constant", DoubleValue(constant));
    NS_TEST_ASSERT_MSG_EQ_TOL(c->GetValue(), constant, TOLERANCE, "Constant value changed");
    c->SetAttribute("Constant", DoubleValue(20.0));
    NS_TEST_ASSERT_MSG_NE(c->GetValue(), constant, "Constant value not changed");

    // Test that the constant value does not change.
    constant = c->GetValue();
    for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
    {
        NS_TEST_ASSERT_MSG_EQ_TOL(c->GetValue(),
                                  constant,
                                  TOLERANCE,
                                  "Constant value changed in loop");
    }
}

/**
 * \ingroup rng-tests
 * Test case for sequential random variable stream generator
 */
class SequentialTestCase : public TestCaseBase
{
  public:
    // Constructor
    SequentialTestCase();

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation. */
    static constexpr double TOLERANCE{1e-8};
};

SequentialTestCase::SequentialTestCase()
    : TestCaseBase("Sequential Random Variable Stream Generator")
{
}

void
SequentialTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    Ptr<SequentialRandomVariable> s = CreateObject<SequentialRandomVariable>();

    // The following four attributes should give the sequence
    //
    //    4, 4, 7, 7, 10, 10
    //
    s->SetAttribute("Min", DoubleValue(4));
    s->SetAttribute("Max", DoubleValue(11));
    s->SetAttribute("Increment", StringValue("ns3::UniformRandomVariable[Min=3.0|Max=3.0]"));
    s->SetAttribute("Consecutive", IntegerValue(2));

    double value;

    // Test that the sequencet is correct.
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 4, TOLERANCE, "Sequence value 1 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 4, TOLERANCE, "Sequence value 2 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 7, TOLERANCE, "Sequence value 3 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 7, TOLERANCE, "Sequence value 4 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 10, TOLERANCE, "Sequence value 5 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 10, TOLERANCE, "Sequence value 6 wrong.");
}

/**
 * \ingroup rng-tests
 * Test case for normal distribution random variable stream generator
 */
class NormalTestCase : public TestCaseBase
{
  public:
    // Constructor
    NormalTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation, in rms. */
    static constexpr double TOLERANCE{5};
};

NormalTestCase::NormalTestCase()
    : TestCaseBase("Normal Random Variable Stream Generator")
{
}

double
NormalTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, -4., 4.);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has mean equal to zero and standard
    // deviation equal to one, which are their default values for this
    // distribution.
    double sigma = 1.;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_gaussian_P(range[i + 1], sigma) - gsl_cdf_gaussian_P(range[i], sigma);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);
    gsl_histogram_free(h);
    return chiSquared;
}

void
NormalTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<NormalRandomVariable>();
    auto rng = generator.Create();

    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mean = 5.0;
    double variance = 2.0;

    // Create the RNG with the specified range.
    Ptr<NormalRandomVariable> x = CreateObject<NormalRandomVariable>();
    x->SetAttribute("Mean", DoubleValue(mean));
    x->SetAttribute("Variance", DoubleValue(variance));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // normally distributed random variable is equal to mean.
    double expectedMean = mean;
    double expectedRms = mean / std::sqrt(variance * N_MEASUREMENTS);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedRms * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic normal distribution random variable stream generator
 */
class NormalAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    NormalAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation, in rms. */
    static constexpr double TOLERANCE{5};
};

NormalAntitheticTestCase::NormalAntitheticTestCase()
    : TestCaseBase("Antithetic Normal Random Variable Stream Generator")
{
}

double
NormalAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, -4, 4);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has mean equal to zero and standard
    // deviation equal to one, which are their default values for this
    // distribution.
    double sigma = 1.;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_gaussian_P(range[i + 1], sigma) - gsl_cdf_gaussian_P(range[i], sigma);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
NormalAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<NormalRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mean = 5.0;
    double variance = 2.0;

    // Create the RNG with the specified range.
    Ptr<NormalRandomVariable> x = CreateObject<NormalRandomVariable>();
    x->SetAttribute("Mean", DoubleValue(mean));
    x->SetAttribute("Variance", DoubleValue(variance));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // normally distributed random variable is equal to mean.
    double expectedMean = mean;
    double expectedRms = mean / std::sqrt(variance * N_MEASUREMENTS);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedRms * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for exponential distribution random variable stream generator
 */
class ExponentialTestCase : public TestCaseBase
{
  public:
    // Constructor
    ExponentialTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation, in rms. */
    static constexpr double TOLERANCE{5};
};

ExponentialTestCase::ExponentialTestCase()
    : TestCaseBase("Exponential Random Variable Stream Generator")
{
}

double
ExponentialTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that e has mean equal to one, which is the
    // default value for this distribution.
    double mu = 1.;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_exponential_P(range[i + 1], mu) - gsl_cdf_exponential_P(range[i], mu);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ExponentialTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ExponentialRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mean = 3.14;
    double bound = 0.0;

    // Create the RNG with the specified range.
    Ptr<ExponentialRandomVariable> x = CreateObject<ExponentialRandomVariable>();
    x->SetAttribute("Mean", DoubleValue(mean));
    x->SetAttribute("Bound", DoubleValue(bound));

    // Calculate the mean of these values.
    double valueMean = Average(x);
    double expectedMean = mean;
    double expectedRms = std::sqrt(mean / N_MEASUREMENTS);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedRms * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic exponential distribution random variable stream generator
 */
class ExponentialAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    ExponentialAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation, in rms. */
    static constexpr double TOLERANCE{5};
};

ExponentialAntitheticTestCase::ExponentialAntitheticTestCase()
    : TestCaseBase("Antithetic Exponential Random Variable Stream Generator")
{
}

double
ExponentialAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that e has mean equal to one, which is the
    // default value for this distribution.
    double mu = 1.;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_exponential_P(range[i + 1], mu) - gsl_cdf_exponential_P(range[i], mu);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ExponentialAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ExponentialRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mean = 3.14;
    double bound = 0.0;

    // Create the RNG with the specified range.
    Ptr<ExponentialRandomVariable> x = CreateObject<ExponentialRandomVariable>();
    x->SetAttribute("Mean", DoubleValue(mean));
    x->SetAttribute("Bound", DoubleValue(bound));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);
    double expectedMean = mean;
    double expectedRms = std::sqrt(mean / N_MEASUREMENTS);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedRms * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for Pareto distribution random variable stream generator
 */
class ParetoTestCase : public TestCaseBase
{
  public:
    // Constructor
    ParetoTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ParetoTestCase::ParetoTestCase()
    : TestCaseBase("Pareto Random Variable Stream Generator")
{
}

double
ParetoTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 1, 10, false);

    std::vector<double> expected(N_BINS);

    double shape = 2.0;
    double scale = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_pareto_P(range[i + 1], shape, scale) - gsl_cdf_pareto_P(range[i], shape, scale);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ParetoTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ParetoRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double shape = 2.0;
    double scale = 1.0;

    // Create the RNG with the specified range.
    Ptr<ParetoRandomVariable> x = CreateObject<ParetoRandomVariable>();
    x->SetAttribute("Shape", DoubleValue(shape));
    x->SetAttribute("Scale", DoubleValue(scale));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean is given by
    //
    //                   shape * scale
    //     E[value]  =  ---------------  ,
    //                     shape - 1
    //
    // where
    //
    //     scale  =  mean * (shape - 1.0) / shape .
    double expectedMean = (shape * scale) / (shape - 1.0);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic Pareto distribution random variable stream generator
 */
class ParetoAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    ParetoAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ParetoAntitheticTestCase::ParetoAntitheticTestCase()
    : TestCaseBase("Antithetic Pareto Random Variable Stream Generator")
{
}

double
ParetoAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 1, 10, false);

    std::vector<double> expected(N_BINS);

    double shape = 2.0;
    double scale = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_pareto_P(range[i + 1], shape, scale) - gsl_cdf_pareto_P(range[i], shape, scale);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ParetoAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ParetoRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double shape = 2.0;
    double scale = 1.0;

    // Create the RNG with the specified range.
    Ptr<ParetoRandomVariable> x = CreateObject<ParetoRandomVariable>();
    x->SetAttribute("Shape", DoubleValue(shape));
    x->SetAttribute("Scale", DoubleValue(scale));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean is given by
    //
    //                   shape * scale
    //     E[value]  =  ---------------  ,
    //                     shape - 1
    //
    // where
    //
    //     scale  =  mean * (shape - 1.0) / shape .
    //
    double expectedMean = (shape * scale) / (shape - 1.0);

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for Weibull distribution random variable stream generator
 */
class WeibullTestCase : public TestCaseBase
{
  public:
    // Constructor
    WeibullTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

WeibullTestCase::WeibullTestCase()
    : TestCaseBase("Weibull Random Variable Stream Generator")
{
}

double
WeibullTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 1, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that p has shape equal to one and scale
    // equal to one, which are their default values for this
    // distribution.
    double a = 1.0;
    double b = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_weibull_P(range[i + 1], a, b) - gsl_cdf_weibull_P(range[i], a, b);
        expected[i] *= N_MEASUREMENTS;
        NS_LOG_INFO("weibull: " << expected[i]);
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
WeibullTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<WeibullRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double scale = 5.0;
    double shape = 1.0;

    // Create the RNG with the specified range.
    Ptr<WeibullRandomVariable> x = CreateObject<WeibullRandomVariable>();
    x->SetAttribute("Scale", DoubleValue(scale));
    x->SetAttribute("Shape", DoubleValue(shape));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Weibull distributed random variable is
    //
    //     E[value]  =  scale * Gamma(1 + 1 / shape)  ,
    //
    // where Gamma() is the Gamma function.  Note that
    //
    //     Gamma(n)  =  (n - 1)!
    //
    // if n is a positive integer.
    //
    // For this test,
    //
    //     Gamma(1 + 1 / shape)  =  Gamma(1 + 1 / 1)
    //                           =  Gamma(2)
    //                           =  (2 - 1)!
    //                           =  1
    //
    // which means
    //
    //     E[value]  =  scale  .
    //
    double expectedMean = scale;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic Weibull distribution random variable stream generator
 */
class WeibullAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    WeibullAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

WeibullAntitheticTestCase::WeibullAntitheticTestCase()
    : TestCaseBase("Antithetic Weibull Random Variable Stream Generator")
{
}

double
WeibullAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 1, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that p has shape equal to one and scale
    // equal to one, which are their default values for this
    // distribution.
    double a = 1.0;
    double b = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] = gsl_cdf_weibull_P(range[i + 1], a, b) - gsl_cdf_weibull_P(range[i], a, b);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
WeibullAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<WeibullRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double scale = 5.0;
    double shape = 1.0;

    // Create the RNG with the specified range.
    Ptr<WeibullRandomVariable> x = CreateObject<WeibullRandomVariable>();
    x->SetAttribute("Scale", DoubleValue(scale));
    x->SetAttribute("Shape", DoubleValue(shape));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Weibull distributed random variable is
    //
    //     E[value]  =  scale * Gamma(1 + 1 / shape)  ,
    //
    // where Gamma() is the Gamma function.  Note that
    //
    //     Gamma(n)  =  (n - 1)!
    //
    // if n is a positive integer.
    //
    // For this test,
    //
    //     Gamma(1 + 1 / shape)  =  Gamma(1 + 1 / 1)
    //                           =  Gamma(2)
    //                           =  (2 - 1)!
    //                           =  1
    //
    // which means
    //
    //     E[value]  =  scale  .
    //
    double expectedMean = scale;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for log-normal distribution random variable stream generator
 */
class LogNormalTestCase : public TestCaseBase
{
  public:
    // Constructor
    LogNormalTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{3e-2};
};

LogNormalTestCase::LogNormalTestCase()
    : TestCaseBase("Log-Normal Random Variable Stream Generator")
{
}

double
LogNormalTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has mu equal to zero and sigma
    // equal to one, which are their default values for this
    // distribution.
    double mu = 0.0;
    double sigma = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_lognormal_P(range[i + 1], mu, sigma) - gsl_cdf_lognormal_P(range[i], mu, sigma);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
LogNormalTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<LogNormalRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);

    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mu = 5.0;
    double sigma = 2.0;

    // Create the RNG with the specified range.
    Ptr<LogNormalRandomVariable> x = CreateObject<LogNormalRandomVariable>();
    x->SetAttribute("Mu", DoubleValue(mu));
    x->SetAttribute("Sigma", DoubleValue(sigma));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // log-normally distributed random variable is equal to
    //
    //                             2
    //                   mu + sigma  / 2
    //     E[value]  =  e                 .
    //
    double expectedMean = std::exp(mu + sigma * sigma / 2.0);

    // Test that values have approximately the right mean value.
    //
    /**
     * \todo This test fails sometimes if the required tolerance is less
     * than 3%, which may be because there is a bug in the
     * implementation or that the mean of this distribution is more
     * sensitive to its parameters than the others are.
     */
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic log-normal distribution random variable stream generator
 */
class LogNormalAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    LogNormalAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{3e-2};
};

LogNormalAntitheticTestCase::LogNormalAntitheticTestCase()
    : TestCaseBase("Antithetic Log-Normal Random Variable Stream Generator")
{
}

double
LogNormalAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has mu equal to zero and sigma
    // equal to one, which are their default values for this
    // distribution.
    double mu = 0.0;
    double sigma = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_lognormal_P(range[i + 1], mu, sigma) - gsl_cdf_lognormal_P(range[i], mu, sigma);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
LogNormalAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<LogNormalRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double mu = 5.0;
    double sigma = 2.0;

    // Create the RNG with the specified range.
    Ptr<LogNormalRandomVariable> x = CreateObject<LogNormalRandomVariable>();
    x->SetAttribute("Mu", DoubleValue(mu));
    x->SetAttribute("Sigma", DoubleValue(sigma));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // log-normally distributed random variable is equal to
    //
    //                             2
    //                   mu + sigma  / 2
    //     E[value]  =  e                 .
    //
    double expectedMean = std::exp(mu + sigma * sigma / 2.0);

    // Test that values have approximately the right mean value.
    //
    /**
     * \todo This test fails sometimes if the required tolerance is less
     * than 3%, which may be because there is a bug in the
     * implementation or that the mean of this distribution is more
     * sensitive to its parameters than the others are.
     */
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for gamma distribution random variable stream generator
 */
class GammaTestCase : public TestCaseBase
{
  public:
    // Constructor
    GammaTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

GammaTestCase::GammaTestCase()
    : TestCaseBase("Gamma Random Variable Stream Generator")
{
}

double
GammaTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has alpha equal to one and beta
    // equal to one, which are their default values for this
    // distribution.
    double alpha = 1.0;
    double beta = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_gamma_P(range[i + 1], alpha, beta) - gsl_cdf_gamma_P(range[i], alpha, beta);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
GammaTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<GammaRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double alpha = 5.0;
    double beta = 2.0;

    // Create the RNG with the specified range.
    Ptr<GammaRandomVariable> x = CreateObject<GammaRandomVariable>();
    x->SetAttribute("Alpha", DoubleValue(alpha));
    x->SetAttribute("Beta", DoubleValue(beta));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // gammaly distributed random variable is equal to
    //
    //     E[value]  =  alpha * beta  .
    //
    double expectedMean = alpha * beta;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic gamma distribution random variable stream generator
 */
class GammaAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    GammaAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

GammaAntitheticTestCase::GammaAntitheticTestCase()
    : TestCaseBase("Antithetic Gamma Random Variable Stream Generator")
{
}

double
GammaAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has alpha equal to one and beta
    // equal to one, which are their default values for this
    // distribution.
    double alpha = 1.0;
    double beta = 1.0;

    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_gamma_P(range[i + 1], alpha, beta) - gsl_cdf_gamma_P(range[i], alpha, beta);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
GammaAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<GammaRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    double alpha = 5.0;
    double beta = 2.0;

    // Create the RNG with the specified range.
    Ptr<GammaRandomVariable> x = CreateObject<GammaRandomVariable>();

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    x->SetAttribute("Alpha", DoubleValue(alpha));
    x->SetAttribute("Beta", DoubleValue(beta));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // gammaly distributed random variable is equal to
    //
    //     E[value]  =  alpha * beta  .
    //
    double expectedMean = alpha * beta;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for Erlang distribution random variable stream generator
 */
class ErlangTestCase : public TestCaseBase
{
  public:
    // Constructor
    ErlangTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ErlangTestCase::ErlangTestCase()
    : TestCaseBase("Erlang Random Variable Stream Generator")
{
}

double
ErlangTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has k equal to one and lambda
    // equal to one, which are their default values for this
    // distribution.
    uint32_t k = 1;
    double lambda = 1.0;

    // Note that Erlang distribution is equal to the gamma distribution
    // when k is an integer, which is why the gamma distribution's cdf
    // function can be used here.
    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_gamma_P(range[i + 1], k, lambda) - gsl_cdf_gamma_P(range[i], k, lambda);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ErlangTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ErlangRandomVariable>();
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    uint32_t k = 5;
    double lambda = 2.0;

    // Create the RNG with the specified range.
    Ptr<ErlangRandomVariable> x = CreateObject<ErlangRandomVariable>();
    x->SetAttribute("K", IntegerValue(k));
    x->SetAttribute("Lambda", DoubleValue(lambda));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Erlangly distributed random variable is equal to
    //
    //     E[value]  =  k * lambda  .
    //
    double expectedMean = k * lambda;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic Erlang distribution random variable stream generator
 */
class ErlangAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    ErlangAntitheticTestCase();

    // Inherited
    double ChiSquaredTest(Ptr<RandomVariableStream> rng) const override;

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ErlangAntitheticTestCase::ErlangAntitheticTestCase()
    : TestCaseBase("Antithetic Erlang Random Variable Stream Generator")
{
}

double
ErlangAntitheticTestCase::ChiSquaredTest(Ptr<RandomVariableStream> rng) const
{
    gsl_histogram* h = gsl_histogram_alloc(N_BINS);
    auto range = UniformHistogramBins(h, 0, 10, false);

    std::vector<double> expected(N_BINS);

    // Note that this assumes that n has k equal to one and lambda
    // equal to one, which are their default values for this
    // distribution.
    uint32_t k = 1;
    double lambda = 1.0;

    // Note that Erlang distribution is equal to the gamma distribution
    // when k is an integer, which is why the gamma distribution's cdf
    // function can be used here.
    for (std::size_t i = 0; i < N_BINS; ++i)
    {
        expected[i] =
            gsl_cdf_gamma_P(range[i + 1], k, lambda) - gsl_cdf_gamma_P(range[i], k, lambda);
        expected[i] *= N_MEASUREMENTS;
    }

    double chiSquared = ChiSquared(h, expected, rng);

    gsl_histogram_free(h);
    return chiSquared;
}

void
ErlangAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    auto generator = RngGenerator<ErlangRandomVariable>(true);
    double sum = ChiSquaredsAverage(&generator, N_RUNS);
    double maxStatistic = gsl_cdf_chisq_Qinv(0.05, N_BINS);
    NS_TEST_ASSERT_MSG_LT(sum, maxStatistic, "Chi-squared statistic out of range");

    uint32_t k = 5;
    double lambda = 2.0;

    // Create the RNG with the specified range.
    Ptr<ErlangRandomVariable> x = CreateObject<ErlangRandomVariable>();

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    x->SetAttribute("K", IntegerValue(k));
    x->SetAttribute("Lambda", DoubleValue(lambda));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Erlangly distributed random variable is equal to
    //
    //     E[value]  =  k * lambda  .
    //
    double expectedMean = k * lambda;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for Zipf distribution random variable stream generator
 */
class ZipfTestCase : public TestCaseBase
{
  public:
    // Constructor
    ZipfTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ZipfTestCase::ZipfTestCase()
    : TestCaseBase("Zipf Random Variable Stream Generator")
{
}

void
ZipfTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    uint32_t n = 1;
    double alpha = 2.0;

    // Create the RNG with the specified range.
    Ptr<ZipfRandomVariable> x = CreateObject<ZipfRandomVariable>();
    x->SetAttribute("N", IntegerValue(n));
    x->SetAttribute("Alpha", DoubleValue(alpha));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Zipfly distributed random variable is equal to
    //
    //                   H
    //                    N, alpha - 1
    //     E[value]  =  ---------------
    //                     H
    //                      N, alpha
    //
    // where
    //
    //                    N
    //                   ---
    //                   \     -alpha
    //     H          =  /    m        .
    //      N, alpha     ---
    //                   m=1
    //
    // For this test,
    //
    //                      -(alpha - 1)
    //                     1
    //     E[value]  =  ---------------
    //                      -alpha
    //                     1
    //
    //               =  1  .
    //
    double expectedMean = 1.0;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic Zipf distribution random variable stream generator
 */
class ZipfAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    ZipfAntitheticTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ZipfAntitheticTestCase::ZipfAntitheticTestCase()
    : TestCaseBase("Antithetic Zipf Random Variable Stream Generator")
{
}

void
ZipfAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    uint32_t n = 1;
    double alpha = 2.0;

    // Create the RNG with the specified range.
    Ptr<ZipfRandomVariable> x = CreateObject<ZipfRandomVariable>();
    x->SetAttribute("N", IntegerValue(n));
    x->SetAttribute("Alpha", DoubleValue(alpha));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // Zipfly distributed random variable is equal to
    //
    //                   H
    //                    N, alpha - 1
    //     E[value]  =  ---------------
    //                     H
    //                      N, alpha
    //
    // where
    //
    //                    N
    //                   ---
    //                   \     -alpha
    //     H          =  /    m        .
    //      N, alpha     ---
    //                   m=1
    //
    // For this test,
    //
    //                      -(alpha - 1)
    //                     1
    //     E[value]  =  ---------------
    //                      -alpha
    //                     1
    //
    //               =  1  .
    //
    double expectedMean = 1.0;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for Zeta distribution random variable stream generator
 */
class ZetaTestCase : public TestCaseBase
{
  public:
    // Constructor
    ZetaTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ZetaTestCase::ZetaTestCase()
    : TestCaseBase("Zeta Random Variable Stream Generator")
{
}

void
ZetaTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    double alpha = 5.0;

    // Create the RNG with the specified range.
    Ptr<ZetaRandomVariable> x = CreateObject<ZetaRandomVariable>();
    x->SetAttribute("Alpha", DoubleValue(alpha));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // zetaly distributed random variable is equal to
    //
    //                   zeta(alpha - 1)
    //     E[value]  =  ---------------   for alpha > 2 ,
    //                     zeta(alpha)
    //
    // where zeta(alpha) is the Riemann zeta function.
    //
    // There are no simple analytic forms for the Riemann zeta function,
    // which is why the gsl library is used in this test to calculate
    // the known mean of the values.
    double expectedMean =
        gsl_sf_zeta_int(static_cast<int>(alpha - 1)) / gsl_sf_zeta_int(static_cast<int>(alpha));

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic Zeta distribution random variable stream generator
 */
class ZetaAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    ZetaAntitheticTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

ZetaAntitheticTestCase::ZetaAntitheticTestCase()
    : TestCaseBase("Antithetic Zeta Random Variable Stream Generator")
{
}

void
ZetaAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    double alpha = 5.0;

    // Create the RNG with the specified range.
    Ptr<ZetaRandomVariable> x = CreateObject<ZetaRandomVariable>();
    x->SetAttribute("Alpha", DoubleValue(alpha));

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Calculate the mean of these values.
    double valueMean = Average(x);

    // The expected value for the mean of the values returned by a
    // zetaly distributed random variable is equal to
    //
    //                   zeta(alpha - 1)
    //     E[value]  =  ---------------   for alpha > 2 ,
    //                     zeta(alpha)
    //
    // where zeta(alpha) is the Riemann zeta function.
    //
    // There are no simple analytic forms for the Riemann zeta function,
    // which is why the gsl library is used in this test to calculate
    // the known mean of the values.
    double expectedMean =
        gsl_sf_zeta_int(static_cast<int>(alpha) - 1) / gsl_sf_zeta_int(static_cast<int>(alpha));

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for deterministic random variable stream generator
 */
class DeterministicTestCase : public TestCaseBase
{
  public:
    // Constructor
    DeterministicTestCase();

  private:
    // Inherited
    void DoRun() override;

    /** Tolerance for testing rng values against expectation. */
    static constexpr double TOLERANCE{1e-8};
};

DeterministicTestCase::DeterministicTestCase()
    : TestCaseBase("Deterministic Random Variable Stream Generator")
{
}

void
DeterministicTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    Ptr<DeterministicRandomVariable> s = CreateObject<DeterministicRandomVariable>();

    // The following array should give the sequence
    //
    //    4, 4, 7, 7, 10, 10 .
    //
    double array1[] = {4, 4, 7, 7, 10, 10};
    std::size_t count1 = 6;
    s->SetValueArray(array1, count1);

    double value;

    // Test that the first sequence is correct.
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 4, TOLERANCE, "Sequence 1 value 1 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 4, TOLERANCE, "Sequence 1 value 2 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 7, TOLERANCE, "Sequence 1 value 3 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 7, TOLERANCE, "Sequence 1 value 4 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 10, TOLERANCE, "Sequence 1 value 5 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 10, TOLERANCE, "Sequence 1 value 6 wrong.");

    // The following array should give the sequence
    //
    //    1000, 2000, 7, 7 .
    //
    double array2[] = {1000, 2000, 3000, 4000};
    std::size_t count2 = 4;
    s->SetValueArray(array2, count2);

    // Test that the second sequence is correct.
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 1000, TOLERANCE, "Sequence 2 value 1 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 2000, TOLERANCE, "Sequence 2 value 2 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 3000, TOLERANCE, "Sequence 2 value 3 wrong.");
    value = s->GetValue();
    NS_TEST_ASSERT_MSG_EQ_TOL(value, 4000, TOLERANCE, "Sequence 2 value 4 wrong.");
    value = s->GetValue();
}

/**
 * \ingroup rng-tests
 * Test case for empirical distribution random variable stream generator
 */
class EmpiricalTestCase : public TestCaseBase
{
  public:
    // Constructor
    EmpiricalTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

EmpiricalTestCase::EmpiricalTestCase()
    : TestCaseBase("Empirical Random Variable Stream Generator")
{
}

void
EmpiricalTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    // Create the RNG with a uniform distribution between 0 and 10.
    Ptr<EmpiricalRandomVariable> x = CreateObject<EmpiricalRandomVariable>();
    x->SetInterpolate(false);
    x->CDF(0.0, 0.0);
    x->CDF(5.0, 0.25);
    x->CDF(10.0, 1.0);

    // Check that only the correct values are returned
    for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
    {
        double value = x->GetValue();
        NS_TEST_EXPECT_MSG_EQ((value == 5) || (value == 10),
                              true,
                              "Incorrect value returned, expected only 5 or 10.");
    }

    // Calculate the mean of the sampled values.
    double valueMean = Average(x);

    // The expected distribution with sampled values is
    //     Value     Probability
    //      5        25%
    //     10        75%
    //
    // The expected mean is
    //
    //     E[value]  =  5 * 25%  +  10 * 75%  =  8.75
    //
    // Test that values have approximately the right mean value.
    double expectedMean = 8.75;
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");

    // Calculate the mean of the interpolated values.
    x->SetInterpolate(true);
    valueMean = Average(x);

    // The expected distribution (with interpolation) is
    //     Bin     Probability
    //     [0, 5)     25%
    //     [5, 10)    75%
    //
    // Each bin is uniformly sampled, so the average of the samples in the
    // bin is the center of the bin.
    //
    // The expected mean is
    //
    //     E[value]  =  2.5 * 25% + 7.5 * 75% = 6.25
    //
    expectedMean = 6.25;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");

    // Bug 2082: Create the RNG with a uniform distribution between -1 and 1.
    Ptr<EmpiricalRandomVariable> y = CreateObject<EmpiricalRandomVariable>();
    y->SetInterpolate(false);
    y->CDF(-1.0, 0.0);
    y->CDF(0.0, 0.5);
    y->CDF(1.0, 1.0);
    NS_TEST_ASSERT_MSG_LT(y->GetValue(), 2, "Empirical variable with negative domain");
}

/**
 * \ingroup rng-tests
 * Test case for antithetic empirical distribution random variable stream generator
 */
class EmpiricalAntitheticTestCase : public TestCaseBase
{
  public:
    // Constructor
    EmpiricalAntitheticTestCase();

  private:
    // Inherited
    void DoRun() override;

    /**
     * Tolerance for testing rng values against expectation,
     * as a fraction of mean value.
     */
    static constexpr double TOLERANCE{1e-2};
};

EmpiricalAntitheticTestCase::EmpiricalAntitheticTestCase()
    : TestCaseBase("EmpiricalAntithetic Random Variable Stream Generator")
{
}

void
EmpiricalAntitheticTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    // Create the RNG with a uniform distribution between 0 and 10.
    Ptr<EmpiricalRandomVariable> x = CreateObject<EmpiricalRandomVariable>();
    x->SetInterpolate(false);
    x->CDF(0.0, 0.0);
    x->CDF(5.0, 0.25);
    x->CDF(10.0, 1.0);

    // Make this generate antithetic values.
    x->SetAttribute("Antithetic", BooleanValue(true));

    // Check that only the correct values are returned
    for (uint32_t i = 0; i < N_MEASUREMENTS; ++i)
    {
        double value = x->GetValue();
        NS_TEST_EXPECT_MSG_EQ((value == 5) || (value == 10),
                              true,
                              "Incorrect value returned, expected only 5 or 10.");
    }

    // Calculate the mean of these values.
    double valueMean = Average(x);
    // Expected
    //    E[value] = 5 * 25%  + 10 * 75%  = 8.75
    double expectedMean = 8.75;
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");

    // Check interpolated sampling
    x->SetInterpolate(true);
    valueMean = Average(x);

    // The expected value for the mean of the values returned by this
    // empirical distribution with interpolation is
    //
    //     E[value]  =  2.5 * 25% + 7.5 * 75% = 6.25
    //
    expectedMean = 6.25;

    // Test that values have approximately the right mean value.
    NS_TEST_ASSERT_MSG_EQ_TOL(valueMean,
                              expectedMean,
                              expectedMean * TOLERANCE,
                              "Wrong mean value.");
}

/**
 * \ingroup rng-tests
 * Test case for caching of Normal RV parameters (see issue #302)
 */
class NormalCachingTestCase : public TestCaseBase
{
  public:
    // Constructor
    NormalCachingTestCase();

  private:
    // Inherited
    void DoRun() override;
};

NormalCachingTestCase::NormalCachingTestCase()
    : TestCaseBase("NormalRandomVariable caching of parameters")
{
}

void
NormalCachingTestCase::DoRun()
{
    NS_LOG_FUNCTION(this);
    SetTestSuiteSeed();

    Ptr<NormalRandomVariable> n = CreateObject<NormalRandomVariable>();
    double v1 = n->GetValue(-10, 1, 10); // Mean -10, variance 1, bounded to [-20,0]
    double v2 = n->GetValue(10, 1, 10);  // Mean 10, variance 1, bounded to [0,20]

    NS_TEST_ASSERT_MSG_LT(v1, 0, "Incorrect value returned, expected < 0");
    NS_TEST_ASSERT_MSG_GT(v2, 0, "Incorrect value returned, expected > 0");
}

/**
 * \ingroup rng-tests
 * RandomVariableStream test suite, covering all random number variable
 * stream generator types.
 */
class RandomVariableSuite : public TestSuite
{
  public:
    // Constructor
    RandomVariableSuite();
};

RandomVariableSuite::RandomVariableSuite()
    : TestSuite("random-variable-stream-generators", UNIT)
{
    AddTestCase(new UniformTestCase);
    AddTestCase(new UniformAntitheticTestCase);
    AddTestCase(new ConstantTestCase);
    AddTestCase(new SequentialTestCase);
    AddTestCase(new NormalTestCase);
    AddTestCase(new NormalAntitheticTestCase);
    AddTestCase(new ExponentialTestCase);
    AddTestCase(new ExponentialAntitheticTestCase);
    AddTestCase(new ParetoTestCase);
    AddTestCase(new ParetoAntitheticTestCase);
    AddTestCase(new WeibullTestCase);
    AddTestCase(new WeibullAntitheticTestCase);
    AddTestCase(new LogNormalTestCase);
    /// \todo This test is currently disabled because it fails sometimes.
    /// A possible reason for the failure is that the antithetic code is
    /// not implemented properly for this log-normal case.
    /*
    AddTestCase (new LogNormalAntitheticTestCase);
    */
    AddTestCase(new GammaTestCase);
    /// \todo This test is currently disabled because it fails sometimes.
    /// A possible reason for the failure is that the antithetic code is
    /// not implemented properly for this gamma case.
    /*
    AddTestCase (new GammaAntitheticTestCase);
    */
    AddTestCase(new ErlangTestCase);
    AddTestCase(new ErlangAntitheticTestCase);
    AddTestCase(new ZipfTestCase);
    AddTestCase(new ZipfAntitheticTestCase);
    AddTestCase(new ZetaTestCase);
    AddTestCase(new ZetaAntitheticTestCase);
    AddTestCase(new DeterministicTestCase);
    AddTestCase(new EmpiricalTestCase);
    AddTestCase(new EmpiricalAntitheticTestCase);
    /// Issue #302:  NormalRandomVariable produces stale values
    AddTestCase(new NormalCachingTestCase);
}

static RandomVariableSuite randomVariableSuite; //!< Static variable for test initialization

} // namespace RandomVariable

} // namespace test

} // namespace ns3
