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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.commons.math3.distribution;
+
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.OutOfRangeException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.util.CombinatoricsUtils;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.ResizableDoubleArray;
+
+/**
+ * Implementation of the exponential distribution.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Exponential distribution
+ *     (Wikipedia)</a>
+ * @see <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">Exponential distribution
+ *     (MathWorld)</a>
+ */
+public class ExponentialDistribution extends AbstractRealDistribution {
+    /**
+     * Default inverse cumulative probability accuracy.
+     *
+     * @since 2.1
+     */
+    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
+
+    /** Serializable version identifier */
+    private static final long serialVersionUID = 2401296428283614780L;
+
+    /**
+     * Used when generating Exponential samples. Table containing the constants q_i = sum_{j=1}^i
+     * (ln 2)^j/j! = ln 2 + (ln 2)^2/2 + ... + (ln 2)^i/i! until the largest representable fraction
+     * below 1 is exceeded.
+     *
+     * <p>Note that 1 = 2 - 1 = exp(ln 2) - 1 = sum_{n=1}^infty (ln 2)^n / n! thus q_i -> 1 as i ->
+     * +inf, so the higher i, the closer to one we get (the series is not alternating).
+     *
+     * <p>By trying, n = 16 in Java is enough to reach 1.0.
+     */
+    private static final double[] EXPONENTIAL_SA_QI;
+
+    /** The mean of this distribution. */
+    private final double mean;
+
+    /** The logarithm of the mean, stored to reduce computing time. * */
+    private final double logMean;
+
+    /** Inverse cumulative probability accuracy. */
+    private final double solverAbsoluteAccuracy;
+
+    /** Initialize tables. */
+    static {
+        /** Filling EXPONENTIAL_SA_QI table. Note that we don't want qi = 0 in the table. */
+        final double LN2 = FastMath.log(2);
+        double qi = 0;
+        int i = 1;
+
+        /**
+         * ArithmeticUtils provides factorials up to 20, so let's use that limit together with
+         * Precision.EPSILON to generate the following code (a priori, we know that there will be 16
+         * elements, but it is better to not hardcode it).
+         */
+        final ResizableDoubleArray ra = new ResizableDoubleArray(20);
+
+        while (qi < 1) {
+            qi += FastMath.pow(LN2, i) / CombinatoricsUtils.factorial(i);
+            ra.addElement(qi);
+            ++i;
+        }
+
+        EXPONENTIAL_SA_QI = ra.getElements();
+    }
+
+    /**
+     * Create an exponential distribution with the given mean.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param mean mean of this distribution.
+     */
+    public ExponentialDistribution(double mean) {
+        this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Create an exponential distribution with the given mean.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param mean Mean of this distribution.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code mean <= 0}.
+     * @since 2.1
+     */
+    public ExponentialDistribution(double mean, double inverseCumAccuracy) {
+        this(new Well19937c(), mean, inverseCumAccuracy);
+    }
+
+    /**
+     * Creates an exponential distribution.
+     *
+     * @param rng Random number generator.
+     * @param mean Mean of this distribution.
+     * @throws NotStrictlyPositiveException if {@code mean <= 0}.
+     * @since 3.3
+     */
+    public ExponentialDistribution(RandomGenerator rng, double mean)
+            throws NotStrictlyPositiveException {
+        this(rng, mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Creates an exponential distribution.
+     *
+     * @param rng Random number generator.
+     * @param mean Mean of this distribution.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code mean <= 0}.
+     * @since 3.1
+     */
+    public ExponentialDistribution(RandomGenerator rng, double mean, double inverseCumAccuracy)
+            throws NotStrictlyPositiveException {
+        super(rng);
+
+        if (mean <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);
+        }
+        this.mean = mean;
+        logMean = FastMath.log(mean);
+        solverAbsoluteAccuracy = inverseCumAccuracy;
+    }
+
+    /**
+     * Access the mean.
+     *
+     * @return the mean.
+     */
+    public double getMean() {
+        return mean;
+    }
+
+    /** {@inheritDoc} */
+    public double density(double x) {
+        final double logDensity = logDensity(x);
+        return logDensity == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logDensity);
+    }
+
+    /** {@inheritDoc} * */
+    @Override
+    public double logDensity(double x) {
+        if (x < 0) {
+            return Double.NEGATIVE_INFINITY;
+        }
+        return -x / mean - logMean;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The implementation of this method is based on:
+     *
+     * <ul>
+     *   <li><a href="http://mathworld.wolfram.com/ExponentialDistribution.html">Exponential
+     *       Distribution</a>, equation (1).
+     * </ul>
+     */
+    public double cumulativeProbability(double x) {
+        double ret;
+        if (x <= 0.0) {
+            ret = 0.0;
+        } else {
+            ret = 1.0 - FastMath.exp(-x / mean);
+        }
+        return ret;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>Returns {@code 0} when {@code p= = 0} and {@code Double.POSITIVE_INFINITY} when {@code p
+     * == 1}.
+     */
+    @Override
+    public double inverseCumulativeProbability(double p) throws OutOfRangeException {
+        double ret;
+
+        if (p < 0.0 || p > 1.0) {
+            throw new OutOfRangeException(p, 0.0, 1.0);
+        } else if (p == 1.0) {
+            ret = Double.POSITIVE_INFINITY;
+        } else {
+            ret = -mean * FastMath.log(1.0 - p);
+        }
+
+        return ret;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p><strong>Algorithm Description</strong>: this implementation uses the <a
+     * href="http://www.jesus.ox.ac.uk/~clifford/a5/chap1/node5.html">Inversion Method</a> to
+     * generate exponentially distributed random values from uniform deviates.
+     *
+     * @return a random value.
+     * @since 2.2
+     */
+    @Override
+    public double sample() {
+        // Step 1:
+        double a = 0;
+        double u = random.nextDouble();
+
+        // Step 2 and 3:
+        while (u < 0.5) {
+            a += EXPONENTIAL_SA_QI[0];
+            u *= 2;
+        }
+
+        // Step 4 (now u >= 0.5):
+        u += u - 1;
+
+        // Step 5:
+        if (u <= EXPONENTIAL_SA_QI[0]) {
+            return mean * (a + u);
+        }
+
+        // Step 6:
+        int i = 0; // Should be 1, be we iterate before it in while using 0
+        double u2 = random.nextDouble();
+        double umin = u2;
+
+        // Step 7 and 8:
+        do {
+            ++i;
+            u2 = random.nextDouble();
+
+            if (u2 < umin) {
+                umin = u2;
+            }
+
+            // Step 8:
+        } while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1
+
+        return mean * (a + umin * EXPONENTIAL_SA_QI[0]);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return solverAbsoluteAccuracy;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>For mean parameter {@code k}, the mean is {@code k}.
+     */
+    public double getNumericalMean() {
+        return getMean();
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>For mean parameter {@code k}, the variance is {@code k^2}.
+     */
+    public double getNumericalVariance() {
+        final double m = getMean();
+        return m * m;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The lower bound of the support is always 0 no matter the mean parameter.
+     *
+     * @return lower bound of the support (always 0)
+     */
+    public double getSupportLowerBound() {
+        return 0;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The upper bound of the support is always positive infinity no matter the mean parameter.
+     *
+     * @return upper bound of the support (always Double.POSITIVE_INFINITY)
+     */
+    public double getSupportUpperBound() {
+        return Double.POSITIVE_INFINITY;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportLowerBoundInclusive() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportUpperBoundInclusive() {
+        return false;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The support of this distribution is connected.
+     *
+     * @return {@code true}
+     */
+    public boolean isSupportConnected() {
+        return true;
+    }
+}