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 * 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
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 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math3.distribution;

import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;

Implementation of the uniform integer distribution.
See Also:
Uniform distribution (discrete), at Wikipedia
Since:
3.0/**
 * Implementation of the uniform integer distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Uniform_distribution_(discrete)"
 * >Uniform distribution (discrete), at Wikipedia</a>
 *
 * @since 3.0
 */
public class UniformIntegerDistribution extends AbstractIntegerDistribution {
    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 20120109L;
    
Lower bound (inclusive) of this distribution. /** Lower bound (inclusive) of this distribution. */
    private final int lower;
    
Upper bound (inclusive) of this distribution. /** Upper bound (inclusive) of this distribution. */
    private final int upper;

    
Creates a new uniform integer distribution using the given lower and
upper bounds (both inclusive).

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractIntegerDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead. 
Params:
lower – Lower bound (inclusive) of this distribution.
upper – Upper bound (inclusive) of this distribution.
Throws:
NumberIsTooLargeException – if lower >= upper./**
     * Creates a new uniform integer distribution using the given lower and
     * upper bounds (both inclusive).
     * <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 lower Lower bound (inclusive) of this distribution.
     * @param upper Upper bound (inclusive) of this distribution.
     * @throws NumberIsTooLargeException if {@code lower >= upper}.
     */
    public UniformIntegerDistribution(int lower, int upper)
        throws NumberIsTooLargeException {
        this(new Well19937c(), lower, upper);
    }

    
Creates a new uniform integer distribution using the given lower and
upper bounds (both inclusive).
Params:
rng – Random number generator.
lower – Lower bound (inclusive) of this distribution.
upper – Upper bound (inclusive) of this distribution.
Throws:
NumberIsTooLargeException – if lower > upper.
Since:
3.1/**
     * Creates a new uniform integer distribution using the given lower and
     * upper bounds (both inclusive).
     *
     * @param rng Random number generator.
     * @param lower Lower bound (inclusive) of this distribution.
     * @param upper Upper bound (inclusive) of this distribution.
     * @throws NumberIsTooLargeException if {@code lower > upper}.
     * @since 3.1
     */
    public UniformIntegerDistribution(RandomGenerator rng,
                                      int lower,
                                      int upper)
        throws NumberIsTooLargeException {
        super(rng);

        if (lower > upper) {
            throw new NumberIsTooLargeException(
                            LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,
                            lower, upper, true);
        }
        this.lower = lower;
        this.upper = upper;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double probability(int x) {
        if (x < lower || x > upper) {
            return 0;
        }
        return 1.0 / (upper - lower + 1);
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public double cumulativeProbability(int x) {
        if (x < lower) {
            return 0;
        }
        if (x > upper) {
            return 1;
        }
        return (x - lower + 1.0) / (upper - lower + 1.0);
    }

    
{@inheritDoc} For lower bound lower and upper bound upper, the mean is 0.5 * (lower + upper). /**
     * {@inheritDoc}
     *
     * For lower bound {@code lower} and upper bound {@code upper}, the mean is
     * {@code 0.5 * (lower + upper)}.
     */
    public double getNumericalMean() {
        return 0.5 * (lower + upper);
    }

    
{@inheritDoc} For lower bound lower and upper bound upper, and n = upper - lower + 1, the variance is (n^2 - 1) / 12. /**
     * {@inheritDoc}
     *
     * For lower bound {@code lower} and upper bound {@code upper}, and
     * {@code n = upper - lower + 1}, the variance is {@code (n^2 - 1) / 12}.
     */
    public double getNumericalVariance() {
        double n = upper - lower + 1;
        return (n * n - 1) / 12.0;
    }

    
{@inheritDoc}
The lower bound of the support is equal to the lower bound parameter
of the distribution.
Returns:
lower bound of the support/**
     * {@inheritDoc}
     *
     * The lower bound of the support is equal to the lower bound parameter
     * of the distribution.
     *
     * @return lower bound of the support
     */
    public int getSupportLowerBound() {
        return lower;
    }

    
{@inheritDoc}
The upper bound of the support is equal to the upper bound parameter
of the distribution.
Returns:
upper bound of the support/**
     * {@inheritDoc}
     *
     * The upper bound of the support is equal to the upper bound parameter
     * of the distribution.
     *
     * @return upper bound of the support
     */
    public int getSupportUpperBound() {
        return upper;
    }

    
{@inheritDoc}
The support of this distribution is connected.
Returns:
true/**
     * {@inheritDoc}
     *
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    public boolean isSupportConnected() {
        return true;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    public int sample() {
        final int max = (upper - lower) + 1;
        if (max <= 0) {
            // The range is too wide to fit in a positive int (larger
            // than 2^31); as it covers more than half the integer range,
            // we use a simple rejection method.
            while (true) {
                final int r = random.nextInt();
                if (r >= lower &&
                    r <= upper) {
                    return r;
                }
            }
        } else {
            // We can shift the range and directly generate a positive int.
            return lower + random.nextInt(max);
        }
    }
}