MersenneTwisterFast

package ec.util;

import java.io.DataInputStream;
import java.io.DataOutputStream;
import java.io.IOException;
import java.io.Serializable;
import java.util.Random;

/**
 * <h3>MersenneTwister and MersenneTwisterFast</h3>
 * <p>
 * <b>Version 20</b>, based on version MT199937(99/10/29) of the Mersenne
 * Twister algorithm found at <a
 * href="http://www.math.keio.ac.jp/matumoto/emt.html"> The Mersenne Twister
 * Home Page</a>, with the initialization improved using the new 2002/1/26
 * initialization algorithm By Sean Luke, October 2004.
 *
 * <p>
 * <b>MersenneTwister</b> is a drop-in subclass replacement for
 * java.util.Random. It is properly synchronized and can be used in a
 * multithreaded environment. On modern VMs such as HotSpot, it is approximately
 * 1/3 slower than java.util.Random.
 *
 * <p>
 * <b>MersenneTwisterFast</b> is not a subclass of java.util.Random. It has the
 * same public methods as Random does, however, and it is algorithmically
 * identical to MersenneTwister. MersenneTwisterFast has hard-code inlined all
 * of its methods directly, and made all of them final (well, the ones of
 * consequence anyway). Further, these methods are <i>not</i> synchronized, so
 * the same MersenneTwisterFast instance cannot be shared by multiple threads.
 * But all this helps MersenneTwisterFast achieve well over twice the speed of
 * MersenneTwister. java.util.Random is about 1/3 slower than
 * MersenneTwisterFast.
 *
 * <h3>About the Mersenne Twister</h3>
 * <p>
 * This is a Java version of the C-program for MT19937: Integer version. The
 * MT19937 algorithm was created by Makoto Matsumoto and Takuji Nishimura, who
 * ask: "When you use this, send an email to: matumoto@math.keio.ac.jp with an
 * appropriate reference to your work". Indicate that this is a translation of
 * their algorithm into Java.
 *
 * <p>
 * <b>Reference. </b> Makato Matsumoto and Takuji Nishimura, "Mersenne Twister:
 * A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator",
 * <i>ACM Transactions on Modeling and. Computer Simulation,</i> Vol. 8, No. 1,
 * January 1998, pp 3--30.
 *
 * <h3>About this Version</h3>
 *
 * <p>
 * <b>Changes since V19:</b> nextFloat(boolean, boolean) now returns float, not
 * double.
 *
 * <p>
 * <b>Changes since V18:</b> Removed old final declarations, which used to
 * potentially speed up the code, but no longer.
 *
 * <p>
 * <b>Changes since V17:</b> Removed vestigial references to &= 0xffffffff which
 * stemmed from the original C code. The C code could not guarantee that ints
 * were 32 bit, hence the masks. The vestigial references in the Java code were
 * likely optimized out anyway.
 *
 * <p>
 * <b>Changes since V16:</b> Added nextDouble(includeZero, includeOne) and
 * nextFloat(includeZero, includeOne) to allow for half-open, fully-closed, and
 * fully-open intervals.
 *
 * <p>
 * <b>Changes Since V15:</b> Added serialVersionUID to quiet compiler warnings
 * from Sun's overly verbose compilers as of JDK 1.5.
 *
 * <p>
 * <b>Changes Since V14:</b> made strictfp, with StrictMath.log and
 * StrictMath.sqrt in nextGaussian instead of Math.log and Math.sqrt. This is
 * largely just to be safe, as it presently makes no difference in the speed,
 * correctness, or results of the algorithm.
 *
 * <p>
 * <b>Changes Since V13:</b> clone() method CloneNotSupportedException removed.
 *
 * <p>
 * <b>Changes Since V12:</b> clone() method added.
 *
 * <p>
 * <b>Changes Since V11:</b> stateEquals(...) method added. MersenneTwisterFast
 * is equal to other MersenneTwisterFasts with identical state; likewise
 * MersenneTwister is equal to other MersenneTwister with identical state. This
 * isn't equals(...) because that requires a contract of immutability to compare
 * by value.
 *
 * <p>
 * <b>Changes Since V10:</b> A documentation error suggested that setSeed(int[])
 * required an int[] array 624 long. In fact, the array can be any non-zero
 * length. The new version also checks for this fact.
 *
 * <p>
 * <b>Changes Since V9:</b> readState(stream) and writeState(stream) provided.
 *
 * <p>
 * <b>Changes Since V8:</b> setSeed(int) was only using the first 28 bits of the
 * seed; it should have been 32 bits. For small-number seeds the behavior is
 * identical.
 *
 * <p>
 * <b>Changes Since V7:</b> A documentation error in MersenneTwisterFast (but
 * not MersenneTwister) stated that nextDouble selects uniformly from the
 * full-open interval [0,1]. It does not. nextDouble's contract is identical
 * across MersenneTwisterFast, MersenneTwister, and java.util.Random, namely,
 * selection in the half-open interval [0,1). That is, 1.0 should not be
 * returned. A similar contract exists in nextFloat.
 *
 * <p>
 * <b>Changes Since V6:</b> License has changed from LGPL to BSD. New timing
 * information to compare against java.util.Random. Recent versions of HotSpot
 * have helped Random increase in speed to the point where it is faster than
 * MersenneTwister but slower than MersenneTwisterFast (which should be the
 * case, as it's a less complex algorithm but is synchronized).
 *
 * <p>
 * <b>Changes Since V5:</b> New empty constructor made to work the same as
 * java.util.Random -- namely, it seeds based on the current time in
 * milliseconds.
 *
 * <p>
 * <b>Changes Since V4:</b> New initialization algorithms. See (see <a
 * href="http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html"</a>
 * http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html</a>)
 *
 * <p>
 * The MersenneTwister code is based on standard MT19937 C/C++ code by Takuji
 * Nishimura, with suggestions from Topher Cooper and Marc Rieffel, July 1997.
 * The code was originally translated into Java by Michael Lecuyer, January
 * 1999, and the original code is Copyright (c) 1999 by Michael Lecuyer.
 *
 * <h3>Java notes</h3>
 *
 * <p>
 * This implementation implements the bug fixes made in Java 1.2's version of
 * Random, which means it can be used with earlier versions of Java. See <a
 * href=
 * "http://www.javasoft.com/products/jdk/1.2/docs/api/java/util/Random.html">
 * the JDK 1.2 java.util.Random documentation</a> for further documentation on
 * the random-number generation contracts made. Additionally, there's an
 * undocumented bug in the JDK java.util.Random.nextBytes() method, which this
 * code fixes.
 *
 * <p>
 * Just like java.util.Random, this generator accepts a long seed but doesn't
 * use all of it. java.util.Random uses 48 bits. The Mersenne Twister instead
 * uses 32 bits (int size). So it's best if your seed does not exceed the int
 * range.
 *
 * <p>
 * MersenneTwister can be used reliably on JDK version 1.1.5 or above. Earlier
 * Java versions have serious bugs in java.util.Random; only MersenneTwisterFast
 * (and not MersenneTwister nor java.util.Random) should be used with them.
 *
 * <h3>License</h3>
 *
 * Copyright (c) 2003 by Sean Luke. <br>
 * Portions copyright (c) 1993 by Michael Lecuyer. <br>
 * All rights reserved. <br>
 *
 * <p>
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * <ul>
 * <li>Redistributions of source code must retain the above copyright notice,
 * this list of conditions and the following disclaimer.
 * <li>Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.
 * <li>Neither the name of the copyright owners, their employers, nor the names
 * of its contributors may be used to endorse or promote products derived from
 * this software without specific prior written permission.
 * </ul>
 * <p>
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNERS OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 * @version 20
 */

// Note: this class is hard-inlined in all of its methods. This makes some of
// the methods well-nigh unreadable in their complexity. In fact, the Mersenne
// Twister is fairly easy code to understand: if you're trying to get a handle
// on the code, I strongly suggest looking at MersenneTwister.java first.
// -- Sean

public strictfp class MersenneTwisterFast implements Serializable, Cloneable {
    // Serialization
    private static final long serialVersionUID = -8219700664442619525L; // locked
                                                                        // as of
                                                                        // Version
                                                                        // 15

    // Period parameters
    private static final int N = 624;
    private static final int M = 397;
    private static final int MATRIX_A = 0x9908b0df; // private static final *
                                                    // constant vector a
    private static final int UPPER_MASK = 0x80000000; // most significant w-r
                                                        // bits
    private static final int LOWER_MASK = 0x7fffffff; // least significant r
                                                        // bits

    // Tempering parameters
    private static final int TEMPERING_MASK_B = 0x9d2c5680;
    private static final int TEMPERING_MASK_C = 0xefc60000;

    private int mt[]; // the array for the state vector
    private int mti; // mti==N+1 means mt[N] is not initialized
    private int mag01[];

    // a good initial seed (of int size, though stored in a long)
    // private static final long GOOD_SEED = 4357;

    private double __nextNextGaussian;
    private boolean __haveNextNextGaussian;

    /*
     * We're overriding all internal data, to my knowledge, so this should be
     * okay
     */
    @Override
    public Object clone() {
        try {
            final MersenneTwisterFast f = (MersenneTwisterFast) (super.clone());
            f.mt = (mt.clone());
            f.mag01 = (mag01.clone());
            return f;
        } catch (final CloneNotSupportedException e) {
            throw new InternalError();
        } // should never happen
    }

    public boolean stateEquals(final Object o) {
        if (o == this) {
            return true;
        }
        if (o == null || !(o instanceof MersenneTwisterFast)) {
            return false;
        }
        final MersenneTwisterFast other = (MersenneTwisterFast) o;
        if (mti != other.mti) {
            return false;
        }
        for (int x = 0; x < mag01.length; x++) {
            if (mag01[x] != other.mag01[x]) {
                return false;
            }
        }
        for (int x = 0; x < mt.length; x++) {
            if (mt[x] != other.mt[x]) {
                return false;
            }
        }
        return true;
    }

    /** Reads the entire state of the MersenneTwister RNG from the stream */
    public void readState(final DataInputStream stream) throws IOException {
        int len = mt.length;
        for (int x = 0; x < len; x++) {
            mt[x] = stream.readInt();
        }

        len = mag01.length;
        for (int x = 0; x < len; x++) {
            mag01[x] = stream.readInt();
        }

        mti = stream.readInt();
        __nextNextGaussian = stream.readDouble();
        __haveNextNextGaussian = stream.readBoolean();
    }

    /** Writes the entire state of the MersenneTwister RNG to the stream */
    public void writeState(final DataOutputStream stream) throws IOException {
        int len = mt.length;
        for (int x = 0; x < len; x++) {
            stream.writeInt(mt[x]);
        }

        len = mag01.length;
        for (int x = 0; x < len; x++) {
            stream.writeInt(mag01[x]);
        }

        stream.writeInt(mti);
        stream.writeDouble(__nextNextGaussian);
        stream.writeBoolean(__haveNextNextGaussian);
    }

    /**
     * Constructor using the default seed.
     */
    public MersenneTwisterFast() {
        this(System.currentTimeMillis());
    }

    /**
     * Constructor using a given seed. Though you pass this seed in as a long,
     * it's best to make sure it's actually an integer.
     *
     */
    public MersenneTwisterFast(final long seed) {
        setSeed(seed);
    }

    /**
     * Constructor using an array of integers as seed. Your array must have a
     * non-zero length. Only the first 624 integers in the array are used; if
     * the array is shorter than this then integers are repeatedly used in a
     * wrap-around fashion.
     */
    public MersenneTwisterFast(final int[] array) {
        setSeed(array);
    }

    /**
     * Initalize the pseudo random number generator. Don't pass in a long that's
     * bigger than an int (Mersenne Twister only uses the first 32 bits for its
     * seed).
     */

    synchronized public void setSeed(final long seed) {
        // Due to a bug in java.util.Random clear up to 1.2, we're
        // doing our own Gaussian variable.
        __haveNextNextGaussian = false;

        mt = new int[N];

        mag01 = new int[2];
        mag01[0] = 0x0;
        mag01[1] = MATRIX_A;

        mt[0] = (int) (seed & 0xffffffff);
        for (mti = 1; mti < N; mti++) {
            mt[mti] = (1812433253 * (mt[mti - 1] ^ (mt[mti - 1] >>> 30)) + mti);
            /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
            /* In the previous versions, MSBs of the seed affect */
            /* only MSBs of the array mt[]. */
            /* 2002/01/09 modified by Makoto Matsumoto */
            // mt[mti] &= 0xffffffff;
            /* for >32 bit machines */
        }
    }

    /**
     * Sets the seed of the MersenneTwister using an array of integers. Your
     * array must have a non-zero length. Only the first 624 integers in the
     * array are used; if the array is shorter than this then integers are
     * repeatedly used in a wrap-around fashion.
     */

    synchronized public void setSeed(final int[] array) {
        if (array.length == 0) {
            throw new IllegalArgumentException("Array length must be greater than zero");
        }
        int i, j, k;
        setSeed(19650218);
        i = 1;
        j = 0;
        k = (N > array.length ? N : array.length);
        for (; k != 0; k--) {
            mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >>> 30)) * 1664525)) + array[j] + j; /*
                                                                                             * non
                                                                                             * linear
                                                                                             */
            // mt[i] &= 0xffffffff; /* for WORDSIZE > 32 machines */
            i++;
            j++;
            if (i >= N) {
                mt[0] = mt[N - 1];
                i = 1;
            }
            if (j >= array.length) {
                j = 0;
            }
        }
        for (k = N - 1; k != 0; k--) {
            mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >>> 30)) * 1566083941)) - i; /*
                                                                                     * non
                                                                                     * linear
                                                                                     */
            // mt[i] &= 0xffffffff; /* for WORDSIZE > 32 machines */
            i++;
            if (i >= N) {
                mt[0] = mt[N - 1];
                i = 1;
            }
        }
        mt[0] = 0x80000000; /* MSB is 1; assuring non-zero initial array */
    }

    public int nextInt() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return y;
    }

    public short nextShort() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (short) (y >>> 16);
    }

    public char nextChar() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (char) (y >>> 16);
    }

    public boolean nextBoolean() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (y >>> 31) != 0;
    }

    /**
     * This generates a coin flip with a probability <tt>probability</tt> of
     * returning true, else returning false. <tt>probability</tt> must be
     * between 0.0 and 1.0, inclusive. Not as precise a random real event as
     * nextBoolean(double), but twice as fast. To explicitly use this, remember
     * you may need to cast to float first.
     */

    public boolean nextBoolean(final float probability) {
        int y;

        if (probability < 0.0f || probability > 1.0f) {
            throw new IllegalArgumentException("probability must be between 0.0 and 1.0 inclusive.");
        }
        if (probability == 0.0f) {
            return false; // fix half-open issues
        } else if (probability == 1.0f) {
            return true; // fix half-open issues
        }
        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (y >>> 8) / ((float) (1 << 24)) < probability;
    }

    /**
     * This generates a coin flip with a probability <tt>probability</tt> of
     * returning true, else returning false. <tt>probability</tt> must be
     * between 0.0 and 1.0, inclusive.
     */

    public boolean nextBoolean(final double probability) {
        int y;
        int z;

        if (probability < 0.0 || probability > 1.0) {
            throw new IllegalArgumentException("probability must be between 0.0 and 1.0 inclusive.");
        }
        if (probability == 0.0) {
            return false; // fix half-open issues
        } else if (probability == 1.0) {
            return true; // fix half-open issues
        }
        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            for (; kk < N - 1; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1];

            mti = 0;
        }

        z = mt[mti++];
        z ^= z >>> 11; // TEMPERING_SHIFT_U(z)
        z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z)
        z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z)
        z ^= (z >>> 18); // TEMPERING_SHIFT_L(z)

        /* derived from nextDouble documentation in jdk 1.2 docs, see top */
        return ((((long) (y >>> 6)) << 27) + (z >>> 5)) / (double) (1L << 53) < probability;
    }

    public byte nextByte() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (byte) (y >>> 24);
    }

    public void nextBytes(final byte[] bytes) {
        int y;

        for (int x = 0; x < bytes.length; x++) {
            if (mti >= N) // generate N words at one time
            {
                int kk;
                final int[] mt = this.mt; // locals are slightly faster
                final int[] mag01 = this.mag01; // locals are slightly faster

                for (kk = 0; kk < N - M; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                for (; kk < N - 1; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

                mti = 0;
            }

            y = mt[mti++];
            y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

            bytes[x] = (byte) (y >>> 24);
        }
    }

    public long nextLong() {
        int y;
        int z;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            for (; kk < N - 1; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1];

            mti = 0;
        }

        z = mt[mti++];
        z ^= z >>> 11; // TEMPERING_SHIFT_U(z)
        z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z)
        z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z)
        z ^= (z >>> 18); // TEMPERING_SHIFT_L(z)

        return (((long) y) << 32) + z;
    }

    /**
     * Returns a long drawn uniformly from 0 to n-1. Suffice it to say, n must
     * be > 0, or an IllegalArgumentException is raised.
     */
    public long nextLong(final long n) {
        if (n <= 0) {
            throw new IllegalArgumentException("n must be positive, got: " + n);
        }

        long bits, val;
        do {
            int y;
            int z;

            if (mti >= N) // generate N words at one time
            {
                int kk;
                final int[] mt = this.mt; // locals are slightly faster
                final int[] mag01 = this.mag01; // locals are slightly faster

                for (kk = 0; kk < N - M; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                for (; kk < N - 1; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

                mti = 0;
            }

            y = mt[mti++];
            y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

            if (mti >= N) // generate N words at one time
            {
                int kk;
                final int[] mt = this.mt; // locals are slightly faster
                final int[] mag01 = this.mag01; // locals are slightly faster

                for (kk = 0; kk < N - M; kk++) {
                    z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
                for (; kk < N - 1; kk++) {
                    z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1];
                }
                z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1];

                mti = 0;
            }

            z = mt[mti++];
            z ^= z >>> 11; // TEMPERING_SHIFT_U(z)
            z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z)
            z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z)
            z ^= (z >>> 18); // TEMPERING_SHIFT_L(z)

            bits = (((((long) y) << 32) + z) >>> 1);
            val = bits % n;
        } while (bits - val + (n - 1) < 0);
        return val;
    }

    /**
     * Returns a random double in the half-open range from [0.0,1.0). Thus 0.0
     * is a valid result but 1.0 is not.
     */
    public double nextDouble() {
        int y;
        int z;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            for (; kk < N - 1; kk++) {
                z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1];
            }
            z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1];

            mti = 0;
        }

        z = mt[mti++];
        z ^= z >>> 11; // TEMPERING_SHIFT_U(z)
        z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z)
        z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z)
        z ^= (z >>> 18); // TEMPERING_SHIFT_L(z)

        /* derived from nextDouble documentation in jdk 1.2 docs, see top */
        return ((((long) (y >>> 6)) << 27) + (z >>> 5)) / (double) (1L << 53);
    }

    /**
     * Returns a double in the range from 0.0 to 1.0, possibly inclusive of 0.0
     * and 1.0 themselves. Thus:
     *
     * <p>
     * <table border=0>
     * <th>
     * <td>Expression
     * <td>Interval
     * <tr>
     * <td>nextDouble(false, false)
     * <td>(0.0, 1.0)
     * <tr>
     * <td>nextDouble(true, false)
     * <td>[0.0, 1.0)
     * <tr>
     * <td>nextDouble(false, true)
     * <td>(0.0, 1.0]
     * <tr>
     * <td>nextDouble(true, true)
     * <td>[0.0, 1.0]
     * </table>
     *
     * <p>
     * This version preserves all possible random values in the double range.
     */
    public double nextDouble(final boolean includeZero, final boolean includeOne) {
        double d = 0.0;
        do {
            d = nextDouble(); // grab a value, initially from half-open [0.0,
                                // 1.0)
            if (includeOne && nextBoolean()) {
                d += 1.0; // if includeOne, with 1/2 probability, push to [1.0,
                            // 2.0)
            }
        } while ((d > 1.0) || // everything above 1.0 is always invalid
                (!includeZero && d == 0.0)); // if we're not including zero, 0.0
                                                // is invalid
        return d;
    }

    public double nextGaussian() {
        if (__haveNextNextGaussian) {
            __haveNextNextGaussian = false;
            return __nextNextGaussian;
        } else {
            double v1, v2, s;
            do {
                int y;
                int z;
                int a;
                int b;

                if (mti >= N) // generate N words at one time
                {
                    int kk;
                    final int[] mt = this.mt; // locals are slightly faster
                    final int[] mag01 = this.mag01; // locals are slightly
                                                    // faster

                    for (kk = 0; kk < N - M; kk++) {
                        y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                    for (; kk < N - 1; kk++) {
                        y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                    }
                    y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

                    mti = 0;
                }

                y = mt[mti++];
                y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
                y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
                y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
                y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

                if (mti >= N) // generate N words at one time
                {
                    int kk;
                    final int[] mt = this.mt; // locals are slightly faster
                    final int[] mag01 = this.mag01; // locals are slightly
                                                    // faster

                    for (kk = 0; kk < N - M; kk++) {
                        z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1];
                    }
                    for (; kk < N - 1; kk++) {
                        z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1];
                    }
                    z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1];

                    mti = 0;
                }

                z = mt[mti++];
                z ^= z >>> 11; // TEMPERING_SHIFT_U(z)
                z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z)
                z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z)
                z ^= (z >>> 18); // TEMPERING_SHIFT_L(z)

                if (mti >= N) // generate N words at one time
                {
                    int kk;
                    final int[] mt = this.mt; // locals are slightly faster
                    final int[] mag01 = this.mag01; // locals are slightly
                                                    // faster

                    for (kk = 0; kk < N - M; kk++) {
                        a = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + M] ^ (a >>> 1) ^ mag01[a & 0x1];
                    }
                    for (; kk < N - 1; kk++) {
                        a = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + (M - N)] ^ (a >>> 1) ^ mag01[a & 0x1];
                    }
                    a = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N - 1] = mt[M - 1] ^ (a >>> 1) ^ mag01[a & 0x1];

                    mti = 0;
                }

                a = mt[mti++];
                a ^= a >>> 11; // TEMPERING_SHIFT_U(a)
                a ^= (a << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(a)
                a ^= (a << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(a)
                a ^= (a >>> 18); // TEMPERING_SHIFT_L(a)

                if (mti >= N) // generate N words at one time
                {
                    int kk;
                    final int[] mt = this.mt; // locals are slightly faster
                    final int[] mag01 = this.mag01; // locals are slightly
                                                    // faster

                    for (kk = 0; kk < N - M; kk++) {
                        b = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + M] ^ (b >>> 1) ^ mag01[b & 0x1];
                    }
                    for (; kk < N - 1; kk++) {
                        b = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                        mt[kk] = mt[kk + (M - N)] ^ (b >>> 1) ^ mag01[b & 0x1];
                    }
                    b = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                    mt[N - 1] = mt[M - 1] ^ (b >>> 1) ^ mag01[b & 0x1];

                    mti = 0;
                }

                b = mt[mti++];
                b ^= b >>> 11; // TEMPERING_SHIFT_U(b)
                b ^= (b << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(b)
                b ^= (b << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(b)
                b ^= (b >>> 18); // TEMPERING_SHIFT_L(b)

                /*
                 * derived from nextDouble documentation in jdk 1.2 docs, see
                 * top
                 */
                v1 = 2 * (((((long) (y >>> 6)) << 27) + (z >>> 5)) / (double) (1L << 53)) - 1;
                v2 = 2 * (((((long) (a >>> 6)) << 27) + (b >>> 5)) / (double) (1L << 53)) - 1;
                s = v1 * v1 + v2 * v2;
            } while (s >= 1 || s == 0);
            final double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s) / s);
            __nextNextGaussian = v2 * multiplier;
            __haveNextNextGaussian = true;
            return v1 * multiplier;
        }
    }

    /**
     * Returns a random float in the half-open range from [0.0f,1.0f). Thus 0.0f
     * is a valid result but 1.0f is not.
     */
    public float nextFloat() {
        int y;

        if (mti >= N) // generate N words at one time
        {
            int kk;
            final int[] mt = this.mt; // locals are slightly faster
            final int[] mag01 = this.mag01; // locals are slightly faster

            for (kk = 0; kk < N - M; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            for (; kk < N - 1; kk++) {
                y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
            }
            y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
            mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

            mti = 0;
        }

        y = mt[mti++];
        y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
        y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
        y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
        y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

        return (y >>> 8) / ((float) (1 << 24));
    }

    /**
     * Returns a float in the range from 0.0f to 1.0f, possibly inclusive of
     * 0.0f and 1.0f themselves. Thus:
     *
     * <p>
     * <table border=0>
     * <th>
     * <td>Expression
     * <td>Interval
     * <tr>
     * <td>nextFloat(false, false)
     * <td>(0.0f, 1.0f)
     * <tr>
     * <td>nextFloat(true, false)
     * <td>[0.0f, 1.0f)
     * <tr>
     * <td>nextFloat(false, true)
     * <td>(0.0f, 1.0f]
     * <tr>
     * <td>nextFloat(true, true)
     * <td>[0.0f, 1.0f]
     * </table>
     *
     * <p>
     * This version preserves all possible random values in the float range.
     */
    public float nextFloat(final boolean includeZero, final boolean includeOne) {
        float d = 0.0f;
        do {
            d = nextFloat(); // grab a value, initially from half-open [0.0f,
                                // 1.0f)
            if (includeOne && nextBoolean()) {
                d += 1.0f; // if includeOne, with 1/2 probability, push to
                            // [1.0f, 2.0f)
            }
        } while ((d > 1.0f) || // everything above 1.0f is always invalid
                (!includeZero && d == 0.0f)); // if we're not including zero,
                                                // 0.0f is invalid
        return d;
    }

    /**
     * Returns an integer drawn uniformly from 0 to n-1. Suffice it to say, n
     * must be > 0, or an IllegalArgumentException is raised.
     */
    public int nextInt(final int n) {
        if (n <= 0) {
            throw new IllegalArgumentException("n must be positive, got: " + n);
        }

        if ((n & -n) == n) // i.e., n is a power of 2
        {
            int y;

            if (mti >= N) // generate N words at one time
            {
                int kk;
                final int[] mt = this.mt; // locals are slightly faster
                final int[] mag01 = this.mag01; // locals are slightly faster

                for (kk = 0; kk < N - M; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                for (; kk < N - 1; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

                mti = 0;
            }

            y = mt[mti++];
            y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

            return (int) ((n * (long) (y >>> 1)) >> 31);
        }

        int bits, val;
        do {
            int y;

            if (mti >= N) // generate N words at one time
            {
                int kk;
                final int[] mt = this.mt; // locals are slightly faster
                final int[] mag01 = this.mag01; // locals are slightly faster

                for (kk = 0; kk < N - M; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                for (; kk < N - 1; kk++) {
                    y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
                    mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1];
                }
                y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
                mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1];

                mti = 0;
            }

            y = mt[mti++];
            y ^= y >>> 11; // TEMPERING_SHIFT_U(y)
            y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y)
            y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y)
            y ^= (y >>> 18); // TEMPERING_SHIFT_L(y)

            bits = (y >>> 1);
            val = bits % n;
        } while (bits - val + (n - 1) < 0);
        return val;
    }

    /**
     * Tests the code.
     */
    public static void main(final String args[]) {
        int j;

        MersenneTwisterFast r;

        // CORRECTNESS TEST
        // COMPARE WITH
        // http://www.math.keio.ac.jp/matumoto/CODES/MT2002/mt19937ar.out

        r = new MersenneTwisterFast(new int[] { 0x123, 0x234, 0x345, 0x456 });
        System.out.println("Output of MersenneTwisterFast with new (2002/1/26) seeding mechanism");
        for (j = 0; j < 1000; j++) {
            // first, convert the int from signed to "unsigned"
            long l = r.nextInt();
            if (l < 0) {
                l += 4294967296L; // max int value
            }
            String s = String.valueOf(l);
            while (s.length() < 10) {
                s = " " + s; // buffer
            }
            System.out.print(s + " ");
            if (j % 5 == 4) {
                System.out.println();
            }
        }

        // SPEED TEST

        final long SEED = 4357;

        int xx;
        long ms;
        System.out.println("\nTime to test grabbing 100000000 ints");

        final Random rr = new Random(SEED);
        xx = 0;
        ms = System.currentTimeMillis();
        for (j = 0; j < 100000000; j++) {
            xx += rr.nextInt();
        }
        System.out.println("java.util.Random: " + (System.currentTimeMillis() - ms) + "          Ignore this: " + xx);

        r = new MersenneTwisterFast(SEED);
        ms = System.currentTimeMillis();
        xx = 0;
        for (j = 0; j < 100000000; j++) {
            xx += r.nextInt();
        }
        System.out.println("Mersenne Twister Fast: " + (System.currentTimeMillis() - ms) + "          Ignore this: " + xx);

        // TEST TO COMPARE TYPE CONVERSION BETWEEN
        // MersenneTwisterFast.java AND MersenneTwister.java

        System.out.println("\nGrab the first 1000 booleans");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextBoolean() + " ");
            if (j % 8 == 7) {
                System.out.println();
            }
        }
        if (!(j % 8 == 7)) {
            System.out.println();
        }

        System.out.println("\nGrab 1000 booleans of increasing probability using nextBoolean(double)");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextBoolean(j / 999.0) + " ");
            if (j % 8 == 7) {
                System.out.println();
            }
        }
        if (!(j % 8 == 7)) {
            System.out.println();
        }

        System.out.println("\nGrab 1000 booleans of increasing probability using nextBoolean(float)");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextBoolean(j / 999.0f) + " ");
            if (j % 8 == 7) {
                System.out.println();
            }
        }
        if (!(j % 8 == 7)) {
            System.out.println();
        }

        final byte[] bytes = new byte[1000];
        System.out.println("\nGrab the first 1000 bytes using nextBytes");
        r = new MersenneTwisterFast(SEED);
        r.nextBytes(bytes);
        for (j = 0; j < 1000; j++) {
            System.out.print(bytes[j] + " ");
            if (j % 16 == 15) {
                System.out.println();
            }
        }
        if (!(j % 16 == 15)) {
            System.out.println();
        }

        byte b;
        System.out.println("\nGrab the first 1000 bytes -- must be same as nextBytes");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print((b = r.nextByte()) + " ");
            if (b != bytes[j]) {
                System.out.print("BAD ");
            }
            if (j % 16 == 15) {
                System.out.println();
            }
        }
        if (!(j % 16 == 15)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 shorts");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextShort() + " ");
            if (j % 8 == 7) {
                System.out.println();
            }
        }
        if (!(j % 8 == 7)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 ints");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextInt() + " ");
            if (j % 4 == 3) {
                System.out.println();
            }
        }
        if (!(j % 4 == 3)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 ints of different sizes");
        r = new MersenneTwisterFast(SEED);
        int max = 1;
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextInt(max) + " ");
            max *= 2;
            if (max <= 0) {
                max = 1;
            }
            if (j % 4 == 3) {
                System.out.println();
            }
        }
        if (!(j % 4 == 3)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 longs");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextLong() + " ");
            if (j % 3 == 2) {
                System.out.println();
            }
        }
        if (!(j % 3 == 2)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 longs of different sizes");
        r = new MersenneTwisterFast(SEED);
        long max2 = 1;
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextLong(max2) + " ");
            max2 *= 2;
            if (max2 <= 0) {
                max2 = 1;
            }
            if (j % 4 == 3) {
                System.out.println();
            }
        }
        if (!(j % 4 == 3)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 floats");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextFloat() + " ");
            if (j % 4 == 3) {
                System.out.println();
            }
        }
        if (!(j % 4 == 3)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 doubles");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextDouble() + " ");
            if (j % 3 == 2) {
                System.out.println();
            }
        }
        if (!(j % 3 == 2)) {
            System.out.println();
        }

        System.out.println("\nGrab the first 1000 gaussian doubles");
        r = new MersenneTwisterFast(SEED);
        for (j = 0; j < 1000; j++) {
            System.out.print(r.nextGaussian() + " ");
            if (j % 3 == 2) {
                System.out.println();
            }
        }
        if (!(j % 3 == 2)) {
            System.out.println();
        }

    }
}