/*
 * #%L
 * SciJava Common shared library for SciJava software.
 * %%
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 * Wisconsin-Madison, Broad Institute of MIT and Harvard, Max Planck
 * Institute of Molecular Cell Biology and Genetics, University of
 * Konstanz, and KNIME GmbH.
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 * 1. Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
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 *    this list of conditions and the following disclaimer in the documentation
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package org.scijava.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 17</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 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
 * <a href="http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html">
 * 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.
 *
 * @author Sean Luke
 * @version 17
 */
@SuppressWarnings("all")
public strictfp class MersenneTwisterFast implements Serializable, Cloneable
    {

    // 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

    // 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
            {
            MersenneTwisterFast f = (MersenneTwisterFast)(super.clone());
            f.mt = (int[])(mt.clone());
            f.mag01 = (int[])(mag01.clone());
            return f;
            }
        catch (CloneNotSupportedException e) { throw new InternalError(); } // should never happen
        }
    
    public boolean stateEquals(Object o)
        {
        if (o==this) return true;
        if (o == null || !(o instanceof MersenneTwisterFast))
            return false;
        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(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(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 final 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 final 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 final 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 final 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 (boolean)((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 final 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 final 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 final 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 final void nextBytes(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 final 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) + (long)z;
        }



    /** Returns a long drawn uniformly from 0 to n-1.  Suffice it to say,
        n must be &gt; 0, or an IllegalArgumentException is raised. */
    public final 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) + (long)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 final 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:

        <table border=0 summary="Table">
        <tr><th>Expression</th><th>Interval</th></tr>
        <tr><td>nextDouble(false, false)</td><td>(0.0, 1.0)</td></tr>
        <tr><td>nextDouble(true, false)</td><td>[0.0, 1.0)</td></tr>
        <tr><td>nextDouble(false, true)</td><td>(0.0, 1.0]</td></tr>
        <tr><td>nextDouble(true, true)</td><td>[0.0, 1.0]</td></tr>
        </table>
        
        <p>This version preserves all possible random values in the double range.
        */
    public double nextDouble(boolean includeZero, 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 final 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);
            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 final 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:

        <table border=0 summary="Table">
        <tr><th>Expression</th><th>Interval</th></tr>
        <tr><td>nextFloat(false, false)</td><td>(0.0f, 1.0f)</td></tr>
        <tr><td>nextFloat(true, false)</td><td>[0.0f, 1.0f)</td></tr>
        <tr><td>nextFloat(false, true)</td><td>(0.0f, 1.0f]</td></tr>
        <tr><td>nextFloat(true, true)</td><td>[0.0f, 1.0f]</td></tr>
        </table>
        
        <p>This version preserves all possible random values in the float range.
        */
    public double nextFloat(boolean includeZero, 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 &gt; 0, or an IllegalArgumentException is raised. */
    public final 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(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 = (long)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");
          
        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((double)(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((float)(j/999.0f)) + " ");
            if (j%8==7) System.out.println();
            }
        if (!(j%8==7)) System.out.println();
          
        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();
        
        }
    }
