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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;

/**
 * 

MersenneTwister and MersenneTwisterFast

*

* Version 17, based on version MT199937(99/10/29) of the Mersenne * Twister algorithm found at * The Mersenne Twister * Home Page, with the initialization improved using the new 2002/1/26 * initialization algorithm By Sean Luke, October 2004. *

* MersenneTwister 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. *

* MersenneTwisterFast 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 not 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. *

About the Mersenne Twister

*

* 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: [email protected] with an * appropriate reference to your work". Indicate that this is a translation of * their algorithm into Java. *

* Reference. Makato Matsumoto and Takuji Nishimura, "Mersenne Twister: * A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator", * ACM Transactions on Modeling and. Computer Simulation, Vol. 8, No. 1, * January 1998, pp 3--30. *

About this Version

*

* Changes since V16: Added nextDouble(includeZero, includeOne) and * nextFloat(includeZero, includeOne) to allow for half-open, fully-closed, and * fully-open intervals. *

* Changes Since V15: Added serialVersionUID to quiet compiler warnings * from Sun's overly verbose compilers as of JDK 1.5. *

* Changes Since V14: 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. *

* Changes Since V13: clone() method CloneNotSupportedException removed. *

* Changes Since V12: clone() method added. *

* Changes Since V11: 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. *

* Changes Since V10: 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. *

* Changes Since V9: readState(stream) and writeState(stream) provided. *

* Changes Since V8: 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. *

* Changes Since V7: 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. *

* Changes Since V6: 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). *

* Changes Since V5: New empty constructor made to work the same as * java.util.Random -- namely, it seeds based on the current time in * milliseconds. *

* Changes Since V4: New initialization algorithms (see * * http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html). *

* 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. *

Java notes

*

* 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 * * the JDK 1.2 java.util.Random documentation 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. *

* 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. *

* 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. *

License

Copyright (c) 2003 by Sean Luke.
* Portions copyright (c) 1993 by Michael Lecuyer.
* All rights reserved.
*

* Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: *

    *
  • Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. *
  • 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. *
  • 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. *
*

* 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>> 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 probability of returning true, else returning false. probability 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 probability of returning true, else returning false. probability 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= 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 > 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:

ExpressionInterval
nextDouble(false, false)(0.0, 1.0)
nextDouble(true, false)[0.0, 1.0)
nextDouble(false, true)(0.0, 1.0]
nextDouble(true, true)[0.0, 1.0]

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:

ExpressionInterval
nextFloat(false, false)(0.0f, 1.0f)
nextFloat(true, false)[0.0f, 1.0f)
nextFloat(false, true)(0.0f, 1.0f]
nextFloat(true, true)[0.0f, 1.0f]

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 > 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(); } }





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