package edu.northwestern.at.utils.math.randomnumbers; /* Please see the license information in the header below. */ import java.io.*; import java.util.*; /** MersenneTwister and MersenneTwisterFast. * * <p> * <strong>Version 8</strong>, * 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, April 2004. * </p> * * <p> * <strong>MersenneTwister</strong> 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> * * <p> * <strong>MersenneTwisterFast</strong> 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 <em>not</em> 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. * </p> * * <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> * * <p> * <strong>Reference.</strong> * Makato Matsumoto and Takuji Nishimura, * "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform * Pseudo-Random Number Generator", * <em>ACM Transactions on Modeling and Computer Simulation,</em> * Vol. 8, No. 1, January 1998, pp 3--30. * </p> * * <h3> * About this Version * </h3> * * <p> * <strong>Changes Since V7:</strong> 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> * * <p> * <strong>Changes Since V6:</strong> 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> * * <p> * <strong>Changes Since V5:</strong> New empty constructor made to work the same * as java.util.Random -- namely, it seeds based on the current time in * milliseconds. * </p> * * <p> * <strong>Changes Since V4:</strong> New initialization algorithms. See * (see <a href="http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html"</a> * http://www.math.keio.ac.jp/matumoto/MT2002/emt19937ar.html</a>) * </p> * * <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. * </p> * * <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> * <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> * * <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. * </p> * * <h3> * License * </h3> * * <p> * Copyright (c) 2003 by Sean Luke. <br> * Portions copyright (c) 1993 by Michael Lecuyer. <br> * All rights reserved. <br> * </p> * * <p> * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * </p> * * <ul> * <li> Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer.</li> * <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> * <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.</li> * </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. * </p> * * @version 8 */ public class MersenneTwister extends java.util.Random implements Serializable { // 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; /* implemented here because there's a bug in Random's implementation of the Gaussian code (divide by zero, and log(0), ugh!), yet its gaussian variables are private so we can't access them here. :-( */ private double __nextNextGaussian; private boolean __haveNextNextGaussian; /** * Constructor using the default seed. */ public MersenneTwister() { 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 MersenneTwister(final long seed) { super(seed); /* just in case */ setSeed(seed); } /** * Constructor using an array. */ public MersenneTwister(final int[] array) { super(System.currentTimeMillis()); /* pick something at random just in case */ 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) { // it's always good style to call super super.setSeed(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 & 0xfffffff); 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 */ } } /** * An alternative, more complete, method of seeding the * pseudo random number generator. array must be an * array of 624 ints, and they can be any value as long as * they're not *all* zero. */ synchronized public void setSeed(final int[] array) { 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 */ } /** * Returns an integer with <em>bits</em> bits filled with a random number. */ synchronized protected int next(final int bits) { 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 >>> (32 - bits); // hope that's right! } /* If you've got a truly old version of Java, you can omit these two next methods. */ private synchronized void writeObject(final ObjectOutputStream out) throws IOException { // just so we're synchronized. out.defaultWriteObject(); } private synchronized void readObject(final ObjectInputStream in) throws IOException, ClassNotFoundException { // just so we're synchronized. in.defaultReadObject(); } /** This method is missing from jdk 1.0.x and below. JDK 1.1 includes this for us, but what the heck.*/ public boolean nextBoolean() { return next(1) != 0; } /** This generates a coin flip with a probability <tt>probability</tt> of returning true, else returning false. <tt>probability</tt> must be between 0.0 and 1.0, inclusive. Not as precise a random real event as nextBoolean(double), but twice as fast. To explicitly use this, remember you may need to cast to float first. */ public boolean nextBoolean(final float probability) { 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 return nextFloat() < probability; } /** This generates a coin flip with a probability <tt>probability</tt> of returning true, else returning false. <tt>probability</tt> must be between 0.0 and 1.0, inclusive. */ public boolean nextBoolean(final double probability) { 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 return nextDouble() < probability; } /** This method is missing from JDK 1.1 and below. JDK 1.2 includes this for us, but what the heck. */ public int nextInt(final int n) { if (n <= 0) throw new IllegalArgumentException("n must be >= 0"); if ((n & -n) == n) return (int) ((n * (long) next(31)) >> 31); int bits, val; do { bits = next(31); val = bits % n; } while (bits - val + (n - 1) < 0); return val; } /** This method is for completness' sake. Returns a long drawn uniformly from 0 to n-1. Suffice it to say, n must be > 0, or an IllegalArgumentException is raised. */ public long nextLong(final long n) { if (n <= 0) throw new IllegalArgumentException("n must be >= 0"); long bits, val; do { bits = (nextLong() >>> 1); val = bits % n; } while (bits - val + (n - 1) < 0); return val; } /** A bug fix for versions of JDK 1.1 and below. JDK 1.2 fixes this for us, but what the heck. */ public double nextDouble() { return (((long) next(26) << 27) + next(27)) / (double) (1L << 53); } /** A bug fix for versions of JDK 1.1 and below. JDK 1.2 fixes this for us, but what the heck. */ public float nextFloat() { return next(24) / ((float) (1 << 24)); } /** A bug fix for all versions of the JDK. The JDK appears to use all four bytes in an integer as independent byte values! Totally wrong. I've submitted a bug report. */ public void nextBytes(final byte[] bytes) { for (int x = 0; x < bytes.length; x++) bytes[x] = (byte) next(8); } /** For completeness' sake, though it's not in java.util.Random. */ public char nextChar() { // chars are 16-bit UniCode values return (char) (next(16)); } /** For completeness' sake, though it's not in java.util.Random. */ public short nextShort() { return (short) (next(16)); } /** For completeness' sake, though it's not in java.util.Random. */ public byte nextByte() { return (byte) (next(8)); } /** A bug fix for all JDK code including 1.2. nextGaussian can theoretically ask for the log of 0 and divide it by 0! See Java bug <a href="http://developer.java.sun.com/developer/bugParade/bugs/4254501.html"> http://developer.java.sun.com/developer/bugParade/bugs/4254501.html</a> */ synchronized public double nextGaussian() { if (__haveNextNextGaussian) { __haveNextNextGaussian = false; return __nextNextGaussian; } else { double v1, v2, s; do { v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0 v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0 s = v1 * v1 + v2 * v2; } while (s >= 1 || s == 0); double multiplier = /* Strict*/Math.sqrt(-2 * /* Strict*/Math.log(s) / s); __nextNextGaussian = v2 * multiplier; __haveNextNextGaussian = true; return v1 * multiplier; } } }