package ec.util; import java.io.*; /** *

MersenneTwister and MersenneTwisterFast

*

Version 16, 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: matumoto@math.keio.ac.jp * 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 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 * (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: *

*

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNERS OR CONTRIBUTORS BE * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * @version 16 */ public strictfp class MersenneTwister extends java.util.Random implements Serializable, Cloneable { // Serialization private static final long serialVersionUID = -4035832775130174188L; // 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; /* 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; /* We're overriding all internal data, to my knowledge, so this should be okay */ public Object clone() { try { MersenneTwister f = (MersenneTwister)(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 MersenneTwister)) return false; MersenneTwister other = (MersenneTwister) 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 */ } /** * Returns an integer with bits 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 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 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 probability of returning true, else returning false. probability 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 positive, got: " + n); 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 positive, got: " + n); 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 http://developer.java.sun.com/developer/bugParade/bugs/4254501.html */ 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 = StrictMath.sqrt(-2 * StrictMath.log(s)/s); __nextNextGaussian = v2 * multiplier; __haveNextNextGaussian = true; return v1 * multiplier; } } /** * Tests the code. */ public static void main(String args[]) { int j; MersenneTwister r; // CORRECTNESS TEST // COMPARE WITH http://www.math.keio.ac.jp/matumoto/CODES/MT2002/mt19937ar.out r = new MersenneTwister(new int[]{0x123, 0x234, 0x345, 0x456}); System.out.println("Output of MersenneTwister 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"); r = new MersenneTwister(SEED); ms = System.currentTimeMillis(); xx=0; for (j = 0; j < 100000000; j++) xx += r.nextInt(); System.out.println("Mersenne Twister: " + (System.currentTimeMillis()-ms) + " Ignore this: " + xx); System.out.println("To compare this with java.util.Random, run this same test on MersenneTwisterFast."); System.out.println("The comparison with Random is removed from MersenneTwister because it is a proper"); System.out.println("subclass of Random and this unfairly makes some of Random's methods un-inlinable,"); System.out.println("so it would make Random look worse than it is."); // TEST TO COMPARE TYPE CONVERSION BETWEEN // MersenneTwisterFast.java AND MersenneTwister.java System.out.println("\nGrab the first 1000 booleans"); r = new MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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 MersenneTwister(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(); } }