Class MersenneTwister

Object
MersenneTwister

public class MersenneTwister extends Object

MersenneTwister and MersenneTwisterFast

Version 22, 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 V21: Minor documentation HTML fixes.

Changes since V20: Added clearGuassian(). Modified stateEquals() to be synchronizd on both objects for MersenneTwister, and changed its documentation. Added synchronization to both setSeed() methods, to writeState(), and to readState() in MersenneTwister. Removed synchronization from readObject() in MersenneTwister.

Changes since V19: nextFloat(boolean, boolean) now returns float, not double.

Changes since V18: Removed old final declarations, which used to potentially speed up the code, but no longer.

Changes since V17: Removed vestigial references to &= 0xffffffff which stemmed from the original C code. The C code could not guarantee that ints were 32 bit, hence the masks. The vestigial references in the Java code were likely optimized out anyway.

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 (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.

Version:
22
  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static interface 
    The minimal Chronometer interface is only used to hide differences for measuring execution time in JRE and GWT.
    (package private) static class 
    Minimal implementation of Chronometer.
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private boolean
    The flag to indicate that the next Gaussian has already been generated.
    private double
    Gaussian random numbers are generated in pairs.
    private static final int
     
    private static StringBuilder
    ChH: for testing on GWT/JRE platforms logging needs to be rewritten
    private static final double
    Constant: 1/(2^-31 - 1).
    private static final int
     
    private static final int
     
    private static final int
     
    private int[]
    The array for the state vector
    private int
    The current index for the state vector.
    private static final int
    Period parameters
    private static final int
    Tempering parameters
    private static final int
     
    private static final double
    Constant: 2^27.
    private static final float
    Constant: 2^31.
    private static final double
    Constant: 2^31 - 1.
    private static final double
    Constant: 2^32.
    private static final double
    Constant: 2^53.
    private static final double
    Constant: 2^-24.
    private static final double
    Constant: 2^-25.
    private static final double
    Constant: 2^-27.
    private static final double
    Constant: 1/2^-31.
    private static final float
    Constant: 2^-31.
    private static final double
    Constant: 2^-52.
    private static final double
    Constant: 2^-53.
    private static final int
     
  • Constructor Summary

    Constructors
    Constructor
    Description
    Constructor using the default seed.
    MersenneTwister(int[] array)
    Constructor using an array of integers as seed.
    MersenneTwister(long seed)
    Constructor using a given seed.
  • Method Summary

    Modifier and Type
    Method
    Description
    private static void
    Append message to buffer (no newline added).
    void
    Clears the internal Gaussian variable from the RNG.
    Clone this MersenneTwister to ensure both objects return identical sequences of random numbers.
    Encode state of random number generator as plist for saving.
    private static void
    Append newline to buffer.
    private static void
    Append message to buffer (adding newline).
    static void
    main(String[] args)
    Tests the code.
    boolean
    Generates a random boolean.
    boolean
    nextBoolean(double probability)
    This generates a coin flip with a probability probability of returning true, else returning false.
    boolean
    nextBoolean(float probability)
    This generates a coin flip with a probability probability of returning true, else returning false.
    byte
    Generates a random byte on [0, 0xff]-interval.
    void
    nextBytes(byte[] bytes)
    Fill array bytes with random bytes.
    char
    generates a random char on [0, 0xffff]-interval.
    double
    Generate random double on half-open [0, 1)-interval.
    double
    Generate random double on closed [0, 1]-interval
    double
    Generates a random high-precision double on half-open [0, 1)-interval.
    double
    Generate random double on open (0, 1)-interval
    float
    Generates a random float on half-open [0, 1)-interval.
    double
    Generate random number from standard normal distribution (Gaussian distribution).
    int
    Generate a 31bit (signed) random int in [0, Integer.MAX_VALUE).
    int
    nextInt(int n)
    Generate a random int in [0, n-1]-interval.
    long
    Generate a 63bit (signed) random long integer in [0, Long.MAX_VALUE).
    long
    nextLong(long n)
    Generate a random long integer in [0, n) with n > 0.
    short
    Generates a random short integer on [0, 0xffff]-interval.
    private int
    Generates a 32bit 'unsigned' random int in [0, 2^33-1].
    private long
    Generate a 64bit unsigned random long in [0, 2^65-1].
    boolean
    Restore state of random number generator from plist encoded string.
    void
    setSeed(int[] array)
    Sets the seed of the MersenneTwister using an array of integers.
    void
    setSeed(long seed)
    Initialize the pseudo random number generator.
    boolean
    Returns true if the MersenneTwister's current internal state is equal to another MersenneTwister.
    static void
    Tests if generated random numbers comply with reference mt19937ar.c.
    static void
    testSpeed(Logger logger, MersenneTwister.Chronometer clock, int nSamples)
    Tests speed of MersenneTwister as compared to Random.
    private void
    The twister: core mechanism for generating pseudo random numbers.

    Methods inherited from class Object

    equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Field Details

    • N

      private static final int N
      Period parameters
      See Also:
    • M

      private static final int M
      See Also:
    • MATRIX_A

      private static final int MATRIX_A
      See Also:
    • BIT32_MASK

      private static final int BIT32_MASK
      See Also:
    • UPPER_MASK

      private static final int UPPER_MASK
      See Also:
    • LOWER_MASK

      private static final int LOWER_MASK
      See Also:
    • TEMPERING_MASK_B

      private static final int TEMPERING_MASK_B
      Tempering parameters
      See Also:
    • TEMPERING_MASK_C

      private static final int TEMPERING_MASK_C
      See Also:
    • TWO_TO_27

      private static final double TWO_TO_27
      Constant: 2^27.
      See Also:
    • TWO_TO_31f

      private static final float TWO_TO_31f
      Constant: 2^31.
      See Also:
    • TWO_TO_31M1

      private static final double TWO_TO_31M1
      Constant: 2^31 - 1.
      See Also:
    • TWO_TO_32

      private static final double TWO_TO_32
      Constant: 2^32.
      See Also:
    • TWO_TO_53

      private static final double TWO_TO_53
      Constant: 2^53.
      See Also:
    • TWO_TO_NEG24

      private static final double TWO_TO_NEG24
      Constant: 2^-24.
      See Also:
    • TWO_TO_NEG25

      private static final double TWO_TO_NEG25
      Constant: 2^-25.
      See Also:
    • TWO_TO_NEG27

      private static final double TWO_TO_NEG27
      Constant: 2^-27.
      See Also:
    • TWO_TO_NEG31f

      private static final float TWO_TO_NEG31f
      Constant: 2^-31.
      See Also:
    • TWO_TO_NEG31

      private static final double TWO_TO_NEG31
      Constant: 1/2^-31.
      See Also:
    • INV_TWO_TO_31M1

      private static final double INV_TWO_TO_31M1
      Constant: 1/(2^-31 - 1).
      See Also:
    • TWO_TO_NEG52

      private static final double TWO_TO_NEG52
      Constant: 2^-52.
      See Also:
    • TWO_TO_NEG53

      private static final double TWO_TO_NEG53
      Constant: 2^-53.
      See Also:
    • mt

      private int[] mt
      The array for the state vector
    • mti

      private int mti
      The current index for the state vector. mti == N+1 means mt[N] is not initialized.
    • __nextNextGaussian

      private double __nextNextGaussian
      Gaussian random numbers are generated in pairs. This is the second of the two.
    • __haveNextNextGaussian

      private boolean __haveNextNextGaussian
      The flag to indicate that the next Gaussian has already been generated.
      See Also:
    • buffer

      private static StringBuilder buffer
      ChH: for testing on GWT/JRE platforms logging needs to be rewritten
  • Constructor Details

    • MersenneTwister

      public MersenneTwister()
      Constructor using the default seed.
    • MersenneTwister

      public MersenneTwister(long seed)
      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.
      Parameters:
      seed - for random number generator
    • MersenneTwister

      public MersenneTwister(int[] array)
      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.
      Parameters:
      array - of integers for seeding the random number generator
  • Method Details

    • encodeState

      public String encodeState()
      Encode state of random number generator as plist for saving.
      Returns:
      plist string encoding state of random number generator
    • restoreState

      public boolean restoreState(Plist plist)
      Restore state of random number generator from plist encoded string.
      Parameters:
      plist - encoded state of random number generator
      Returns:
      true if state successfully restored
    • stateEquals

      public boolean stateEquals(MersenneTwister other)
      Returns true if the MersenneTwister's current internal state is equal to another MersenneTwister. This is roughly the same as equals(other), except that it compares based on value but does not guarantee the contract of immutability (obviously random number generators are immutable). Note that this does NOT check to see if the internal gaussian storage is the same for both. You can guarantee that the internal gaussian storage is the same (and so the nextGaussian() methods will return the same values) by calling clearGaussian() on both objects.
      Parameters:
      other - another MersenneTwister
      Returns:
      true the two MersenneTwister's are identical.
    • setSeed

      public void setSeed(long seed)
      Initialize 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).

      Implementation Notes:

      1. Writing java code that GWT can translate into equivalent JavaScript turns out to be challenging. Stephan Brumme's JavaScript implementation supplied the essential tricks. For details see https://create.stephan-brumme.com/mersenne-twister/
      2. In order to avoid multiplication overflow split 32 bits into 2x 16 bits and process them individually (see mtmti1 in code).
      3. See Knuth TAOCP Vol2. 3rd Ed. p.106 for multiplier
      Parameters:
      seed - the seed for the random number generator
    • setSeed

      public void setSeed(int[] array)
      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.
      Parameters:
      array - of integers for seeding the random number generator
    • twist

      private void twist()
      The twister: core mechanism for generating pseudo random numbers.

      Note: Adapted from mersenne.js, JavaScript version of MersenneTwister by Stephan Brumme.

      See Also:
    • nextUInt

      private int nextUInt()
      Generates a 32bit 'unsigned' random int in [0, 2^33-1]. All 32bits represent random number - use with care! Allows to verify output with original mt19937ar.c output.

      From mt19937ar.c: generates a random number on [0, 0xffffffff]-interval corresponds to: unsigned long genrand_int32

      Returns:
      random int in [0, 2^33-1]
    • nextInt

      public int nextInt()
      Generate a 31bit (signed) random int in [0, Integer.MAX_VALUE).

      From mt19937ar.c: generates a random number on [0, 0x7fffffff]-interval corresponds to: unsigned long genrand_int31

      Returns:
      random int in [0, 2^32-1]
    • nextInt

      public int nextInt(int n)
      Generate a random int in [0, n-1]-interval.
      Parameters:
      n - integer upper bound (exclusive)
      Returns:
      random integer in [0, n)
      Throws:
      IllegalArgumentException - if n ≤ 0
    • nextULong

      private long nextULong()
      Generate a 64bit unsigned random long in [0, 2^65-1].
      Returns:
      random long integer in [0, 2^65-1]
    • nextLong

      public long nextLong()
      Generate a 63bit (signed) random long integer in [0, Long.MAX_VALUE).

      Note:

      • Twice as expensive as nextInt().
      • Do not use in GWT applications (long integers are CPU hogs).
      Returns:
      random long integer in [0, 2^63-1]
    • nextLong

      public long nextLong(long n)
      Generate a random long integer in [0, n) with n > 0.

      Note:

      • Twice as expensive as nextInt(int).
      • Do not use in GWT applications (long integers are CPU hogs).
      Parameters:
      n - integer upper bound (exclusive)
      Returns:
      random long integer in [0, n]
      Throws:
      IllegalArgumentException - if n ≤ 0
    • nextShort

      public short nextShort()
      Generates a random short integer on [0, 0xffff]-interval.

      Note:

      • same as nextChar() but different return type.
      • Do not use in GWT applications (short integers are not supported).
      Returns:
      random short integer in [0, 65536)
    • nextChar

      public char nextChar()
      generates a random char on [0, 0xffff]-interval.

      Note: same as nextShort() but different return type.

      Returns:
      random short integer in [0, 65536)
    • nextByte

      public byte nextByte()
      Generates a random byte on [0, 0xff]-interval.
      Returns:
      random short integer in [0, 16)
    • nextBytes

      public void nextBytes(byte[] bytes)
      Fill array bytes with random bytes.
      Parameters:
      bytes - random bytes stored here
      See Also:
    • nextBoolean

      public boolean nextBoolean()
      Generates a random boolean.
      Returns:
      true with 50% chance
    • nextBoolean

      public boolean nextBoolean(float probability)
      This generates a coin flip with a probability probability of returning true, else returning false. probability must be in [0, 1]. Not as precise as nextBoolean(double), but twice as fast. To explicitly use this, remember you may need to cast to float first.

      Note: Do not use in GWT applications (float's create overhead).

      Parameters:
      probability - for returning true
      Returns:
      true with probability
      Throws:
      IllegalArgumentException - if probability<0 or probability>1
    • nextBoolean

      public boolean nextBoolean(double probability)
      This generates a coin flip with a probability probability of returning true, else returning false. probability must be in [0, 1].

      Note: More accurate than nextBoolean(float), but twice as expensive

      Parameters:
      probability - for returning true
      Returns:
      true with probability
      Throws:
      IllegalArgumentException - if probability<0 or probability>1
    • nextDoubleHigh

      public double nextDoubleHigh()
      Generates a random high-precision double on half-open [0, 1)-interval.

      From mt19937ar.c: generates a random number on [0,1) with 53-bit resolution corresponds to: double genrand_res53(void).

      Note: Twice as expensive as nextDouble() or the equivalent nextFloat().

      Returns:
      random high-precision double in [0, 1)
    • nextDouble

      public double nextDouble()
      Generate random double on half-open [0, 1)-interval.

      From mt19937ar.c: generates a random number on [0,1)-real-interval corresponds to: double genrand_real2(void).

      Note:

      Returns:
      random double in [0, 1)
    • nextDoubleClosed

      public double nextDoubleClosed()
      Generate random double on closed [0, 1]-interval

      From mt19937ar.c: generates a random number on [0,1]-real-interval corresponds to: double genrand_real1(void).

      Note: one bit lost compared to original due to signed int.

      Returns:
      random double in [0, 1]
    • nextDoubleOpen

      public double nextDoubleOpen()
      Generate random double on open (0, 1)-interval

      From mt19937ar.c: generates a random number on (0,1)-real-interval corresponds to: double genrand_real3(void).

      Note: one bit lost compared to original due to signed int.

      Returns:
      random double in (0, 1)
    • nextFloat

      public float nextFloat()
      Generates a random float on half-open [0, 1)-interval.

      Note:

      • Twice as fast as nextDouble().
      • Do not use in GWT applications (float's create overhead).
      Returns:
      random float in [0, 1)
    • clearGaussian

      public void clearGaussian()
      Clears the internal Gaussian variable from the RNG. You only need to do this in the rare case that you need to guarantee that two RNGs have identical internal state. Otherwise, disregard this method.
      See Also:
    • nextGaussian

      public double nextGaussian()
      Generate random number from standard normal distribution (Gaussian distribution).
      Returns:
      random number
    • clone

      public MersenneTwister clone()
      Clone this MersenneTwister to ensure both objects return identical sequences of random numbers.

      IMPORTANT:

      1. overrides clone() in Object but conflicts with GWT's aversion to clone()ing...
      2. remove @SuppressWarnings("all") to ensure that no other issues crept in when modifying method.
      Overrides:
      clone in class Object
      Returns:
      clone of MersenneTwister random number generator
    • appendProgress

      private static void appendProgress(String msg)
      Append message to buffer (no newline added).
      Parameters:
      msg - message to append
    • logProgress

      private static void logProgress()
      Append newline to buffer.
    • logProgress

      private static void logProgress(String msg)
      Append message to buffer (adding newline).
      Parameters:
      msg - message to append
    • testCorrectness

      public static void testCorrectness(Logger logger)
      Tests if generated random numbers comply with reference mt19937ar.c.
      Parameters:
      logger - for reporting progress and results
    • testSpeed

      public static void testSpeed(Logger logger, MersenneTwister.Chronometer clock, int nSamples)
      Tests speed of MersenneTwister as compared to Random.
      Parameters:
      logger - for reporting progress and results
      clock - device for measuring elapsed time
      nSamples - number of samples for testing speed
    • main

      public static void main(String[] args)
      Tests the code.
      Parameters:
      args - command line arguments - ignored