Package org.evoludo.math

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	MersenneTwister.Chronometer	The minimal Chronometer interface is only used to hide differences for measuring execution time in JRE and GWT.
(package private) static class	MersenneTwister.StopWatch	Minimal implementation of Chronometer.

Field Summary

Fields

Modifier and Type	Field	Description
private boolean	__haveNextNextGaussian	The flag to indicate that the next Gaussian has already been generated.
private double	__nextNextGaussian	Gaussian random numbers are generated in pairs.
private static final int	BIT32_MASK
private static StringBuilder	buffer	ChH: for testing on GWT/JRE platforms logging needs to be rewritten
private static final double	INV_TWO_TO_31M1	Constant: 1/(2^-31 - 1).
private static final int	LOWER_MASK
private static final int	M
private static final int	MATRIX_A
private int[]	mt	The array for the state vector
private int	mti	The current index for the state vector.
private static final int	N	Period parameters
private static final int	TEMPERING_MASK_B	Tempering parameters
private static final int	TEMPERING_MASK_C
private static final double	TWO_TO_27	Constant: 2^27.
private static final float	TWO_TO_31f	Constant: 2^31.
private static final double	TWO_TO_31M1	Constant: 2^31 - 1.
private static final double	TWO_TO_32	Constant: 2^32.
private static final double	TWO_TO_53	Constant: 2^53.
private static final double	TWO_TO_NEG24	Constant: 2^-24.
private static final double	TWO_TO_NEG25	Constant: 2^-25.
private static final double	TWO_TO_NEG27	Constant: 2^-27.
private static final double	TWO_TO_NEG31	Constant: 1/2^-31.
private static final float	TWO_TO_NEG31f	Constant: 2^-31.
private static final double	TWO_TO_NEG52	Constant: 2^-52.
private static final double	TWO_TO_NEG53	Constant: 2^-53.
private static final int	UPPER_MASK

Constructor Summary

Constructors

Constructor	Description
MersenneTwister()	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	appendProgress(String msg)	Append message to buffer (no newline added).
void	clearGaussian()	Clears the internal Gaussian variable from the RNG.
MersenneTwister	clone()	Clone this MersenneTwister to ensure both objects return identical sequences of random numbers.
String	encodeState()	Encode state of random number generator as plist for saving.
private static void	logProgress()	Append newline to buffer.
private static void	logProgress(String msg)	Append message to buffer (adding newline).
static void	main(String[] args)	Tests the code.
boolean	nextBoolean()	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	nextByte()	Generates a random byte on [0, 0xff]-interval.
void	nextBytes(byte[] bytes)	Fill array bytes with random bytes.
char	nextChar()	generates a random char on [0, 0xffff]-interval.
double	nextDouble()	Generate random double on half-open [0, 1)-interval.
double	nextDoubleClosed()	Generate random double on closed [0, 1]-interval
double	nextDoubleHigh()	Generates a random high-precision double on half-open [0, 1)-interval.
double	nextDoubleOpen()	Generate random double on open (0, 1)-interval
float	nextFloat()	Generates a random float on half-open [0, 1)-interval.
double	nextGaussian()	Generate random number from standard normal distribution (Gaussian distribution).
int	nextInt()	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	nextLong()	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	nextShort()	Generates a random short integer on [0, 0xffff]-interval.
private int	nextUInt()	Generates a 32bit 'unsigned' random int in [0, 2^33-1].
private long	nextULong()	Generate a 64bit unsigned random long in [0, 2^65-1].
boolean	restoreState(Plist plist)	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	stateEquals(MersenneTwister other)	Returns true if the MersenneTwister's current internal state is equal to another MersenneTwister.
static void	testCorrectness(Logger logger)	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	twist()	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:

• Constant Field Values

M

private static final int M

See Also:

• Constant Field Values

MATRIX_A

private static final int MATRIX_A

See Also:

• Constant Field Values

BIT32_MASK

private static final int BIT32_MASK

See Also:

• Constant Field Values

UPPER_MASK

private static final int UPPER_MASK

See Also:

• Constant Field Values

LOWER_MASK

private static final int LOWER_MASK

See Also:

• Constant Field Values

TEMPERING_MASK_B

private static final int TEMPERING_MASK_B

Tempering parameters

See Also:

• Constant Field Values

TEMPERING_MASK_C

private static final int TEMPERING_MASK_C

See Also:

• Constant Field Values

TWO_TO_27

private static final double TWO_TO_27

Constant: 2^27.

See Also:

• Constant Field Values

TWO_TO_31f

private static final float TWO_TO_31f

Constant: 2^31.

See Also:

• Constant Field Values

TWO_TO_31M1

private static final double TWO_TO_31M1

Constant: 2^31 - 1.

See Also:

• Constant Field Values

TWO_TO_32

private static final double TWO_TO_32

Constant: 2^32.

See Also:

• Constant Field Values

TWO_TO_53

private static final double TWO_TO_53

Constant: 2^53.

See Also:

• Constant Field Values

TWO_TO_NEG24

private static final double TWO_TO_NEG24

Constant: 2^-24.

See Also:

• Constant Field Values

TWO_TO_NEG25

private static final double TWO_TO_NEG25

Constant: 2^-25.

See Also:

• Constant Field Values

TWO_TO_NEG27

private static final double TWO_TO_NEG27

Constant: 2^-27.

See Also:

• Constant Field Values

TWO_TO_NEG31f

private static final float TWO_TO_NEG31f

Constant: 2^-31.

See Also:

• Constant Field Values

TWO_TO_NEG31

private static final double TWO_TO_NEG31

Constant: 1/2^-31.

See Also:

• Constant Field Values

INV_TWO_TO_31M1

private static final double INV_TWO_TO_31M1

Constant: 1/(2^-31 - 1).

See Also:

• Constant Field Values

TWO_TO_NEG52

private static final double TWO_TO_NEG52

Constant: 2^-52.

See Also:

• Constant Field Values

TWO_TO_NEG53

private static final double TWO_TO_NEG53

Constant: 2^-53.

See Also:

• Constant Field Values

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:

• __nextNextGaussian

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:

• https://create.stephan-brumme.com/mersenne-twister/

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:

• nextByte()

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:

• Twice as fast as nextDoubleHigh()
• Equivalent to nextFloat()
• One bit lost compared to original due to signed int

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:

• stateEquals(MersenneTwister)

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