cern.jet.random.engine

Class MersenneTwister

java.lang.Object

cern.colt.PersistentObject

cern.jet.random.engine.RandomEngine

cern.jet.random.engine.MersenneTwister

All Implemented Interfaces:

DoubleFunction, IntFunction, Serializable, Cloneable

public class MersenneTwister
extends RandomEngine

MersenneTwister (MT19937) is one of the strongest uniform pseudo-random number generators known so far; at the same time it is quick. Produces uniformly distributed int's and long's in the closed intervals [Integer.MIN_VALUE,Integer.MAX_VALUE] and [Long.MIN_VALUE,Long.MAX_VALUE], respectively, as well as float's and double's in the open unit intervals (0.0f,1.0f) and (0.0,1.0), respectively. The seed can be any 32-bit integer except 0. Shawn J. Cokus commented that perhaps the seed should preferably be odd.

Quality: MersenneTwister is designed to pass the k-distribution test. It has an astronomically large period of 2¹⁹⁹³⁷-1 (=10⁶⁰⁰¹) and 623-dimensional equidistribution up to 32-bit accuracy. It passes many stringent statistical tests, including the diehard test of G. Marsaglia and the load test of P. Hellekalek and S. Wegenkittl.

Performance: Its speed is comparable to other modern generators (in particular, as fast as java.util.Random.nextFloat()). 2.5 million calls to raw() per second (Pentium Pro 200 Mhz, JDK 1.2, NT). Be aware, however, that there is a non-negligible amount of overhead required to initialize the data structures used by a MersenneTwister. Code like

        double sum = 0.0;
        for (int i=0; i<100000; ++i) {
           RandomElement twister = new MersenneTwister(new java.util.Date());
           sum += twister.raw();
        }

will be wildly inefficient. Consider using

        double sum = 0.0;
        RandomElement twister = new MersenneTwister(new java.util.Date());
        for (int i=0; i<100000; ++i) {
           sum += twister.raw();
        }

instead. This allows the cost of constructing the MersenneTwister object to be borne only once, rather than once for each iteration in the loop.

Implementation: After M. Matsumoto and T. 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.

More info on Masumoto's homepage.

More info on Pseudo-random number generators is on the Web.

Yet some more info.

The correctness of this implementation has been verified against the published output sequence mt19937-2.out of the C-implementation mt19937-2.c. (Call test(1000) to print the sequence). Note that this implementation is not synchronized.

Details: MersenneTwister is designed with consideration of the flaws of various existing generators in mind. It is an improved version of TT800, a very successful generator. MersenneTwister is based on linear recurrences modulo 2. Such generators are very fast, have extremely long periods, and appear quite robust. MersenneTwister produces 32-bit numbers, and every k-dimensional vector of such numbers appears the same number of times as k successive values over the period length, for each k <= 623 (except for the zero vector, which appears one time less). If one looks at only the first n <= 16 bits of each number, then the property holds for even larger k, as shown in the following table (taken from the publication cited above):

n	1	2	3	4	5	6	7	8	9	10	11	12 .. 16	17 .. 32
k	19937	9968	6240	4984	3738	3115	2493	2492	1869	1869	1248	1246	623

MersenneTwister generates random numbers in batches of 624 numbers at a time, so the caching and pipelining of modern systems is exploited. The generator is implemented to generate the output by using the fastest arithmetic operations only: 32-bit additions and bit operations (no division, no multiplication, no mod). These operations generate sequences of 32 random bits (int's). long's are formed by concatenating two 32 bit int's. float's are formed by dividing the interval [0.0,1.0] into 2³² sub intervals, then randomly choosing one subinterval. double's are formed by dividing the interval [0.0,1.0] into 2⁶⁴ sub intervals, then randomly choosing one subinterval.

Version:

1.0, 09/24/99

Author:

wolfgang.hoschek@cern.ch

See Also:

Random, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_SEED

Constructor Summary

Constructors

Constructor and Description
MersenneTwister() Constructs and returns a random number generator with a default seed, which is a constant.
MersenneTwister(Date d) Constructs and returns a random number generator seeded with the given date.
MersenneTwister(int seed) Constructs and returns a random number generator with the given seed.

Method Summary

Modifier and Type	Method and Description
Object	clone() Returns a copy of the receiver; the copy will produce identical sequences.
protected void	nextBlock() Generates N words at one time.
int	nextInt() Returns a 32 bit uniformly distributed random number in the closed interval [Integer.MIN_VALUE,Integer.MAX_VALUE] (including Integer.MIN_VALUE and Integer.MAX_VALUE).
protected void	setSeed(int seed) Sets the receiver's seed.

Methods inherited from class cern.jet.random.engine.RandomEngine

apply, apply, makeDefault, nextDouble, nextFloat, nextLong, raw

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_SEED

public static final int DEFAULT_SEED

See Also:

Constant Field Values

Constructor Detail

MersenneTwister

public MersenneTwister()

Constructs and returns a random number generator with a default seed, which is a constant. Thus using this constructor will yield generators that always produce exactly the same sequence. This method is mainly intended to ease testing and debugging.

MersenneTwister

public MersenneTwister(int seed)

Constructs and returns a random number generator with the given seed.

MersenneTwister

public MersenneTwister(Date d)

Constructs and returns a random number generator seeded with the given date.

Parameters:

d - typically new java.util.Date()

Method Detail

clone

public Object clone()

Returns a copy of the receiver; the copy will produce identical sequences. After this call has returned, the copy and the receiver have equal but separate state.

Overrides:

clone in class PersistentObject

Returns:

a copy of the receiver.

nextBlock

protected void nextBlock()

Generates N words at one time.

nextInt

public int nextInt()

Returns a 32 bit uniformly distributed random number in the closed interval [Integer.MIN_VALUE,Integer.MAX_VALUE] (including Integer.MIN_VALUE and Integer.MAX_VALUE).

Specified by:

nextInt in class RandomEngine

setSeed

protected void setSeed(int seed)

Sets the receiver's seed. This method resets the receiver's entire internal state.