## 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

- Direct Known Subclasses:
- MersenneTwister64

public class MersenneTwisterextends 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 2^{19937}-1 (=10^{6001}) 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 datastructures used by a MersenneTwister. Code likedouble 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 usingdouble 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 objectto 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-implementationmt19937-2.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 theperiod 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):n123456789101112 .. 1617 .. 32k1993799686240498437383115249324921869186912481246623MersenneTwister 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 2^{32}sub intervals, then randomly choosing one subinterval.`double`'s are formed by dividing the interval`[0.0,1.0]`into 2^{64}sub intervals, then randomly choosing one subinterval.- See Also:
`Random`

, Serialized Form

### Field Summary

Fields Modifier and Type Field and Description `static int`

**DEFAULT_SEED**### Fields inherited from class cern.colt.PersistentObject

`serialVersionUID`

### 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

Methods Modifier and Type Method and Description `Object`

**clone**()Returns a copy of the receiver; the copy will produce identical sequences.`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`).### Methods inherited from class cern.jet.random.engine.RandomEngine

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

### 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.

#### 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`

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