## Class MersenneTwister

• All Implemented Interfaces:
Serializable, Cloneable, DoubleUnaryOperator, IntUnaryOperator
Direct Known Subclasses:
MersenneTwister64

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.

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
Random, Serialized Form
• ### Field Summary

Fields
Modifier and Type Field Description
static int DEFAULT_SEED
• ### Constructor Summary

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

All Methods
Modifier and Type Method 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)
• ### Methods inherited from class com.opengamma.strata.math.impl.cern.RandomEngine

applyAsDouble, applyAsInt, makeDefault, nextDouble, nextFloat, nextLong, raw
• ### Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface java.util.function.DoubleUnaryOperator

andThen, compose
• ### Methods inherited from interface java.util.function.IntUnaryOperator

andThen, compose
• ### Field Detail

• #### DEFAULT_SEED

public static final int DEFAULT_SEED
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.
Parameters:
seed - the 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.
Returns:
• #### 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
Returns:
the random number
• #### setSeed

protected void setSeed​(int seed)
Sets the receiver's seed. This method resets the receiver's entire internal state.
Parameters:
seed - the seed