public final class MersenneTwister extends RandomEngine
Quality: MersenneTwister is designed to pass the kdistribution test. It has an astronomically large period of 2^{19937}1 (=10^{6001}) and 623dimensional equidistribution up to 32bit 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 nonnegligible 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 Date());
sum += twister.raw();
}
will be wildly inefficient. Consider using
double sum = 0.0;
RandomElement twister = new MersenneTwister(new 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 623Dimensionally Equidistributed Uniform PseudoRandom Number Generator", ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 330.
The correctness of this implementation has been verified against the published output sequence mt199372.out of the Cimplementation mt199372.c. (Call test(1000) to print the sequence).
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 32bit numbers, and every kdimensional 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: 32bit 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.
Random
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.

Modifier and Type  Method and Description 

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).

apply, apply, nextDouble, nextFloat, nextLong, raw
isDensifying
public MersenneTwister()
public MersenneTwister(int seed)
seed
 A number that is used to initialize the internal state of the generator.public MersenneTwister(Date d)
d
 typically new Date()public int nextInt()
nextInt
in class RandomEngine
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