Re: [Help-gsl] Random Number Generator

[John Lamb]

Dr Jekyll wrote:
> Can someone explain to me the following three "gsl_rng_type" pointers, where
> does they come from? I only know some generators such as LeCuyer... but
> never heards generators whose name contains "19937" or something like that!
> gsl_rng_mt19937
> gsl_rng_mt19937_1999
> gsl_rng_mt19937_1998

See below for details: the 1998 and 1999 versions are older 
implementations that are not as good but preserved, presumably for the 
sake of consistency.

Mersenne twister: a 623-dimensionally equidistributed uniform 
pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation
Volume 8 ,  Issue 1  (January 1998)
Pages: 3 - 30

ISSN:1049-3301
Authors         
Makoto Matsumoto 	 Keio Univ., Yakohama; and the Max-Planch-Institut Für 
Mathematik, Japan
Takuji Nishimura         Keio Univ., Yokohama, Japan

 A new algorithm called Mersenne Twister (MT) is proposed for 
generating uniform pseudorandom numbers. For a particular choice of 
parameters, the algorithm provides a super astronomical period of 219937 
-1 and 623-dimensional equidistribution up to 32-bit accuracy, while 
using a working area of only 624 words. This is a new variant of the 
previously proposed generators, TGFSR, modified so as to admit a 
Mersenne-prime period. The characteristic polynomial has many terms. The 
distribution up to v bits accuracy for 1 ? v ? 32 is also shown to be 
good. An algorithm is also given that checks the primitivity of the 
characteristic polynomial of MT with computational complexity O(p2) 
where p is the degree of the polynomial.We implemented this generator in 
portable C-code. It passed several stringent statistical tests, 
including diehard. Its speed is comparable to other modern generators. 
Its merits are due to the efficient algorithms that are unique to 
polynomial calculations over the two-element field.

--
JDL