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Re: Random Number Generator of large period

  • Subject: [mg3351] Re: Random Number Generator of large period
  • From: withoff (David Withoff)
  • Date: 29 Feb 1996 15:31:40 -0600
  • Approved:
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Wolfram Research, Inc.
  • Sender: daemon at

In article <4gro5a$1d6 at> ross at writes:
> Here is a request for information.
> Does anyone know of the whereabout of (code for) 
> a Random-Number Generator (Linear-Congruential or otherwise) 
> that produces output ``uniformally distributed''
> amongst at least 2^96 objects?
> i.e. integers: {1, ..., 2^96 }  
> The code can be in any language: Mathematica, C, APL, Maple, ....
> Concerning Mathematica...
> What are the technical specs on the RNG used by Mathematica?
> What is its period?
> How many distinct ``seeds'' are accepted by  SeedRandom[] 
> and/or how many distinct starting-points for Random[]
> are generated by seeding?
> Indeed, does Mathematica even provide an RNG distinct from that
> which may be built-in to the host-computer's operating system?
> Please email replies to myself and  timbourk at,
> posting to the group only if you think there is general interest.
> Thanks,
> 	Ross
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Ross Moore                         Internet: ross at
> Mathematics Department                Work:       +61 2 850-8955
> Macquarie University                   Home:   please do not try
> North Ryde, Sydney                     Fax:       +61 2 850-8114
> Australia  2109
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The machine real random number generator is based on

    George Marsaglia and Arif Zaman, "A New Class of Random Number
    Generators", The Annals of Applied Probability, 1991, Vol. 1,
    No. 3, p462-480.

There are several variants that are listed in that paper.  The
one used by Mathematica is the one that is listed in that paper
as having a period of 10^445.  I believe that the number of possible
seeds is comparable, but I think that the reference above has a more
thorough discussion of that.

Dave Withoff
Research and Development
Wolfram Research

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