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From: anonymous-remailer@shell.portal.com
Date: Wed, 4 Oct 95 11:23:15 PDT
To: cypherpunks@toad.com
Subject: Random number generators
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http://www.uni-karlsruhe.de/~RNG/
> Random number generators
>
> --------------------------------------------------------------------
> Diese Seite gibt es noch nicht in Deutsch.
> --------------------------------------------------------------------
>
> Classification of random numbers
>
> Random numbers for use in computer programs can be classified into 3
> different categories:
>
> * Truely random numbers:
> Truely random numbers obviosly cannot be produced by computer
> programs, they must be supplied by an external source like
> radioactive decay. Such sequences are available (e.g. on
> magnetic tape), but clumsy to use and often not sufficient in
> terms of speed and number.
> * Pseudorandom numbers:
> A sequence of numbers is generated by an algorithm in a way
> that the resulting numbers look statistically independent and
> uniformly distributed. This is the prevailing method used in
> random number generators.
> * Quasirandom numbers:
> These are generated by algorithms tuned to optimize the
> sequences uniform distribution, which can improve the accuracy
> of Monte-Carlo integration. These numbers are not independent
> and thus cannot be used generally.
>
> Other than uniform distributions can be generated by suitable
> transformations of the basic uniformly distributed sequence.
> Numerical libraries often offer a rich set of distributions.
>
> Desirable properties of (pseudo) random numbers
>
> A good random number generator (RNG) should have the following
> properties:
>
> * Good statistical properties:
> There are theoretical and empirical tests to judge a RNGs
> quality. Every generator should always be tested with one's
> actual application: the standard tests can only disqualify a
> RNG and may not check for the properties the application
> requires.
> * Long period:
> RNG algorithms are iteration formulae. The state is often
> stored in a single integer, in this case there cannot be more
> states than representable integers (recall 2^30 \approx 10^9).
> * Reproducibility:
> All generators can initialize the sequence by a starting seed.
> Storing and reloading a generator's internal state is also
> useful.
> * Portability:
> This concerns both programming language (e.g. Fortran 90 or
> ANSI C) as well as machine-dependent (e.g. floating point
> representation) aspects. The ideal RNG produces (bit-)
> identical results in every environment.
> * Efficient implementation:
> This may be irrelevant for "general purpose" generators. But
> time-critical applications may require inline coding and/or the
> generation of whole vectors of random numbers at once. Vector
> and parallel computers need special RNG methods.
>
> Which of these aspects is most important depends on the actual
> application, of course.
>
> Miscellaneous RNG material
>
> What follows is a collection of material on pseudorandom number
> generators. I hope to improve this soon...
>
> * The RNG Chapter of Designing and Building Parallel Programs by
> Ian Foster
> * The pLab pages at Salzburg University
> * The RNG Document of ORNL's Computational Science Education
> Project
> * My publications on RNGs are available online, also some slides
> * My BiBTeX-bibliographies of articles and books on random number
> generation
> * The RAND/VP package contains a RNG tuned for our vector
> computer SNI S600/20
> * The NAG and IMSL Fortran libraries contain random number
> generators for various distributions
> * Popular public-domain sources include the StatLib and NetLib
> libraries
> * My publications on RNGs and the RANEXP library are available by
> anonymous ftp also.
> URL: ftp://ftp.rz.uni-karlsruhe.de/pub/misc/random/
> * A good source of RNG codes and articles is the journal Computer
> Physics Communications, ISSN 0010-4655, published by
> North-Holland.
>
> --------------------------------------------------------------------
> Michael Hennecke / 21.07.1995
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1995-10-04 (Wed, 4 Oct 95 11:23:15 PDT) - Random number generators - anonymous-remailer@shell.portal.com