Random Number Generators for Parallel Computers
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Over the years many widely-used methods for generating pseudo-random numbers
have been shown to be inadequate,
either by theoretical arguments, or empirical tests, or both.
In some cases theoretical arguments can show that there are correlations in
the sequence of numbers, however in many cases the problems only show up in
empirical tests that statistically compare the results produced by the
random number generators with results expected from a truly random sequence
of numbers. Many standard tests of this kind are available
[1, 2, 18].
In addition to standard statistical tests, it is useful to apply
application-specific tests that are more relevant to some of the various
applications for which random numbers are used.
As with the statistical tests, these tests generally
compare the results obtained using a pseudo-random number
generator with known exact results that would occur if the numbers
were truly random.
Tests of this kind include Monte Carlo simulation [19, 20]
of exactly solvable systems such as the two dimensional
Ising model [10, 21, 13, 15, 16, 17],
simulations of percolation models [22],
and random walks [14, 22, 17].
Generators that pass standard statistical tests have sometimes been found
to fail these application-specific tests. It is therefore important to
use as wide a variety of empirical tests as possible.
Any application can in principle be used to test random number generators,
by comparing results obtained with two different
generators [8, 9, 10].
Copyright © 1996
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Paul Coddington, paulc@npac.syr.edu