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From: "Robert I. Eachus" <eachus@mitre.org>
Subject: Re: Array of Variant Records Question...
Date: 1999/09/22
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Robert A Duff wrote:
 
> I don't know much about the theory of these things, but I was under the
> impression that Random can never ever return the same value twice in a
> row.  Robert Eachus or somebody can tell us for sure.

   See previous post.  There is a major distiction here between a
floating-point generator and an integer or fixed-point generator.  In an
idealized enivronment, a floating-point generator would have zero chance
of
returning the same value twice in a row.  (There are aleph-one possible
return values and any generator can only return aleph-null of them. 
Therefore the probabilty of returning the same value the next time it is
called is one over aleph-one.)  But in a computer environment where
floating point values are represented by a finite set of values, there
should be a small but finite probability that two succesive values are
the same.

   In the fixed-point or integer case, the number of possible return
values is very small, so that the probability of repeated values in a
long sequence approaches unity.  (Even in a boolean generator, if it is
truly random, there is a finite probability that you will see a long
sequence of True, False, True, False, True, etc...)
> 
> I do know that in fact the Random function is *not* random.
 
    (Okay, you asked.) Which Random function?  How do you know that? 
Linear Congruential Generators have a lot of faults, including that it
is possible to look at a short sequence and predict the next value.  Or
to put it differently successive  values are highly correlated.  In
fact, if you look at the unscaled output of an LCG you will never see
the same value repeated until the generator runs through its entire
period.

    The generator used by GNAT is much different.  You can only tell it
is not random by knowing its period, either by running the generator
that long, looking at interior details, or by being a very good
cryptographer.  If the generator does not behave that way, there is a
bug in the code.  (And there was a minor bug in the 3.10p code for the
integer generator...)  Pseudo-random number generators of this type are
technically "more random than random," and are used to "whiten" the
outpot of physical generators that sample the environment.
-- 

                                        Robert I. Eachus

with Standard_Disclaimer;
use  Standard_Disclaimer;
function Message (Text: in Clever_Ideas) return Better_Ideas is...