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From: tmoran@acm.org
Newsgroups: comp.lang.ada
Subject: Re: Ada2005 random
References: <uadf5s8pi.fsf@wanadoo.fr>
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> Ok, but integer has a range of -(2 ** 31) .. +(2 ** 31 - 1) so the difference
> could be something around +/- (x / (2 ** 31 - 1)) !
  A small error if x is small, but rather large if x is, say, 3/8 * 2**31
If the generator's range = a*x+b, then (random mod x) will take
values < b a+1 times and values >= b only a times.  If a is small,
a/(a+1) will differ substantially from 1.0
  Also, there's no guarantee that the generator's range is Integer or
that it is 32 bits wide.