Eric De Mund wrote:
Ron,
John Hasler:
] echo $(( $(( $RANDOM - $RANDOM )) % 3 ))
Ron Johnson:
] Does this burn through entropy faster than other methods?
Yes. Twice as fast. And, more importantly, it's mathematically
incorrect. It does not have the same probability density function as:
echo $(( $(($RANDOM % 5)) - 2))
To be complete, (( $(($RANDOM % 5)) - 2)) is not perfect either, but
closer to perfection if $RANDOM is a true random generator.
To simplify things, let's assume that the numbers we work on are 4 bits
long. The possible values are:
$RANDOM -> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
$RANDOM % 5 -> 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0
You see that 0 has a higher probability than the other values.
If Max is the biggest int that can be generated by $RANDOM, and N is the
number of different values we need, we should throw away any value of
$RANDOM that is >= int(Max / N) * N.
Just my 2 cents ;-)
François.
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