Re: Entropy (was Re: how to generate random negative numbers)

[Eric De Mund <ead-debian-user@ixian.com>]

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 illustrate, assuming that each $RANDOM value is uniform over {0,1,2}
mod 3, here is the table of the function b-a:

              b
     +-------------
     | |  0   1   2
     +-+-----------
     |0|  0   1   2
    a|1| -1   0   1
     |2| -2  -1   0

5 (the number of values in {-2,-1,0,1,2}) simply doesn't divide 9 (the
number of values in {0,1,2}x{0,1,2})

(Also, remember that when one adds multiple random deviates, as the
number of deviates approaches infinity, the distribution approaches
Gaussian. Here, with two deviates, one ends up with a "triangle"
distribution.)

Programmatic cleverness sometimes works, but it's a sharp knife. One
must be careful not to accidentally cut oneself.

Regards,
Eric
--
Eric De Mund   |  Y!: ead0002
ead@ixian.com  |  ICQ: 811788