Question

rand(n) returns a number between 0 and n. Will rand work as expected, with regard to “randomness”, for all arguments up to the integer limit on my platform?

Answer 1

This is going to depend on your randbits value:

rand calls your system’s random number generator (or whichever one was
compiled into your copy of Perl). For this discussion, I’ll call that
generator RAND to distinguish it from rand, Perl’s function. RAND produces
an integer from 0 to 2**randbits – 1, inclusive, where randbits is a small
integer. To see what it is in your perl, use the command ‘perl
-V:randbits’. Common values are 15, 16, or 31.

When you call rand with an argument arg, perl takes that value as an
integer and calculates this value.

                        arg * RAND
          rand(arg) = ---------------
                        2**randbits

This value will always fall in the range required.

          0  <=  rand(arg)  < arg

But as arg becomes large in comparison to 2**randbits, things become
problematic. Let’s imagine a machine where randbits = 15, so RAND ranges
from 0..32767. That is, whenever we call RAND, we get one of 32768
possible values. Therefore, when we call rand(arg), we get one of 32768
possible values.