How big can the argument to Perl's rand be? - perl

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.

Answer 2

It depends on the number of bits used by your system's (pseudo)random number generator. You can find this value via
perl -V:randbits
or within a program via
use Config;
my $randbits = $Config{randbits};
rand can generate 2^randbits distinct random numbers. While you can generate numbers larger than 2^randbits, you can't generate all of the integer values in the range [0, N) when N > 2^randbits.
Values of N which aren't a power of two can also be problematic, as the distribution of (integer truncated) random values won't quite be flat. Some values will be slightly over-represented, others slightly under-represented.
It's worth noting that randbits is a paltry 15 on Windows. This means you can only get 32768 (2**15) distinct values. You can improve the situation by making multiple calls to rand and combining the values:
use Config;
use constant RANDBITS => $Config{randbits};
use constant RAND_MAX => 2**RANDBITS;
sub double_rand {
my $max = shift || 1;
my $iv =
int rand(RAND_MAX) << RANDBITS
| int rand(RAND_MAX);
return $max * ($iv / 2**(2*RANDBITS));
}
Assuming randbits = 15, double_rand mimics randbits = 30, providing 1073741824 (2**30) possible distinct values. This alleviates (but can never eliminate) both of the problems mentioned above.

Answer 3

We are talking about big random integers and whether it is possible to get them. It should be noted that the concatenation of two random integers is also a random integer. So if your system, for any reason, cannot go beyond 999999999999, then just write
$bigrand = int(rand(999999999999)).int(rand(999999999999));
and you'll get a random integer of (maximally) twice the length.
(Actually this is not a numeric answer to the question “how big a rand number can be” but rather the answer “you can get as big as you want, just concatenate small numbers”.)