bignum isn't needed. The example only requires 11 bits, for example.

Perl uses doubles which have 52 bits of precision. The above algorithms can safely handle strings
(((2^52)-1)/((2^8)-1))*2 = 17,661,175,009,296 chararacters long.

Using just ints on a 32 bit system, the above algorithms can safely handle strings
(((2^32)-1)/((2^8)-1))*2 = 16,843,008 chararacters long.