I assume we're supposed to take constant time comparison as an axiom?

use Math::BigInt;
use Benchmark qw( cmpthese ) ;

my $x = (new Math::BigInt 2)**(2**16);
my $y = $x - 1;
my $m = new Math::BigInt 2;
my $n = $m + 1;

cmpthese(-1, { large => sub{ $y < $x },
               small => sub{ $m < $n } });
[download]