Instead of mucking around with Windows 3.0-esque pseudo-threading and polling, you could just use proper threading:

#! perl -slw
use strict;
use bignum;
use threads;
use threads::shared;

my $result :shared;
async {
    my $comp = 0;
    for my $i ( 1 .. 1e6 ) {
        $comp += $i ** $i;
    }
    $result = '' . $comp;
}->detach;

while( sleep 1 ) {
    print "timer event";
    last if $result;
}

print $result;
[download]

It's simpler, and actually works!