ObCounter: if you're so concerned about speed, why are you doing numerics in Perl? :-) In case of the reverse join, I don't see why your code is better anyway: you are constantly replacing the string by a character+string.

In any case, it could probably be sped up a little by using string reverse vs list reverse:

sub mul2 {
    my ( $str, $have_overflow ) = @_;

    my $ret = reverse join '', map {
        my $c = $_ * 2 + ( $have_overflow ? 1 : 0 );
        $have_overflow = ( $c >= 10 );
        ( $c % 10 );
    } split //, scalar reverse $str;

    ( $have_overflow ? 1 : '' ) . $ret;
}
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Makeshifts last the longest.