Brute-force algorithm:

sub is_power {
    # Some algorithm to determine if a number is a power of two.
}

sub closest_power_of_two_brute {
    my $m = my $n = shift;

    return $n if is_power( $n, 2 );

    while (1) {
        return $n if is_power( $++n, 2 );
        return $m if is_power( $--m, 2 );
    }
}

##</code><code>##

Predictive algorithm:

sub iterate_over {
    my $v = shift;
    return sub {
        $v *= $v;
    };
}

sub closest_power_of_two_predictive {
    my $n = shift;

    my $it = iterate_over( 2 );

    my $l = $it->();
    while ( my $v = $it->() ) {
        last if $v > $n;
        $l = $v;
    }

    abs( $n - $l ) > abs( $n - $v ) ? $v : $l;
}