GrandFather already explained why your code was not doing what you thought it was.

Here's an additional solution for achieving what you want though:

use Cwd qw(abs_path);
use File::Basename qw(dirname);

my $dirname = dirname(__FILE__);
my $db_dir_qfn = abs_path("$dirname/../db");

print "$db_dir_qfn\n";
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