HTTP authenticate a directory via an existing users table in a database.

Question

I wish to tie my user accounts into HTTP for a specific directory of my website and normally that wouldn't be too much of a problem, because I could either edit the htpasswd file or use mod_auth_mysql (which I'm not too familiar with). However, the passwords are encrypted using SHA1 and a salt. How can I HTTP authentication password an entire directory from my database using this method?

I'm aware that PHP has an authentication method: http://php.net/manual/en/features.http-auth.php But that doesn't work, because I would prefer to password protect the entire directory via an AuthUserFile or some other method that would not involve me modifying the open source software I wish to place in the directory.