phpass the best solution for secure password-storing?

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I'm creating a service which handles a lot of personal data, and therefor it's not appropriate to let the passwords simply fly out. I've been diggin' around to find any possible solutions, and one that caught my attention is phpass. I did read about it on StackOverflow over here.

I'm aware that there are a lot of questions about this subject, but I'd just like to clarify, that phpass is a secure way of storing passwords. The reason to my suspiciousness is that it doesn't use any salts (at least doesn't seem to use), which are, I've been told, the key to secure storing.

My current method is simply a sha512-hash with one user-specific salt, and another site-specific hash. Here's a clip of my PHP-code:

hash_hmac('sha512', $password.$account_specific, $site_specific);

It would be great to hear some expert-ish opinions on this matter. I apologize for creating another thread for the subject that's been and will always be asked about. Thanks in advance.

EDIT:
I've also heard that hashing a password, let's say, 1000 times is also a good way to store passwords. This way hashing only takes a few seconds (at max), but breaking the hashed password takes literally ages?

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