The smart thing is not to write the crypto yourself but to use something like passlib: https://bitbucket.org/ecollins/passlib/wiki/Home
It is easy to mess up writing your crypto code in a secure way. The nasty thing is that with non crypto code you often immediately notice it when it is not working since your program crashes. While with crypto code you often only find out after it is to late and your data has been compromised. Therefor I think it is better to use a package written by someone else who is knowledgable about the subject and which is based on battle tested protocols.
Also passlib has some nice features which make it easy to use and also easy to upgrade to a newer password hashing protocol if an old protocol turns out to be broken.
Also just a single round of sha512 is more vulnerable to dictionary attacks. sha512 is designed to be fast and this is actually a bad thing when trying to store passwords securely. Other people have thought long and hard about all this sort issues so you better take advantage of this.