sha512 hasn't shown collisions, afaik
SHA512 has 512 bits (64 bytes).
Computing all hashes from all possible unique files of 65 bytes, you will find at least 256 collisions.
Computing all hashes from all possible unique files of 66 bytes, you will find at least 65536 collisions.
Computing all hashes from all possible unique files of 67 bytes, you will find at least 16777216 collisions.
I'm no security expert.
http://en.wikipedia.org/wiki/SHA-2SHA-2 - SHA-512/384, Collisions found: none
So I thought, with everything below SHA-2, including obviously stuff like md5, collisions have been found; therefore they are insecure.