I want to use SHA-512 for hashing in a system that must be FIPS-compliant. When I look at the FIPS 140 list of approved providers, I don't see SHA from any provider as being an approved algorithm, I only see it as an "other" algorithm. In FIPS 180, SHA-512 is listed as being approved, although I don't see any specific references for approved providers.
Is there another list of approved providers of SHA-512 (or SHA-256, or whatever) that I have not found? Or is there no list of approved providers because they are all acceptable for use?