SHA512/224 and SHA512/256 are truncated versions of SHA512. Just like SHA384 they use the same algorithm but different initial values and a smaller digest. I took the start vectors and test values from libtomcrypt.

Like in my blake2 branch I have add tp_new to the types and removed the old factory methods. Now it is possible to instantiate the types.

The code is also in my github fork https://github.com/tiran/cpython/tree/feature/sha512truncated

Would it be appropriate to mention these hashes higher up in the documentation, e.g. where it lists the names of the always-present constructors?

I haven’t had a close look at the C code. It looks like you are also adding better multithreading support for SHA-512 objects (? related to Issue 4821).

Was this patch mostly ready to go? The additional SHA512 variants are appealing because they run ~40% faster than SHA256 on 64-bit hardware for longer messages.

OpenSSL 1.1.1 comes with sha512_256 and sha512_224. I propose that we use the OpenSSL implementation and don't add the variants to our _sha512 module.

>>> hashlib.new("sha512_256").hexdigest()
'c672b8d1ef56ed28ab87c3622c5114069bdd3ad7b8f9737498d0c01ecef0967a'
>>> hashlib.new("sha512_224").hexdigest()
'6ed0dd02806fa89e25de060c19d3ac86cabb87d6a0ddd05c333b84f4'