Intel has upcoming instructions for accelerating the calculation of SHA1 /256 hashes.
You can read more about them, how to detect if your CPU support them and how to use them here.
(But not SHA-512, you’ll still need to manually vectorize that with regular SIMD instructions. AVX512 should help for SHA-512 (and for SHA-1 / SHA-256 on CPUs with AVX512 but not SHA extensions), providing SIMD rotates as well as shifts, for example https://github.com/minio/sha256-simd)
It was hoped that Intel’s Skylake microarchitecture would have them, but it doesn’t. Intel CPU’s with it are low-power Goldmont in 2016, then Goldmont Plus in 2017. Intel’s first mainstream CPU with SHA extensions will be Cannon Lake. Skylake / Kaby Lake / Coffee Lake do not.
AMD Ryzen (2017) has SHA extension.
A C/C++ programmer is probably best off using OpenSSL, which will use whatever CPU features it can to hash quickly. (Including SHA extensions on CPUs that have them, if your version of OpenSSL is new enough.)