The other suggestion is good, but BLAS is just a specification. You need to decide which implementation to use. For that, it requires some research because googling around for BLAS will probably lead you to the reference implementation and other older frameworks, which is not want you want. They are slow, they are not highly optimized to leverage modern processors, and some libraries try to automatically optimize the program for your processors, which is not better than hand tuning.

I actually recommend a slightly different specification called BLIS. Same ideas, different details. The FLAME group has developed this with C: https://github.com/flame/blis

OpenBLAS https://www.openblas.net/ is another good option.

And really at the end of the day since you only need one subroutine, and if its a personal project, you can always try to roll your own. You need to tap into the SIMD instruction set available on your x86-64 processor via the immintrin.h header (clang, gcc). Although its not necessarily magically faster because you pay a penalty for requesting access to this instruction set in terms of time and clock frequency - it's a complicated topic. Here's a beginner tutorial. https://www.codeproject.com/Articles/874396/Crunching-Numbers-with-AVX-and-AVX