Libraries don’t cut it, IMO. Sometimes you want your complete input data in registers, 4x4 matrices fit there nicely. Other times you want to stream stuff from memory, the above-mentioned 24x24 multiplication streams the complete matrix, while loading 4-long chunks of the vector.

I’ve wrote an introduction article some time ago: http://const.me/articles/simd/simd.pdf

Here’s more practical one: https://stackoverflow.blog/2020/07/08/improving-performance-...