About the template stuff, I think their main performance advantage over traditional BLAS is not even SIMD, it’s lazy evaluation. Expressions like x=a*b+c never compute the complete a*b matrix or vector. The a*b expression returns a small placeholder object on the stack, of a scary type with couple lines of template arguments in the type name. This way the complete expression runs without making temporary matrices, instead it streams data from all 3 arguments and only writes to memory once. And if the `x` is of the correct size already, it doesn’t call malloc/free.
I'm sure someone has already looked at this, but I wonder if Eigen can just somehow nab kernels directly from BLIS, haha.