As far as I can tell from glancing through Gaius.jl is no longer maintained and both it and Tullio still consistently lose out to MKL across a wide range of matrix sizes and usually lose out to OpenBLAS on larger matrices. Moreover most victories for Tullio seem to be very machine dependent with different users reporting OpenBLAS still beating Tullio even on smaller matrix sizes.
It has mostly been replaced by PaddedMatrices.jl
>Moreover most victories for Tullio seem to be very machine dependent with different users reporting OpenBLAS still beating Tullio even on smaller matrix sizes.
On kernels which OpenBLAS directly represents. But Tullio is building more general kernels and has a pretty big win on tensor calculations that are not just one GEMM.
Besides handling operations which aren't standard kernels, handling weird number types efficiently would be nice. (Being able to compile lighter-weight Julia images without BLAS libraries might be nice too, for other purposes.)