Cascadelake

Cascadelake CPUs feature 2 512-bit-fma units, and thus can achieve high FLOPS in BLAS-like operations. The particular CPU on which these benchmarks were run had its heavy-AVX512 clock speed set to 4.1 GHz, providing a theoretical peak of 131.2 GFLOPS/core.

Statically sized benchmarks vs StaticArrays.jl:

The SMatrix and MMatrix are the immutable and immutable matrix types from StaticArrays.jl, respectively, while StrideArray.jl and PtrArray.jl are mutable array types with optional static sizing providing by PaddedMatrices.jl. The benchmarks also included jmul! on base Matrix{Float64}, demonstrating the performance of PaddedMatrices's fully dynamic multiplication function.

SMatrix were only benchmarked up to size 20x20. As their performance at larger sizes recently increased, I'll increase the size range at which I benchmark them in the future.

The fully dynamic multiplication is competitive with MKL and OpenBLAS from around 2x2 to 256x256: However, beyond this size, performance begins to fall behind: OpenBLAS eventually ascends to about 120 GFLOPS, but PaddedMatrices seems stuck at around 100 GFLOPS.

The packing and blocking need work.

Multithreading is coming.