cadabra2 VS array

If you're into tensor algebra i can only recommend the beautiful piece of Software Cadabra is:

https://cadabra.science/

We wrote an article with it once, 40th order in the Lagrangian, perhaps 50k pages of calculations when all printed. Amazing tool! Thanks Kasper!

Before these suggestions come up, let me note that I did submit a bug report about a month ago, which was so far unaddressed by the developer. If I can't get it to work here, I also plan to email the developer directly since he said

I wrote a library in C++ (I know, probably a non-starter for most reading this) that I think does most of what you want, as well as some other requests in this thread (generalized to more than just multiply-add): https://github.com/dsharlet/array?tab=readme-ov-file#einstei....

A matrix multiply written with this looks like this:

    enum { i = 2, j = 0, k = 1 };

I should have mentioned somewhere, I disabled threading for OpenBLAS, so it is comparing one thread to one thread. Parallelism would be easy to add, but I tend to want the thread parallelism outside code like this anyways.

As for the inner loop not being well optimized... the disassembly looks like the same basic thing as OpenBLAS. There's disassembly in the comments of that file to show what code it generates, I'd love to know what you think is lacking! The only difference between the one I linked and this is prefetching and outer loop ordering: https://github.com/dsharlet/array/blob/master/examples/linea...

If you are looking for something like this in C++, here's my attempt at implementing it: https://github.com/dsharlet/array#einstein-reductions

It doesn't do any automatic optimization of the loops like some of the projects linked in this thread, but, it provides all the tools needed for humans to express the code in a way that a good compiler can turn it into really good code.