marshallward

> I hope you can list all of the groups of order < 8 without having to think too hard.

Welp, guess I'm out.

> “The pyramids seem like pretty monumental work”

You don't say...

I ran with OMP_NUM_THREADS=1, but your point is well taken.

As for the original post, I felt a bit embarrassed about my original comments, but I think the compilers actually did fairly well based on what they were given, which I think is what you are saying in your first part.

I'm sure there's more to it, but just comparing the profile output shows aggressive use of prefetch and broadcast instructions.

I just did a test of OpenBLAS with Intel-compiled BLAS, and it was about 6 GFLOP/s vs 150 GFLOP/s, so I must admit that I was wrong here. Maybe in some sense 4% is not bad, but it's certainly not good. My faith in current compilers has certainly been shattered quite a bit today.

Anyway, I have come to eat crow. Thank you for your insight and helping me to get a much better perspective on this problem. I mostly work with scalar and vector updates, and do not work with matrices very often.

You are right, I just tested this out and my speed from BLAS to OpenBLAS went from 6 GFLOP/s to 150 GFLOP/s. I can only imagine what BLIS and MKL would give. I apologize for my ignorance. Apparently my faith in the compilers was wildly misplaced.

I don't disagree, but where are those techniques presented in the article? It seems like she exploits the particular shape of her matrix to align better with cache. No BLAS library is going to figure that out.

I am not trying to say that a simple 50+ year old matrix solver is somehow competitive with existing BLAS libraries. But I disagreed with its portrayal in the article, which associated the block with NumPy performance. Give that to a 2024 Fortran compiler, and it's going to get enough right to produce reasonable bytecode.

How do you feel about Nvidia endorsing do concurrent migration to GPUs? Would that be classified as parallelization?

Fair enough, this is not meant to be some endorsement of the standard Fortran BLAS implementations over the optimized versions cited above. Only that the mainstream compilers cited above appear capable of applying these optimizations to the standard BLAS Fortran without any additional effort.

I am basing these comments on quick inspection of the assembly output. Timings would be equally interesting to compare at each stage, but I'm only willing to go so far for a Hacker News comment. So all I will say is perhaps let's keep an open mind about the capability of simple Fortran code.

There is an implication here that the Fortran implementation of `SGEMM` is somehow inadequate. But any modern Fortran compiler will quite easily apply the AVX and FMA optimizations presented here without any additional changes. Both GNU and Intel make these substitutions with the correct flags.

The unrolling optimization is also just another flag away (`-funroll-all-loops`). The Intel Compiler will even do this without prompting. In fact, it appears to only do a modest 2x unroll on my machine, suggesting that the extreme unroll in this article would have been overkill.

Parallelization certainly a lot to ask of Fortran 77 source, but there there is little stopping you from adding OpenMP statements to the `SGEMM` function. In fact, modern Fortran even offers its own parallelization constructs if you're willing to go there.

Which is to say: Let's not belittle this old Fortran 77 function. Yes it is old, and does not even resemble modern Fortran. But the whole point of Fortran is to free the developer from these platform-specific details, and hand the job off to the compiler. If you don't like that approach, then you're welcome to go to C or C++. But this little block of Fortran code is already capable of doing just about everything in this article.

Unfortunately I don't think the compilers will add it in time.

I have only looked at the GCC Fortran frontend. I would not say it is necessarily difficult but rather very ad-hoc and disconnected from the rest of gcc. I don't see many tools for specifying a grammar or tokens. Instead, there are a lot of constructs custom-written to handle Fortran. Looking around, the Go and Rust frontends feel equally disconnected.

I'm told that you eventually make your way to the "GCC IR", but it seems like you are largely on your own with how to get there.

I did not invest a lot of time here, so I could be wildly off base, but thought I'd at least try to give a very-slightly-hands-on perspective.

I know someone who took that course. They did not have fond memories of it.

My impression is that it can be a very frustrating way to learn mechanics if you don't have much interest in functional programming.

It's an excellent essay, and the Fortran community owes you a major gratitude for promoting these issues. But surely there loops can be safely parallelized if the iterations do not interact, e.g. per-element array arithmetic, and a compiler ought to safely identify such arithmetic.

Also, isn't your employer promoting do concurrent as a method of GPU parallelization? Has this been controversial within Nvidia?