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Could you expand on the 24x24 unrolling with AVX? How big of a benefit did you obtain, compared to say using a library such as Armadillo, Fastor, Eigen, etc?

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Eigen was my baseline. As far as I remember, my best AVX version (which unrolls 24x4 blocks, running 6 iterations of the loop) was about 50% faster.

Eigen is designed in the assumption these vectors/matrices are large. 24 is not large, fits in 3 vector registers out of the 16 available. Eliminating data access latency of the accumulators is what caused the speedup.

In my experience Eigen is not very good either for small matrices, whilst Fastor performs much better.

Interesting

Libraries don’t cut it, IMO. Sometimes you want your complete input data in registers, 4x4 matrices fit there nicely. Other times you want to stream stuff from memory, the above-mentioned 24x24 multiplication streams the complete matrix, while loading 4-long chunks of the vector.

I’ve wrote an introduction article some time ago: http://const.me/articles/simd/simd.pdf

Here’s more practical one: https://stackoverflow.blog/2020/07/08/improving-performance-...

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