Remove a register

[lemire]

We can simplify the algorithm. This should not affect the performance, although it might be slightly beneficial because we need one fewer register.

The gist of it is that we replace

_mm512_madd52lo_epu64(zmmzero, bcstq_h, ifma_const);

by

_mm512_madd52lo_epu64(ifma_const, bcstq_h, ifma_const);

So instead of loading zmmzero and ifma_const, we just need ifma_const.

I am also trimming out shift_and_insert_dot as it is not needed.

[jaja360]

Very cool !!!

I ran some benchmarks to see if it impacts performance. It doesn't at all with clang. With g++, however, I get that the new version is 7% faster on the Twitter dataset, but 15% slower on Uniform-8 (it goes from 4.01 to 4.62 c/n). g++ has always given us suboptimal results (it generates 30 instructions instead of 27 for clang, on Uniform-8), so it seems more like a GCC codegen quirk than a problem on our side.

I think we can merge !

[lemire]

@jaja360 Logically, it should not make a difference... We save one named register, but that's not a limitation. We also save loading the register, which might help a little bit (maybe save one instruction) but it was almost surely not a bottleneck.

Of course, the main point is to simplify the algorithm and the code.

Merging.

[jaja360]

Indeed, it should not do a difference (and it does not on clang !)
I think g++ just have some code alignment issues (that we already observed earlier), this time due to the static const variables we removed.