Optimizing Acsint

[lukas-weber]

I had some time to optimize Acsint. It is much faster now, but quite a bit slower than libcint still. Maybe it is a starting point for someone who wants to use nonstandard types.

The biggest issue was excessive compilation time due to needless specialization on the shell sizes. I fixed it by making the shells have runtime shell sizes. This should also benefit type stability throughout other parts of GaussianBasis.

Simple benchmark

using GaussianBasis

bset = BasisSet("cc-pvtz", "N 0 0 1\nN 0 0 -1", spherical=false, lib=:acsint)
@time ERI_2e4c(bset);
@time ERI_2e4c(bset);

bset2 = BasisSet("cc-pvtz", "N 0 0 1\nN 0 0 -1")
@time ERI_2e4c(bset2);
@time ERI_2e4c(bset2);

Before

135.987606 seconds (66.29 M allocations: 3.037 GiB, 0.38% gc time, 95.69% compilation time)
  5.489963 seconds (5.90 M allocations: 493.756 MiB, 1.76% gc time)

This PR

  2.742417 seconds (8.55 M allocations: 1.060 GiB, 4.38% gc time, 55.30% compilation time)
  1.324503 seconds (366.76 k allocations: 681.408 MiB, 6.15% gc time)

Libcint backend

  0.517454 seconds (964.76 k allocations: 146.260 MiB, 0.74% gc time, 63.17% compilation time)
  0.187572 seconds (6.70 k allocations: 99.609 MiB, 1.67% gc time)

Compatibility

The results of ERI_2e4c(bset) are the same as before up to a relative tolerance of 1e-15. This can probably be further reduced using the new cutoff parameter of generate_ERI_quartet.

One thing I found though is that ERI_2e4c(bset) does not match ERI_2e4c(bset2), neither now nor before the PR. Possibly that has to do something with spherical vs cartesian.

[gustavojra]

Thank you very much @lukas-weber . I am in the middle of changing jobs, so very busy. But this weekend I will take some time to review this PR! At a first glance it looks like great work, I just want to understand it better!