Improve performance of inv(::ComplexF64)

[thchr]

This is essentially just a rebase of #29058 (but my fork of that had gotten deleted so I had to open it anew): leads to a speedup of about 30% for inv(::ComplexF64) without changing the output.

The gist of the changes are the same as in the original PR: speed up inv(::ComplexF64) by combining two if statements into an if-elseif and opt for a cheaper variant of max, because we know we won't benefit from checking NaN or Inf values in this context. Also now use muladd explicitly in one spot.

Benchmarks:

v = rand(ComplexF64, 100000);

1.6-beta:

@btime inv($v) # 2.244 ms (2 allocations: 1.53 MiB)

PR:

@btime inv($v) # 1.562 ms (2 allocations: 1.53 MiB)

Tagging @simonbyrne again, in case you still recall the PR that #29058 branched off originally (~2 years ago now 😮 ).

[thchr]

Test error in spawn testset doesn't seem related afaict.

[thchr]

Bump; just so I don't forget this for 2 years again.

(I suspect nothing here is too controversial: maybe the main point to consider is whether to use muladd or not - using it can change the output of inv very slightly when fma is available, but it should be an improvement in both accuracy and speed, afaiu)

[oscardssmith]

In my opinion, the use of muladd here is perfectly justified. We very explicitly do not guarantee exact outputs of floating point arithmatic. I'm also assigning myself as a reviewer for this so we can hopefully get it merged soon.

[oscardssmith]

Overall, the code for this looks good. The worst error I've seen from this is 2.6 ULP (about the same as before the PR), but I don't really know what we aim for for the accuracy of complex arithmatic.

[thchr]

The worst error I've seen from this is 2.6 ULP (about the same as before the PR).

Thanks for checking this explicitly; good to know.

[oscardssmith]

@thchr any idea why the windows tests are failing? I don't want this to get lost. It might be worth rebasing and hoping they just go away.

[thchr]

@thchr any idea why the windows tests are failing? I don't want this to get lost. It might be worth rebasing and hoping they just go away.

Hmm, no; when I looked at it originally, it didn't look related.
Anyway, I've rebased and pushed again, so let's see if it's clear now; thanks for the prompt to do so :).

[thchr]

Oki, all green now test-wise.

[oscardssmith]

Anyone have objections to this merging?