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You could also use SIMD to compute N independent Kahan sums in parallel and reduce them at the end.

I tried this, it was the same speed as orlp_sum with worse accuracy.

How was the final reduction performed? Also Kahan?

Yes, although to be fair I did discard the c values for the final reduction I perhaps should've incorporated somehow.

The code from the blog post is all on Github, feel free to try and add/benchmark it yourself: https://github.com/orlp/sum-bench/.