An aside, but I recently learned -- if one is willing to use a very modest amount of memory -- summing floating-point numbers with no loss of precision is effectively a solved problem with the XSUM algorithm.

https://glizen.com/radfordneal/ftp/xsum.pdf

That paper explains some useful optimisation details, but obviously since the floats are all (either infinity or) some multiple of a known tiny fraction (their smallest non-zero number), we can definitely sum them accurately.