Let's close this one.  As Uncle Timmy says, it would be a mistake to "funkify" the signature for math.fsum.

If something like a Summer() class is born, it should start it life outside the standard library, gain a following, and let both the API and implementation mature.

I'm sympathic about the loss of information in the final step of math.fsum() but don't think the standard library is the place for this to be born.