Exact computation of sums and means

A while ago, I came across a mention of the Python math.fsum function, which sums a set of floating-point values exactly, then rounds to the closest floating point value. This seemed useful. In particular, I thought that if it’s fast enough it could be used instead of R’s rather primitive two-pass approach to trying to compute the sample mean more accurately (but still not exactly). My initial thought was to just implement the algorithm Python uses in pqR. But I soon discovered that there were newer (and faster) algorithms. And then I thought that I might be able to do even better…

The result is a new paper of mine on Fast exact summation using small and large superaccumulators (also available from arxiv.org).