This is quite interesting, and I'll be examining your method more closely in the future. A skim of the paper convinces me that there is merit.
The main upside to the Kahan method is that it can be incremental and online. Imagine that one is writing a Prometheus-like metrics client, and keeping a running tally. One cannot reorder the summation, and one cannot take advantage of parallelism. In these cases, a small Kahan accumulator can perform incredibly well.
> The main upside to the Kahan method is that it can be incremental and online.
I got excited when I heard the claims of a method better than Kahan/Neumaier summation, but the storage requirements are enormous (6700% versus for the "small" version, versus 200% for Kahan), so I definitely wouldn't call Kahan summation "pointless". It's in fact one of the most amazing and underutilised bits of CS out there IMO.
The main upside to the Kahan method is that it can be incremental and online. Imagine that one is writing a Prometheus-like metrics client, and keeping a running tally. One cannot reorder the summation, and one cannot take advantage of parallelism. In these cases, a small Kahan accumulator can perform incredibly well.