Accurate summation algorithm

[certik]

I think the reason we can’t reach an agreement is that there are a lot of sub-problems that we never agreed upon a clear “yes” or “no”, and the overall subject is very complicated, and impossible to make progress on unless we can at least agree on these simple sub-problems. So I have asked one such sub-problem here: Can the following list of transformations turn a stable well conditioned algorithm into an unstable one?, let’s discuss that one. After we reach a clear agreement on that, we can tackle the rest.