On Tuesday, February 3, 2015 at 4:48:20 AM UTC-5, Christoph Ortner wrote: > > > On Monday, 2 February 2015 16:59:19 UTC, Steven G. Johnson wrote: >> >> It might be nice to submit a patch to OpenBLAS to make their dot >> functions use pairwise summation; this is almost as accurate as KBN >> summation but with negligible performance penalty (for a large base case), >> so it should be possible to put together an attractive pull request. >> > > intersting - but wouldn't performance suffer, or does nobody care about > Level1-BLAS performance? (this is really outside my domain) >
No, there is no performance penalty. (Or rather, the performance penalty can easily be made 1% or less…basically unmeasurable.) That is the whole advantage of pairwise summation — you get nearly the accuracy of Kahan summation (with only a logarithmic penalty) with nearly the performance of naive summation. That's why pairwise sums are the default algorithm for Julia's sum function (and cumsum etc.).
