If you make a binary tree and sum it, the rounding errors aren't that bad and this algorithm is easy to parallelise.
Higham, Nicholas J 1993 the accuracy of floating point summation SIAM Sci Comp 14 (4) 783-799 Also see Wikipedia for a description of Kahan summation and a general discussion of this topic. Why not commit to binary tree reductions and that will allow everyone to understand what is going on and design lambdas accordingly. -- Howard. Sent from my iPad On 13/01/2013, at 2:04 AM, Doug Lea <d...@cs.oswego.edu> wrote: > On 01/11/13 21:37, Joe Darcy wrote: > >> I would prefer to cautionary note along the lines of "if you want numerical >> accuracy, take care to use a summation algorithm with defined worst-case >> behavior." >> >> (Varying magnitude is not so much of a problem if you add things up in the >> right >> order.) > > Thanks. I do not believe such an algorithm exists, because > no ordering control is possible, and all other known accuracy > improvements (like Kahn) require multiword atomicity, which we > explicitly do not provide. > > Which leaves me thinking that the current disclaimer (below) > is the best we can do. > > -Doug > >>>> "The order of accumulation within or across threads is not guaranteed. >>>> Thus, this class may not be applicable if numerical stability is >>>> required, especially when combining values of substantially different >>>> orders of magnitude." >>>>
