Right, wasn't sure if we kept that around or not.
> On Nov 15, 2014, at 7:56 PM, Ivar Nesje <[email protected]> wrote: > > Seems like this thread is missing a reference to the standard library > function sum_kbn. > > kl. 12:33:31 UTC+1 lørdag 15. november 2014 skrev [email protected] følgende: >> >> Dear Stefan, >> >> Thank you for your quick answer. That's what I had in mind. I just thought, >> very naively I must admit, that sum(a) would have computed the total sum in >> the same order as one of the other 4 approaches. >> I'll have a look at compensated summation. >> >> Thanks again, >> >> Le samedi 15 novembre 2014 12:18:46 UTC+1, Stefan Karpinski a écrit : >>> >>> This is expected. Floating-point addition is non-associative and these >>> codes add values in different orders. Julia's built-in sum function uses >>> recursive pairwise summation, which is the most accurate of these three >>> approaches but nearly as fast as linear scanning. A slower but more >>> accurate algorithm is compensated summation. Even compensated summation is >>> not completely accurate; completely accurate floating-point summation is >>> tricky. >>> >>> On Sat, Nov 15, 2014 at 11:52 AM, <[email protected]> wrote: >>>> Dear all, >>>> >>>> Some (serious?) issue was raised on a mailing list concerning the "sum" >>>> functions involved in computing the sum of elements of an array. >>>> >>>> It seems that we obtain different results for the three following >>>> procedures: >>>> >>>> - using sum over the whole matrix >>>> - using sum over the columns/rows of the matrix and summing these results >>>> within a loop >>>> - computing the sum with a double loop over all the elements of the matrix >>>> >>>> Attached is a file with the different procedures and their results for a >>>> particular matrix. >>>> >>>> What is wrong with the implementation of the sum function? >>>> This could have important consequences with iterative procedures. >>>> >>>> Many thanks, >>>
