From: minforth@gmx.net   
      
   Am 16.07.2025 um 18:23 schrieb Anton Ertl:   
   > minforth  writes:   
   >> Am 16.07.2025 um 13:25 schrieb Anton Ertl:   
   >>> I did not do any accuracy measurements, but I did performance   
   >>> measurements   
   >> YMMV but "fast but wrong" would not be my goal.  ;-)   
   >   
   > I did test correctness with cases where roundoff errors do not play a   
   > role.   
   >   
   > As mentioned, the RECursive balanced-tree sum (which is also the   
   > fastest on several systems and absolutely) is expected to be more   
   > accurate in those cases where roundoff errors do play a role.  But if   
   > you care about that, better design a test and test it yourself.  It   
   > will be interesting to see how you find out which result is more   
   > accurate when they differ.   
      
   Meanwhile many years ago, comparative tests were carried out with a   
   couple of representative archived serial data (~50k samples) by   
   using a Java 128-bit quadruple fp-math class to perform summations   
   and calculate dot-product results.   
      
   The results were compared with those of naive linear summation and   
   multiplication and pairwise divide&conquer summation at different   
   rounding modes, for float32 and float64. Ultimately, Kahan summation   
   was the winner. It is slow, but there were no in-the-loop   
   requirements, so for a background task, Kahan was fast enough.   
      
   --- SoupGate-Win32 v1.05   
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