https://bugs.documentfoundation.org/show_bug.cgi?id=137679

--- Comment #72 from b. <[email protected]> ---
just one point which wasn't clear enough to me in the past:  

the difference of a FP calculation vs. the user intended decimal calculation
adds up from:  
a.) the imprecision in the bin representation of the operands,  
b.) in operation rounding,  

e.g. '= 0.2 + 0.1' with doubles:  
0.2 bin representation is about 1.11E-17 overshot,  
0.1 bin representation is about 5.55E-18 overshot,  
and as the sum doesn't meet a double value it's rounded, in this case rounded
up, by additional 2.77E-17.  
this way we get the irritating 0.30000000000000004 as result.  

with 'Kahaning' or Neumaier we have access to the 2.77E-17 rounding difference,
not! to the representation deviations.  

thus 'by chance' a set with randomly distributed up and down deviations will
produce improved results with Kahan or Neumaier, while sets with 'systematic
drift' - e.g. all positive - will gain less benefit.

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