Tamas, I agree with you that 'unbiased rounding' is a strong argument in favor of the "round-to-even" rule. It appears natural that e.g. R falls for this rule.
The interpolation case seems to favor a rule that moves all ties in the same direction, being it upwards or downwards, and independent of the sign. Because otherwise the length of interpolation intervals is not so easily predictable. This thread is getting too long now. If you want your arguments to be taken into account, I suggest you join the discussion at Simon Byrne's issue #9464. Thanks to all for your patience. For those interested, have a look at PARI/GP home <http://pari.math.u-bordeaux.fr/> . On Saturday, December 27, 2014 3:22:53 PM UTC+1, Tamas Papp wrote: > > Hi Hans, > > If I understand corretly, #13 is a potential problem arising from a > change in behavior, not an argument in favor of one rounding mode vs > another per se. > > The only reasonably cogent argument I know is mentioned in #8750 > (unbiasedness). I am glad that the issue is now closed, since that means > no more electrons are wasted on it, but I am still curious about > practical examples where rounding mode makes a difference in numerical > code. All I have seen rely on ill-conditioning, which is a separate > issue. > > Best, > > Tamas > > On Sat, Dec 27 2014, Hans W Borchers <[email protected] <javascript:>> > wrote: > > >> However, these discussions are necessarily very abstract. Having a > >> concrete issue or use case where you find one rounding mode preferable > >> to another would help focus the discussion. > > > > @Tamas For an example where it might have the potential to cause > problems, > > see > > > > Potential future problem: rounding mode changed in core Julia #13 > > https://github.com/tlycken/Interpolations.jl/issues/13 > >
