[Haskell-cafe] Why 'round' does not just round numbers ?
daniel.is.fischer at web.de
Mon Oct 27 07:17:43 EDT 2008
Am Montag, 27. Oktober 2008 11:46 schrieb Henning Thielemann:
> On Mon, 27 Oct 2008, Janis Voigtlaender wrote:
> > Henning Thielemann wrote:
> >> I think one reason is that repeated rounding should not be worse than
> >> rounding in one go. Consider the rule 'use ceiling when the first
> >> removed digit is 5'. Then
> >> 0.45 - (round to one place) -> 0.5 - (round to integer) -> 1
> > But repeated rounding *is* worse than rounding in one go, under any
> > reasonable scheme:
> > 3.46 -> 3.5 -> 4
> With the rounding-to-even route this would be
> 3.46 -> 3.4 -> 3
Wait, that cannot be. 6 > 5, so 3.46 -> 3.5 even with banker's rounding.
> so rounding in passes is no worse than rounding in one go for this
Rounding in passes is bad per se, because there are pretty large intervals
where that gives a different result from a direct rounding.
> > vs.
> > 3.46 -> 3
> > That was actually the debate with that teacher. Unbelievable as that
> > still is to me today, she advocated the 3.46 -> 3.5 -> 4 route ...
> I also know a didact which tells teachers that 1 has no prime
> decomposition. Oh, I see, she may have copied that from Wikipedia:
I can believe that makes sense to somebody who considers 0 an unnatural
number, an empty product must be frightening for them.
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