floating point woes

[Hans-Peter Jansen]

On Wednesday 16 February 2011, 01:06:08 Benjamin Kaplan wrote:
> On Tue, Feb 15, 2011 at 6:49 PM, Hans-Peter Jansen <hpj at urpla.net> 
wrote:
> > Hi,
> >
> > while I usually cope with the woes of floating point issues, this
> > is
> >
> > one, that I didn't expect:
> >>>> round(2.385, 2)
> >
> > 2.3799999999999999
> >
> > Doesn't the docs say, it's rounded up for this case?
> >
> > <quote>
> > Values are rounded to the closest multiple of 10 to the power minus
> > n; if two multiples are equally close, rounding is done away from 0
> > </quote>
> >
> > Well, that one is clearly rounding down.
> >
> > What's up, eh, down here?
> >
> > Pete
>
> The number you are rounding is not 2.385. It is not possible to
> represent that number in binary, just like you cannot represent the
> value 1/3 in decimal. So instead, you're using the nearest
> approximation that an IEEE 754 Double-Precision Floating Point number
> can get you, which happens to be about 2.3849999999999998. And that
> rounds down to 2.38. Which also cannot be precisely represented in
> binary, so you get 2.3799999999999999 instead.

Thanks for the explanation, Benjamin. Not that I like it, but anyway.
If I hadn't quitted smoking a long time ago, I would go and ask, what 
these engineers smoked during the course of inventing this sh*t. Even 
more probably, they took way too much of a special form of lysergic 
acid.

OTOH, cdecimals, as in Stefan Krah's package are long overdue to get 
into the core.

Pete