floating point woes

[Benjamin Kaplan]

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.