[Haskell-cafe] Re: Why purely in haskell?

[Lennart Augustsson]

If you can't stomach the weirdness of floating point then perhaps you should
try to define your own type that obeys all the expected laws? :)

On Jan 11, 2008 3:36 AM, Wolfgang Jeltsch <g9ks157k at acme.softbase.org>
wrote:

> Am Freitag, 11. Januar 2008 11:03 schrieb Felipe Lessa:
> > Another thing for the record: Goldberg says
> >
> > "The introduction of NaNs can be confusing, because a NaN is never
> > equal to any other number (including another NaN), so x = x is no
> > longer always true. In fact, the expression x /= x is the simplest way
> > to test for a NaN if the IEEE recommended function Isnan is not
> > provided. Furthermore, NaNs are unordered with respect to all other
> > numbers, so x <= y cannot be defined as not x > y. Since the
> > introduction of NaNs causes floating-point numbers to become partially
> > ordered, a compare function that returns one of <, =, >, or unordered
> > can make it easier for the programmer to deal with comparisons."
> >
> > Goldberg, David. What Every Computer Scientist Should Know About
> > Floating-Point Arithmetic.
> > http://docs.sun.com/source/806-3568/ncg_goldberg.html .
> >
> > As GNU is not Unix, NaN is not a number, so what is standard about
> > numbers doesn't work for them. I don't think there's a compeling
> > reason about changing this behavior, specially because it's what's
> > specified in the IEEE 754.
>
> There is a really compelling reason: If the order on floating point
> numbers is
> partial then there is no meaningful Ord instance for them.
>
> And what do Hugs and GHCi say?  Their answers are plain horror:
>
>    Hugs, version 20050308:
>
>        compare (0 / 0) (0 / 0) => EQ
>
>        0 / 0 == 0 / 0 => False
>
>    GHCi 6.8.2:
>
>        compare (0 / 0) (0 / 0) => GT
>
>        0 / 0 > 0 / 0 => False
>
> Anyone interested in filing bug reports?
>
> > […]
>
> Best wishes,
> Wolfgang
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