Fix prelude definitions of abs/signum for Floats/Doubles

[Shachaf Ben-Kiki]

On Wed, Apr 10, 2013 at 11:24 AM, Levent Erkok <erkokl at gmail.com> wrote:
> The current definition of "abs" and "signum" for the types Float/Double is
> not IEEE-754 compliant. To wit:
>
>    Prelude> abs (-0.0::Float)
>    -0.0
>    Prelude> signum (-0.0::Float)
>    0.0
>
> The correct result should be the other way around; abs returning 0.0 and
> signum returning -0.0 when they receive a negative-zero. The same also holds
> for the type Double.
>
> The issue came up several times in several forums, with general consensus
> that the behavior should match the IEEE-754 specs. Here're three different
> discussions on this matter:
>
>         http://www.haskell.org/pipermail/libraries/2011-January/015761.html
>
> http://stackoverflow.com/questions/10395761/absolute-value-of-negative-zero-bug-or-a-part-of-the-floating-point-standard
>         http://www.haskell.org/pipermail/haskell-cafe/2013-April/107471.html
>
> Proposed fix: Section 6.4.4 of the report
> http://www.haskell.org/onlinereport/basic.html#sect6.4 gives "default"
> definitions for abs/signum; which fails to take into account of
> negative-zero values for floating-point types. An easy fix would be to add
> to the report a note on the status of negative-zero for Real/Float
> instances; with individual implementations explicitly checking for
> negative-0 first. For instance GHC's implementation can be changed as
> follows:
>
> instance Num Float where
>     signum x | isNegativeZero x = x
>              | x == 0           = 0
>              | x > 0.0          = 1
>              | otherwise        = negate 1
>     abs x    | isNegativeZero x = 0
>              | x >= 0           = x
>              | otherwise        = negate x
>
> A similar change would need to be done for the "Num Double" instance as
> well. Of course, implementations can take advantage of the underlying CPU's
> native floating-point abs/sign functions if available as well, avoiding
> explicit tests at the Haskell code; based on the underlying platform.
>
> Library guidelines suggest a discussion period of 2 weeks on this issue. I'm
> hoping that we can resolve the issue in a timely manner, and at least GHC's
> implementation can match the desired semantics in the next release. If
> there's consensus at the end of 2-weeks; I'll go ahead and create a
> corresponding ticket for GHC.
>
> Thanks,
>
> -Levent.
>

While we're at it: abs NaN is NaN, but signum NaN is currently -1.0.
Maybe it should also be NaN?

    Shachaf