[Haskell-cafe] Ordering of BigFloats in numbers-3000.0.0.0

[Carter Schonwald]

you should probably file a ticket on the DanBurton repo if he's the one
doing the uploading
 :-)


On Tue, Oct 9, 2012 at 12:55 PM, Michael Orlitzky <michael at orlitzky.com>wrote:

> On 10/09/2012 12:29 PM, Chaddaï Fouché wrote:
> > On Sun, Oct 7, 2012 at 8:00 PM, Michael Orlitzky <michael at orlitzky.com>
> wrote:
> >> I'm trying to use,
> >>
> >>   http://hackage.haskell.org/package/numbers-3000.0.0.0
> >>
> >> to get better precision "for free" out of some numerical code. I ran
> >> into an issue pretty quickly, though. In Data.Number.BigFloat, we have,
> >>
> >>   data BigFloat e = BF (Fixed e) Integer
> >>     deriving (Eq, Ord)
> >>
> >> and the derived Ord is obviously incorrect:
> >>
> >>   Prelude Data.Number.BigFloat> let x = 0.1 :: BigFloat Prec50
> >>   Prelude Data.Number.BigFloat> let y = 0.02 :: BigFloat Prec50
> >>   Prelude Data.Number.BigFloat> x < y
> >>   True
> >>
> >
> > That's pretty strange since the derived Ord should be the same as
> > Fixed Ord, which itself is just a newtype over Rational (and 1%10 <
> > 2%100 == False), did you try to convert those BigFloat back to
> > Rational to see if they're still correct ? That may be worse than a
> > misbehaving Ord instance.
> >
>
> The BigFloat constructor doesn't do what you think it does... I chose a
> bad spot to snip the comments:
>
>   -- This representation is stupid, two Integers makes more sense,
>   -- but is more work.
>   -- | Floating point number where the precision is determined by the
>   --   type /e/.
>   data BigFloat e = BF (Fixed e) Integer
>     deriving (Eq)
>
> If it was two Integers, I think it would be more clear that this is what
> will happen:
>
>   *Data.Number.BigFloat> let x = 0.1 :: BigFloat Prec50
>   *Data.Number.BigFloat> let y = 0.02 :: BigFloat Prec50
>   *Data.Number.BigFloat> let BF m1 e1 = x
>   *Data.Number.BigFloat> let BF m2 e2 = y
>   *Data.Number.BigFloat> (m1,e1)
>   (1.00000000000000000000000000000000000000000000000000,-1)
>   *Data.Number.BigFloat> (m2,e2)
>   (2.00000000000000000000000000000000000000000000000000,-2)
>
> The fast way to compare them would be to check the mantissa/exponent
> directly, but toRational works just fine. I made a pull request
> yesterday that compares them as rationals.
>
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