[Haskell-cafe] Re: Double -> CDouble, realToFrac doesn't work

[Robert Dockins]

My guess is because irrationals can't be represented on a discrete 
computer (unless you consider a computaion, the limit of which is the 
irrational number in question).  A single irrational might not just be 
arbitrarily long, but it may have an _infinite_ length representation! 
What you have described is arbitrary (not infinite) precision floating 
point.

What IEEE has done is shoehorned in some values that aren't really 
numbers into their representation (NaN certainly; one could make a 
convincing argument that +Inf and -Inf aren't numbers).  Perhaps it 
would make more sense to add constructors to the Rational type to 
represent these additional "values", ie, make Rational look like
(edited from section 12.1 of the Report)

data (Integral a) => Ratio a = a! :% a! |
                      Nan | PosInf | NegInf
         deriving(Eq)
type Rational = Ratio Integer

This has the effect that pattern matching :% when the value is NaN etc. 
gives an error instead of doing bizarre things (by succeeding against 
non numeric values).  This is an advantage or a disadvantage depending 
on your viewpoint.

Unfortunately, that isn't how its defined in the Report, so it may not 
be an option.


MR K P SCHUPKE wrote:
>>I would be very careful of adding non-rationals to the Rational type.
> 
> 
> Why is there no Irrational class. This would make more sense for
> Floats and Doubles than the fraction based Rational class. We could
> also add an implementation of infinite precision irrationals using
> a
> pair of Integers for exponent and mantissa.
> 
> 	Keean.
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