Henning Thielemann
On Thu, 12 Jul 2007, Jon Fairbairn wrote:
Now, a proper exact real type is doubtless very inefficient, but wouldn't it be possible to define something that had a fairly efficient head, and a lazy tail? So you'd have, say
data Real = R {big::(Ratio !Int !Int), small:: More_Precision}
Interesting approach.
But flawed as I put it: the big part can't express big numbers! The big part needs to be either Rational (and the precision of that part limited during arithmetic) or BigFloat where
Data BigFloat = BF {mantissa:: Int, exponent:: Integer}
(ie limited precision, but unbounded magnitude). If we were to use BigFloat the base would need to be a power of ten to get the desired results for things like Don's example)
Somehow similar to making Integer a sum of Int and BigInt. Indeed, I have used transcendent arithmetic on Doubles to speedup computations for real numbers. However real numbers cannot be checked for equality. This can be also considered an advantage, because using (==) for floating point numbers is most oftenly a bug.
Agreed. That should be part of the change to the numeric hierarchy.
I think that this hybrid type is nice and could be used by default. But it should not replace native floating point types, since they have guaranteed speed in favor of not guaranteed precision. And we need a correct implementation.
Absolutely! -- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2007-05-07)