Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Josh Lee wrote: On Tue, 27 Nov 2007 14:41:59 -0500 Isaac Dupree [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Using Infinity would go against the meaning of Enum. In the Double/Float types, succ and pred mean add/subtract 1.0, as opposed to the unit of least precision. In fact, succ and pred lose meaning once the precision of the floats exceeds a certain value. That's not the meaning of Enum. That's brokenness :) It's there so that [1..10] :: [Double] works, but it's a horrible horrible thing. The overloaded [a..b] notation should not be in Enum but some other class (I suggest ICanHazInturval as the class name). Oh well. Jules ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Isaac ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
On Tue, 27 Nov 2007 14:41:59 -0500 Isaac Dupree [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Using Infinity would go against the meaning of Enum. In the Double/Float types, succ and pred mean add/subtract 1.0, as opposed to the unit of least precision. In fact, succ and pred lose meaning once the precision of the floats exceeds a certain value. until (\x - x == succ x) succ 1.0 :: Float 1.6777216e7 It would be interesting to have an enumeration for Double/Float that goes from -Infinity to Infinity, reaching every single number on the way. Josh Lee ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
On Tue, 27 Nov 2007, Josh Lee wrote: On Tue, 27 Nov 2007 14:41:59 -0500 Isaac Dupree [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Using Infinity would go against the meaning of Enum. In the Double/Float types, succ and pred mean add/subtract 1.0, as opposed to the unit of least precision. In fact, succ and pred lose meaning once the precision of the floats exceeds a certain value. until (\x - x == succ x) succ 1.0 :: Float 1.6777216e7 It would be interesting to have an enumeration for Double/Float that goes from -Infinity to Infinity, reaching every single number on the way. Actually, IEEE numbers are designed in such a way, that if you interpret their bits as integer number, then 'succ' leads you to the next larger representable number. Thus you only have to cast from Float or Double to Int32 or Int64 respectively, call enumFromTo, then cast back to Float or Double, respectively. :-] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Actually, IEEE numbers are designed in such a way, that if you interpret their bits as integer number, then 'succ' leads you to the next larger representable number. Thus you only have to cast from Float or Double to Int32 or Int64 respectively, call enumFromTo, then cast back to Float or Double, respectively. :-] How do you cast from Float to Int32(or Word32), and back again? I couldn't find an appropriate function. Only thing I can see is going through the Storable interface, but that seems cumbersome and I imagine slow. Also, a related question: How do you convert from Float - Double, and the reverse? Only thing I could find is (fromRational . toRational) which I also imagine to be slow, and I also wonder about accuracy. Thanks, Bit ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Josh Lee wrote: On Tue, 27 Nov 2007 14:41:59 -0500 Isaac Dupree [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Using Infinity would go against the meaning of Enum. Perhaps. But we're talking about Bounded, not Enum. ;-) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
On Tue, 27 Nov 2007, Bit Connor wrote: Actually, IEEE numbers are designed in such a way, that if you interpret their bits as integer number, then 'succ' leads you to the next larger representable number. Thus you only have to cast from Float or Double to Int32 or Int64 respectively, call enumFromTo, then cast back to Float or Double, respectively. :-] How do you cast from Float to Int32(or Word32), and back again? I couldn't find an appropriate function. Only thing I can see is going through the Storable interface, but that seems cumbersome and I imagine slow. As Don pointed out correctly I'm evil. Storable is a fine way, since it makes a hack look like a hack. Or you might use castSTUArray. Also, a related question: How do you convert from Float - Double, and the reverse? Only thing I could find is (fromRational . toRational) which I also imagine to be slow, and I also wonder about accuracy. Rational keeps full precision. Performance - I don't know, maybe it's fused away? When I started with Haskell I regularly needed conversion between Float and Double. I don't know why. I haven't needed it for a long time now. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Bit Connor wrote: Also, a related question: How do you convert from Float - Double, and the reverse? Only thing I could find is (fromRational . toRational) which I also imagine to be slow, and I also wonder about accuracy. realToFrac -Yitz ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
On Tue, 27 Nov 2007, Yitzchak Gale wrote: Bit Connor wrote: Also, a related question: How do you convert from Float - Double, and the reverse? Only thing I could find is (fromRational . toRational) which I also imagine to be slow, and I also wonder about accuracy. realToFrac added to http://www.haskell.org/haskellwiki/Converting_numbers ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
But IEEE can be run with projective infinity in which case there is only one of them. On Nov 27, 2007 7:41 PM, Isaac Dupree [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 26 Nov 2007, Jason Dusek wrote: Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? Isaac ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why aren't Float and Double Bounded?
Among numeric types, it seems that only integer types are Bounded. Maybe because IEEE format supports Infinity? therefore, maxBound is Infinity and minBound negative infinity? But IEEE can be run with projective infinity in which case there is only one of them. Well, if Double becomes a proper member of Ord (which it already almost never is, because of NaN), then, since it is defined by a finite number of bits, it can be Bounded. Maybe this means projective infinity breaks Ord like NaN does. Any of this potential variation in Double obviously breaks referential transparency too, if it depends on what implementation you're using. succ/pred are odd for Double too; even if Bounded and defined by a finite number of bits, you would not be able to have a finite [minBound..0] or [minBound..maxBound]. Basically, it's not Bounded, not for a particular reason, but just because it's rather broken from a Haskell point of view anyway, IMHO. Isaac ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Why aren't Float and Double Bounded?
Among numeric types, it seems that only integer types are Bounded. -- _jsn ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
