On Sat, Apr 29, 2006 at 04:51:40PM -0400, Cale Gibbard wrote:
Floating point computations are always approximate and have some level of error associated with them. If you want proper real numbers, things like equality testing become impossible in general. If you look around, I think there are a couple of libraries in Haskell which let you work with arbitrary precision reals though.
That's not really true. The exact cases of floating point arithmetic can be important, and it's really annoying when compilers break them. For small integers, floating point arithmetic *is* exact, for example, and also for arithmetic (not division) involving integers divided by powers of two, provided there's no overflow or underflow. These exact properties allow the moderately careful programmer to do exact calculations that could have done using clever integer arithmetic while reusing code that works with floating point numbers. It can be handy, for example, when computing the symmetries of a basis set, since you don't need a separate integer 3-vector class (in C++, for example). This isn't a big deal, and it's much less of a deal in Haskell, where you can profitably use typeclasses to make the integer 3-vectors relatively easy to work with, but on the other hand, why bother with an integer class that will behave identically to the floating-point one whenever it's used? (Yes, the answer is the safety of *knowing* that you made no approximation, but for such a small piece of easily audited code, that's not likely to be worth the effort.) -- David Roundy http://www.darcs.net