On Wednesday 07 September 2011, 22:38:21, Brandon Allbery wrote:
On Wed, Sep 7, 2011 at 16:25, Christopher Howard <
christopher.howard@frigidcode.com> wrote:
Hi. I'm working with simple functions involving rational exponents. I noticed that the (**) function seems to do okay with negative powers, but
that something else is needed for rational exponents: Nothing else is needed; you're just seeing the inevitable failure mode of floating point math (once you get into exponents that aren't integers, you can't escape it).
One could have an exact (??) :: Rational -> Rational -> Maybe Rational so that (r % s) ?? (p % q) = Just (n % d) if r^p == n^q && s^p == d^q, Nothing otherwise (if r < 0, p even, q odd, then n has to be chosen negative). But when dealing with floating point numbers, you can only get the occasional correct result by accident.
You may want to restrict printing precision.
Or round to k bits. Or write a function rationalPower :: Floating a => a -> Rational -> a which calculates the power e.g. by Newton's method. That would still give incorrect results most of the time, but could produce exact results in cases where the exact result is representable and all involved numbers are such that no overflow occurs.