Few of us have mentioned that Random is no longer useful, because Uniform and UniformRange was introduced as a more correct interface. Complex is an example of a type where Random can be very useful. We can't compare them and we can't produce a uniform distribution due to infinite many values, so there never can be neither Uniform nor UniformRange instances. But should it also mean that we can't have random complex numbers at all? For example I can see this as a sensible instance for complex numbers:
-- | /Note/ - `randomR (z1, z2)` will produce values in a rectangle with a diagonal
-- defined by a difference of `z1 - z2` and `random` will rely on `a` to produce value for
-- both real and imaginary parts.
instance Random a => Random (Complex a) where
randomR ((al :+ bl), (ah :+ bh)) = runState $
(:+) <$> state (randomR (al, ah)) <*> state (randomR (bl, bh))
random = runState $ (:+) <$> state random <*> state randomor even better and more useful alternative could be this definition:
-- | /Note/ - `randomR` produces values in the annulus between two complex numbers and
-- `random` generates values within the unit circle.
instance (RealFloat a, Random a) => Random (Complex a) where
randomR (z1, z2) = runState $
mkPolar <$> state (randomR (magnitude z1, magnitude z2)) <*> state (randomR (0, 2*pi))
random = random = runState $ mkPolar <$> state (randomR (0, 1)) <*> state (randomR (0, 2*pi))Thoughts?
Note - randomR (0, 2*pi) would need to be adjusted not to include 2*pi, but that is an implementation detail
Few of us have mentioned that
Randomis no longer useful, becauseUniformandUniformRangewas introduced as a more correct interface.Complexis an example of a type whereRandomcan be very useful. We can't compare them and we can't produce a uniform distribution due to infinite many values, so there never can be neitherUniformnorUniformRangeinstances. But should it also mean that we can't have random complex numbers at all? For example I can see this as a sensible instance for complex numbers:or even better and more useful alternative could be this definition:
Thoughts?
Note -
randomR (0, 2*pi)would need to be adjusted not to include2*pi, but that is an implementation detail