AD with Accelerate types

[alang9]

It would be nice to be able to use AD with Accelerate types (like Exp Double or Exp (Complex Double))

I think the big issues are:

1. A lot of typeclass methods on accelerate types result in bottoms. e.g.

instance P.Eq (Exp a) where
  (==) = preludeError "Eq.==" "(==)"
  (/=) = preludeError "Eq./=" "(/=)"

instance Ord a => P.Ord (Exp a) where
  compare = error "Prelude.Ord.compare applied to EDSL types"
  (<)     = preludeError "Ord.<"  "(<)"
  (<=)    = preludeError "Ord.<=" "(<=)"
  (>)     = preludeError "Ord.>"  "(>)"
  (>=)    = preludeError "Ord.>=" "(>=)"
  min     = min
  max     = max

instance P.Enum (Exp a) where
  toEnum   = preludeError "toEnum"
  fromEnum = preludeError "fromEnum"

instance (Num a, Ord a) => P.Real (Exp a) where
  toRational = P.error "Prelude.toRational not supported for Accelerate types"

2. Accelerate appears to be very slow at compiling code with recursive functions. It seems better to iterate with Data.Array.Accelerate.while or Data.Array.Accelerate.iterate.

[tmcdonell]

For anybody who stumbles onto this: AccelerateHS/accelerate#398