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{-# LANGUAGE UndecidableInstances #-}

module Feldspar.Core.Constructs.Complex
where

import Language.Syntactic
import Language.Syntactic.Interpretation.Semantics
import Language.Syntactic.Constructs.Binding

import Data.Complex

import Feldspar.Core.Types
import Feldspar.Core.Interpretation

data COMPLEX a
  where
    MkComplex :: (Type a, RealFloat a) => COMPLEX (a :-> a :-> Full (Complex a))
    RealPart  :: (Type a, RealFloat a) => COMPLEX (Complex a :-> Full a)
    ImagPart  :: (Type a, RealFloat a) => COMPLEX (Complex a :-> Full a)
    Conjugate :: (Type a, RealFloat a) => COMPLEX (Complex a :-> Full (Complex a))
    MkPolar   :: (Type a, RealFloat a) => COMPLEX (a :-> a :-> Full (Complex a))
    Magnitude :: (Type a, RealFloat a) => COMPLEX (Complex a :-> Full a)
    Phase     :: (Type a, RealFloat a) => COMPLEX (Complex a :-> Full a)
    Cis       :: (Type a, RealFloat a) => COMPLEX (a :-> Full (Complex a))

instance WitnessCons COMPLEX
  where
    witnessCons MkComplex = ConsWit
    witnessCons RealPart  = ConsWit
    witnessCons ImagPart  = ConsWit
    witnessCons Conjugate = ConsWit
    witnessCons MkPolar   = ConsWit
    witnessCons Magnitude = ConsWit
    witnessCons Phase     = ConsWit
    witnessCons Cis       = ConsWit

instance WitnessSat COMPLEX
  where
    type SatContext COMPLEX = TypeCtx
    witnessSat MkComplex = SatWit
    witnessSat RealPart  = SatWit
    witnessSat ImagPart  = SatWit
    witnessSat Conjugate = SatWit
    witnessSat MkPolar   = SatWit
    witnessSat Magnitude = SatWit
    witnessSat Phase     = SatWit
    witnessSat Cis       = SatWit

instance MaybeWitnessSat TypeCtx COMPLEX
  where
    maybeWitnessSat = maybeWitnessSatDefault

instance Semantic COMPLEX
  where
    semantics MkComplex = Sem "complex"   (:+)
    semantics RealPart  = Sem "creal"     realPart
    semantics ImagPart  = Sem "cimag"     imagPart
    semantics Conjugate = Sem "conjugate" conjugate
    semantics MkPolar   = Sem "mkPolar"   mkPolar
    semantics Magnitude = Sem "magnitude" magnitude
    semantics Phase     = Sem "phase"     phase
    semantics Cis       = Sem "cis"       cis

instance ExprEq   COMPLEX where exprEq = exprEqSem; exprHash = exprHashSem
instance Render   COMPLEX where renderPart = renderPartSem
instance ToTree   COMPLEX
instance Eval     COMPLEX where evaluate = evaluateSem
instance EvalBind COMPLEX where evalBindSym = evalBindSymDefault
instance Sharable COMPLEX
instance SizeProp COMPLEX where sizeProp = sizePropDefault

instance AlphaEq dom dom dom env => AlphaEq COMPLEX COMPLEX dom env
  where
    alphaEqSym = alphaEqSymDefault

instance (COMPLEX :<: dom, Optimize dom dom) => Optimize COMPLEX dom
  where
    constructFeatUnOpt = constructFeatUnOptDefault
      -- TODO Optimize e.g.
      --
      --        complex (realPart a) (imagPart a)  ==>  a
      --        conjugate . conjugate              ==>  id