Complex.hs

{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}

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{-# LANGUAGE UndecidableInstances #-}

module Feldspar.Core.Constructs.Complex
where

import Language.Syntactic
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 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 Equality COMPLEX where equal = equalDefault; exprHash = exprHashDefault
instance Render   COMPLEX where renderArgs = renderArgsDefault
instance ToTree   COMPLEX
instance Eval     COMPLEX where evaluate = evaluateDefault
instance EvalBind COMPLEX where evalBindSym = evalBindSymDefault
instance Sharable COMPLEX

instance SizeProp (COMPLEX :|| Type)
  where
    sizeProp (C' s) = sizePropDefault s

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

instance ( (COMPLEX :|| Type) :<: dom
         , OptimizeSuper dom)
      => Optimize (COMPLEX :|| Type) dom
  where
    constructFeatOpt (C' MkComplex) ((rp :$ a) :* (ip :$ b) :* Nil)
        | Just (C' RealPart) <- prjF rp
        , Just (C' ImagPart) <- prjF ip
        , alphaEq a b
        = return a

    constructFeatOpt (C' RealPart) ((mkc :$ r :$ _) :* Nil)
        | Just (C' MkComplex) <- prjF mkc
        = return r

    constructFeatOpt (C' ImagPart) ((mkc :$ _ :$ i) :* Nil)
        | Just (C' MkComplex) <- prjF mkc
        = return i

    constructFeatOpt (C' MkPolar) ((mag :$ a) :* (ph :$ b) :* Nil)
        | Just (C' Magnitude) <- prjF mag
        , Just (C' Phase)     <- prjF ph
        , alphaEq a b
        = return a

    constructFeatOpt (C' Magnitude) ((mkp :$ m :$ _) :* Nil)
        | Just (C' MkPolar) <- prjF mkp
        = return m

    constructFeatOpt (C' Phase) ((mkp :$ _ :$ p) :* Nil)
        | Just (C' MkPolar) <- prjF mkp
        = return p

    constructFeatOpt (C' Conjugate) ((conj :$ a) :* Nil)
        | Just (C' Conjugate) <- prjF conj
        = return a

    constructFeatOpt sym args = constructFeatUnOpt sym args

    constructFeatUnOpt x@(C' _) = constructFeatUnOptDefault x