{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}
module Synthesizer.LLVM.Filter.ComplexFirstOrderPacked (
   Parameter, parameter,
   causal, causalP,
   ) where

import qualified Synthesizer.LLVM.CausalParameterized.Process as CausalP
import qualified Synthesizer.LLVM.Causal.Process as Causal
import qualified Synthesizer.LLVM.Simple.Value as Value

import qualified Synthesizer.LLVM.Frame.Stereo as Stereo

import qualified LLVM.Extra.ScalarOrVector as SoV
import qualified LLVM.Extra.Vector as Vector
import qualified LLVM.Extra.Arithmetic as A
import qualified LLVM.Extra.Memory as Memory
import LLVM.Extra.Class (Undefined, undefTuple, )

import qualified LLVM.Core as LLVM
import LLVM.Core
   (Value, valueOf, Struct,
    IsPrimitive, IsFloating, IsSized,
    Vector, insertelement,
    CodeGenFunction, )
import LLVM.Util.Loop (Phi, phis, addPhis, )

import qualified Type.Data.Num.Decimal as TypeNum
import Type.Data.Num.Decimal (D4, d0, d1, (:*:), )

import Control.Applicative (liftA2, )

import NumericPrelude.Numeric
import NumericPrelude.Base


-- the pair should also be replaced by a Vector
data Parameter a =
   Parameter (Value (Vector D4 a)) (Value (Vector D4 a))

instance IsPrimitive a => Phi (Parameter a) where
   phis bb (Parameter r i) = do
      r' <- phis bb r
      i' <- phis bb i
      return (Parameter r' i')
   addPhis bb
        (Parameter r i)
        (Parameter r' i') = do
      addPhis bb r r'
      addPhis bb i i'

instance IsPrimitive a => Undefined (Parameter a) where
   undefTuple = Parameter undefTuple undefTuple


type ParameterStruct a = Struct (Vector D4 a, (Vector D4 a, ()))

parameterMemory ::
   (Memory.FirstClass a, Memory.Stored a ~ am,
    IsPrimitive a, IsPrimitive am,
    TypeNum.Positive (TypeNum.D4 :*: LLVM.SizeOf am),
    IsSized am) =>
   Memory.Record r (ParameterStruct am) (Parameter a)
parameterMemory =
   liftA2 Parameter
      (Memory.element (\(Parameter kr _) -> kr) d0)
      (Memory.element (\(Parameter _ ki) -> ki) d1)

{-
The complicated Add constraints are caused by the IsType superclass of Memory.

instance (IsPrimitive l, IsSized (Vector D4 l) ss) =>
      Memory.C (Parameter l) (Struct (Vector D4 l, (Vector D4 l, ()))) where

Mul constraint seems to be not enough, GHC urges to give constraints in terms of Add
instance (IsPrimitive l, IsSized l s, Mul D4 s ss, Sets.Pos ss) =>
      Memory.C (Parameter l) (Struct (Vector D4 l, (Vector D4 l, ()))) where
-}
instance
   (Memory.FirstClass a, Memory.Stored a ~ am,
    IsPrimitive a, IsPrimitive am,
    IsSized am,
    TypeNum.Positive (TypeNum.D4 :*: LLVM.SizeOf am)) =>
      Memory.C (Parameter a) where
   type Struct (Parameter a) = ParameterStruct (Memory.Stored a)
   load = Memory.loadRecord parameterMemory
   store = Memory.storeRecord parameterMemory
   decompose = Memory.decomposeRecord parameterMemory
   compose = Memory.composeRecord parameterMemory

parameter ::
   (SoV.TranscendentalConstant a, IsFloating a, IsPrimitive a) =>
   Value a -> Value a -> CodeGenFunction r (Parameter a)
parameter reson freq = do
   amp <- A.fdiv A.one reson
   k   <- A.sub  A.one amp
   w  <- A.mul freq =<< Value.decons Value.twoPi
   kr <- A.mul k =<< A.cos w
   ki <- A.mul k =<< A.sin w

   kin <- A.neg ki
   kvr <- Vector.assemble [kr,kin,amp, A.zero]
   kvi <- Vector.assemble [ki,kr, amp, A.zero]
   return (Parameter kvr kvi)


type State a = Vector D4 a

{-
The handling of Vector D2 Float in LLVM-2.5 and LLVM-2.6 is at least unexpected.
Because of compatibility reasons, LLVM chooses MMX registers
which requires to call EMMS occasionally.
Thus I choose Vector D4 for Float computations.
Actually, I have now rearranged the data
such that we can make use of SSE4's dot product operation.
This would even require a vector of size 3.
-}
next ::
   (Vector.Arithmetic a) =>
   (Parameter a, Stereo.T (Value a)) ->
   Value (State a) ->
   CodeGenFunction r (Stereo.T (Value a), (Value (State a)))
next (Parameter kr ki, x) s = do
   sr <- insertelement s (Stereo.left  x) (valueOf 2)
   yr <- Vector.dotProduct kr sr

   si <- insertelement s (Stereo.right x) (valueOf 2)
   yi <- Vector.dotProduct ki si

   sv <- Vector.assemble [yr,yi]
   return (Stereo.cons yr yi, sv)

start ::
   (Vector.Arithmetic a) =>
   CodeGenFunction r (Value (State a))
start = return A.zero

causal ::
   (Causal.C process, Vector.Arithmetic a, Memory.C (Value (State a))) =>
   process
      (Parameter a, Stereo.T (Value a))
      (Stereo.T (Value a))
causal =
   Causal.mapAccum next start

{-# DEPRECATED causalP "use causal instead" #-}
causalP ::
   (Vector.Arithmetic a, Memory.C (Value (State a))) =>
   CausalP.T p
      (Parameter a, Stereo.T (Value a))
      (Stereo.T (Value a))
causalP =
   CausalP.mapAccumSimple next start