{- |
ToDo:
How to handle dimensional values as control parameters?
How to combine control parameters with antialiasing waveforms?

Actually, a waveform is like a Map where one parameter is of type Phase.T.
A waveform with dimensional control parameter
should be treated like a dimensional Map.
If we do not use the Map type for waveforms
we must at least provide a function for applying a Map to a Wave.

I think the oscillators should always provide the frequency
to the apply method of a wave.
Then the waveform can decide whether it wants to use it or not.
We could make a type class for simple and bandlimited waveforms.
However, there is a fundamental problem:
Distortion of a waveform (wave shaping)
can turn bandlimited waveforms into ones without band limits.
-}
module Synthesizer.Dimensional.Wave.Controlled where

import qualified Synthesizer.Basic.Wave as Wave
import qualified Synthesizer.Generic.Wave as WaveG
import qualified Synthesizer.Generic.Signal as SigG

import qualified Synthesizer.Interpolation as Interpolation

import qualified Synthesizer.Dimensional.Signal.Private as SigA
import qualified Synthesizer.Dimensional.Amplitude as Amp
import qualified Synthesizer.Dimensional.Rate as Rate

import qualified Algebra.Transcendental as Trans
import qualified Algebra.RealField      as RealField
import qualified Algebra.Ring           as Ring

import qualified Number.DimensionTerm        as DN
import qualified Algebra.DimensionTerm       as Dim

import NumericPrelude
import PreludeBase
import Prelude ()


data T amp c t y =
   Cons {
      amplitude :: amp,
      body :: c -> Wave.T t y
   }

{-
data T amp body =
   Cons {
      amplitude :: amp,
      body :: body
   }
-}

{- |
Interpolate first within waves and then across waves,
which is simpler but maybe less efficient for lists.
However for types with fast indexing/drop like StorableVector this is optimal.
-}
sampledTone ::
   (RealField.C t, SigG.Transform sig y, Dim.C u) =>
   Interpolation.T t y ->
   Interpolation.T t y ->
   DN.T u t -> SigA.T (Rate.Dimensional u t) amp (sig y) -> T amp t t y
sampledTone ipLeap ipStep period tone =
   Cons (SigA.amplitude tone) $
   WaveG.sampledTone ipLeap ipStep
      (DN.mulToScalar period (SigA.actualSampleRate tone))
      (SigA.body tone)



{-# INLINE flat #-}
flat :: (Ring.C y) =>
   (c -> Wave.T t y) ->
   T (Amp.Flat y) c t y
flat = Cons Amp.Flat


{-# INLINE abstract #-}
abstract ::
   (c -> Wave.T t y) ->
   T Amp.Abstract c t y
abstract = Cons Amp.Abstract


{-# INLINE amplified #-}
amplified :: (Ring.C y, Dim.C u) =>
   DN.T u y ->
   (c -> Wave.T t y) ->
   T (Amp.Dimensional u y) c t y
amplified = Cons . Amp.Numeric


{-# INLINE mapLinear #-}
mapLinear :: (Ring.C y, Dim.C u) =>
   y ->
   DN.T u y ->
   (c -> Wave.T t y) ->
   T (Amp.Dimensional u y) c t y
mapLinear depth center =
   amplified center . (Wave.distort (\x -> one+x*depth) .)

{-# INLINE mapExponential #-}
mapExponential :: (Trans.C y, Dim.C u) =>
   y ->
   DN.T u y ->
   (c -> Wave.T t y) ->
   T (Amp.Dimensional u y) c t y
mapExponential depth center =
   -- amplified center . Wave.distort (depth**)
   -- should be faster
   amplified center .
      let logDepth = log depth
      in  (Wave.distort (exp . (logDepth*)) .)