{-# LANGUAGE NoImplicitPrelude #-} {- | Copyright : (c) Henning Thielemann 2006 License : GPL Maintainer : synthesizer@henning-thielemann.de Stability : provisional Portability : requires multi-parameter type classes Avoid importing this module. Better use functions from "Synthesizer.Plain.Oscillator" and "Synthesizer.Basic.Wave" Input data is interpreted as samples of data on a cylinder in the following form: > |* | > | * | > | * | > | * | > | * | > | * | > | * | > | *| > | * | > | * | > | * | > ----------- > * > * > * > * > * > * > * > * > * > * > * > ----------- We have to interpolate in the parallelograms. -} module Synthesizer.Plain.ToneModulation where import qualified Synthesizer.Basic.ToneModulation as ToneMod import qualified Synthesizer.Basic.Phase as Phase import qualified Synthesizer.Plain.Signal as Sig import qualified Synthesizer.Plain.Interpolation as Interpolation import Synthesizer.Interpolation (Margin, ) -- import qualified Data.Array as Array import Data.Array (Array, (!), listArray, ) -- import qualified Algebra.Transcendental as Trans import qualified Algebra.RealField as RealField import qualified Algebra.Field as Field import qualified Algebra.RealRing as RealRing import qualified Algebra.Ring as Ring import qualified Algebra.Additive as Additive import qualified Number.NonNegative as NonNeg import qualified Number.NonNegativeChunky as Chunky import Control.Monad (guard, ) import qualified Data.List as List import qualified Data.List.HT as ListHT import qualified Data.List.Match as ListMatch import Data.Ord.HT (limit, ) import Data.Tuple.HT (mapPair, mapSnd, forcePair, ) import NumericPrelude.Numeric -- import qualified Prelude as P import NumericPrelude.Base -- * general helpers type Cell y = Sig.T (Sig.T y) interpolateCell :: Interpolation.T a y -> Interpolation.T b y -> (a, b) -> Cell y -> y interpolateCell ipLeap ipStep (qLeap,qStep) = Interpolation.func ipStep qStep . map (Interpolation.func ipLeap qLeap) -- * array based shape variable wave data Prototype t y = Prototype { protoMarginLeap, protoMarginStep :: Margin, protoIpOffset :: Int, protoPeriod :: t, protoPeriodInt :: Int, protoShapeLimits :: (t,t), protoArray :: Array Int y } makePrototype :: (RealField.C t) => Margin -> Margin -> Int -> t -> Sig.T y -> Prototype t y makePrototype marginLeap marginStep periodInt period tone = let ipOffset = ToneMod.interpolationOffset marginLeap marginStep periodInt len = length tone (lower,upper) = ToneMod.shapeLimits marginLeap marginStep periodInt len limits = if lower > upper then error "min>max" else (fromIntegral lower, fromIntegral upper) arr = listArray (0, pred len) tone in Prototype { protoMarginLeap = marginLeap, protoMarginStep = marginStep, protoIpOffset = ipOffset, protoPeriod = period, protoPeriodInt = periodInt, protoShapeLimits = limits, protoArray = arr } sampledToneCell :: (RealField.C t) => Prototype t y -> t -> Phase.T t -> ((t,t), Cell y) sampledToneCell p shape phase = let (n, q) = ToneMod.flattenShapePhase (protoPeriodInt p) (protoPeriod p) (limit (protoShapeLimits p) shape, phase) in (q, map (map (protoArray p ! ) . iterate (protoPeriodInt p +)) $ enumFrom (n - protoIpOffset p)) {- M = ((1,1)^T, (periodRound, period-periodRound)^T) equation for the line 0 = (nStep - offset ipStep) + (nLeap - offset ipLeap) * periodInt <(1,periodInt), (offset ipStep, offset ipLeap)> = <(1,periodInt), (nStep,nLeap)> d = <a,x> = <a,M^-1*M*x> = <(M^-T)*a,M*x> = <(M^-T)*a,y> b = (M^-T)*a required: y0 such that y1=0 y0 such that y1=period The line {x : d = <a,x>} converted to (shape,phase) coordinates has constant shape and meets all phases. -} -- * lazy oscillator oscillatorCells :: (RealField.C t) => Margin -> Margin -> Int -> t -> Sig.T y -> (t, Sig.T t) -> (Phase.T t, Sig.T t) -> Sig.T ((t,t), Cell y) oscillatorCells marginLeap marginStep periodInt period sampledTone shapes freqs = map (seekCell periodInt period) $ oscillatorSuffixes marginLeap marginStep periodInt period sampledTone shapes freqs seekCell :: (RealField.C t) => Int -> t -> ((t, Phase.T t), Cell y) -> ((t,t), Cell y) seekCell periodInt period = {- n will be zero within the data. We would need it only for extrapolation at the end. But this does not happen, since we limit the shape control parameter accordingly. -} (\(coords, ptr) -> let (k,q) = ToneMod.flattenShapePhase periodInt period coords in if k>0 then error "ToneModulation.oscillatorCells: k>0" else (q, drop (periodInt+k) ptr)) oscillatorSuffixes :: (RealField.C t) => Margin -> Margin -> Int -> t -> Sig.T y -> (t, Sig.T t) -> (Phase.T t, Sig.T t) -> Sig.T ((t, Phase.T t), Cell y) oscillatorSuffixes marginLeap marginStep periodInt period sampledTone shapes freqs = let ptrs = List.transpose $ takeWhile (not . null) $ iterate (drop periodInt) sampledTone ipOffset = periodInt + ToneMod.interpolationOffset marginLeap marginStep periodInt {- I tried to switch integrateFractional and limitRelativeShapes in order to have a position where I can easily add phase distortion. However, limitting skip values after integrateFractional does not work this way, since once we start setting skip values to zero, we had to clear the fractional parts of the shape coordinate, too. (firstSkip:allSkips,coords) = unzip $ integrateFractional period shapes freqs (skip,skips) = limitRelativeShapes marginLeap marginStep periodInt sampledTone (firstSkip,allSkips) -} (skip:skips,coords) = unzip $ integrateFractional period (limitRelativeShapes marginLeap marginStep periodInt sampledTone shapes) freqs in zip coords $ map (\(n,ptr) -> if n>0 then error $ "ToneModulation.oscillatorCells: " ++ "limit of shape parameter is buggy" else ptr) $ tail $ scanl {- since we clip the coordinates before calling oscillatorCells we do not need 'dropRem', since 'drop' would never go beyond the list end -} (\ (n,ptr0) d0 -> dropRem (n+d0) ptr0) (0,ptrs) ((skip - ipOffset) : skips) dropFrac :: RealField.C i => i -> Sig.T a -> (Int, i, Sig.T a) dropFrac = let recourse acc n xt = if n>=1 then case xt of _:xs -> recourse (succ acc) (n-1) xs [] -> (acc, n, []) else (acc,n,xt) in recourse 0 dropFrac' :: RealField.C i => i -> Sig.T a -> (Int, i, Sig.T a) dropFrac' = let recourse acc n xt = maybe (acc,n,xt) (recourse (succ acc) (n-1) . snd) (guard (n>=1) >> ListHT.viewL xt) in recourse 0 propDropFrac :: (RealField.C i, Eq a) => i -> Sig.T a -> Bool propDropFrac n xs = dropFrac n xs == dropFrac' n xs dropRem :: Int -> Sig.T a -> (Int, Sig.T a) dropRem = let recourse n xt = if n>0 then case xt of _:xs -> recourse (pred n) xs [] -> (n, []) else (n,xt) in recourse dropRem' :: Int -> Sig.T a -> (Int, Sig.T a) dropRem' = let recourse n xt = maybe (n,xt) (recourse (pred n) . snd) (guard (n>0) >> ListHT.viewL xt) in recourse propDropRem :: (Eq a) => Int -> Sig.T a -> Bool propDropRem n xs = dropRem n xs == dropRem' n xs {- *Synthesizer.Plain.ToneModulation> Test.QuickCheck.quickCheck (\n xs -> propDropRem n (xs::[Int])) OK, passed 100 tests. *Synthesizer.Plain.ToneModulation> Test.QuickCheck.quickCheck (\n xs -> propDropFrac (n::Rational) (xs::[Int])) OK, passed 100 tests. -} oscillatorCoords :: (RealField.C t) => Int -> t -> (t, Sig.T t) -> (Phase.T t, Sig.T t) -> Sig.T (ToneMod.Coords t) oscillatorCoords periodInt period shapes freqs = map (mapSnd (ToneMod.flattenShapePhase periodInt period)) $ integrateFractional period shapes freqs {- mapM print $ take 30 $ let period = 1/0.07::Double in oscillatorCoords (round period) period 0 0 (repeat 0.1) (repeat 0.01) *Synthesizer.Plain.Oscillator> mapM print $ take 30 $ let period = 1/0.07::Rational in oscillatorCoords (round period) period 0 0 (repeat 1) (repeat 0.07) *Synthesizer.Plain.Oscillator> mapM print $ take 30 $ let period = 1/0.07::Rational in oscillatorCoords (round period) period 0 0 (repeat 0.25) (repeat 0.0175) -} integrateFractional :: (RealField.C t) => t -> (t, Sig.T t) -> (Phase.T t, Sig.T t) -> Sig.T (ToneMod.Skip t) integrateFractional period (shape0, shapes) (phase, freqs) = let shapeOffsets = scanl (\(_,s) c -> splitFraction (s+c)) (splitFraction shape0) shapes phases = let (s:ss) = map (\(n,_) -> fromIntegral n / period) shapeOffsets in freqsToPhases (Phase.decrement s phase) -- phase - s (zipWith (-) freqs ss) in zipWith (\(d,s) p -> (d, (s,p))) shapeOffsets phases -- this function fits better in the Oscillator module {- | Convert a list of phase steps into a list of momentum phases phase is a number in the interval [0,1) freq contains the phase steps -} freqsToPhases :: RealRing.C a => Phase.T a -> Sig.T a -> Sig.T (Phase.T a) freqsToPhases phase freq = scanl (flip Phase.increment) phase freq limitRelativeShapes :: (Ring.C t, Ord t) => Margin -> Margin -> Int -> Sig.T y -> (t, Sig.T t) -> (t, Sig.T t) limitRelativeShapes marginLeap marginStep periodInt sampledTone = let -- len = List.genericLength sampledTone len = Chunky.fromChunks (ListMatch.replicate sampledTone one) (minShape, maxShape) = ToneMod.shapeLimits marginLeap marginStep periodInt len fromChunky = NonNeg.toNumber . Chunky.toNumber toChunky = Chunky.fromNumber . NonNeg.fromNumber in mapPair (fromChunky, map fromChunky) . uncurry (limitMaxRelativeValuesNonNeg maxShape) . mapPair (toChunky, map toChunky) . uncurry (limitMinRelativeValues (fromChunky minShape)) {- *Synthesizer.Plain.Oscillator> let ip = Interpolation.linear in limitRelativeShapes ip ip 13 (take 100 $ iterate (1+) (0::Double)) (0::Double, cycle [0.5,1.5]) (13.0,[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5,1.5,0.5*** Exception: Numeric.NonNegative.Chunky.-: negative number -} limitMinRelativeValues :: (Additive.C a, Ord a) => a -> a -> Sig.T a -> (a, Sig.T a) limitMinRelativeValues xMin x0 xs = let (ys,zs) = span ((<zero).fst) (zip (scanl (+) (x0-xMin) xs) (x0:xs)) in case ys of [] -> (x0,xs) (_:yr) -> (xMin, ListMatch.replicate yr zero ++ case zs of [] -> [] (z:zr) -> fst z : map snd zr) limitMaxRelativeValues :: (Additive.C a, Ord a) => a -> a -> Sig.T a -> (a, Sig.T a) limitMaxRelativeValues xMax x0 xs = let (ys,zs) = span (>zero) (scanl (-) (xMax-x0) xs) in forcePair $ ListHT.switchR (xMax, ListMatch.replicate xs zero) (\ yl yr -> (x0, ListMatch.take yl xs ++ ListMatch.take zs (yr : repeat zero))) ys {- | Avoids negative numbers and thus can be used with Chunky numbers. -} limitMaxRelativeValuesNonNeg :: (Additive.C a, Ord a) => a -> a -> Sig.T a -> (a, Sig.T a) limitMaxRelativeValuesNonNeg xMax x0 xs = let (ys,zs) = span fst (scanl (\(_,acc) d -> safeSub acc d) (safeSub xMax x0) xs) in forcePair $ ListHT.switchR (xMax, ListMatch.replicate xs zero) (\ yl ~(_,yr) -> (x0, ListMatch.take yl xs ++ ListMatch.take zs (yr : repeat zero))) ys {- *Synthesizer.Plain.Oscillator> limitMaxRelativeValuesNonNeg (let inf = 1+inf in inf) (0::Chunky.T NonNeg.Rational) (repeat 2.5) -} safeSub :: (Additive.C a, Ord a) => a -> a -> (Bool, a) safeSub a b = (a>=b, a-b)