{-# LANGUAGE NoImplicitPrelude #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE FlexibleContexts #-} {- | Signal generators that generate the signal in chunks that can be processed natively by the processor. Some of the functions for plain signals can be re-used without modification. E.g. rendering a signal and reading from and to signals work because the vector type as element type warrents correct alignment. We can convert between atomic and chunked signals. The article explains the difference between Vector and SIMD computing. According to that the SSE extensions in Intel processors must be called Vector computing. But since we use the term Vector already in the mathematical sense, I like to use the term "packed" that is used in Intel mnemonics like mulps. -} module Synthesizer.LLVM.Generator.SignalPacked ( pack, packRotate, packSmall, unpack, unpackRotate, constant, exponential2, exponentialBounded2, osciCore, osci, parabolaFadeInInf, parabolaFadeOutInf, rampInf, rampSlope, noise, noiseCore, noiseCoreAlt, ) where import qualified Synthesizer.LLVM.Causal.Process as Causal import qualified Synthesizer.LLVM.Generator.Private as Priv import qualified Synthesizer.LLVM.Generator.Core as Core import qualified Synthesizer.LLVM.Generator.Signal as Sig import qualified Synthesizer.LLVM.Frame.SerialVector.Class as SerialClass import qualified Synthesizer.LLVM.Frame.SerialVector.Code as SerialCode import qualified Synthesizer.LLVM.Frame.SerialVector as Serial import qualified Synthesizer.LLVM.Random as Rnd import Synthesizer.Causal.Class (($*)) import qualified LLVM.DSL.Expression as Expr import LLVM.DSL.Expression (Exp) import qualified LLVM.Extra.Multi.Vector as MultiVector import qualified LLVM.Extra.Multi.Value.Marshal as Marshal import qualified LLVM.Extra.Multi.Value.Vector as MultiValueVec import qualified LLVM.Extra.Multi.Value as MultiValue import qualified LLVM.Extra.Memory as Memory import qualified LLVM.Extra.MaybeContinuation as Maybe import qualified LLVM.Extra.Control as U import qualified LLVM.Extra.Arithmetic as A import qualified LLVM.Extra.Tuple as Tuple import qualified Type.Data.Num.Decimal as TypeNum import Type.Data.Num.Decimal ((:*:)) import qualified LLVM.Core as LLVM import qualified Control.Monad.Trans.Class as MT import qualified Control.Monad.Trans.State as MS import Control.Monad.HT ((<=<)) import Control.Monad (replicateM) import Control.Applicative ((<$>)) import qualified Algebra.Ring as Ring import Data.Tuple.HT (mapSnd) import Data.Word (Word32, Word) import Data.Int (Int32) import NumericPrelude.Numeric import NumericPrelude.Base {- | Convert a signal of scalar values into one using processor vectors. If the signal length is not divisible by the chunk size, then the last chunk is dropped. -} pack, packRotate :: (SerialClass.Write v, a ~ SerialClass.Element v) => Sig.T a -> Sig.T v pack = packRotate packRotate (Priv.Cons next start stop) = Priv.Cons (\global local s -> do wInit <- Maybe.lift $ SerialClass.writeStart (w2,_,s2) <- Maybe.fromBool $ U.whileLoop (LLVM.valueOf True, (wInit, LLVM.valueOf $ (SerialClass.sizeOfIterator wInit :: Word), s)) (\(cont,(_w0,i0,_s0)) -> A.and cont =<< A.cmp LLVM.CmpGT i0 A.zero) (\(_,(w0,i0,s0)) -> Maybe.toBool $ do (a,s1) <- next global local s0 Maybe.lift $ do w1 <- SerialClass.writeNext a w0 i1 <- A.dec i0 return (w1,i1,s1)) v <- Maybe.lift $ SerialClass.writeStop w2 return (v, s2)) start stop {- We could reformulate it in terms of WriteIterator that accesses elements using LLVM.extract. We might move the loop counter into the Iterator, but we have to assert that the counter is not duplicated. packIndex :: (SerialClass.Write v, a ~ SerialClass.Element v) => Sig.T a -> Sig.T v packIndex = alter (\(Core next start stop) -> Core (\param s -> do (v2,_,s2) <- Maybe.fromBool $ U.whileLoop (LLVM.valueOf True, (Tuple.undef, A.zero, s)) (\(cont,(v0,i0,_s0)) -> A.and cont =<< A.cmp LLVM.CmpLT i0 (LLVM.valueOf $ SerialClass.size v0)) (\(_,(v0,i0,s0)) -> Maybe.toBool $ do (a,s1) <- next param s0 Maybe.lift $ do v1 <- Vector.insert i0 a v0 i1 <- A.inc i0 return (v1,i1,s1)) return (v2, s2)) start stop) -} {- | Like 'pack' but duplicates the code for creating elements. That is, for vectors of size n, the code of the input signal will be emitted n times. This is efficient only for simple input generators. -} packSmall :: (SerialClass.Write v, a ~ SerialClass.Element v) => Sig.T a -> Sig.T v packSmall (Priv.Cons next start stop) = Priv.Cons (\global local -> MS.runStateT $ SerialClass.withSize $ \n -> MT.lift . Maybe.lift . SerialClass.assemble =<< replicateM n (MS.StateT $ next global local)) start stop unpack, unpackRotate :: (SerialClass.Read v, a ~ SerialClass.Element v, SerialClass.ReadIt v ~ itv, Memory.C itv) => Sig.T v -> Sig.T a unpack = unpackRotate unpackRotate (Priv.Cons next start stop) = Priv.Cons (\global local (i0,r0,s0) -> do endOfVector <- Maybe.lift $ A.cmp LLVM.CmpEQ i0 (LLVM.valueOf (0::Word)) (i2,r2,s2) <- Maybe.fromBool $ U.ifThen endOfVector (LLVM.valueOf True, (i0,r0,s0)) $ do (cont1, (v1,s1)) <- Maybe.toBool $ next global local s0 r1 <- SerialClass.readStart v1 return (cont1, (LLVM.valueOf $ SerialClass.size v1, r1, s1)) Maybe.lift $ do (a,r3) <- SerialClass.readNext r2 i3 <- A.dec i2 return (a, (i3,r3,s2))) (mapSnd (\s -> (A.zero, Tuple.undef, s)) <$> start) stop {- We could reformulate it in terms of ReadIterator that accesses elements using LLVM.extract. We might move the loop counter into the Iterator, but we have to assert that the counter is not duplicated. unpackIndex :: (SerialClass.Write v, a ~ SerialClass.Element v, Memory.C v) => Sig.T v -> Sig.T a unpackIndex = alter (\(Core next start stop) -> Core (\param (i0,v0,s0) -> do endOfVector <- Maybe.lift $ A.cmp LLVM.CmpGE i0 (LLVM.valueOf $ SerialClass.size v0) (i2,v2,s2) <- Maybe.fromBool $ U.ifThen endOfVector (LLVM.valueOf True, (i0,v0,s0)) $ do (cont1, (v1,s1)) <- Maybe.toBool $ next param s0 return (cont1, (A.zero, v1, s1)) Maybe.lift $ do a <- Vector.extract i2 v2 i3 <- A.inc i2 return (a, (i3,v2,s2))) (\p -> do s <- start p let v = Tuple.undef return (LLVM.valueOf $ SerialClass.size v, v, s)) stop) -} type Serial n a = SerialCode.Value n a withSize :: (TypeNum.Positive n) => (TypeNum.Singleton n -> Sig.T (Serial n a)) -> Sig.T (Serial n a) withSize f = f TypeNum.singleton withSizeRing :: (Ring.C b, TypeNum.Positive n) => (b -> Sig.T (Serial n a)) -> Sig.T (Serial n a) withSizeRing f = withSize $ f . fromInteger . TypeNum.integerFromSingleton constant :: (Marshal.Vector n a) => Exp a -> Sig.T (Serial n a) constant = Sig.constant . Serial.upsample exponential2 :: (Marshal.Vector n a, MultiVector.Transcendental a, MultiValue.RationalConstant a) => Exp a -> Exp a -> Sig.T (Serial n a) exponential2 halfLife start = withSizeRing $ \n -> Core.exponential (Serial.upsample (0.5 ** (n / halfLife))) (Serial.iterate (0.5 ** recip halfLife *) start) exponentialBounded2 :: (Marshal.Vector n a, MultiVector.Transcendental a, MultiValue.RationalConstant a, MultiVector.IntegerConstant a, MultiVector.Real a) => Exp a -> Exp a -> Exp a -> Sig.T (Serial n a) exponentialBounded2 bound halfLife start = withSizeRing $ \n -> Core.exponentialBounded (Serial.upsample bound) (Serial.upsample (0.5 ** (n / halfLife))) (Serial.iterate (0.5 ** recip halfLife *) start) osciCore :: (Marshal.Vector n t, MultiVector.PseudoRing t, MultiVector.Fraction t, MultiValue.IntegerConstant t) => Exp t -> Exp t -> Sig.T (Serial n t) osciCore phase freq = withSizeRing $ \n -> Core.osci (Serial.iterate (Expr.fraction . (freq +)) phase) (Serial.upsample (Expr.fraction (n * freq))) osci :: (Marshal.Vector n t, MultiVector.PseudoRing t, MultiVector.Fraction t, MultiValue.IntegerConstant t) => (forall r. Serial n t -> LLVM.CodeGenFunction r y) -> Exp t -> Exp t -> Sig.T y osci wave phase freq = Priv.map wave $ osciCore phase freq rampInf, rampSlope, parabolaFadeInInf, parabolaFadeOutInf :: (Marshal.Vector n a, MultiVector.Field a, MultiVector.IntegerConstant a, MultiValue.RationalConstant a) => Exp a -> Sig.T (Serial n a) rampSlope slope = withSizeRing $ \n -> Core.ramp (Serial.upsample (n * slope)) (Serial.iterate (slope +) 0) rampInf dur = rampSlope (Expr.recip dur) parabolaFadeInInf dur = withSizeRing $ \n -> let d = n/dur in Core.parabola (Serial.upsample (-2*d*d)) (Serial.iterate (subtract $ 2 / dur ^ 2) (d*(2-d))) ((\t -> t*(2-t)) $ Serial.iterate (recip dur +) 0) parabolaFadeOutInf dur = withSizeRing $ \n -> let d = n/dur in Core.parabola (Serial.upsample (-2*d*d)) (Serial.iterate (subtract $ 2 / dur ^ 2) (-d*d)) ((\t -> 1-t*t) $ Serial.iterate (recip dur +) 0) {- | For the mysterious rate parameter see 'Sig.noise'. -} noise :: (MultiVector.NativeFloating n a ar) => (MultiVector.PseudoRing a, MultiVector.IntegerConstant a) => (MultiValue.Algebraic a, MultiValue.RationalConstant a) => (TypeNum.Positive n, TypeNum.Positive (n :*: TypeNum.D32)) => Exp Word32 -> Exp a -> Sig.T (Serial n a) noise seed rate = let m2 = div Rnd.modulus 2 r = Serial.upsample $ Expr.sqrt (3*rate) / Expr.fromInteger' m2 in Causal.map (\y -> r * (Expr.liftM int31tofp y - Expr.fromInteger' (m2+1))) $* noiseCoreAlt seed {- sitofp is a single instruction on x86 and thus we use it, since the arguments are below 2^31. It would be better to use LLVM's range annotation, instead. -} int31tofp :: (MultiVector.NativeFloating n a ar, TypeNum.Positive n, TypeNum.Positive (n :*: TypeNum.D32)) => Serial n Word32 -> LLVM.CodeGenFunction r (Serial n a) int31tofp = fmap SerialCode.fromOrdinary . MultiValueVec.fromIntegral . SerialCode.toOrdinary . forceInt32 <=< MultiValue.liftM LLVM.bitcast type Id a = a -> a forceInt32 :: Id (Serial n Int32) forceInt32 = id noiseCore, noiseCoreAlt :: (TypeNum.Positive n, TypeNum.Positive (n :*: TypeNum.D32)) => Exp Word32 -> Sig.T (Serial n Word32) noiseCore = Sig.iterate (Expr.liftReprM Rnd.nextVector) . vectorSeed noiseCoreAlt = Sig.iterate (Expr.liftReprM Rnd.nextVector64) . vectorSeed vectorSeed :: (TypeNum.Positive n) => Exp Word32 -> Exp (Serial.T n Word32) vectorSeed seed = Serial.iterate (Expr.liftReprM Rnd.nextCG) $ Expr.irem seed (fromInteger Rnd.modulus - 1) + 1