{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE FlexibleContexts #-}
module Synthesizer.Generic.Filter.NonRecursive (
negate,
amplify,
amplifyVector,
normalize,
envelope,
envelopeVector,
fadeInOut,
delay,
delayPad,
delayPos,
delayNeg,
delayLazySize,
delayPadLazySize,
delayPosLazySize,
binomialMask,
binomial,
binomial1,
sums,
sumsDownsample2,
downsample2,
downsample,
sumRange,
pyramid,
sumRangeFromPyramid,
sumsPosModulated,
sumsPosModulatedPyramid,
movingAverageModulatedPyramid,
inverseFrequencyModulationFloor,
differentiate,
differentiateCenter,
differentiate2,
generic,
karatsubaFinite,
karatsubaFiniteInfinite,
karatsubaInfinite,
Pair,
convolvePair,
sumAndConvolvePair,
Triple,
convolvePairTriple,
convolveTriple,
sumAndConvolveTriple,
sumAndConvolveTripleAlt,
Quadruple,
convolveQuadruple,
sumAndConvolveQuadruple,
sumAndConvolveQuadrupleAlt,
maybeAccumulateRangeFromPyramid,
accumulatePosModulatedFromPyramid,
withPaddedInput,
addShiftedSimple,
consumeRangeFromPyramid,
sumRangeFromPyramidReverse,
sumRangeFromPyramidFoldr,
) where
import qualified Synthesizer.Generic.Signal as SigG
import qualified Synthesizer.Generic.Cut as CutG
import qualified Synthesizer.Generic.Control as Ctrl
import qualified Synthesizer.Generic.LengthSignal as SigL
import qualified Synthesizer.Basic.Filter.NonRecursive as Filt
import qualified Synthesizer.State.Filter.NonRecursive as FiltS
import qualified Synthesizer.State.Signal as SigS
import Control.Monad (mplus, )
import Data.Function.HT (nest, )
import Data.Tuple.HT (mapSnd, mapPair, )
import Data.Maybe.HT (toMaybe, )
import qualified Algebra.Transcendental as Trans
import qualified Algebra.Module as Module
import qualified Algebra.RealField as RealField
import qualified Algebra.Field as Field
import qualified Algebra.Ring as Ring
import qualified Algebra.Additive as Additive
import qualified NumericPrelude.Numeric as NP
import NumericPrelude.Numeric hiding (negate, )
import NumericPrelude.Base
{-# INLINE negate #-}
negate ::
(Additive.C a, SigG.Transform sig a) =>
sig a -> sig a
negate :: forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
negate = (a -> a) -> sig a -> sig a
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map a -> a
forall a. C a => a -> a
Additive.negate
{-# INLINE amplify #-}
amplify ::
(Ring.C a, SigG.Transform sig a) =>
a -> sig a -> sig a
amplify :: forall a (sig :: * -> *).
(C a, Transform sig a) =>
a -> sig a -> sig a
amplify a
v = (a -> a) -> sig a -> sig a
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map (a
va -> a -> a
forall a. C a => a -> a -> a
*)
{-# INLINE amplifyVector #-}
amplifyVector ::
(Module.C a v, SigG.Transform sig v) =>
a -> sig v -> sig v
amplifyVector :: forall a v (sig :: * -> *).
(C a v, Transform sig v) =>
a -> sig v -> sig v
amplifyVector a
v = (v -> v) -> sig v -> sig v
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map (a
va -> v -> v
forall a v. C a v => a -> v -> v
*>)
{-# INLINE normalize #-}
normalize ::
(Field.C a, SigG.Transform sig a) =>
(sig a -> a) -> sig a -> sig a
normalize :: forall a (sig :: * -> *).
(C a, Transform sig a) =>
(sig a -> a) -> sig a -> sig a
normalize sig a -> a
volume sig a
xs =
a -> sig a -> sig a
forall a (sig :: * -> *).
(C a, Transform sig a) =>
a -> sig a -> sig a
amplify (a -> a
forall a. C a => a -> a
recip (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ sig a -> a
volume sig a
xs) sig a
xs
{-# INLINE envelope #-}
envelope ::
(Ring.C a, SigG.Transform sig a) =>
sig a
-> sig a
-> sig a
envelope :: forall a (sig :: * -> *).
(C a, Transform sig a) =>
sig a -> sig a -> sig a
envelope = (a -> a -> a) -> sig a -> sig a -> sig a
forall (sig :: * -> *) a b c.
(Read sig a, Transform sig b, Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
SigG.zipWith a -> a -> a
forall a. C a => a -> a -> a
(*)
{-# INLINE envelopeVector #-}
envelopeVector ::
(Module.C a v, SigG.Read sig a, SigG.Transform sig v) =>
sig a
-> sig v
-> sig v
envelopeVector :: forall a v (sig :: * -> *).
(C a v, Read sig a, Transform sig v) =>
sig a -> sig v -> sig v
envelopeVector = (a -> v -> v) -> sig a -> sig v -> sig v
forall (sig :: * -> *) a b c.
(Read sig a, Transform sig b, Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
SigG.zipWith a -> v -> v
forall a v. C a v => a -> v -> v
(*>)
{-# INLINE fadeInOut #-}
fadeInOut ::
(Field.C a, SigG.Write sig a) =>
Int -> Int -> Int -> sig a -> sig a
fadeInOut :: forall a (sig :: * -> *).
(C a, Write sig a) =>
Int -> Int -> Int -> sig a -> sig a
fadeInOut Int
tIn Int
tHold Int
tOut sig a
xs =
let slopeIn :: a
slopeIn = a -> a
forall a. C a => a -> a
recip (Int -> a
forall a b. (C a, C b) => a -> b
fromIntegral Int
tIn)
slopeOut :: a
slopeOut = a -> a
forall a. C a => a -> a
Additive.negate (a -> a
forall a. C a => a -> a
recip (Int -> a
forall a b. (C a, C b) => a -> b
fromIntegral Int
tOut))
leadIn :: sig a
leadIn = Int -> sig a -> sig a
forall sig. Transform sig => Int -> sig -> sig
SigG.take Int
tIn (sig a -> sig a) -> sig a -> sig a
forall a b. (a -> b) -> a -> b
$ LazySize -> a -> a -> sig a
forall y (sig :: * -> *).
(C y, Write sig y) =>
LazySize -> y -> y -> sig y
Ctrl.linear LazySize
SigG.defaultLazySize a
slopeIn a
0
leadOut :: sig a
leadOut = Int -> sig a -> sig a
forall sig. Transform sig => Int -> sig -> sig
SigG.take Int
tOut (sig a -> sig a) -> sig a -> sig a
forall a b. (a -> b) -> a -> b
$ LazySize -> a -> a -> sig a
forall y (sig :: * -> *).
(C y, Write sig y) =>
LazySize -> y -> y -> sig y
Ctrl.linear LazySize
SigG.defaultLazySize a
slopeOut a
1
(sig a
partIn, sig a
partHoldOut) = Int -> sig a -> (sig a, sig a)
forall sig. Transform sig => Int -> sig -> (sig, sig)
SigG.splitAt Int
tIn sig a
xs
(sig a
partHold, sig a
partOut) = Int -> sig a -> (sig a, sig a)
forall sig. Transform sig => Int -> sig -> (sig, sig)
SigG.splitAt Int
tHold sig a
partHoldOut
in sig a -> sig a -> sig a
forall a (sig :: * -> *).
(C a, Transform sig a) =>
sig a -> sig a -> sig a
envelope sig a
leadIn sig a
partIn sig a -> sig a -> sig a
forall sig. Monoid sig => sig -> sig -> sig
`SigG.append`
sig a
partHold sig a -> sig a -> sig a
forall sig. Monoid sig => sig -> sig -> sig
`SigG.append`
sig a -> sig a -> sig a
forall a (sig :: * -> *).
(C a, Transform sig a) =>
sig a -> sig a -> sig a
envelope sig a
leadOut sig a
partOut
{-# INLINE delay #-}
delay :: (Additive.C y, SigG.Write sig y) =>
Int -> sig y -> sig y
delay :: forall y (sig :: * -> *).
(C y, Write sig y) =>
Int -> sig y -> sig y
delay =
y -> Int -> sig y -> sig y
forall (sig :: * -> *) y. Write sig y => y -> Int -> sig y -> sig y
delayPad y
forall a. C a => a
zero
{-# INLINE delayPad #-}
delayPad :: (SigG.Write sig y) =>
y -> Int -> sig y -> sig y
delayPad :: forall (sig :: * -> *) y. Write sig y => y -> Int -> sig y -> sig y
delayPad y
z Int
n =
if Int
nInt -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
0
then Int -> sig y -> sig y
forall sig. Transform sig => Int -> sig -> sig
SigG.drop (Int -> Int
forall a. C a => a -> a
Additive.negate Int
n)
else sig y -> sig y -> sig y
forall sig. Monoid sig => sig -> sig -> sig
SigG.append (LazySize -> Int -> y -> sig y
forall y. Storage (sig y) => LazySize -> Int -> y -> sig y
forall (sig :: * -> *) y.
(Write0 sig, Storage (sig y)) =>
LazySize -> Int -> y -> sig y
SigG.replicate LazySize
SigG.defaultLazySize Int
n y
z)
{-# INLINE delayPos #-}
delayPos :: (Additive.C y, SigG.Write sig y) =>
Int -> sig y -> sig y
delayPos :: forall y (sig :: * -> *).
(C y, Write sig y) =>
Int -> sig y -> sig y
delayPos Int
n =
sig y -> sig y -> sig y
forall sig. Monoid sig => sig -> sig -> sig
SigG.append (LazySize -> Int -> y -> sig y
forall y. Storage (sig y) => LazySize -> Int -> y -> sig y
forall (sig :: * -> *) y.
(Write0 sig, Storage (sig y)) =>
LazySize -> Int -> y -> sig y
SigG.replicate LazySize
SigG.defaultLazySize Int
n y
forall a. C a => a
zero)
{-# INLINE delayNeg #-}
delayNeg :: (SigG.Transform sig y) =>
Int -> sig y -> sig y
delayNeg :: forall (sig :: * -> *) y. Transform sig y => Int -> sig y -> sig y
delayNeg = Int -> sig y -> sig y
forall sig. Transform sig => Int -> sig -> sig
SigG.drop
{-# INLINE delayLazySize #-}
delayLazySize :: (Additive.C y, SigG.Write sig y) =>
SigG.LazySize -> Int -> sig y -> sig y
delayLazySize :: forall y (sig :: * -> *).
(C y, Write sig y) =>
LazySize -> Int -> sig y -> sig y
delayLazySize LazySize
size =
LazySize -> y -> Int -> sig y -> sig y
forall (sig :: * -> *) y.
Write sig y =>
LazySize -> y -> Int -> sig y -> sig y
delayPadLazySize LazySize
size y
forall a. C a => a
zero
{-# INLINE delayPadLazySize #-}
delayPadLazySize :: (SigG.Write sig y) =>
SigG.LazySize -> y -> Int -> sig y -> sig y
delayPadLazySize :: forall (sig :: * -> *) y.
Write sig y =>
LazySize -> y -> Int -> sig y -> sig y
delayPadLazySize LazySize
size y
z Int
n =
if Int
nInt -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
0
then Int -> sig y -> sig y
forall sig. Transform sig => Int -> sig -> sig
SigG.drop (Int -> Int
forall a. C a => a -> a
Additive.negate Int
n)
else sig y -> sig y -> sig y
forall sig. Monoid sig => sig -> sig -> sig
SigG.append (LazySize -> Int -> y -> sig y
forall y. Storage (sig y) => LazySize -> Int -> y -> sig y
forall (sig :: * -> *) y.
(Write0 sig, Storage (sig y)) =>
LazySize -> Int -> y -> sig y
SigG.replicate LazySize
size Int
n y
z)
{-# INLINE delayPosLazySize #-}
delayPosLazySize :: (Additive.C y, SigG.Write sig y) =>
SigG.LazySize -> Int -> sig y -> sig y
delayPosLazySize :: forall y (sig :: * -> *).
(C y, Write sig y) =>
LazySize -> Int -> sig y -> sig y
delayPosLazySize LazySize
size Int
n =
sig y -> sig y -> sig y
forall sig. Monoid sig => sig -> sig -> sig
SigG.append (LazySize -> Int -> y -> sig y
forall y. Storage (sig y) => LazySize -> Int -> y -> sig y
forall (sig :: * -> *) y.
(Write0 sig, Storage (sig y)) =>
LazySize -> Int -> y -> sig y
SigG.replicate LazySize
size Int
n y
forall a. C a => a
zero)
binomialMask ::
(Field.C a, SigG.Write sig a) =>
SigG.LazySize ->
Int -> sig a
binomialMask :: forall a (sig :: * -> *).
(C a, Write sig a) =>
LazySize -> Int -> sig a
binomialMask LazySize
size Int
n =
LazySize
-> ((a, Integer, Integer) -> Maybe (a, (a, Integer, Integer)))
-> (a, Integer, Integer)
-> sig a
forall y s.
Storage (sig y) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
forall (sig :: * -> *) y s.
(Write0 sig, Storage (sig y)) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
SigG.unfoldR LazySize
size
(\(a
x, Integer
a, Integer
b) ->
Bool
-> (a, (a, Integer, Integer)) -> Maybe (a, (a, Integer, Integer))
forall a. Bool -> a -> Maybe a
toMaybe (Integer
bInteger -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
>=Integer
0)
(a
x, (a
x a -> a -> a
forall a. C a => a -> a -> a
* Integer -> a
forall a. C a => Integer -> a
fromInteger Integer
b a -> a -> a
forall a. C a => a -> a -> a
/ Integer -> a
forall a. C a => Integer -> a
fromInteger (Integer
aInteger -> Integer -> Integer
forall a. C a => a -> a -> a
+Integer
1), Integer
aInteger -> Integer -> Integer
forall a. C a => a -> a -> a
+Integer
1, Integer
bInteger -> Integer -> Integer
forall a. C a => a -> a -> a
-Integer
1)))
(a -> a
forall a. C a => a -> a
recip (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ a
2 a -> Integer -> a
forall a. C a => a -> Integer -> a
^ Int -> Integer
forall a b. (C a, C b) => a -> b
fromIntegral Int
n, Integer
0, Int -> Integer
forall a b. (C a, C b) => a -> b
fromIntegral Int
n)
{-# INLINE binomial #-}
binomial ::
(Trans.C a, RealField.C a, Module.C a v, SigG.Transform sig v) =>
a -> a -> sig v -> sig v
binomial :: forall a v (sig :: * -> *).
(C a, C a, C a v, Transform sig v) =>
a -> a -> sig v -> sig v
binomial a
ratio a
freq =
let width :: Int
width = a -> Int
forall b. C b => a -> b
forall a b. (C a, C b) => a -> b
ceiling (a
2 a -> a -> a
forall a. C a => a -> a -> a
* a -> a -> a
forall a. C a => a -> a -> a
Filt.ratioFreqToVariance a
ratio a
freq a -> Integer -> a
forall a. C a => a -> Integer -> a
^ Integer
2)
in Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
width (sig v -> sig v) -> (sig v -> sig v) -> sig v -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
Int -> (sig v -> sig v) -> sig v -> sig v
forall a. Int -> (a -> a) -> a -> a
nest (Int
2Int -> Int -> Int
forall a. C a => a -> a -> a
*Int
width) (a -> sig v -> sig v
forall a v (sig :: * -> *).
(C a v, Transform sig v) =>
a -> sig v -> sig v
amplifyVector (a -> a -> a
forall a. a -> a -> a
asTypeOf a
0.5 a
freq) (sig v -> sig v) -> (sig v -> sig v) -> sig v -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
. sig v -> sig v
forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
binomial1)
{-# INLINE binomial1 #-}
binomial1 ::
(Additive.C v, SigG.Transform sig v) => sig v -> sig v
binomial1 :: forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
binomial1 = (v -> v -> v) -> sig v -> sig v
forall (sig :: * -> *) a.
(Read sig a, Transform sig a) =>
(a -> a -> a) -> sig a -> sig a
SigG.mapAdjacent v -> v -> v
forall a. C a => a -> a -> a
(+)
{-# INLINE sums #-}
sums ::
(Additive.C v, SigG.Transform sig v) =>
Int -> sig v -> sig v
sums :: forall v (sig :: * -> *).
(C v, Transform sig v) =>
Int -> sig v -> sig v
sums Int
n = (sig v -> v) -> sig v -> sig v
forall (sig :: * -> *) a.
Transform sig a =>
(sig a -> a) -> sig a -> sig a
SigG.mapTails (sig v -> v
forall a (sig :: * -> *). (C a, Read sig a) => sig a -> a
SigG.sum (sig v -> v) -> (sig v -> sig v) -> sig v -> v
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.take Int
n)
sumsDownsample2 ::
(Additive.C v, SigG.Write sig v) =>
SigG.LazySize -> sig v -> sig v
sumsDownsample2 :: forall v (sig :: * -> *).
(C v, Write sig v) =>
LazySize -> sig v -> sig v
sumsDownsample2 LazySize
cs =
LazySize -> (sig v -> Maybe (v, sig v)) -> sig v -> sig v
forall y s.
Storage (sig y) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
forall (sig :: * -> *) y s.
(Write0 sig, Storage (sig y)) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
SigG.unfoldR LazySize
cs (\sig v
xs ->
(((v, sig v) -> (v, sig v))
-> Maybe (v, sig v) -> Maybe (v, sig v))
-> Maybe (v, sig v)
-> ((v, sig v) -> (v, sig v))
-> Maybe (v, sig v)
forall a b c. (a -> b -> c) -> b -> a -> c
flip ((v, sig v) -> (v, sig v)) -> Maybe (v, sig v) -> Maybe (v, sig v)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (sig v -> Maybe (v, sig v)
forall y. Storage (sig y) => sig y -> Maybe (y, sig y)
forall (sig :: * -> *) y.
(Transform0 sig, Storage (sig y)) =>
sig y -> Maybe (y, sig y)
SigG.viewL sig v
xs) (((v, sig v) -> (v, sig v)) -> Maybe (v, sig v))
-> ((v, sig v) -> (v, sig v)) -> Maybe (v, sig v)
forall a b. (a -> b) -> a -> b
$ \xxs0 :: (v, sig v)
xxs0@(v
x0,sig v
xs0) ->
(v, sig v) -> (v -> sig v -> (v, sig v)) -> sig v -> (v, sig v)
forall (sig :: * -> *) y a.
Transform sig y =>
a -> (y -> sig y -> a) -> sig y -> a
SigG.switchL (v, sig v)
xxs0
(\ v
x1 sig v
xs1 -> (v
x0v -> v -> v
forall a. C a => a -> a -> a
+v
x1, sig v
xs1))
sig v
xs0)
downsample2 ::
(SigG.Write sig v) =>
SigG.LazySize -> sig v -> sig v
downsample2 :: forall (sig :: * -> *) v. Write sig v => LazySize -> sig v -> sig v
downsample2 LazySize
cs =
LazySize -> (sig v -> Maybe (v, sig v)) -> sig v -> sig v
forall y s.
Storage (sig y) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
forall (sig :: * -> *) y s.
(Write0 sig, Storage (sig y)) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
SigG.unfoldR LazySize
cs
(((v, sig v) -> (v, sig v)) -> Maybe (v, sig v) -> Maybe (v, sig v)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((sig v -> sig v) -> (v, sig v) -> (v, sig v)
forall b c a. (b -> c) -> (a, b) -> (a, c)
mapSnd sig v -> sig v
forall (sig :: * -> *) y. Transform sig y => sig y -> sig y
SigG.laxTail) (Maybe (v, sig v) -> Maybe (v, sig v))
-> (sig v -> Maybe (v, sig v)) -> sig v -> Maybe (v, sig v)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. sig v -> Maybe (v, sig v)
forall y. Storage (sig y) => sig y -> Maybe (y, sig y)
forall (sig :: * -> *) y.
(Transform0 sig, Storage (sig y)) =>
sig y -> Maybe (y, sig y)
SigG.viewL)
downsample ::
(SigG.Write sig v) =>
SigG.LazySize -> Int -> sig v -> sig v
downsample :: forall (sig :: * -> *) v.
Write sig v =>
LazySize -> Int -> sig v -> sig v
downsample LazySize
cs Int
n =
LazySize -> (sig v -> Maybe (v, sig v)) -> sig v -> sig v
forall y s.
Storage (sig y) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
forall (sig :: * -> *) y s.
(Write0 sig, Storage (sig y)) =>
LazySize -> (s -> Maybe (y, s)) -> s -> sig y
SigG.unfoldR LazySize
cs
(\sig v
xs -> ((v, sig v) -> (v, sig v)) -> Maybe (v, sig v) -> Maybe (v, sig v)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((sig v -> sig v) -> (v, sig v) -> (v, sig v)
forall b c a. (b -> c) -> (a, b) -> (a, c)
mapSnd (sig v -> sig v -> sig v
forall a b. a -> b -> a
const (Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
n sig v
xs))) (Maybe (v, sig v) -> Maybe (v, sig v))
-> Maybe (v, sig v) -> Maybe (v, sig v)
forall a b. (a -> b) -> a -> b
$ sig v -> Maybe (v, sig v)
forall y. Storage (sig y) => sig y -> Maybe (y, sig y)
forall (sig :: * -> *) y.
(Transform0 sig, Storage (sig y)) =>
sig y -> Maybe (y, sig y)
SigG.viewL sig v
xs)
sumRange ::
(Additive.C v, SigG.Transform sig v) =>
sig v -> (Int,Int) -> v
sumRange :: forall v (sig :: * -> *).
(C v, Transform sig v) =>
sig v -> (Int, Int) -> v
sumRange =
((Int, Int) -> sig v -> v) -> sig v -> (Int, Int) -> v
forall v source.
C v =>
((Int, Int) -> source -> v) -> source -> (Int, Int) -> v
Filt.sumRangePrepare (((Int, Int) -> sig v -> v) -> sig v -> (Int, Int) -> v)
-> ((Int, Int) -> sig v -> v) -> sig v -> (Int, Int) -> v
forall a b. (a -> b) -> a -> b
$ \ (Int
l,Int
r) ->
sig v -> v
forall a (sig :: * -> *). (C a, Read sig a) => sig a -> a
SigG.sum (sig v -> v) -> (sig v -> sig v) -> sig v -> v
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.take (Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
l) (sig v -> sig v) -> (sig v -> sig v) -> sig v -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
l
pyramid ::
(Additive.C v, SigG.Write sig v) =>
Int -> sig v -> ([Int], [sig v])
pyramid :: forall v (sig :: * -> *).
(C v, Write sig v) =>
Int -> sig v -> ([Int], [sig v])
pyramid Int
height sig v
sig =
let sizes :: [Int]
sizes = [Int] -> [Int]
forall a. [a] -> [a]
reverse ([Int] -> [Int]) -> [Int] -> [Int]
forall a b. (a -> b) -> a -> b
$ Int -> [Int] -> [Int]
forall a. Int -> [a] -> [a]
take (Int
1Int -> Int -> Int
forall a. C a => a -> a -> a
+Int
height) ([Int] -> [Int]) -> [Int] -> [Int]
forall a b. (a -> b) -> a -> b
$ (Int -> Int) -> Int -> [Int]
forall a. (a -> a) -> a -> [a]
iterate (Int
2Int -> Int -> Int
forall a. C a => a -> a -> a
*) Int
1
in ([Int]
sizes,
(sig v -> LazySize -> sig v) -> sig v -> [LazySize] -> [sig v]
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl ((LazySize -> sig v -> sig v) -> sig v -> LazySize -> sig v
forall a b c. (a -> b -> c) -> b -> a -> c
flip LazySize -> sig v -> sig v
forall v (sig :: * -> *).
(C v, Write sig v) =>
LazySize -> sig v -> sig v
sumsDownsample2) sig v
sig ((Int -> LazySize) -> [Int] -> [LazySize]
forall a b. (a -> b) -> [a] -> [b]
map Int -> LazySize
SigG.LazySize ([Int] -> [LazySize]) -> [Int] -> [LazySize]
forall a b. (a -> b) -> a -> b
$ [Int] -> [Int]
forall a. HasCallStack => [a] -> [a]
tail [Int]
sizes))
{-# INLINE sumRangeFromPyramid #-}
sumRangeFromPyramid ::
(Additive.C v, SigG.Transform sig v) =>
[sig v] -> (Int,Int) -> v
sumRangeFromPyramid :: forall v (sig :: * -> *).
(C v, Transform sig v) =>
[sig v] -> (Int, Int) -> v
sumRangeFromPyramid =
((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall v source.
C v =>
((Int, Int) -> source -> v) -> source -> (Int, Int) -> v
Filt.sumRangePrepare (((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v)
-> ((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall a b. (a -> b) -> a -> b
$ \(Int, Int)
lr0 [sig v]
pyr0 ->
(v -> (v -> v) -> v -> v)
-> (v -> v) -> [sig v] -> (Int, Int) -> v -> v
forall (sig :: * -> *) v a.
Transform sig v =>
(v -> a -> a) -> a -> [sig v] -> (Int, Int) -> a
consumeRangeFromPyramid (\v
v v -> v
k v
s -> v -> v
k (v
sv -> v -> v
forall a. C a => a -> a -> a
+v
v)) v -> v
forall a. a -> a
id [sig v]
pyr0 (Int, Int)
lr0 v
forall a. C a => a
zero
sumRangeFromPyramidReverse ::
(Additive.C v, SigG.Transform sig v) =>
[sig v] -> (Int,Int) -> v
sumRangeFromPyramidReverse :: forall v (sig :: * -> *).
(C v, Transform sig v) =>
[sig v] -> (Int, Int) -> v
sumRangeFromPyramidReverse =
((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall v source.
C v =>
((Int, Int) -> source -> v) -> source -> (Int, Int) -> v
Filt.sumRangePrepare (((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v)
-> ((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall a b. (a -> b) -> a -> b
$ \(Int, Int)
lr0 [sig v]
pyr0 ->
(v -> v -> v) -> v -> [sig v] -> (Int, Int) -> v
forall (sig :: * -> *) v a.
Transform sig v =>
(v -> a -> a) -> a -> [sig v] -> (Int, Int) -> a
consumeRangeFromPyramid v -> v -> v
forall a. C a => a -> a -> a
(+) v
forall a. C a => a
zero [sig v]
pyr0 (Int, Int)
lr0
sumRangeFromPyramidFoldr ::
(Additive.C v, SigG.Transform sig v) =>
[sig v] -> (Int,Int) -> v
sumRangeFromPyramidFoldr :: forall v (sig :: * -> *).
(C v, Transform sig v) =>
[sig v] -> (Int, Int) -> v
sumRangeFromPyramidFoldr =
((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall v source.
C v =>
((Int, Int) -> source -> v) -> source -> (Int, Int) -> v
Filt.sumRangePrepare (((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v)
-> ((Int, Int) -> [sig v] -> v) -> [sig v] -> (Int, Int) -> v
forall a b. (a -> b) -> a -> b
$ \(Int, Int)
lr0 [sig v]
pyr0 ->
case [sig v]
pyr0 of
[] -> [Char] -> v
forall a. HasCallStack => [Char] -> a
error [Char]
"empty pyramid"
(sig v
ps0:[sig v]
pss) ->
(sig v
-> ((Int, Int) -> sig v -> v -> v)
-> (Int, Int)
-> sig v
-> v
-> v)
-> ((Int, Int) -> sig v -> v -> v)
-> [sig v]
-> (Int, Int)
-> sig v
-> v
-> v
forall a b. (a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr
(\sig v
psNext (Int, Int) -> sig v -> v -> v
k (Int
l,Int
r) sig v
ps v
s ->
case Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
l of
Int
0 -> v
s
Int
1 -> v
s v -> v -> v
forall a. C a => a -> a -> a
+ sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps Int
l
Int
_ ->
let (Int
lh,Int
ll) = (Int, Int) -> (Int, Int)
forall a. C a => a -> a
NP.negate ((Int, Int) -> (Int, Int)) -> (Int, Int) -> (Int, Int)
forall a b. (a -> b) -> a -> b
$ Int -> Int -> (Int, Int)
forall a. C a => a -> a -> (a, a)
divMod (Int -> Int
forall a. C a => a -> a
NP.negate Int
l) Int
2
(Int
rh,Int
rl) = Int -> Int -> (Int, Int)
forall a. C a => a -> a -> (a, a)
divMod Int
r Int
2
{-# INLINE inc #-}
inc :: a -> a -> a -> a
inc a
b a
x = if a
ba -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
0 then a -> a
forall a. a -> a
id else (a
xa -> a -> a
forall a. C a => a -> a -> a
+)
in (Int, Int) -> sig v -> v -> v
k (Int
lh,Int
rh) sig v
psNext (v -> v) -> v -> v
forall a b. (a -> b) -> a -> b
$
Int -> v -> v -> v
forall {a} {a}. (Eq a, C a, C a) => a -> a -> a -> a
inc Int
ll (sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps Int
l) (v -> v) -> v -> v
forall a b. (a -> b) -> a -> b
$
Int -> v -> v -> v
forall {a} {a}. (Eq a, C a, C a) => a -> a -> a -> a
inc Int
rl (sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps (Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
1)) (v -> v) -> v -> v
forall a b. (a -> b) -> a -> b
$
v
s)
(\(Int
l,Int
r) sig v
ps v
s ->
v
s v -> v -> v
forall a. C a => a -> a -> a
+ (sig v -> v
forall a (sig :: * -> *). (C a, Read sig a) => sig a -> a
SigG.sum (sig v -> v) -> sig v -> v
forall a b. (a -> b) -> a -> b
$ Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.take (Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
l) (sig v -> sig v) -> sig v -> sig v
forall a b. (a -> b) -> a -> b
$ Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
l sig v
ps))
[sig v]
pss (Int, Int)
lr0 sig v
ps0 v
forall a. C a => a
zero
{-# INLINE maybeAccumulateRangeFromPyramid #-}
maybeAccumulateRangeFromPyramid ::
(SigG.Transform sig v) =>
(v -> v -> v) ->
[sig v] -> (Int,Int) -> Maybe v
maybeAccumulateRangeFromPyramid :: forall (sig :: * -> *) v.
Transform sig v =>
(v -> v -> v) -> [sig v] -> (Int, Int) -> Maybe v
maybeAccumulateRangeFromPyramid v -> v -> v
acc =
((Int, Int) -> [sig v] -> Maybe v)
-> [sig v] -> (Int, Int) -> Maybe v
forall source v.
((Int, Int) -> source -> v) -> source -> (Int, Int) -> v
Filt.symmetricRangePrepare (((Int, Int) -> [sig v] -> Maybe v)
-> [sig v] -> (Int, Int) -> Maybe v)
-> ((Int, Int) -> [sig v] -> Maybe v)
-> [sig v]
-> (Int, Int)
-> Maybe v
forall a b. (a -> b) -> a -> b
$ \(Int, Int)
lr0 [sig v]
pyr0 ->
(v -> (Maybe v -> Maybe v) -> Maybe v -> Maybe v)
-> (Maybe v -> Maybe v)
-> [sig v]
-> (Int, Int)
-> Maybe v
-> Maybe v
forall (sig :: * -> *) v a.
Transform sig v =>
(v -> a -> a) -> a -> [sig v] -> (Int, Int) -> a
consumeRangeFromPyramid
(\v
v Maybe v -> Maybe v
k Maybe v
s -> Maybe v -> Maybe v
k ((v -> v) -> Maybe v -> Maybe v
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (v -> v -> v
acc v
v) Maybe v
s Maybe v -> Maybe v -> Maybe v
forall a. Maybe a -> Maybe a -> Maybe a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
`mplus` v -> Maybe v
forall a. a -> Maybe a
Just v
v))
Maybe v -> Maybe v
forall a. a -> a
id [sig v]
pyr0 (Int, Int)
lr0 Maybe v
forall a. Maybe a
Nothing
{-# INLINE consumeRangeFromPyramid #-}
consumeRangeFromPyramid ::
(SigG.Transform sig v) =>
(v -> a -> a) -> a ->
[sig v] -> (Int,Int) -> a
consumeRangeFromPyramid :: forall (sig :: * -> *) v a.
Transform sig v =>
(v -> a -> a) -> a -> [sig v] -> (Int, Int) -> a
consumeRangeFromPyramid v -> a -> a
acc a
init0 [sig v]
pyr0 (Int, Int)
lr0 =
case [sig v]
pyr0 of
[] -> [Char] -> a
forall a. HasCallStack => [Char] -> a
error [Char]
"empty pyramid"
(sig v
ps0:[sig v]
pss) ->
(sig v -> ((Int, Int) -> sig v -> a) -> (Int, Int) -> sig v -> a)
-> ((Int, Int) -> sig v -> a)
-> [sig v]
-> (Int, Int)
-> sig v
-> a
forall a b. (a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr
(\sig v
psNext (Int, Int) -> sig v -> a
k (Int
l,Int
r) sig v
ps ->
case Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
l of
Int
0 -> a
init0
Int
1 -> v -> a -> a
acc (sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps Int
l) a
init0
Int
_ ->
let (Int
lh,Int
ll) = (Int, Int) -> (Int, Int)
forall a. C a => a -> a
NP.negate ((Int, Int) -> (Int, Int)) -> (Int, Int) -> (Int, Int)
forall a b. (a -> b) -> a -> b
$ Int -> Int -> (Int, Int)
forall a. C a => a -> a -> (a, a)
divMod (Int -> Int
forall a. C a => a -> a
NP.negate Int
l) Int
2
(Int
rh,Int
rl) = Int -> Int -> (Int, Int)
forall a. C a => a -> a -> (a, a)
divMod Int
r Int
2
{-# INLINE inc #-}
inc :: a -> v -> a -> a
inc a
b v
x = if a
ba -> a -> Bool
forall a. Eq a => a -> a -> Bool
==a
0 then a -> a
forall a. a -> a
id else v -> a -> a
acc v
x
in Int -> v -> a -> a
forall {a}. (Eq a, C a) => a -> v -> a -> a
inc Int
ll (sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps Int
l) (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$
Int -> v -> a -> a
forall {a}. (Eq a, C a) => a -> v -> a -> a
inc Int
rl (sig v -> Int -> v
forall y. Storage (sig y) => sig y -> Int -> y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> Int -> y
SigG.index sig v
ps (Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
1)) (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$
(Int, Int) -> sig v -> a
k (Int
lh,Int
rh) sig v
psNext)
(\(Int
l,Int
r) sig v
ps ->
(v -> a -> a) -> a -> sig v -> a
forall y s. Storage (sig y) => (y -> s -> s) -> s -> sig y -> s
forall (sig :: * -> *) y s.
(Read0 sig, Storage (sig y)) =>
(y -> s -> s) -> s -> sig y -> s
SigG.foldR v -> a -> a
acc a
init0 (sig v -> a) -> sig v -> a
forall a b. (a -> b) -> a -> b
$
Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.take (Int
rInt -> Int -> Int
forall a. C a => a -> a -> a
-Int
l) (sig v -> sig v) -> sig v -> sig v
forall a b. (a -> b) -> a -> b
$ Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
l sig v
ps)
[sig v]
pss (Int, Int)
lr0 sig v
ps0
sumsPosModulated ::
(Additive.C v, SigG.Transform sig (Int,Int), SigG.Transform sig v) =>
sig (Int,Int) -> sig v -> sig v
sumsPosModulated :: forall v (sig :: * -> *).
(C v, Transform sig (Int, Int), Transform sig v) =>
sig (Int, Int) -> sig v -> sig v
sumsPosModulated sig (Int, Int)
ctrl sig v
xs =
((Int, Int) -> sig v -> v) -> sig (Int, Int) -> sig v -> sig v
forall (sig :: * -> *) a b c.
(Transform sig a, Transform sig b, Transform sig c) =>
(a -> sig b -> c) -> sig a -> sig b -> sig c
SigG.zipWithTails ((sig v -> (Int, Int) -> v) -> (Int, Int) -> sig v -> v
forall a b c. (a -> b -> c) -> b -> a -> c
flip sig v -> (Int, Int) -> v
forall v (sig :: * -> *).
(C v, Transform sig v) =>
sig v -> (Int, Int) -> v
sumRange) sig (Int, Int)
ctrl sig v
xs
{-# INLINE accumulatePosModulatedFromPyramid #-}
accumulatePosModulatedFromPyramid ::
(SigG.Transform sig (Int,Int), SigG.Write sig v) =>
([sig v] -> (Int,Int) -> v) ->
([Int], [sig v]) ->
sig (Int,Int) -> sig v
accumulatePosModulatedFromPyramid :: forall (sig :: * -> *) v.
(Transform sig (Int, Int), Write sig v) =>
([sig v] -> (Int, Int) -> v)
-> ([Int], [sig v]) -> sig (Int, Int) -> sig v
accumulatePosModulatedFromPyramid [sig v] -> (Int, Int) -> v
accumulate ([Int]
sizes,[sig v]
pyr0) sig (Int, Int)
ctrl =
let blockSize :: Int
blockSize = [Int] -> Int
forall a. HasCallStack => [a] -> a
head [Int]
sizes
pyrStarts :: [[sig v]]
pyrStarts = ([sig v] -> [sig v]) -> [sig v] -> [[sig v]]
forall a. (a -> a) -> a -> [a]
iterate ((Int -> sig v -> sig v) -> [Int] -> [sig v] -> [sig v]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop [Int]
sizes) [sig v]
pyr0
ctrlBlocks :: [sig (Int, Int)]
ctrlBlocks = T (sig (Int, Int)) -> [sig (Int, Int)]
forall y. T y -> [y]
SigS.toList (T (sig (Int, Int)) -> [sig (Int, Int)])
-> T (sig (Int, Int)) -> [sig (Int, Int)]
forall a b. (a -> b) -> a -> b
$ Int -> sig (Int, Int) -> T (sig (Int, Int))
forall sig. Transform sig => Int -> sig -> T sig
SigG.sliceVertical Int
blockSize sig (Int, Int)
ctrl
in [sig v] -> sig v
forall sig. Monoid sig => [sig] -> sig
SigG.concat ([sig v] -> sig v) -> [sig v] -> sig v
forall a b. (a -> b) -> a -> b
$
([sig v] -> sig (Int, Int) -> sig v)
-> [[sig v]] -> [sig (Int, Int)] -> [sig v]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith
(\[sig v]
pyr ->
LazySize -> T v -> sig v
forall (sig :: * -> *) y. Write sig y => LazySize -> T y -> sig y
SigG.fromState (Int -> LazySize
SigG.LazySize Int
blockSize) (T v -> sig v)
-> (sig (Int, Int) -> T v) -> sig (Int, Int) -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
((Int, Int) -> v) -> T (Int, Int) -> T v
forall a b. (a -> b) -> T a -> T b
SigS.map ([sig v] -> (Int, Int) -> v
accumulate [sig v]
pyr) (T (Int, Int) -> T v)
-> (sig (Int, Int) -> T (Int, Int)) -> sig (Int, Int) -> T v
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
(Int -> (Int, Int) -> (Int, Int))
-> T Int -> T (Int, Int) -> T (Int, Int)
forall a b c. (a -> b -> c) -> T a -> T b -> T c
SigS.zipWith (\Int
d -> (Int -> Int, Int -> Int) -> (Int, Int) -> (Int, Int)
forall a c b d. (a -> c, b -> d) -> (a, b) -> (c, d)
mapPair ((Int
dInt -> Int -> Int
forall a. C a => a -> a -> a
+), (Int
dInt -> Int -> Int
forall a. C a => a -> a -> a
+))) ((Int -> Int) -> Int -> T Int
forall a. (a -> a) -> a -> T a
SigS.iterate (Int
1Int -> Int -> Int
forall a. C a => a -> a -> a
+) Int
0) (T (Int, Int) -> T (Int, Int))
-> (sig (Int, Int) -> T (Int, Int))
-> sig (Int, Int)
-> T (Int, Int)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
sig (Int, Int) -> T (Int, Int)
forall y. Storage (sig y) => sig y -> T y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState)
[[sig v]]
pyrStarts [sig (Int, Int)]
ctrlBlocks
sumsPosModulatedPyramid ::
(Additive.C v, SigG.Transform sig (Int,Int), SigG.Write sig v) =>
Int -> sig (Int,Int) -> sig v -> sig v
sumsPosModulatedPyramid :: forall v (sig :: * -> *).
(C v, Transform sig (Int, Int), Write sig v) =>
Int -> sig (Int, Int) -> sig v -> sig v
sumsPosModulatedPyramid Int
height sig (Int, Int)
ctrl sig v
xs =
([sig v] -> (Int, Int) -> v)
-> ([Int], [sig v]) -> sig (Int, Int) -> sig v
forall (sig :: * -> *) v.
(Transform sig (Int, Int), Write sig v) =>
([sig v] -> (Int, Int) -> v)
-> ([Int], [sig v]) -> sig (Int, Int) -> sig v
accumulatePosModulatedFromPyramid
[sig v] -> (Int, Int) -> v
forall v (sig :: * -> *).
(C v, Transform sig v) =>
[sig v] -> (Int, Int) -> v
sumRangeFromPyramid
(Int -> sig v -> ([Int], [sig v])
forall v (sig :: * -> *).
(C v, Write sig v) =>
Int -> sig v -> ([Int], [sig v])
pyramid Int
height sig v
xs) sig (Int, Int)
ctrl
withPaddedInput ::
(SigG.Transform sig Int, SigG.Transform sig (Int, Int),
SigG.Write sig y) =>
y -> (sig (Int, Int) -> sig y -> v) ->
Int ->
sig Int ->
sig y -> v
withPaddedInput :: forall (sig :: * -> *) y v.
(Transform sig Int, Transform sig (Int, Int), Write sig y) =>
y -> (sig (Int, Int) -> sig y -> v) -> Int -> sig Int -> sig y -> v
withPaddedInput y
pad sig (Int, Int) -> sig y -> v
proc Int
maxC sig Int
ctrl sig y
xs =
sig (Int, Int) -> sig y -> v
proc
((Int -> (Int, Int)) -> sig Int -> sig (Int, Int)
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map (\Int
c -> (Int
maxC Int -> Int -> Int
forall a. C a => a -> a -> a
- Int
c, Int
maxC Int -> Int -> Int
forall a. C a => a -> a -> a
+ Int
c Int -> Int -> Int
forall a. C a => a -> a -> a
+ Int
1)) sig Int
ctrl)
(y -> Int -> sig y -> sig y
forall (sig :: * -> *) y. Write sig y => y -> Int -> sig y -> sig y
delayPad y
pad Int
maxC sig y
xs)
movingAverageModulatedPyramid ::
(Field.C a, Module.C a v,
SigG.Transform sig Int, SigG.Transform sig (Int,Int), SigG.Write sig v) =>
a -> Int -> Int -> sig Int -> sig v -> sig v
movingAverageModulatedPyramid :: forall a v (sig :: * -> *).
(C a, C a v, Transform sig Int, Transform sig (Int, Int),
Write sig v) =>
a -> Int -> Int -> sig Int -> sig v -> sig v
movingAverageModulatedPyramid a
amp Int
height Int
maxC sig Int
ctrl0 =
v
-> (sig (Int, Int) -> sig v -> sig v)
-> Int
-> sig Int
-> sig v
-> sig v
forall (sig :: * -> *) y v.
(Transform sig Int, Transform sig (Int, Int), Write sig y) =>
y -> (sig (Int, Int) -> sig y -> v) -> Int -> sig Int -> sig y -> v
withPaddedInput v
forall a. C a => a
zero
(\sig (Int, Int)
ctrl sig v
xs ->
(Int -> v -> v) -> sig Int -> sig v -> sig v
forall (sig :: * -> *) a b c.
(Read sig a, Transform sig b, Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
SigG.zipWith (\Int
c v
x -> (a
amp a -> a -> a
forall a. C a => a -> a -> a
/ Int -> a
forall a b. (C a, C b) => a -> b
fromIntegral (Int
2Int -> Int -> Int
forall a. C a => a -> a -> a
*Int
cInt -> Int -> Int
forall a. C a => a -> a -> a
+Int
1)) a -> v -> v
forall a v. C a v => a -> v -> v
*> v
x) sig Int
ctrl0 (sig v -> sig v) -> sig v -> sig v
forall a b. (a -> b) -> a -> b
$
Int -> sig (Int, Int) -> sig v -> sig v
forall v (sig :: * -> *).
(C v, Transform sig (Int, Int), Write sig v) =>
Int -> sig (Int, Int) -> sig v -> sig v
sumsPosModulatedPyramid Int
height sig (Int, Int)
ctrl sig v
xs)
Int
maxC sig Int
ctrl0
inverseFrequencyModulationFloor ::
(Ord t, Ring.C t, SigG.Write sig v, SigG.Read sig t) =>
SigG.LazySize ->
sig t -> sig v -> sig v
inverseFrequencyModulationFloor :: forall t (sig :: * -> *) v.
(Ord t, C t, Write sig v, Read sig t) =>
LazySize -> sig t -> sig v -> sig v
inverseFrequencyModulationFloor LazySize
chunkSize sig t
ctrl sig v
xs =
LazySize -> T v -> sig v
forall (sig :: * -> *) y. Write sig y => LazySize -> T y -> sig y
SigG.fromState LazySize
chunkSize
(T t -> T v -> T v
forall t v. (Ord t, C t) => T t -> T v -> T v
FiltS.inverseFrequencyModulationFloor
(sig t -> T t
forall y. Storage (sig y) => sig y -> T y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState sig t
ctrl) (sig v -> T v
forall y. Storage (sig y) => sig y -> T y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState sig v
xs))
{-# INLINE differentiate #-}
differentiate ::
(Additive.C v, SigG.Transform sig v) =>
sig v -> sig v
differentiate :: forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
differentiate sig v
x = (v -> v -> v) -> sig v -> sig v
forall (sig :: * -> *) a.
(Read sig a, Transform sig a) =>
(a -> a -> a) -> sig a -> sig a
SigG.mapAdjacent v -> v -> v
forall a. C a => a -> a -> a
subtract sig v
x
{-# INLINE differentiateCenter #-}
differentiateCenter ::
(Field.C v, SigG.Transform sig v) =>
sig v -> sig v
differentiateCenter :: forall v (sig :: * -> *). (C v, Transform sig v) => sig v -> sig v
differentiateCenter =
Int -> sig v -> sig v
forall sig. Transform sig => Int -> sig -> sig
SigG.drop Int
2 (sig v -> sig v) -> (sig v -> sig v) -> sig v -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
(v -> (v, v) -> Maybe (v, (v, v))) -> (v, v) -> sig v -> sig v
forall y0 y1 s.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> s -> Maybe (y1, s)) -> s -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1 s.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> s -> Maybe (y1, s)) -> s -> sig y0 -> sig y1
SigG.crochetL
(\v
x0 (v
x1,v
x2) -> (v, (v, v)) -> Maybe (v, (v, v))
forall a. a -> Maybe a
Just ((v
x2v -> v -> v
forall a. C a => a -> a -> a
-v
x0)v -> v -> v
forall a. C a => a -> a -> a
/v
2, (v
x0,v
x1)))
(v
forall a. C a => a
zero,v
forall a. C a => a
zero)
{-# INLINE differentiate2 #-}
differentiate2 ::
(Additive.C v, SigG.Transform sig v) =>
sig v -> sig v
differentiate2 :: forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
differentiate2 = sig v -> sig v
forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
differentiate (sig v -> sig v) -> (sig v -> sig v) -> sig v -> sig v
forall b c a. (b -> c) -> (a -> b) -> a -> c
. sig v -> sig v
forall a (sig :: * -> *). (C a, Transform sig a) => sig a -> sig a
differentiate
{-# INLINE generic #-}
generic ::
(Module.C a v, SigG.Transform sig a, SigG.Write sig v) =>
sig a -> sig v -> sig v
generic :: forall a v (sig :: * -> *).
(C a v, Transform sig a, Write sig v) =>
sig a -> sig v -> sig v
generic sig a
m sig v
x =
if sig a -> Bool
forall sig. Read sig => sig -> Bool
SigG.null sig a
m Bool -> Bool -> Bool
|| sig v -> Bool
forall sig. Read sig => sig -> Bool
SigG.null sig v
x
then sig v
forall sig. Monoid sig => sig
CutG.empty
else
let mr :: sig a
mr = sig a -> sig a
forall sig. Transform sig => sig -> sig
SigG.reverse sig a
m
xp :: sig v
xp = Int -> sig v -> sig v
forall y (sig :: * -> *).
(C y, Write sig y) =>
Int -> sig y -> sig y
delayPos (Int -> Int
forall a. Enum a => a -> a
pred (sig a -> Int
forall sig. Read sig => sig -> Int
SigG.length sig a
m)) sig v
x
in (sig v -> v) -> sig v -> sig v
forall (sig :: * -> *) a.
Transform sig a =>
(sig a -> a) -> sig a -> sig a
SigG.mapTails (sig a -> sig v -> v
forall t y (sig :: * -> *).
(C t y, Read sig t, Read sig y) =>
sig t -> sig y -> y
SigG.linearComb sig a
mr) sig v
xp
karatsubaFinite ::
(Additive.C a, Additive.C b, Additive.C c,
SigG.Transform sig a, SigG.Transform sig b, SigG.Transform sig c) =>
(a -> b -> c) ->
sig a -> sig b -> sig c
karatsubaFinite :: forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
karatsubaFinite a -> b -> c
mul sig a
a sig b
b =
T (sig c) -> sig c
forall sig. T sig -> sig
SigL.toSignal (T (sig c) -> sig c) -> T (sig c) -> sig c
forall a b. (a -> b) -> a -> b
$
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
karatsubaBounded a -> b -> c
mul
(sig a -> T (sig a)
forall sig. Read sig => sig -> T sig
SigL.fromSignal sig a
a) (sig b -> T (sig b)
forall sig. Read sig => sig -> T sig
SigL.fromSignal sig b
b)
{-# INLINE karatsubaBounded #-}
karatsubaBounded ::
(Additive.C a, Additive.C b, Additive.C c,
SigG.Transform sig a, SigG.Transform sig b, SigG.Transform sig c) =>
(a -> b -> c) ->
SigL.T (sig a) -> SigL.T (sig b) -> SigL.T (sig c)
karatsubaBounded :: forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
karatsubaBounded a -> b -> c
mul T (sig a)
a T (sig b)
b =
case (T (sig a) -> Int
forall sig. T sig -> Int
SigL.length T (sig a)
a, T (sig b) -> Int
forall sig. T sig -> Int
SigL.length T (sig b)
b) of
(Int
0,Int
_) -> T (sig c)
forall sig. Monoid sig => sig
CutG.empty
(Int
_,Int
0) -> T (sig c)
forall sig. Monoid sig => sig
CutG.empty
(Int
1,Int
_) ->
T (sig c) -> (a -> sig a -> T (sig c)) -> sig a -> T (sig c)
forall (sig :: * -> *) y a.
Transform sig y =>
a -> (y -> sig y -> a) -> sig y -> a
SigG.switchL
([Char] -> T (sig c)
forall a. HasCallStack => [Char] -> a
error [Char]
"karatsubaBounded: empty signal")
(\a
y sig a
_ -> (sig b -> sig c) -> T (sig b) -> T (sig c)
forall a b. (a -> b) -> T a -> T b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((b -> c) -> sig b -> sig c
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map (a -> b -> c
mul a
y)) T (sig b)
b) (sig a -> T (sig c)) -> sig a -> T (sig c)
forall a b. (a -> b) -> a -> b
$
T (sig a) -> sig a
forall sig. T sig -> sig
SigL.body T (sig a)
a
(Int
_,Int
1) ->
T (sig c) -> (b -> sig b -> T (sig c)) -> sig b -> T (sig c)
forall (sig :: * -> *) y a.
Transform sig y =>
a -> (y -> sig y -> a) -> sig y -> a
SigG.switchL
([Char] -> T (sig c)
forall a. HasCallStack => [Char] -> a
error [Char]
"karatsubaBounded: empty signal")
(\b
y sig b
_ -> (sig a -> sig c) -> T (sig a) -> T (sig c)
forall a b. (a -> b) -> T a -> T b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> c) -> sig a -> sig c
forall y0 y1.
(Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
forall (sig :: * -> *) y0 y1.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> y1) -> sig y0 -> sig y1
SigG.map ((a -> b -> c) -> b -> a -> c
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> c
mul b
y)) T (sig a)
a) (sig b -> T (sig c)) -> sig b -> T (sig c)
forall a b. (a -> b) -> a -> b
$
T (sig b) -> sig b
forall sig. T sig -> sig
SigL.body T (sig b)
b
(Int
2,Int
2) ->
let [a
a0,a
a1] = sig a -> [a]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig a) -> sig a
forall sig. T sig -> sig
SigL.toSignal T (sig a)
a)
[b
b0,b
b1] = sig b -> [b]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig b) -> sig b
forall sig. T sig -> sig
SigL.toSignal T (sig b)
b)
(c
c0,c
c1,c
c2) = (a -> b -> c) -> Pair a -> Pair b -> (c, c, c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> Triple c
convolvePair a -> b -> c
mul (a
a0,a
a1) (b
b0,b
b1)
in Int -> sig c -> T (sig c)
forall sig. Int -> sig -> T sig
SigL.Cons Int
3 (sig c -> T (sig c)) -> sig c -> T (sig c)
forall a b. (a -> b) -> a -> b
$ T (sig a) -> T (sig b) -> [c] -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b ([c] -> sig c) -> [c] -> sig c
forall a b. (a -> b) -> a -> b
$
c
c0 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c1 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c2 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: []
(Int
2,Int
3) ->
let [a
a0,a
a1] = sig a -> [a]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig a) -> sig a
forall sig. T sig -> sig
SigL.toSignal T (sig a)
a)
[b
b0,b
b1,b
b2] = sig b -> [b]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig b) -> sig b
forall sig. T sig -> sig
SigL.toSignal T (sig b)
b)
(c
c0,c
c1,c
c2,c
c3) =
(a -> b -> c) -> Pair a -> Triple b -> (c, c, c, c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Triple b -> (c, c, c, c)
convolvePairTriple a -> b -> c
mul (a
a0,a
a1) (b
b0,b
b1,b
b2)
in Int -> sig c -> T (sig c)
forall sig. Int -> sig -> T sig
SigL.Cons Int
4 (sig c -> T (sig c)) -> sig c -> T (sig c)
forall a b. (a -> b) -> a -> b
$ T (sig a) -> T (sig b) -> [c] -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b ([c] -> sig c) -> [c] -> sig c
forall a b. (a -> b) -> a -> b
$
c
c0 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c1 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c2 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c3 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: []
(Int
3,Int
2) ->
let [a
a0,a
a1,a
a2] = sig a -> [a]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig a) -> sig a
forall sig. T sig -> sig
SigL.toSignal T (sig a)
a)
[b
b0,b
b1] = sig b -> [b]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig b) -> sig b
forall sig. T sig -> sig
SigL.toSignal T (sig b)
b)
(c
c0,c
c1,c
c2,c
c3) =
(b -> a -> c) -> Pair b -> Triple a -> (c, c, c, c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Triple b -> (c, c, c, c)
convolvePairTriple ((a -> b -> c) -> b -> a -> c
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> c
mul) (b
b0,b
b1) (a
a0,a
a1,a
a2)
in Int -> sig c -> T (sig c)
forall sig. Int -> sig -> T sig
SigL.Cons Int
4 (sig c -> T (sig c)) -> sig c -> T (sig c)
forall a b. (a -> b) -> a -> b
$ T (sig a) -> T (sig b) -> [c] -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b ([c] -> sig c) -> [c] -> sig c
forall a b. (a -> b) -> a -> b
$
c
c0 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c1 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c2 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c3 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: []
(Int
3,Int
3) ->
let [a
a0,a
a1,a
a2] = sig a -> [a]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig a) -> sig a
forall sig. T sig -> sig
SigL.toSignal T (sig a)
a)
[b
b0,b
b1,b
b2] = sig b -> [b]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig b) -> sig b
forall sig. T sig -> sig
SigL.toSignal T (sig b)
b)
(c
c0,c
c1,c
c2,c
c3,c
c4) =
(a -> b -> c) -> Triple a -> Triple b -> (c, c, c, c, c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Triple a -> Triple b -> (c, c, c, c, c)
convolveTriple a -> b -> c
mul (a
a0,a
a1,a
a2) (b
b0,b
b1,b
b2)
in Int -> sig c -> T (sig c)
forall sig. Int -> sig -> T sig
SigL.Cons Int
5 (sig c -> T (sig c)) -> sig c -> T (sig c)
forall a b. (a -> b) -> a -> b
$ T (sig a) -> T (sig b) -> [c] -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b ([c] -> sig c) -> [c] -> sig c
forall a b. (a -> b) -> a -> b
$
c
c0 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c1 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c2 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c3 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c4 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: []
(Int
4,Int
4) ->
let [a
a0,a
a1,a
a2,a
a3] = sig a -> [a]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig a) -> sig a
forall sig. T sig -> sig
SigL.toSignal T (sig a)
a)
[b
b0,b
b1,b
b2,b
b3] = sig b -> [b]
forall y. Storage (sig y) => sig y -> [y]
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> [y]
SigG.toList (T (sig b) -> sig b
forall sig. T sig -> sig
SigL.toSignal T (sig b)
b)
(c
c0,c
c1,c
c2,c
c3,c
c4,c
c5,c
c6) =
(a -> b -> c)
-> Quadruple a -> Quadruple b -> (c, c, c, c, c, c, c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c)
-> Quadruple a -> Quadruple b -> (c, c, c, c, c, c, c)
convolveQuadruple a -> b -> c
mul (a
a0,a
a1,a
a2,a
a3) (b
b0,b
b1,b
b2,b
b3)
in Int -> sig c -> T (sig c)
forall sig. Int -> sig -> T sig
SigL.Cons Int
7 (sig c -> T (sig c)) -> sig c -> T (sig c)
forall a b. (a -> b) -> a -> b
$ T (sig a) -> T (sig b) -> [c] -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b ([c] -> sig c) -> [c] -> sig c
forall a b. (a -> b) -> a -> b
$
c
c0 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c1 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c2 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c3 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c4 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c5 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: c
c6 c -> [c] -> [c]
forall a. a -> [a] -> [a]
: []
(Int
lenA,Int
lenB) ->
let n2 :: Int
n2 = Int -> Int -> Int
forall a. C a => a -> a -> a
div (Int -> Int -> Int
forall a. Ord a => a -> a -> a
max Int
lenA Int
lenB) Int
2
(T (sig a)
a0,T (sig a)
a1) = Int -> T (sig a) -> (T (sig a), T (sig a))
forall sig. Transform sig => Int -> T sig -> (T sig, T sig)
SigL.splitAt Int
n2 T (sig a)
a
(T (sig b)
b0,T (sig b)
b1) = Int -> T (sig b) -> (T (sig b), T (sig b))
forall sig. Transform sig => Int -> T sig -> (T sig, T sig)
SigL.splitAt Int
n2 T (sig b)
b
(T (sig c)
c0,T (sig c)
c1,T (sig c)
c2) =
(T (sig a) -> T (sig b) -> T (sig c))
-> (T (sig a), T (sig a))
-> (T (sig b), T (sig b))
-> (T (sig c), T (sig c), T (sig c))
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> Triple c
convolvePair
((a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
karatsubaBounded a -> b -> c
mul)
(T (sig a)
a0,T (sig a)
a1) (T (sig b)
b0,T (sig b)
b1)
in (sig c -> sig c) -> T (sig c) -> T (sig c)
forall a b. (a -> b) -> T a -> T b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (T (sig a) -> T (sig b) -> sig c -> sig c
forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig a)
a T (sig b)
b) (T (sig c) -> T (sig c)) -> T (sig c) -> T (sig c)
forall a b. (a -> b) -> a -> b
$
Int -> T (sig c) -> T (sig c) -> T (sig c)
forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> T (sig a) -> T (sig a) -> T (sig a)
SigL.addShiftedSimple Int
n2 T (sig c)
c0 (T (sig c) -> T (sig c)) -> T (sig c) -> T (sig c)
forall a b. (a -> b) -> a -> b
$
Int -> T (sig c) -> T (sig c) -> T (sig c)
forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> T (sig a) -> T (sig a) -> T (sig a)
SigL.addShiftedSimple Int
n2 T (sig c)
c1 T (sig c)
c2
{-# INLINE rechunk #-}
rechunk ::
(SigG.Transform sig1 a, SigG.Transform sig1 b, SigG.Transform sig1 c,
SigG.Transform sig0 c) =>
SigL.T (sig1 a) -> SigL.T (sig1 b) -> sig0 c -> sig1 c
rechunk :: forall (sig1 :: * -> *) a b c (sig0 :: * -> *).
(Transform sig1 a, Transform sig1 b, Transform sig1 c,
Transform sig0 c) =>
T (sig1 a) -> T (sig1 b) -> sig0 c -> sig1 c
rechunk T (sig1 a)
a T (sig1 b)
b sig0 c
c =
let (sig0 c
ac,sig0 c
bc) = Int -> sig0 c -> (sig0 c, sig0 c)
forall sig. Transform sig => Int -> sig -> (sig, sig)
CutG.splitAt (T (sig1 a) -> Int
forall sig. T sig -> Int
SigL.length T (sig1 a)
a) sig0 c
c
in sig1 a -> T c -> sig1 c
forall (sig :: * -> *) a b.
(Transform sig a, Transform sig b) =>
sig a -> T b -> sig b
SigG.takeStateMatch (T (sig1 a) -> sig1 a
forall sig. T sig -> sig
SigL.body T (sig1 a)
a) (sig0 c -> T c
forall y. Storage (sig0 y) => sig0 y -> T y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState sig0 c
ac)
sig1 c -> sig1 c -> sig1 c
forall sig. Monoid sig => sig -> sig -> sig
`SigG.append`
sig1 b -> T c -> sig1 c
forall (sig :: * -> *) a b.
(Transform sig a, Transform sig b) =>
sig a -> T b -> sig b
SigG.takeStateMatch (T (sig1 b) -> sig1 b
forall sig. T sig -> sig
SigL.body T (sig1 b)
b) (sig0 c -> T c
forall y. Storage (sig0 y) => sig0 y -> T y
forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState sig0 c
bc)
karatsubaFiniteInfinite ::
(Additive.C a, Additive.C b, Additive.C c,
SigG.Transform sig a, SigG.Transform sig b, SigG.Transform sig c) =>
(a -> b -> c) ->
sig a -> sig b -> sig c
karatsubaFiniteInfinite :: forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
karatsubaFiniteInfinite a -> b -> c
mul sig a
a sig b
b =
let al :: T (sig a)
al = sig a -> T (sig a)
forall sig. Read sig => sig -> T sig
SigL.fromSignal sig a
a
in case T (sig a) -> Int
forall sig. T sig -> Int
SigL.length T (sig a)
al of
Int
0 -> sig c
forall sig. Monoid sig => sig
CutG.empty
Int
alen ->
(sig c -> sig c -> sig c) -> sig c -> T (sig c) -> sig c
forall x acc. (x -> acc -> acc) -> acc -> T x -> acc
SigS.foldR (Int -> sig c -> sig c -> sig c
forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> sig a -> sig a -> sig a
addShiftedSimple Int
alen) sig c
forall sig. Monoid sig => sig
CutG.empty (T (sig c) -> sig c) -> T (sig c) -> sig c
forall a b. (a -> b) -> a -> b
$
(T (sig c) -> sig c) -> T (T (sig c)) -> T (sig c)
forall a b. (a -> b) -> T a -> T b
SigS.map T (sig c) -> sig c
forall sig. T sig -> sig
SigL.toSignal (T (T (sig c)) -> T (sig c)) -> T (T (sig c)) -> T (sig c)
forall a b. (a -> b) -> a -> b
$
(sig b -> T (sig c)) -> T (sig b) -> T (T (sig c))
forall a b. (a -> b) -> T a -> T b
SigS.map ((a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
karatsubaBounded a -> b -> c
mul T (sig a)
al (T (sig b) -> T (sig c))
-> (sig b -> T (sig b)) -> sig b -> T (sig c)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. sig b -> T (sig b)
forall sig. Read sig => sig -> T sig
SigL.fromSignal) (T (sig b) -> T (T (sig c))) -> T (sig b) -> T (T (sig c))
forall a b. (a -> b) -> a -> b
$
Int -> sig b -> T (sig b)
forall sig. Transform sig => Int -> sig -> T sig
SigG.sliceVertical Int
alen sig b
b
karatsubaInfinite ::
(Additive.C a, Additive.C b, Additive.C c,
SigG.Transform sig a, SigG.Transform sig c, SigG.Transform sig b) =>
(a -> b -> c) ->
sig a -> sig b -> sig c
karatsubaInfinite :: forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig c,
Transform sig b) =>
(a -> b -> c) -> sig a -> sig b -> sig c
karatsubaInfinite a -> b -> c
mul =
let recourse :: Int -> sig a -> sig b -> sig c
recourse Int
n sig a
a sig b
b =
let (sig a
a0,sig a
a1) = Int -> sig a -> (sig a, sig a)
forall sig. Transform sig => Int -> sig -> (sig, sig)
SigG.splitAt Int
n sig a
a
(sig b
b0,sig b
b1) = Int -> sig b -> (sig b, sig b)
forall sig. Transform sig => Int -> sig -> (sig, sig)
SigG.splitAt Int
n sig b
b
ab00 :: sig c
ab00 =
T (sig c) -> sig c
forall sig. T sig -> sig
SigL.toSignal (T (sig c) -> sig c) -> T (sig c) -> sig c
forall a b. (a -> b) -> a -> b
$
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> T (sig a) -> T (sig b) -> T (sig c)
karatsubaBounded a -> b -> c
mul
(sig a -> T (sig a)
forall sig. Read sig => sig -> T sig
SigL.fromSignal sig a
a0) (sig b -> T (sig b)
forall sig. Read sig => sig -> T sig
SigL.fromSignal sig b
b0)
ab01 :: sig c
ab01 = (a -> b -> c) -> sig a -> sig b -> sig c
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
karatsubaFiniteInfinite a -> b -> c
mul sig a
a0 sig b
b1
ab10 :: sig c
ab10 = (b -> a -> c) -> sig b -> sig a -> sig c
forall a b c (sig :: * -> *).
(C a, C b, C c, Transform sig a, Transform sig b,
Transform sig c) =>
(a -> b -> c) -> sig a -> sig b -> sig c
karatsubaFiniteInfinite ((a -> b -> c) -> b -> a -> c
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> c
mul) sig b
b0 sig a
a1
ab11 :: sig c
ab11 = Int -> sig a -> sig b -> sig c
recourse (Int
2Int -> Int -> Int
forall a. C a => a -> a -> a
*Int
n) sig a
a1 sig b
b1
in if sig a -> Bool
forall sig. Read sig => sig -> Bool
SigG.null sig a
a Bool -> Bool -> Bool
|| sig b -> Bool
forall sig. Read sig => sig -> Bool
SigG.null sig b
b
then sig c
forall sig. Monoid sig => sig
CutG.empty
else
Int -> sig c -> sig c -> sig c
forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> sig a -> sig a -> sig a
addShiftedSimple Int
n sig c
ab00 (sig c -> sig c) -> sig c -> sig c
forall a b. (a -> b) -> a -> b
$
Int -> sig c -> sig c -> sig c
forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> sig a -> sig a -> sig a
addShiftedSimple Int
n (sig c -> sig c -> sig c
forall y (sig :: * -> *).
(C y, Transform sig y) =>
sig y -> sig y -> sig y
SigG.mix sig c
ab01 sig c
ab10) sig c
ab11
in Int -> sig a -> sig b -> sig c
forall {sig :: * -> *}.
(Transform sig b, Transform sig a, Transform sig c) =>
Int -> sig a -> sig b -> sig c
recourse Int
1
{-# INLINE addShiftedSimple #-}
addShiftedSimple ::
(Additive.C a, SigG.Transform sig a) =>
Int -> sig a -> sig a -> sig a
addShiftedSimple :: forall a (sig :: * -> *).
(C a, Transform sig a) =>
Int -> sig a -> sig a -> sig a
addShiftedSimple Int
del sig a
a sig a
b =
(sig a -> sig a -> sig a) -> (sig a, sig a) -> sig a
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry sig a -> sig a -> sig a
forall sig. Monoid sig => sig -> sig -> sig
CutG.append ((sig a, sig a) -> sig a) -> (sig a, sig a) -> sig a
forall a b. (a -> b) -> a -> b
$
(sig a -> sig a) -> (sig a, sig a) -> (sig a, sig a)
forall b c a. (b -> c) -> (a, b) -> (a, c)
mapSnd ((sig a -> sig a -> sig a) -> sig a -> sig a -> sig a
forall a b c. (a -> b -> c) -> b -> a -> c
flip sig a -> sig a -> sig a
forall y (sig :: * -> *).
(C y, Transform sig y) =>
sig y -> sig y -> sig y
SigG.mix sig a
b) ((sig a, sig a) -> (sig a, sig a))
-> (sig a, sig a) -> (sig a, sig a)
forall a b. (a -> b) -> a -> b
$
Int -> sig a -> (sig a, sig a)
forall sig. Transform sig => Int -> sig -> (sig, sig)
CutG.splitAt Int
del sig a
a
type Pair a = (a,a)
{-# INLINE convolvePair #-}
convolvePair ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Pair a -> Pair b -> Triple c
convolvePair :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> Triple c
convolvePair a -> b -> c
mul Pair a
a Pair b
b =
((a, b), Triple c) -> Triple c
forall a b. (a, b) -> b
snd (((a, b), Triple c) -> Triple c) -> ((a, b), Triple c) -> Triple c
forall a b. (a -> b) -> a -> b
$ (a -> b -> c) -> Pair a -> Pair b -> ((a, b), Triple c)
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> ((a, b), Triple c)
sumAndConvolvePair a -> b -> c
mul Pair a
a Pair b
b
{-# INLINE sumAndConvolvePair #-}
sumAndConvolvePair ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Pair a -> Pair b -> ((a,b), Triple c)
sumAndConvolvePair :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> ((a, b), Triple c)
sumAndConvolvePair a -> b -> c
(!*!) (a
a0,a
a1) (b
b0,b
b1) =
let sa01 :: a
sa01 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a1
sb01 :: b
sb01 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b1
ab0 :: c
ab0 = a
a0a -> b -> c
!*!b
b0
ab1 :: c
ab1 = a
a1a -> b -> c
!*!b
b1
in ((a
sa01, b
sb01), (c
ab0, a
sa01a -> b -> c
!*!b
sb01c -> c -> c
forall a. C a => a -> a -> a
-(c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab1), c
ab1))
type Triple a = (a,a,a)
{-# INLINE convolvePairTriple #-}
convolvePairTriple ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Pair a -> Triple b -> (c,c,c,c)
convolvePairTriple :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Triple b -> (c, c, c, c)
convolvePairTriple a -> b -> c
(!*!) (a
a0,a
a1) (b
b0,b
b1,b
b2) =
let ab0 :: c
ab0 = a
a0a -> b -> c
!*!b
b0
ab1 :: c
ab1 = a
a1a -> b -> c
!*!b
b1
sa01 :: a
sa01 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a1; sb01 :: b
sb01 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b1; ab01 :: c
ab01 = a
sa01a -> b -> c
!*!b
sb01
in (c
ab0, c
ab01 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab1),
a
a0a -> b -> c
!*!b
b2 c -> c -> c
forall a. C a => a -> a -> a
+ c
ab1, a
a1a -> b -> c
!*!b
b2)
{-# INLINE convolveTriple #-}
convolveTriple ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Triple a -> Triple b -> (c,c,c,c,c)
convolveTriple :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Triple a -> Triple b -> (c, c, c, c, c)
convolveTriple a -> b -> c
mul Triple a
a Triple b
b =
((a, b), (c, c, c, c, c)) -> (c, c, c, c, c)
forall a b. (a, b) -> b
snd (((a, b), (c, c, c, c, c)) -> (c, c, c, c, c))
-> ((a, b), (c, c, c, c, c)) -> (c, c, c, c, c)
forall a b. (a -> b) -> a -> b
$ (a -> b -> c) -> Triple a -> Triple b -> ((a, b), (c, c, c, c, c))
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Triple a -> Triple b -> ((a, b), (c, c, c, c, c))
sumAndConvolveTriple a -> b -> c
mul Triple a
a Triple b
b
{-# INLINE sumAndConvolveTriple #-}
sumAndConvolveTriple ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Triple a -> Triple b -> ((a,b), (c,c,c,c,c))
sumAndConvolveTriple :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Triple a -> Triple b -> ((a, b), (c, c, c, c, c))
sumAndConvolveTriple a -> b -> c
(!*!) (a
a0,a
a1,a
a2) (b
b0,b
b1,b
b2) =
let ab0 :: c
ab0 = a
a0a -> b -> c
!*!b
b0
ab1 :: c
ab1 = a
a1a -> b -> c
!*!b
b1
ab2 :: c
ab2 = a
a2a -> b -> c
!*!b
b2
sa01 :: a
sa01 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a1; sb01 :: b
sb01 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b1; ab01 :: c
ab01 = a
sa01a -> b -> c
!*!b
sb01
sa02 :: a
sa02 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a2; sb02 :: b
sb02 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b2; ab02 :: c
ab02 = a
sa02a -> b -> c
!*!b
sb02
sa012 :: a
sa012 = a
sa01a -> a -> a
forall a. C a => a -> a -> a
+a
a2
sb012 :: b
sb012 = b
sb01b -> b -> b
forall a. C a => a -> a -> a
+b
b2
in ((a
sa012, b
sb012),
(c
ab0, c
ab01 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab1),
c
ab02 c -> c -> c
forall a. C a => a -> a -> a
+ c
ab1 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab2),
a
sa012a -> b -> c
!*!b
sb012 c -> c -> c
forall a. C a => a -> a -> a
- c
ab02 c -> c -> c
forall a. C a => a -> a -> a
- c
ab01 c -> c -> c
forall a. C a => a -> a -> a
+ c
ab0, c
ab2))
{-# INLINE sumAndConvolveTripleAlt #-}
sumAndConvolveTripleAlt ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Triple a -> Triple b -> ((a,b), (c,c,c,c,c))
sumAndConvolveTripleAlt :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Triple a -> Triple b -> ((a, b), (c, c, c, c, c))
sumAndConvolveTripleAlt a -> b -> c
(!*!) (a
a0,a
a1,a
a2) (b
b0,b
b1,b
b2) =
let ab0 :: c
ab0 = a
a0a -> b -> c
!*!b
b0
ab1 :: c
ab1 = a
a1a -> b -> c
!*!b
b1
ab2 :: c
ab2 = a
a2a -> b -> c
!*!b
b2
sa01 :: a
sa01 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a1; sb01 :: b
sb01 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b1
ab01 :: c
ab01 = a
sa01a -> b -> c
!*!b
sb01 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab1)
sa02 :: a
sa02 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a2; sb02 :: b
sb02 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b2
ab02 :: c
ab02 = a
sa02a -> b -> c
!*!b
sb02 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab2)
sa12 :: a
sa12 = a
a1a -> a -> a
forall a. C a => a -> a -> a
+a
a2; sb12 :: b
sb12 = b
b1b -> b -> b
forall a. C a => a -> a -> a
+b
b2
ab12 :: c
ab12 = a
sa12a -> b -> c
!*!b
sb12 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab1c -> c -> c
forall a. C a => a -> a -> a
+c
ab2)
in ((a
sa01a -> a -> a
forall a. C a => a -> a -> a
+a
a2, b
sb01b -> b -> b
forall a. C a => a -> a -> a
+b
b2),
(c
ab0, c
ab01, c
ab1c -> c -> c
forall a. C a => a -> a -> a
+c
ab02, c
ab12, c
ab2))
type Quadruple a = (a,a,a,a)
{-# INLINE convolveQuadruple #-}
convolveQuadruple ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Quadruple a -> Quadruple b -> (c,c,c,c,c,c,c)
convolveQuadruple :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c)
-> Quadruple a -> Quadruple b -> (c, c, c, c, c, c, c)
convolveQuadruple a -> b -> c
mul Quadruple a
a Quadruple b
b =
((a, b), (c, c, c, c, c, c, c)) -> (c, c, c, c, c, c, c)
forall a b. (a, b) -> b
snd (((a, b), (c, c, c, c, c, c, c)) -> (c, c, c, c, c, c, c))
-> ((a, b), (c, c, c, c, c, c, c)) -> (c, c, c, c, c, c, c)
forall a b. (a -> b) -> a -> b
$ (a -> b -> c)
-> Quadruple a -> Quadruple b -> ((a, b), (c, c, c, c, c, c, c))
forall a b c.
(C a, C b, C c) =>
(a -> b -> c)
-> Quadruple a -> Quadruple b -> ((a, b), (c, c, c, c, c, c, c))
sumAndConvolveQuadruple a -> b -> c
mul Quadruple a
a Quadruple b
b
{-# INLINE sumAndConvolveQuadruple #-}
sumAndConvolveQuadruple ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Quadruple a -> Quadruple b -> ((a,b), (c,c,c,c,c,c,c))
sumAndConvolveQuadruple :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c)
-> Quadruple a -> Quadruple b -> ((a, b), (c, c, c, c, c, c, c))
sumAndConvolveQuadruple a -> b -> c
(!*!) (a
a0,a
a1,a
a2,a
a3) (b
b0,b
b1,b
b2,b
b3) =
let ab0 :: c
ab0 = a
a0a -> b -> c
!*!b
b0
ab1 :: c
ab1 = a
a1a -> b -> c
!*!b
b1
sa01 :: a
sa01 = a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a1; sb01 :: b
sb01 = b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b1
ab01 :: c
ab01 = a
sa01a -> b -> c
!*!b
sb01 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab1)
ab2 :: c
ab2 = a
a2a -> b -> c
!*!b
b2
ab3 :: c
ab3 = a
a3a -> b -> c
!*!b
b3
sa23 :: a
sa23 = a
a2a -> a -> a
forall a. C a => a -> a -> a
+a
a3; sb23 :: b
sb23 = b
b2b -> b -> b
forall a. C a => a -> a -> a
+b
b3
ab23 :: c
ab23 = a
sa23a -> b -> c
!*!b
sb23 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab2c -> c -> c
forall a. C a => a -> a -> a
+c
ab3)
ab02 :: c
ab02 = (a
a0a -> a -> a
forall a. C a => a -> a -> a
+a
a2)a -> b -> c
!*!(b
b0b -> b -> b
forall a. C a => a -> a -> a
+b
b2)
ab13 :: c
ab13 = (a
a1a -> a -> a
forall a. C a => a -> a -> a
+a
a3)a -> b -> c
!*!(b
b1b -> b -> b
forall a. C a => a -> a -> a
+b
b3)
sa0123 :: a
sa0123 = a
sa01a -> a -> a
forall a. C a => a -> a -> a
+a
sa23
sb0123 :: b
sb0123 = b
sb01b -> b -> b
forall a. C a => a -> a -> a
+b
sb23
ab0123 :: c
ab0123 = a
sa0123a -> b -> c
!*!b
sb0123 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab02c -> c -> c
forall a. C a => a -> a -> a
+c
ab13)
in ((a
sa0123, b
sb0123),
(c
ab0, c
ab01, c
ab1c -> c -> c
forall a. C a => a -> a -> a
+c
ab02c -> c -> c
forall a. C a => a -> a -> a
-(c
ab0c -> c -> c
forall a. C a => a -> a -> a
+c
ab2),
c
ab0123 c -> c -> c
forall a. C a => a -> a -> a
- (c
ab01c -> c -> c
forall a. C a => a -> a -> a
+c
ab23),
c
ab2c -> c -> c
forall a. C a => a -> a -> a
+c
ab13c -> c -> c
forall a. C a => a -> a -> a
-(c
ab1c -> c -> c
forall a. C a => a -> a -> a
+c
ab3), c
ab23, c
ab3))
{-# INLINE sumAndConvolveQuadrupleAlt #-}
sumAndConvolveQuadrupleAlt ::
(Additive.C a, Additive.C b, Additive.C c) =>
(a -> b -> c) ->
Quadruple a -> Quadruple b -> ((a,b), (c,c,c,c,c,c,c))
sumAndConvolveQuadrupleAlt :: forall a b c.
(C a, C b, C c) =>
(a -> b -> c)
-> Quadruple a -> Quadruple b -> ((a, b), (c, c, c, c, c, c, c))
sumAndConvolveQuadrupleAlt a -> b -> c
mul (a
a0,a
a1,a
a2,a
a3) (b
b0,b
b1,b
b2,b
b3) =
let (((a
sa02,a
sa13), (b
sb02,b
sb13)),
((c
c00,c
c01,c
c02), (c
c10,c
c11,c
c12), (c
c20,c
c21,c
c22))) =
(Pair a -> Pair b -> Triple c)
-> Pair (Pair a)
-> Pair (Pair b)
-> ((Pair a, Pair b), Triple (Triple c))
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> ((a, b), Triple c)
sumAndConvolvePair ((a -> b -> c) -> Pair a -> Pair b -> Triple c
forall a b c.
(C a, C b, C c) =>
(a -> b -> c) -> Pair a -> Pair b -> Triple c
convolvePair a -> b -> c
mul)
((a
a0,a
a1),(a
a2,a
a3)) ((b
b0,b
b1),(b
b2,b
b3))
in ((a
sa02a -> a -> a
forall a. C a => a -> a -> a
+a
sa13, b
sb02b -> b -> b
forall a. C a => a -> a -> a
+b
sb13),
(c
c00,c
c01,c
c02c -> c -> c
forall a. C a => a -> a -> a
+c
c10,c
c11,c
c12c -> c -> c
forall a. C a => a -> a -> a
+c
c20,c
c21,c
c22))