-- | In cases where a method takes arguments, these precede the -- collection argument in the haskell variant, so that @c.m(i,j)@ -- becomes @m i j c@. module Sound.SC3.Lang.Collection where import qualified Data.List.Split as S {- split -} import Data.List as L {- base -} import Data.Maybe {- base -} -- * Collection -- | @Collection.*fill@ is 'map' over indices to /n/. -- -- > fill 4 (* 2) == [0,2,4,6] fill :: (Enum n,Num n) => n -> (n -> a) -> [a] fill n f = map f [0 .. n - 1] -- | @Collection.size@ is 'length'. -- -- > size [1,2,3,4] == 4 size :: Integral n => [a] -> n size = genericLength -- | @Collection.isEmpty@ is 'null'. -- -- > isEmpty [] == True isEmpty :: [a] -> Bool isEmpty = null -- | Function equal to 'const' of /f/ of /e/. -- -- > select (ignoringIndex even) [1,2,3,4] == [2,4] ignoringIndex :: (a -> b) -> a -> z -> b ignoringIndex f e = const (f e) -- | @Collection.collect@ is 'map' with element indices. -- -- > collect (\i _ -> i + 10) [1,2,3,4] == [11,12,13,14] -- > collect (\_ j -> j + 11) [1,2,3,4] == [11,12,13,14] collect :: Integral i => (a -> i -> b) -> [a] -> [b] collect f l = zipWith f l [0..] -- | @Collection.select@ is 'filter' with element indices. -- -- > select (\i _ -> even i) [1,2,3,4] == [2,4] -- > select (\_ j -> even j) [1,2,3,4] == [1,3] select :: Integral i => (a -> i -> Bool) -> [a] -> [a] select f l = map fst (filter (uncurry f) (zip l [0..])) -- | @Collection.reject@ is negated 'filter' with element indices. -- -- > reject (\i _ -> even i) [1,2,3,4] == [1,3] -- > reject (\_ j -> even j) [1,2,3,4] == [2,4] reject :: Integral i => (a -> i -> Bool) -> [a] -> [a] reject f l = map fst (filter (not . uncurry f) (zip l [0..])) -- | @Collection.detect@ is 'first' '.' 'select'. -- -- > detect (\i _ -> even i) [1,2,3,4] == Just 2 detect :: Integral i => (a -> i -> Bool) -> [a] -> Maybe a detect f l = fmap fst (find (uncurry f) (zip l [0..])) -- | @Collection.detectIndex@ is the index locating variant of 'detect'. -- -- > detectIndex (\i _ -> even i) [1,2,3,4] == Just 1 detectIndex :: Integral i => (a -> i -> Bool) -> [a] -> Maybe i detectIndex f l = fmap snd (find (uncurry f) (zip l [0..])) -- | @Collection.inject@ is a variant on 'foldl'. -- -- > inject 0 (+) [1..5] == 15 -- > inject 1 (*) [1..5] == 120 inject :: a -> (a -> b -> a) -> [b] -> a inject i f = foldl f i -- | @Collection.any@ is 'True' if 'detect' is not 'Nothing'. -- -- > any' (\i _ -> even i) [1,2,3,4] == True any' :: Integral i => (a -> i -> Bool) -> [a] -> Bool any' f = isJust . detect f -- | @Collection.every@ is 'True' if /f/ applies at all elements. -- -- > every (\i _ -> even i) [1,2,3,4] == False every :: Integral i => (a -> i -> Bool) -> [a] -> Bool every f = let g e = not . f e in not . any' g -- | @Collection.count@ is 'length' '.' 'select'. -- -- > count (\i _ -> even i) [1,2,3,4] == 2 count :: Integral i => (a -> i -> Bool) -> [a] -> i count f = genericLength . select f -- | @Collection.occurencesOf@ is an '==' variant of 'count'. -- -- > occurencesOf 2 [1,2,3,4] == 1 -- > occurencesOf 't' "test" == 2 occurencesOf :: (Integral i,Eq a) => a -> [a] -> i occurencesOf k = count (\e _ -> e == k) -- | @Collection.sum@ is 'sum' '.' 'collect'. -- -- > sum' (ignoringIndex (* 2)) [1,2,3,4] == 20 sum' :: (Num a,Integral i) => (b -> i -> a) -> [b] -> a sum' f = sum . collect f -- | @Collection.maxItem@ is 'maximum' '.' 'collect'. -- -- > maxItem (ignoringIndex (* 2)) [1,2,3,4] == 8 maxItem :: (Ord b,Integral i) => (a -> i -> b) -> [a] -> b maxItem f = maximum . collect f -- | @Collection.minItem@ is 'maximum' '.' 'collect'. -- -- > minItem (ignoringIndex (* 2)) [1,2,3,4] == 2 minItem :: (Integral i,Ord b) => (a -> i -> b) -> [a] -> b minItem f = minimum . collect f -- | Variant of 'zipWith' that cycles the shorter input. -- -- > zipWith_c (+) [1,2] [3,4,5] == [4,6,6] zipWith_c :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith_c f a b = let g [] [] _ = [] g [] b' (_,e) = if e then [] else g a b' (True,e) g a' [] (e,_) = if e then [] else g a' b (e,True) g (a0 : aN) (b0 : bN) e = f a0 b0 : g aN bN e in g a b (False,False) -- | 'zipWith_c' variant of 'zip'. -- -- > zip_c [1,2] [3,4,5] == [(1,3),(2,4),(1,5)] zip_c :: [a] -> [b] -> [(a,b)] zip_c = zipWith_c (,) -- | Variant of 'zipWith3' that cycles the shorter inputs. -- -- > zipWith3_c (,,) [1] [2,3] [4,5,6] == [(1,2,4),(1,3,5),(1,2,6)] zipWith3_c :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] zipWith3_c f p q r = let g = map (const ()) l = [g p,g q,g r] f' _ = f in zipWith4 f' (extension l) (cycle p) (cycle q) (cycle r) -- | 'zipWith3_c' based variant of 'zip3'. -- -- > zip3_c [1] [2,3] [4,5,6] == [(1,2,4),(1,3,5),(1,2,6)] zip3_c :: [a] -> [b] -> [c] -> [(a,b,c)] zip3_c = zipWith3_c (\a b c -> (a,b,c)) -- | 'zipWith_c' based variant of applicative '<*>'. -- -- > zap_c [(+1),negate] [1..6] == [2,-2,4,-4,6,-6] zap_c :: [a -> b] -> [a] -> [b] zap_c = zipWith_c (\f e -> f e) -- * Sequenceable Collection -- | @SequenceableCollection.*series@ is an arithmetic series with -- arguments /size/, /start/ and /step/. -- -- > > Array.series(5,10,2) == [10,12,14,16,18] -- > series 5 10 2 == [10,12 .. 18] -- -- Note that this is quite different from the SimpleNumber.series -- method, which is equal to 'enumFromThenTo'. -- -- > > 5.series(7,10) == [5,7,9] -- > enumFromThenTo 5 7 10 == [5,7,9] series :: (Num a,Integral i) => i -> a -> a -> [a] series n i j = case n of 0 -> [] _ -> i : series (n - 1) (i + j) j -- | @SequenceableCollection.*geom@ is a geometric series with arguments -- /size/, /start/ and /grow/. -- -- > > Array.geom(5,3,6) == [3,18,108,648,3888] -- > geom 5 3 6 == [3,18,108,648,3888] geom :: (Integral i,Num a) => i -> a -> a -> [a] geom n i j = case n of 0 -> [] _ -> i : geom (n - 1) (i * j) j -- | @SequenceableCollection.*fib@ is the Fibonacci series where /n/ -- is number of elements, /i/ is the initial step and /j/ the initial -- value. -- -- > > Array.fib(5,2,32) == [32,34,66,100,166] -- > fib 5 2 32 == [32,34,66,100,166] fib :: (Integral i,Num a) => i -> a -> a -> [a] fib n i j = case n of 0 -> [] _ -> j : fib (n - 1) j (i + j) -- | @SequenceableCollection.first@ is a total variant of 'L.head'. -- -- > > [3,4,5].first == 3 -- > first [3,4,5] == Just 3 -- > first' [3,4,5] == 3 -- -- > > [].first == nil -- > first [] == Nothing first :: [t] -> Maybe t first xs = case xs of [] -> Nothing x:_ -> Just x -- | Synonym for 'L.head'. first' :: [t] -> t first' = head -- | Total variant of 'L.last'. -- -- > > (1..5).last == 5 -- > lastM [1..5] == Just 5 -- > L.last [1..5] == 5 -- -- > > [].last == nil -- > lastM [] == Nothing lastM :: [t] -> Maybe t lastM xs = case xs of [] -> Nothing [x] -> Just x _:xs' -> lastM xs' -- | @SequenceableCollection.last@ is a synonym for 'lastM'. last :: [t] -> Maybe t last = lastM -- | Synonym for 'L.last'. last' :: [t] -> t last' = L.last -- | @SequenceableCollection.indexOf@ is a variant of 'elemIndex' with -- reversed arguments. -- -- > > [3,4,100,5].indexOf(100) == 2 -- > indexOf [3,4,100,5] 100 == Just 2 indexOf :: Eq a => [a] -> a -> Maybe Int indexOf = flip elemIndex -- | 'fromJust' variant of 'indexOf'. indexOf' :: Eq a => [a] -> a -> Int indexOf' l = fromJust . indexOf l -- | @SequenceableCollection.indexOfEqual@ is just 'indexOf'. indexOfEqual :: Eq a => [a] -> a -> Maybe Int indexOfEqual = indexOf -- | @SequenceableCollection.indexOfGreaterThan@ is the index of the -- first greater element. -- -- > indexOfGreaterThan 70 [10,5,77,55,12,123] == Just 2 indexOfGreaterThan :: (Ord a) => a -> [a] -> Maybe Int indexOfGreaterThan e = detectIndex (ignoringIndex (> e)) -- | @SequenceableCollection.indexIn@ is the index of nearest element. -- -- > indexIn 5.2 [2,3,5,6] == 2 indexIn :: (Ord a,Num a) => a -> [a] -> Int indexIn e l = let f 0 = 0 f j = let i = j - 1 right = l !! j left = l !! i in if (e - left) < (right - e) then i else j in maybe (size l - 1) f (indexOfGreaterThan e l) -- | @SequenceableCollection.indexInBetween@ is the linearly -- interpolated fractional index. -- -- > indexInBetween 5.2 [2,3,5,6] == 2.2 indexInBetween :: (Ord a,Fractional a) => a -> [a] -> a indexInBetween e l = let f 0 = 0 f j = let i = fromIntegral j a = l !! (j - 1) b = l !! j d = b - a in if d == 0 then i else ((e - a) / d) + i - 1 in maybe (fromInteger (size l) - 1) f (indexOfGreaterThan e l) -- | @SequenceableCollection.keep@ is, for positive /n/ a synonym for -- 'L.take', and for negative /n/ a variant on 'L.drop' based on the -- 'length' of /l/. -- -- > > [1,2,3,4,5].keep(3) == [1,2,3] -- > keep 3 [1,2,3,4,5] == [1,2,3] -- -- > > [1,2,3,4,5].keep(-3) == [3,4,5] -- > keep (-3) [1,2,3,4,5] == [3,4,5] -- -- > > [1,2].keep(-4) == [1,2] -- > keep (-4) [1,2] == [1,2] keep :: Integral i => i -> [a] -> [a] keep n l = if n < 0 then L.genericDrop (genericLength l + n) l else genericTake n l -- | @SequenceableCollection.drop@ is, for positive /n/ a synonym for -- 'L.drop', for negative /n/ a variant on 'L.take' based on the -- 'L.length' of /l/. -- -- > > [1,2,3,4,5].drop(3) == [4,5] -- > L.drop 3 [1,2,3,4,5] == [4,5] -- -- > > [1,2,3,4,5].drop(-3) == [1,2] -- > Sound.SC3.Lang.Collection.drop (-3) [1,2,3,4,5] == [1,2] -- -- > > [1,2].drop(-4) == [] -- > Sound.SC3.Lang.Collection.drop (-4) [1,2] == [] drop :: Integral i => i -> [a] -> [a] drop n l = if n < 0 then L.genericTake (L.genericLength l + n) l else L.genericDrop n l -- | Function to calculate a list equal in length to the longest input -- list, therefore being productive over infinite lists. -- -- > extension [[1],[2,3],[4,5,6]] == [(),(),()] -- > take 3 (extension [[1],[2..]]) == [(),(),()] extension :: [[a]] -> [()] extension x = if null x then [] else let x' = filter (not . null) (map tail x) in () : extension x' -- | @SequenceableCollection.flop@ is a variant of 'transpose' that -- cycles input sequences and extends rather than truncates. -- -- > > [(1..3),(4..5),(6..9)].flop == [[1,4,6],[2,5,7],[3,4,8],[1,5,9]] -- > flop [[1..3],[4..5],[6..9]] == [[1,4,6],[2,5,7],[3,4,8],[1,5,9]] -- -- > > [[1,2,3],[4,5,6],[7,8]].flop == [[1,4,7],[2,5,8],[3,6,7]] -- > flop [[1,2,3],[4,5,6],[7,8]] == [[1,4,7],[2,5,8],[3,6,7]] -- -- The null case at 'flop' is not handled equivalently to SC3 -- -- > > [].flop == [[]] -- > flop [] /= [[]] -- > flop [] == [] -- -- The 'flop' and 'extendSequences' functions are non-strict and -- productive. -- -- > take 4 (flop [[1..3],[4..]]) == [[1,4],[2,5],[3,6],[1,7]] -- > map (take 4) (extendSequences [[1..3],[4..]]) == [[1,2,3,1],[4,5,6,7]] flop :: [[a]] -> [[a]] flop l = let l' = map cycle l in zipWith (\_ x -> x) (extension l) (transpose l') -- | @SequenceableCollection.integrate@ is the incremental sum of -- elements. -- -- > > [3,4,1,1].integrate == [3,7,8,9] -- > integrate [3,4,1,1] == [3,7,8,9] integrate :: (Num a) => [a] -> [a] integrate = scanl1 (+) -- | @SequenceableCollection.differentiate@ is the pairwise difference -- between elements, with an implicit @0@ at the start. -- -- > > [3,4,1,1].differentiate == [3,1,-3,0] -- > differentiate [3,4,1,1] == [3,1,-3,0] -- -- > > [0,3,1].differentiate == [0,3,-2] -- > differentiate [0,3,1] == [0,3,-2] differentiate :: (Num a) => [a] -> [a] differentiate l = zipWith (-) l (0:l) -- | Variant of 'separate' that performs initial separation. separateAt :: (a -> a -> Bool) -> [a] -> ([a],[a]) separateAt f xs = case xs of (x1:x2:xs') -> if f x1 x2 then ([x1],x2:xs') else let g e (l,r) = (e:l,r) in x1 `g` separateAt f (x2:xs') _ -> (xs,[]) -- | @SequenceableCollection.separate@ applies the predicate 'f' to -- each adjacent pair of elements at /l/. If the predicate is 'True', -- then a separation is made between the elements. -- -- > > [3,2,1,2,3,2].separate({|a,b| a<b}) == [[3,2,1],[2],[3,2]] -- > separate (<) [3,2,1,2,3,2] == [[3,2,1],[2],[3,2]] -- -- > > [1,2,3,5,6,8].separate({|a,b| (b - a) > 1}) == [[1,2,3],[5,6],[8]] -- > separate (\a b -> (b - a) > 1) [1,2,3,5,6,8] == [[1,2,3],[5,6],[8]] separate :: (a -> a -> Bool) -> [a] -> [[a]] separate f l = let (e,r) = separateAt f l in if null r then [e] else e : separate f r -- | @SequenceableCollection.clump@ is a synonym for -- 'Data.List.Split.chunksOf'. -- -- > > [1,2,3,4,5,6,7,8].clump(3) == [[1,2,3],[4,5,6],[7,8]] -- > clump 3 [1,2,3,4,5,6,7,8] == [[1,2,3],[4,5,6],[7,8]] clump :: Int -> [a] -> [[a]] clump = S.chunksOf -- | @SequenceableCollection.clumps@ is a synonym for -- 'Data.List.Split.splitPlaces'. -- -- > > [1,2,3,4,5,6,7,8].clumps([1,2]) == [[1],[2,3],[4],[5,6],[7],[8]] -- > clumps [1,2] [1,2,3,4,5,6,7,8] == [[1],[2,3],[4],[5,6],[7],[8]] clumps :: [Int] -> [a] -> [[a]] clumps m s = let f [] _ = undefined f (n:ns) l = let (e,r) = splitAt n l in if null r then [e] else e : clumps ns r in case m of [] -> [] _ -> f (cycle m) s -- * List and Array -- | @List.lace@ is a concatenated transposition of cycled -- subsequences. -- -- > > [[1,2,3],[6],[8,9]].lace(12) == [1,6,8,2,6,9,3,6,8,1,6,9] -- > lace 12 [[1,2,3],[6],[8,9]] == [1,6,8,2,6,9,3,6,8,1,6,9] lace :: Integral i => i -> [[a]] -> [a] lace n = genericTake n . concat . transpose . map cycle -- | @List.wrapExtend@ extends a sequence by -- /cycling/. 'wrapExtend' is in terms of 'take' and 'cycle'. -- -- > > [1,2,3,4,5].wrapExtend(9) == [1,2,3,4,5,1,2,3,4] -- > wrapExtend 9 [1,2,3,4,5] == [1,2,3,4,5,1,2,3,4] wrapExtend :: Integral i => i -> [a] -> [a] wrapExtend n = genericTake n . cycle -- | Infinite variant of 'foldExtend'. cycleFold :: [a] -> [a] cycleFold = cycle . mirror1 -- | @List.foldExtend@ extends sequence by /folding/ backwards at end. -- 'foldExtend' is in terms of 'cycleFold', which is in terms of -- 'mirror1'. -- -- > > [1,2,3,4,5].foldExtend(10) -- > foldExtend 10 [1,2,3,4,5] == [1,2,3,4,5,4,3,2,1,2] foldExtend :: Integral i => i -> [a] -> [a] foldExtend n = genericTake n . cycleFold -- | @Array.clipExtend@ extends sequence by repeating last element. -- -- > > [1,2,3,4,5].clipExtend(9) == [1,2,3,4,5,5,5,5,5] -- > clipExtend 9 [1,2,3,4,5] == [1,2,3,4,5,5,5,5,5] clipExtend :: Integral i => i -> [a] -> [a] clipExtend n = genericTake n . cycleClip -- | Infinite variant of 'clipExtend'. cycleClip :: [a] -> [a] cycleClip l = case lastM l of Nothing -> [] Just e -> l ++ repeat e -- | Cycle input sequences to 'extension' of input. -- -- > extendSequences [[1],[2,3],[4,5,6]] == [[1,1,1],[2,3,2],[4,5,6]] extendSequences :: [[a]] -> [[a]] extendSequences l = let f = zipWith (\_ x -> x) (extension l) . cycle in map f l -- | @ArrayedCollection.normalizeSum@ ensures sum of elements is one. -- -- > > [1,2,3].normalizeSum == [1/6,1/3,0.5] -- > normalizeSum [1,2,3] == [1/6,2/6,3/6] normalizeSum :: (Fractional a) => [a] -> [a] normalizeSum l = let n = sum l in map (/ n) l -- | @List.slide@ is an identity window function with subsequences of -- length /w/ and stride of /n/. -- -- > > [1,2,3,4,5,6].slide(3,1) -- > slide 3 1 [1,2,3,4,5,6] == [1,2,3,2,3,4,3,4,5,4,5,6] -- -- > > [1,2,3,4,5,6].slide(3,2) -- > slide 3 2 [1,2,3,4,5,6] == [1,2,3,3,4,5] -- -- > > [1,2,3,4,5,6].slide(4,2) -- > slide 4 2 [1,2,3,4,5,6] == [1,2,3,4,3,4,5,6] slide :: Integral i => i -> i -> [a] -> [a] slide w n l = let k = genericLength l in concatMap (\i -> genericTake w (L.genericDrop i l)) [0,n .. k-w] -- | @List.mirror@ concatentates with 'tail' of 'reverse' to make a -- palindrome. -- -- > > [1,2,3,4].mirror == [1,2,3,4,3,2,1] -- > mirror [1,2,3,4] == [1,2,3,4,3,2,1] mirror :: [a] -> [a] mirror l = l ++ tail (reverse l) -- | @List.mirror1@ is as 'mirror' but with last element removed. -- -- > > [1,2,3,4].mirror1 == [1,2,3,4,3,2] -- > mirror1 [1,2,3,4] == [1,2,3,4,3,2] mirror1 :: [a] -> [a] mirror1 l = case l of [] -> [] [e] -> [e] _ -> l ++ tail (reverse (tail l)) -- | @List.mirror2@ concatenate with 'reverse' to make a palindrome, -- as 'mirror' does, but with the center element duplicated. -- -- > > [1,2,3,4].mirror2 == [1,2,3,4,4,3,2,1] -- > mirror2 [1,2,3,4] == [1,2,3,4,4,3,2,1] mirror2 :: [a] -> [a] mirror2 l = l ++ reverse l -- | @List.stutter@ repeats each element /n/ times. -- -- > > [1,2,3].stutter(2) == [1,1,2,2,3,3] -- > stutter 2 [1,2,3] == [1,1,2,2,3,3] stutter :: Integral i => i -> [a] -> [a] stutter n = concatMap (genericReplicate n) -- | Rotate /n/ places to the left. -- -- > rotateLeft 1 [1..5] == [2,3,4,5,1] -- > rotateLeft 3 [1..7] == [4,5,6,7,1,2,3] rotateLeft :: Integral i => i -> [a] -> [a] rotateLeft n p = let (b,a) = genericSplitAt n p in a ++ b -- | Rotate /n/ places to the right. -- -- > rotateRight 1 [1..5] == [5,1,2,3,4] -- > rotateRight 3 [1..7] == [5,6,7,1,2,3,4] rotateRight :: Integral i => i -> [a] -> [a] rotateRight n p = let k = genericLength p (b,a) = genericSplitAt (k - n) p in a ++ b -- | @Array.rotate@ is in terms of 'rotateLeft' and 'rotateRight', -- where negative /n/ rotates left and positive /n/ rotates right. -- -- > > (1..5).rotate(1) == [5,1,2,3,4] -- > rotate 1 [1..5] == [5,1,2,3,4] -- -- > > (1..5).rotate(-1) == [2,3,4,5,1] -- > rotate (-1) [1..5] == [2,3,4,5,1] -- -- > > (1..5).rotate(3) == [3,4,5,1,2] -- > rotate 3 [1..5] == [3,4,5,1,2] rotate :: Integral i => i -> [a] -> [a] rotate n = if n < 0 then rotateLeft (- n) else rotateRight n -- | @ArrayedCollection.windex@ takes a list of probabilities, which -- should sum to /n/, and returns the an index value given a (0,/n/) -- input. -- -- > mapMaybe (windex [0.1,0.3,0.6]) [0,0.1 .. 0.4] == [0,1,1,1,2] windex :: (Ord a,Num a) => [a] -> a -> Maybe Int windex w n = findIndex (n <) (integrate w) -- * Signals & wavetables -- | List of 2-tuples of elements at distance (stride) /n/. -- -- > t2_window 3 [1..9] == [(1,2),(4,5),(7,8)] t2_window :: Integral i => i -> [t] -> [(t,t)] t2_window n x = case x of i:j:_ -> (i,j) : t2_window n (L.genericDrop n x) _ -> [] -- | List of 2-tuples of adjacent elements. -- -- > t2_adjacent [1..6] == [(1,2),(3,4),(5,6)] -- > t2_adjacent [1..5] == [(1,2),(3,4)] t2_adjacent :: [t] -> [(t,t)] t2_adjacent = t2_window (2::Int) -- | List of 2-tuples of overlapping elements. -- -- > t2_overlap [1..4] == [(1,2),(2,3),(3,4)] t2_overlap :: [b] -> [(b,b)] t2_overlap x = zip x (tail x) -- | Concat of 2-tuples. -- -- > t2_concat (t2_adjacent [1..6]) == [1..6] -- > t2_concat (t2_overlap [1..4]) == [1,2,2,3,3,4] t2_concat :: [(a,a)] -> [a] t2_concat x = case x of [] -> [] (i,j):x' -> i : j : t2_concat x' -- | A Signal is half the size of a Wavetable, each element is the sum -- of two adjacent elements of the Wavetable. -- -- > from_wavetable [-0.5,0.5,0,0.5,1.5,-0.5,1,-0.5] == [0.0,0.5,1.0,0.5] -- > let s = [0,0.5,1,0.5] in from_wavetable (to_wavetable s) == s from_wavetable :: Num n => [n] -> [n] from_wavetable = map (uncurry (+)) . t2_adjacent -- | A Wavetable is has /n * 2 + 2/ elements, where /n/ is the number -- of elements of the Signal. Each signal element /e0/ expands to the -- two elements /(2 * e0 - e1, e1 - e0)/ where /e1/ is the next -- element, or zero at the final element. Properly wavetables are -- only of power of two element signals. -- -- > > Signal[0,0.5,1,0.5].asWavetable == Wavetable[-0.5,0.5,0,0.5,1.5,-0.5,1,-0.5] -- -- > to_wavetable [0,0.5,1,0.5] == [-0.5,0.5,0,0.5,1.5,-0.5,1,-0.5] to_wavetable :: Num a => [a] -> [a] to_wavetable = let f (e0,e1) = (2 * e0 - e1,e1 - e0) in t2_concat . map f . t2_overlap . (++ [0])