{-# LANGUAGE Rank2Types, MultiParamTypeClasses, FlexibleContexts, TypeFamilies, ScopedTypeVariables, BangPatterns #-} -- | -- Module : Data.Vector.Generic -- Copyright : (c) Roman Leshchinskiy 2008-2010 -- License : BSD-style -- -- Maintainer : Roman Leshchinskiy <rl@cse.unsw.edu.au> -- Stability : experimental -- Portability : non-portable -- -- Generic interface to pure vectors. -- module Data.Vector.Generic ( -- * Immutable vectors Vector(..), Mutable, -- * Accessors -- ** Length information length, null, -- ** Indexing (!), (!?), head, last, unsafeIndex, unsafeHead, unsafeLast, -- ** Monadic indexing indexM, headM, lastM, unsafeIndexM, unsafeHeadM, unsafeLastM, -- ** Extracting subvectors (slicing) slice, init, tail, take, drop, splitAt, unsafeSlice, unsafeInit, unsafeTail, unsafeTake, unsafeDrop, -- * Construction -- ** Initialisation empty, singleton, replicate, generate, iterateN, -- ** Monadic initialisation replicateM, generateM, create, -- ** Unfolding unfoldr, unfoldrN, constructN, constructrN, -- ** Enumeration enumFromN, enumFromStepN, enumFromTo, enumFromThenTo, -- ** Concatenation cons, snoc, (++), concat, -- ** Restricting memory usage force, -- * Modifying vectors -- ** Bulk updates (//), update, update_, unsafeUpd, unsafeUpdate, unsafeUpdate_, -- ** Accumulations accum, accumulate, accumulate_, unsafeAccum, unsafeAccumulate, unsafeAccumulate_, -- ** Permutations reverse, backpermute, unsafeBackpermute, -- ** Safe destructive updates modify, -- * Elementwise operations -- ** Indexing indexed, -- ** Mapping map, imap, concatMap, -- ** Monadic mapping mapM, mapM_, forM, forM_, -- ** Zipping zipWith, zipWith3, zipWith4, zipWith5, zipWith6, izipWith, izipWith3, izipWith4, izipWith5, izipWith6, zip, zip3, zip4, zip5, zip6, -- ** Monadic zipping zipWithM, zipWithM_, -- ** Unzipping unzip, unzip3, unzip4, unzip5, unzip6, -- * Working with predicates -- ** Filtering filter, ifilter, filterM, takeWhile, dropWhile, -- ** Partitioning partition, unstablePartition, span, break, -- ** Searching elem, notElem, find, findIndex, findIndices, elemIndex, elemIndices, -- * Folding foldl, foldl1, foldl', foldl1', foldr, foldr1, foldr', foldr1', ifoldl, ifoldl', ifoldr, ifoldr', -- ** Specialised folds all, any, and, or, sum, product, maximum, maximumBy, minimum, minimumBy, minIndex, minIndexBy, maxIndex, maxIndexBy, -- ** Monadic folds foldM, foldM', fold1M, fold1M', foldM_, foldM'_, fold1M_, fold1M'_, -- ** Monadic sequencing sequence, sequence_, -- * Prefix sums (scans) prescanl, prescanl', postscanl, postscanl', scanl, scanl', scanl1, scanl1', prescanr, prescanr', postscanr, postscanr', scanr, scanr', scanr1, scanr1', -- * Conversions -- ** Lists toList, fromList, fromListN, -- ** Different vector types convert, -- ** Mutable vectors freeze, thaw, copy, unsafeFreeze, unsafeThaw, unsafeCopy, -- * Fusion support -- ** Conversion to/from Streams stream, unstream, streamR, unstreamR, -- ** Recycling support new, clone, -- * Utilities -- ** Comparisons eq, cmp, -- ** Show and Read showsPrec, readPrec, -- ** @Data@ and @Typeable@ gfoldl, dataCast, mkType ) where import Data.Vector.Generic.Base import Data.Vector.Generic.Mutable ( MVector ) import qualified Data.Vector.Generic.Mutable as M import qualified Data.Vector.Generic.New as New import Data.Vector.Generic.New ( New ) import qualified Data.Vector.Fusion.Stream as Stream import Data.Vector.Fusion.Stream ( Stream, MStream, Step(..), inplace, liftStream ) import qualified Data.Vector.Fusion.Stream.Monadic as MStream import Data.Vector.Fusion.Stream.Size import Data.Vector.Fusion.Util import Control.Monad.ST ( ST, runST ) import Control.Monad.Primitive import qualified Control.Monad as Monad import qualified Data.List as List import Prelude hiding ( length, null, replicate, (++), concat, head, last, init, tail, take, drop, splitAt, reverse, map, concat, concatMap, zipWith, zipWith3, zip, zip3, unzip, unzip3, filter, takeWhile, dropWhile, span, break, elem, notElem, foldl, foldl1, foldr, foldr1, all, any, and, or, sum, product, maximum, minimum, scanl, scanl1, scanr, scanr1, enumFromTo, enumFromThenTo, mapM, mapM_, sequence, sequence_, showsPrec ) import qualified Text.Read as Read import Data.Typeable ( Typeable1, gcast1 ) #include "vector.h" import Data.Data ( Data, DataType ) #if MIN_VERSION_base(4,2,0) import Data.Data ( mkNoRepType ) #else import Data.Data ( mkNorepType ) mkNoRepType :: String -> DataType mkNoRepType = mkNorepType #endif -- Length information -- ------------------ -- | /O(1)/ Yield the length of the vector. length :: Vector v a => v a -> Int {-# INLINE_STREAM length #-} length v = basicLength v {-# RULES "length/unstream [Vector]" forall s. length (new (New.unstream s)) = Stream.length s #-} -- | /O(1)/ Test whether a vector if empty null :: Vector v a => v a -> Bool {-# INLINE_STREAM null #-} null v = basicLength v == 0 {-# RULES "null/unstream [Vector]" forall s. null (new (New.unstream s)) = Stream.null s #-} -- Indexing -- -------- infixl 9 ! -- | O(1) Indexing (!) :: Vector v a => v a -> Int -> a {-# INLINE_STREAM (!) #-} (!) v i = BOUNDS_CHECK(checkIndex) "(!)" i (length v) $ unId (basicUnsafeIndexM v i) infixl 9 !? -- | O(1) Safe indexing (!?) :: Vector v a => v a -> Int -> Maybe a {-# INLINE_STREAM (!?) #-} v !? i | i < 0 || i >= length v = Nothing | otherwise = Just $ unsafeIndex v i -- | /O(1)/ First element head :: Vector v a => v a -> a {-# INLINE_STREAM head #-} head v = v ! 0 -- | /O(1)/ Last element last :: Vector v a => v a -> a {-# INLINE_STREAM last #-} last v = v ! (length v - 1) -- | /O(1)/ Unsafe indexing without bounds checking unsafeIndex :: Vector v a => v a -> Int -> a {-# INLINE_STREAM unsafeIndex #-} unsafeIndex v i = UNSAFE_CHECK(checkIndex) "unsafeIndex" i (length v) $ unId (basicUnsafeIndexM v i) -- | /O(1)/ First element without checking if the vector is empty unsafeHead :: Vector v a => v a -> a {-# INLINE_STREAM unsafeHead #-} unsafeHead v = unsafeIndex v 0 -- | /O(1)/ Last element without checking if the vector is empty unsafeLast :: Vector v a => v a -> a {-# INLINE_STREAM unsafeLast #-} unsafeLast v = unsafeIndex v (length v - 1) {-# RULES "(!)/unstream [Vector]" forall i s. new (New.unstream s) ! i = s Stream.!! i "(!?)/unstream [Vector]" forall i s. new (New.unstream s) !? i = s Stream.!? i "head/unstream [Vector]" forall s. head (new (New.unstream s)) = Stream.head s "last/unstream [Vector]" forall s. last (new (New.unstream s)) = Stream.last s "unsafeIndex/unstream [Vector]" forall i s. unsafeIndex (new (New.unstream s)) i = s Stream.!! i "unsafeHead/unstream [Vector]" forall s. unsafeHead (new (New.unstream s)) = Stream.head s "unsafeLast/unstream [Vector]" forall s. unsafeLast (new (New.unstream s)) = Stream.last s #-} -- Monadic indexing -- ---------------- -- | /O(1)/ Indexing in a monad. -- -- The monad allows operations to be strict in the vector when necessary. -- Suppose vector copying is implemented like this: -- -- > copy mv v = ... write mv i (v ! i) ... -- -- For lazy vectors, @v ! i@ would not be evaluated which means that @mv@ -- would unnecessarily retain a reference to @v@ in each element written. -- -- With 'indexM', copying can be implemented like this instead: -- -- > copy mv v = ... do -- > x <- indexM v i -- > write mv i x -- -- Here, no references to @v@ are retained because indexing (but /not/ the -- elements) is evaluated eagerly. -- indexM :: (Vector v a, Monad m) => v a -> Int -> m a {-# INLINE_STREAM indexM #-} indexM v i = BOUNDS_CHECK(checkIndex) "indexM" i (length v) $ basicUnsafeIndexM v i -- | /O(1)/ First element of a vector in a monad. See 'indexM' for an -- explanation of why this is useful. headM :: (Vector v a, Monad m) => v a -> m a {-# INLINE_STREAM headM #-} headM v = indexM v 0 -- | /O(1)/ Last element of a vector in a monad. See 'indexM' for an -- explanation of why this is useful. lastM :: (Vector v a, Monad m) => v a -> m a {-# INLINE_STREAM lastM #-} lastM v = indexM v (length v - 1) -- | /O(1)/ Indexing in a monad without bounds checks. See 'indexM' for an -- explanation of why this is useful. unsafeIndexM :: (Vector v a, Monad m) => v a -> Int -> m a {-# INLINE_STREAM unsafeIndexM #-} unsafeIndexM v i = UNSAFE_CHECK(checkIndex) "unsafeIndexM" i (length v) $ basicUnsafeIndexM v i -- | /O(1)/ First element in a monad without checking for empty vectors. -- See 'indexM' for an explanation of why this is useful. unsafeHeadM :: (Vector v a, Monad m) => v a -> m a {-# INLINE_STREAM unsafeHeadM #-} unsafeHeadM v = unsafeIndexM v 0 -- | /O(1)/ Last element in a monad without checking for empty vectors. -- See 'indexM' for an explanation of why this is useful. unsafeLastM :: (Vector v a, Monad m) => v a -> m a {-# INLINE_STREAM unsafeLastM #-} unsafeLastM v = unsafeIndexM v (length v - 1) {-# RULES "indexM/unstream [Vector]" forall s i. indexM (new (New.unstream s)) i = liftStream s MStream.!! i "headM/unstream [Vector]" forall s. headM (new (New.unstream s)) = MStream.head (liftStream s) "lastM/unstream [Vector]" forall s. lastM (new (New.unstream s)) = MStream.last (liftStream s) "unsafeIndexM/unstream [Vector]" forall s i. unsafeIndexM (new (New.unstream s)) i = liftStream s MStream.!! i "unsafeHeadM/unstream [Vector]" forall s. unsafeHeadM (new (New.unstream s)) = MStream.head (liftStream s) "unsafeLastM/unstream [Vector]" forall s. unsafeLastM (new (New.unstream s)) = MStream.last (liftStream s) #-} -- Extracting subvectors (slicing) -- ------------------------------- -- | /O(1)/ Yield a slice of the vector without copying it. The vector must -- contain at least @i+n@ elements. slice :: Vector v a => Int -- ^ @i@ starting index -> Int -- ^ @n@ length -> v a -> v a {-# INLINE_STREAM slice #-} slice i n v = BOUNDS_CHECK(checkSlice) "slice" i n (length v) $ basicUnsafeSlice i n v -- | /O(1)/ Yield all but the last element without copying. The vector may not -- be empty. init :: Vector v a => v a -> v a {-# INLINE_STREAM init #-} init v = slice 0 (length v - 1) v -- | /O(1)/ Yield all but the first element without copying. The vector may not -- be empty. tail :: Vector v a => v a -> v a {-# INLINE_STREAM tail #-} tail v = slice 1 (length v - 1) v -- | /O(1)/ Yield the first @n@ elements without copying. The vector may -- contain less than @n@ elements in which case it is returned unchanged. take :: Vector v a => Int -> v a -> v a {-# INLINE_STREAM take #-} take n v = unsafeSlice 0 (delay_inline min n' (length v)) v where n' = max n 0 -- | /O(1)/ Yield all but the first @n@ elements without copying. The vector may -- contain less than @n@ elements in which case an empty vector is returned. drop :: Vector v a => Int -> v a -> v a {-# INLINE_STREAM drop #-} drop n v = unsafeSlice (delay_inline min n' len) (delay_inline max 0 (len - n')) v where n' = max n 0 len = length v -- | /O(1)/ Yield the first @n@ elements paired with the remainder without copying. -- -- Note that @'splitAt' n v@ is equivalent to @('take' n v, 'drop' n v)@ -- but slightly more efficient. {-# INLINE_STREAM splitAt #-} splitAt :: Vector v a => Int -> v a -> (v a, v a) splitAt n v = ( unsafeSlice 0 m v , unsafeSlice m (delay_inline max 0 (len - n')) v ) where m = delay_inline min n' len n' = max n 0 len = length v -- | /O(1)/ Yield a slice of the vector without copying. The vector must -- contain at least @i+n@ elements but this is not checked. unsafeSlice :: Vector v a => Int -- ^ @i@ starting index -> Int -- ^ @n@ length -> v a -> v a {-# INLINE_STREAM unsafeSlice #-} unsafeSlice i n v = UNSAFE_CHECK(checkSlice) "unsafeSlice" i n (length v) $ basicUnsafeSlice i n v -- | /O(1)/ Yield all but the last element without copying. The vector may not -- be empty but this is not checked. unsafeInit :: Vector v a => v a -> v a {-# INLINE_STREAM unsafeInit #-} unsafeInit v = unsafeSlice 0 (length v - 1) v -- | /O(1)/ Yield all but the first element without copying. The vector may not -- be empty but this is not checked. unsafeTail :: Vector v a => v a -> v a {-# INLINE_STREAM unsafeTail #-} unsafeTail v = unsafeSlice 1 (length v - 1) v -- | /O(1)/ Yield the first @n@ elements without copying. The vector must -- contain at least @n@ elements but this is not checked. unsafeTake :: Vector v a => Int -> v a -> v a {-# INLINE unsafeTake #-} unsafeTake n v = unsafeSlice 0 n v -- | /O(1)/ Yield all but the first @n@ elements without copying. The vector -- must contain at least @n@ elements but this is not checked. unsafeDrop :: Vector v a => Int -> v a -> v a {-# INLINE unsafeDrop #-} unsafeDrop n v = unsafeSlice n (length v - n) v {-# RULES "slice/new [Vector]" forall i n p. slice i n (new p) = new (New.slice i n p) "init/new [Vector]" forall p. init (new p) = new (New.init p) "tail/new [Vector]" forall p. tail (new p) = new (New.tail p) "take/new [Vector]" forall n p. take n (new p) = new (New.take n p) "drop/new [Vector]" forall n p. drop n (new p) = new (New.drop n p) "unsafeSlice/new [Vector]" forall i n p. unsafeSlice i n (new p) = new (New.unsafeSlice i n p) "unsafeInit/new [Vector]" forall p. unsafeInit (new p) = new (New.unsafeInit p) "unsafeTail/new [Vector]" forall p. unsafeTail (new p) = new (New.unsafeTail p) #-} -- Initialisation -- -------------- -- | /O(1)/ Empty vector empty :: Vector v a => v a {-# INLINE empty #-} empty = unstream Stream.empty -- | /O(1)/ Vector with exactly one element singleton :: forall v a. Vector v a => a -> v a {-# INLINE singleton #-} singleton x = elemseq (undefined :: v a) x $ unstream (Stream.singleton x) -- | /O(n)/ Vector of the given length with the same value in each position replicate :: forall v a. Vector v a => Int -> a -> v a {-# INLINE replicate #-} replicate n x = elemseq (undefined :: v a) x $ unstream $ Stream.replicate n x -- | /O(n)/ Construct a vector of the given length by applying the function to -- each index generate :: Vector v a => Int -> (Int -> a) -> v a {-# INLINE generate #-} generate n f = unstream (Stream.generate n f) -- | /O(n)/ Apply function n times to value. Zeroth element is original value. iterateN :: Vector v a => Int -> (a -> a) -> a -> v a {-# INLINE iterateN #-} iterateN n f x = unstream (Stream.iterateN n f x) -- Unfolding -- --------- -- | /O(n)/ Construct a vector by repeatedly applying the generator function -- to a seed. The generator function yields 'Just' the next element and the -- new seed or 'Nothing' if there are no more elements. -- -- > unfoldr (\n -> if n == 0 then Nothing else Just (n,n-1)) 10 -- > = <10,9,8,7,6,5,4,3,2,1> unfoldr :: Vector v a => (b -> Maybe (a, b)) -> b -> v a {-# INLINE unfoldr #-} unfoldr f = unstream . Stream.unfoldr f -- | /O(n)/ Construct a vector with at most @n@ by repeatedly applying the -- generator function to the a seed. The generator function yields 'Just' the -- next element and the new seed or 'Nothing' if there are no more elements. -- -- > unfoldrN 3 (\n -> Just (n,n-1)) 10 = <10,9,8> unfoldrN :: Vector v a => Int -> (b -> Maybe (a, b)) -> b -> v a {-# INLINE unfoldrN #-} unfoldrN n f = unstream . Stream.unfoldrN n f -- | /O(n)/ Construct a vector with @n@ elements by repeatedly applying the -- generator function to the already constructed part of the vector. -- -- > constructN 3 f = let a = f <> ; b = f <a> ; c = f <a,b> in f <a,b,c> -- constructN :: forall v a. Vector v a => Int -> (v a -> a) -> v a {-# INLINE constructN #-} -- NOTE: We *CANNOT* wrap this in New and then fuse because the elements -- might contain references to the immutable vector! constructN !n f = runST ( do v <- M.new n v' <- unsafeFreeze v fill v' 0 ) where fill :: forall s. v a -> Int -> ST s (v a) fill !v i | i < n = let x = f (unsafeTake i v) in elemseq v x $ do v' <- unsafeThaw v M.unsafeWrite v' i x v'' <- unsafeFreeze v' fill v'' (i+1) fill v i = return v -- | /O(n)/ Construct a vector with @n@ elements from right to left by -- repeatedly applying the generator function to the already constructed part -- of the vector. -- -- > constructrN 3 f = let a = f <> ; b = f<a> ; c = f <b,a> in f <c,b,a> -- constructrN :: forall v a. Vector v a => Int -> (v a -> a) -> v a {-# INLINE constructrN #-} -- NOTE: We *CANNOT* wrap this in New and then fuse because the elements -- might contain references to the immutable vector! constructrN !n f = runST ( do v <- n `seq` M.new n v' <- unsafeFreeze v fill v' 0 ) where fill :: forall s. v a -> Int -> ST s (v a) fill !v i | i < n = let x = f (unsafeSlice (n-i) i v) in elemseq v x $ do v' <- unsafeThaw v M.unsafeWrite v' (n-i-1) x v'' <- unsafeFreeze v' fill v'' (i+1) fill v i = return v -- Enumeration -- ----------- -- | /O(n)/ Yield a vector of the given length containing the values @x@, @x+1@ -- etc. This operation is usually more efficient than 'enumFromTo'. -- -- > enumFromN 5 3 = <5,6,7> enumFromN :: (Vector v a, Num a) => a -> Int -> v a {-# INLINE enumFromN #-} enumFromN x n = enumFromStepN x 1 n -- | /O(n)/ Yield a vector of the given length containing the values @x@, @x+y@, -- @x+y+y@ etc. This operations is usually more efficient than 'enumFromThenTo'. -- -- > enumFromStepN 1 0.1 5 = <1,1.1,1.2,1.3,1.4> enumFromStepN :: forall v a. (Vector v a, Num a) => a -> a -> Int -> v a {-# INLINE enumFromStepN #-} enumFromStepN x y n = elemseq (undefined :: v a) x $ elemseq (undefined :: v a) y $ unstream $ Stream.enumFromStepN x y n -- | /O(n)/ Enumerate values from @x@ to @y@. -- -- /WARNING:/ This operation can be very inefficient. If at all possible, use -- 'enumFromN' instead. enumFromTo :: (Vector v a, Enum a) => a -> a -> v a {-# INLINE enumFromTo #-} enumFromTo x y = unstream (Stream.enumFromTo x y) -- | /O(n)/ Enumerate values from @x@ to @y@ with a specific step @z@. -- -- /WARNING:/ This operation can be very inefficient. If at all possible, use -- 'enumFromStepN' instead. enumFromThenTo :: (Vector v a, Enum a) => a -> a -> a -> v a {-# INLINE enumFromThenTo #-} enumFromThenTo x y z = unstream (Stream.enumFromThenTo x y z) -- Concatenation -- ------------- -- | /O(n)/ Prepend an element cons :: forall v a. Vector v a => a -> v a -> v a {-# INLINE cons #-} cons x v = elemseq (undefined :: v a) x $ unstream $ Stream.cons x $ stream v -- | /O(n)/ Append an element snoc :: forall v a. Vector v a => v a -> a -> v a {-# INLINE snoc #-} snoc v x = elemseq (undefined :: v a) x $ unstream $ Stream.snoc (stream v) x infixr 5 ++ -- | /O(m+n)/ Concatenate two vectors (++) :: Vector v a => v a -> v a -> v a {-# INLINE (++) #-} v ++ w = unstream (stream v Stream.++ stream w) -- | /O(n)/ Concatenate all vectors in the list concat :: Vector v a => [v a] -> v a {-# INLINE concat #-} concat vs = unstream (Stream.flatten mk step (Exact n) (Stream.fromList vs)) where n = List.foldl' (\k v -> k + length v) 0 vs {-# INLINE_INNER step #-} step (v,i,k) | i < k = case unsafeIndexM v i of Box x -> Stream.Yield x (v,i+1,k) | otherwise = Stream.Done {-# INLINE mk #-} mk v = let k = length v in k `seq` (v,0,k) -- Monadic initialisation -- ---------------------- -- | /O(n)/ Execute the monadic action the given number of times and store the -- results in a vector. replicateM :: (Monad m, Vector v a) => Int -> m a -> m (v a) {-# INLINE replicateM #-} replicateM n m = unstreamM (MStream.replicateM n m) -- | /O(n)/ Construct a vector of the given length by applying the monadic -- action to each index generateM :: (Monad m, Vector v a) => Int -> (Int -> m a) -> m (v a) {-# INLINE generateM #-} generateM n f = unstreamM (MStream.generateM n f) -- | Execute the monadic action and freeze the resulting vector. -- -- @ -- create (do { v \<- 'M.new' 2; 'M.write' v 0 \'a\'; 'M.write' v 1 \'b\' }) = \<'a','b'\> -- @ create :: Vector v a => (forall s. ST s (Mutable v s a)) -> v a {-# INLINE create #-} create p = new (New.create p) -- Restricting memory usage -- ------------------------ -- | /O(n)/ Yield the argument but force it not to retain any extra memory, -- possibly by copying it. -- -- This is especially useful when dealing with slices. For example: -- -- > force (slice 0 2 <huge vector>) -- -- Here, the slice retains a reference to the huge vector. Forcing it creates -- a copy of just the elements that belong to the slice and allows the huge -- vector to be garbage collected. force :: Vector v a => v a -> v a -- FIXME: we probably ought to inline this later as the rules still might fire -- otherwise {-# INLINE_STREAM force #-} force v = new (clone v) -- Bulk updates -- ------------ -- | /O(m+n)/ For each pair @(i,a)@ from the list, replace the vector -- element at position @i@ by @a@. -- -- > <5,9,2,7> // [(2,1),(0,3),(2,8)] = <3,9,8,7> -- (//) :: Vector v a => v a -- ^ initial vector (of length @m@) -> [(Int, a)] -- ^ list of index/value pairs (of length @n@) -> v a {-# INLINE (//) #-} v // us = update_stream v (Stream.fromList us) -- | /O(m+n)/ For each pair @(i,a)@ from the vector of index/value pairs, -- replace the vector element at position @i@ by @a@. -- -- > update <5,9,2,7> <(2,1),(0,3),(2,8)> = <3,9,8,7> -- update :: (Vector v a, Vector v (Int, a)) => v a -- ^ initial vector (of length @m@) -> v (Int, a) -- ^ vector of index/value pairs (of length @n@) -> v a {-# INLINE update #-} update v w = update_stream v (stream w) -- | /O(m+min(n1,n2))/ For each index @i@ from the index vector and the -- corresponding value @a@ from the value vector, replace the element of the -- initial vector at position @i@ by @a@. -- -- > update_ <5,9,2,7> <2,0,2> <1,3,8> = <3,9,8,7> -- -- This function is useful for instances of 'Vector' that cannot store pairs. -- Otherwise, 'update' is probably more convenient. -- -- @ -- update_ xs is ys = 'update' xs ('zip' is ys) -- @ update_ :: (Vector v a, Vector v Int) => v a -- ^ initial vector (of length @m@) -> v Int -- ^ index vector (of length @n1@) -> v a -- ^ value vector (of length @n2@) -> v a {-# INLINE update_ #-} update_ v is w = update_stream v (Stream.zipWith (,) (stream is) (stream w)) update_stream :: Vector v a => v a -> Stream (Int,a) -> v a {-# INLINE update_stream #-} update_stream = modifyWithStream M.update -- | Same as ('//') but without bounds checking. unsafeUpd :: Vector v a => v a -> [(Int, a)] -> v a {-# INLINE unsafeUpd #-} unsafeUpd v us = unsafeUpdate_stream v (Stream.fromList us) -- | Same as 'update' but without bounds checking. unsafeUpdate :: (Vector v a, Vector v (Int, a)) => v a -> v (Int, a) -> v a {-# INLINE unsafeUpdate #-} unsafeUpdate v w = unsafeUpdate_stream v (stream w) -- | Same as 'update_' but without bounds checking. unsafeUpdate_ :: (Vector v a, Vector v Int) => v a -> v Int -> v a -> v a {-# INLINE unsafeUpdate_ #-} unsafeUpdate_ v is w = unsafeUpdate_stream v (Stream.zipWith (,) (stream is) (stream w)) unsafeUpdate_stream :: Vector v a => v a -> Stream (Int,a) -> v a {-# INLINE unsafeUpdate_stream #-} unsafeUpdate_stream = modifyWithStream M.unsafeUpdate -- Accumulations -- ------------- -- | /O(m+n)/ For each pair @(i,b)@ from the list, replace the vector element -- @a@ at position @i@ by @f a b@. -- -- > accum (+) <5,9,2> [(2,4),(1,6),(0,3),(1,7)] = <5+3, 9+6+7, 2+4> accum :: Vector v a => (a -> b -> a) -- ^ accumulating function @f@ -> v a -- ^ initial vector (of length @m@) -> [(Int,b)] -- ^ list of index/value pairs (of length @n@) -> v a {-# INLINE accum #-} accum f v us = accum_stream f v (Stream.fromList us) -- | /O(m+n)/ For each pair @(i,b)@ from the vector of pairs, replace the vector -- element @a@ at position @i@ by @f a b@. -- -- > accumulate (+) <5,9,2> <(2,4),(1,6),(0,3),(1,7)> = <5+3, 9+6+7, 2+4> accumulate :: (Vector v a, Vector v (Int, b)) => (a -> b -> a) -- ^ accumulating function @f@ -> v a -- ^ initial vector (of length @m@) -> v (Int,b) -- ^ vector of index/value pairs (of length @n@) -> v a {-# INLINE accumulate #-} accumulate f v us = accum_stream f v (stream us) -- | /O(m+min(n1,n2))/ For each index @i@ from the index vector and the -- corresponding value @b@ from the the value vector, -- replace the element of the initial vector at -- position @i@ by @f a b@. -- -- > accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4> -- -- This function is useful for instances of 'Vector' that cannot store pairs. -- Otherwise, 'accumulate' is probably more convenient: -- -- @ -- accumulate_ f as is bs = 'accumulate' f as ('zip' is bs) -- @ accumulate_ :: (Vector v a, Vector v Int, Vector v b) => (a -> b -> a) -- ^ accumulating function @f@ -> v a -- ^ initial vector (of length @m@) -> v Int -- ^ index vector (of length @n1@) -> v b -- ^ value vector (of length @n2@) -> v a {-# INLINE accumulate_ #-} accumulate_ f v is xs = accum_stream f v (Stream.zipWith (,) (stream is) (stream xs)) accum_stream :: Vector v a => (a -> b -> a) -> v a -> Stream (Int,b) -> v a {-# INLINE accum_stream #-} accum_stream f = modifyWithStream (M.accum f) -- | Same as 'accum' but without bounds checking. unsafeAccum :: Vector v a => (a -> b -> a) -> v a -> [(Int,b)] -> v a {-# INLINE unsafeAccum #-} unsafeAccum f v us = unsafeAccum_stream f v (Stream.fromList us) -- | Same as 'accumulate' but without bounds checking. unsafeAccumulate :: (Vector v a, Vector v (Int, b)) => (a -> b -> a) -> v a -> v (Int,b) -> v a {-# INLINE unsafeAccumulate #-} unsafeAccumulate f v us = unsafeAccum_stream f v (stream us) -- | Same as 'accumulate_' but without bounds checking. unsafeAccumulate_ :: (Vector v a, Vector v Int, Vector v b) => (a -> b -> a) -> v a -> v Int -> v b -> v a {-# INLINE unsafeAccumulate_ #-} unsafeAccumulate_ f v is xs = unsafeAccum_stream f v (Stream.zipWith (,) (stream is) (stream xs)) unsafeAccum_stream :: Vector v a => (a -> b -> a) -> v a -> Stream (Int,b) -> v a {-# INLINE unsafeAccum_stream #-} unsafeAccum_stream f = modifyWithStream (M.unsafeAccum f) -- Permutations -- ------------ -- | /O(n)/ Reverse a vector reverse :: (Vector v a) => v a -> v a {-# INLINE reverse #-} -- FIXME: make this fuse better, add support for recycling reverse = unstream . streamR -- | /O(n)/ Yield the vector obtained by replacing each element @i@ of the -- index vector by @xs'!'i@. This is equivalent to @'map' (xs'!') is@ but is -- often much more efficient. -- -- > backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a> backpermute :: (Vector v a, Vector v Int) => v a -- ^ @xs@ value vector -> v Int -- ^ @is@ index vector (of length @n@) -> v a {-# INLINE backpermute #-} -- This somewhat non-intuitive definition ensures that the resulting vector -- does not retain references to the original one even if it is lazy in its -- elements. This would not be the case if we simply used map (v!) backpermute v is = seq v $ seq n $ unstream $ Stream.unbox $ Stream.map index $ stream is where n = length v {-# INLINE index #-} -- NOTE: we do it this way to avoid triggering LiberateCase on n in -- polymorphic code index i = BOUNDS_CHECK(checkIndex) "backpermute" i n $ basicUnsafeIndexM v i -- | Same as 'backpermute' but without bounds checking. unsafeBackpermute :: (Vector v a, Vector v Int) => v a -> v Int -> v a {-# INLINE unsafeBackpermute #-} unsafeBackpermute v is = seq v $ seq n $ unstream $ Stream.unbox $ Stream.map index $ stream is where n = length v {-# INLINE index #-} -- NOTE: we do it this way to avoid triggering LiberateCase on n in -- polymorphic code index i = UNSAFE_CHECK(checkIndex) "unsafeBackpermute" i n $ basicUnsafeIndexM v i -- Safe destructive updates -- ------------------------ -- | Apply a destructive operation to a vector. The operation will be -- performed in place if it is safe to do so and will modify a copy of the -- vector otherwise. -- -- @ -- modify (\\v -> 'M.write' v 0 \'x\') ('replicate' 3 \'a\') = \<\'x\',\'a\',\'a\'\> -- @ modify :: Vector v a => (forall s. Mutable v s a -> ST s ()) -> v a -> v a {-# INLINE modify #-} modify p = new . New.modify p . clone -- We have to make sure that this is strict in the stream but we can't seq on -- it while fusion is happening. Hence this ugliness. modifyWithStream :: Vector v a => (forall s. Mutable v s a -> Stream b -> ST s ()) -> v a -> Stream b -> v a {-# INLINE modifyWithStream #-} modifyWithStream p v s = new (New.modifyWithStream p (clone v) s) -- Indexing -- -------- -- | /O(n)/ Pair each element in a vector with its index indexed :: (Vector v a, Vector v (Int,a)) => v a -> v (Int,a) {-# INLINE indexed #-} indexed = unstream . Stream.indexed . stream -- Mapping -- ------- -- | /O(n)/ Map a function over a vector map :: (Vector v a, Vector v b) => (a -> b) -> v a -> v b {-# INLINE map #-} map f = unstream . inplace (MStream.map f) . stream -- | /O(n)/ Apply a function to every element of a vector and its index imap :: (Vector v a, Vector v b) => (Int -> a -> b) -> v a -> v b {-# INLINE imap #-} imap f = unstream . inplace (MStream.map (uncurry f) . MStream.indexed) . stream -- | Map a function over a vector and concatenate the results. concatMap :: (Vector v a, Vector v b) => (a -> v b) -> v a -> v b {-# INLINE concatMap #-} -- NOTE: We can't fuse concatMap anyway so don't pretend we do. -- This seems to be slightly slower -- concatMap f = concat . Stream.toList . Stream.map f . stream -- Slowest -- concatMap f = unstream . Stream.concatMap (stream . f) . stream -- Seems to be fastest concatMap f = unstream . Stream.flatten mk step Unknown . stream where {-# INLINE_INNER step #-} step (v,i,k) | i < k = case unsafeIndexM v i of Box x -> Stream.Yield x (v,i+1,k) | otherwise = Stream.Done {-# INLINE mk #-} mk x = let v = f x k = length v in k `seq` (v,0,k) -- Monadic mapping -- --------------- -- | /O(n)/ Apply the monadic action to all elements of the vector, yielding a -- vector of results mapM :: (Monad m, Vector v a, Vector v b) => (a -> m b) -> v a -> m (v b) {-# INLINE mapM #-} mapM f = unstreamM . Stream.mapM f . stream -- | /O(n)/ Apply the monadic action to all elements of a vector and ignore the -- results mapM_ :: (Monad m, Vector v a) => (a -> m b) -> v a -> m () {-# INLINE mapM_ #-} mapM_ f = Stream.mapM_ f . stream -- | /O(n)/ Apply the monadic action to all elements of the vector, yielding a -- vector of results. Equvalent to @flip 'mapM'@. forM :: (Monad m, Vector v a, Vector v b) => v a -> (a -> m b) -> m (v b) {-# INLINE forM #-} forM as f = mapM f as -- | /O(n)/ Apply the monadic action to all elements of a vector and ignore the -- results. Equivalent to @flip 'mapM_'@. forM_ :: (Monad m, Vector v a) => v a -> (a -> m b) -> m () {-# INLINE forM_ #-} forM_ as f = mapM_ f as -- Zipping -- ------- -- | /O(min(m,n))/ Zip two vectors with the given function. zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> v a -> v b -> v c {-# INLINE zipWith #-} zipWith f xs ys = unstream (Stream.zipWith f (stream xs) (stream ys)) -- | Zip three vectors with the given function. zipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (a -> b -> c -> d) -> v a -> v b -> v c -> v d {-# INLINE zipWith3 #-} zipWith3 f as bs cs = unstream (Stream.zipWith3 f (stream as) (stream bs) (stream cs)) zipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (a -> b -> c -> d -> e) -> v a -> v b -> v c -> v d -> v e {-# INLINE zipWith4 #-} zipWith4 f as bs cs ds = unstream (Stream.zipWith4 f (stream as) (stream bs) (stream cs) (stream ds)) zipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (a -> b -> c -> d -> e -> f) -> v a -> v b -> v c -> v d -> v e -> v f {-# INLINE zipWith5 #-} zipWith5 f as bs cs ds es = unstream (Stream.zipWith5 f (stream as) (stream bs) (stream cs) (stream ds) (stream es)) zipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (a -> b -> c -> d -> e -> f -> g) -> v a -> v b -> v c -> v d -> v e -> v f -> v g {-# INLINE zipWith6 #-} zipWith6 f as bs cs ds es fs = unstream (Stream.zipWith6 f (stream as) (stream bs) (stream cs) (stream ds) (stream es) (stream fs)) -- | /O(min(m,n))/ Zip two vectors with a function that also takes the -- elements' indices. izipWith :: (Vector v a, Vector v b, Vector v c) => (Int -> a -> b -> c) -> v a -> v b -> v c {-# INLINE izipWith #-} izipWith f xs ys = unstream (Stream.zipWith (uncurry f) (Stream.indexed (stream xs)) (stream ys)) izipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (Int -> a -> b -> c -> d) -> v a -> v b -> v c -> v d {-# INLINE izipWith3 #-} izipWith3 f as bs cs = unstream (Stream.zipWith3 (uncurry f) (Stream.indexed (stream as)) (stream bs) (stream cs)) izipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (Int -> a -> b -> c -> d -> e) -> v a -> v b -> v c -> v d -> v e {-# INLINE izipWith4 #-} izipWith4 f as bs cs ds = unstream (Stream.zipWith4 (uncurry f) (Stream.indexed (stream as)) (stream bs) (stream cs) (stream ds)) izipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (Int -> a -> b -> c -> d -> e -> f) -> v a -> v b -> v c -> v d -> v e -> v f {-# INLINE izipWith5 #-} izipWith5 f as bs cs ds es = unstream (Stream.zipWith5 (uncurry f) (Stream.indexed (stream as)) (stream bs) (stream cs) (stream ds) (stream es)) izipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (Int -> a -> b -> c -> d -> e -> f -> g) -> v a -> v b -> v c -> v d -> v e -> v f -> v g {-# INLINE izipWith6 #-} izipWith6 f as bs cs ds es fs = unstream (Stream.zipWith6 (uncurry f) (Stream.indexed (stream as)) (stream bs) (stream cs) (stream ds) (stream es) (stream fs)) -- | /O(min(m,n))/ Zip two vectors zip :: (Vector v a, Vector v b, Vector v (a,b)) => v a -> v b -> v (a, b) {-# INLINE zip #-} zip = zipWith (,) zip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v a -> v b -> v c -> v (a, b, c) {-# INLINE zip3 #-} zip3 = zipWith3 (,,) zip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v a -> v b -> v c -> v d -> v (a, b, c, d) {-# INLINE zip4 #-} zip4 = zipWith4 (,,,) zip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v a -> v b -> v c -> v d -> v e -> v (a, b, c, d, e) {-# INLINE zip5 #-} zip5 = zipWith5 (,,,,) zip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v a -> v b -> v c -> v d -> v e -> v f -> v (a, b, c, d, e, f) {-# INLINE zip6 #-} zip6 = zipWith6 (,,,,,) -- Monadic zipping -- --------------- -- | /O(min(m,n))/ Zip the two vectors with the monadic action and yield a -- vector of results zipWithM :: (Monad m, Vector v a, Vector v b, Vector v c) => (a -> b -> m c) -> v a -> v b -> m (v c) -- FIXME: specialise for ST and IO? {-# INLINE zipWithM #-} zipWithM f as bs = unstreamM $ Stream.zipWithM f (stream as) (stream bs) -- | /O(min(m,n))/ Zip the two vectors with the monadic action and ignore the -- results zipWithM_ :: (Monad m, Vector v a, Vector v b) => (a -> b -> m c) -> v a -> v b -> m () {-# INLINE zipWithM_ #-} zipWithM_ f as bs = Stream.zipWithM_ f (stream as) (stream bs) -- Unzipping -- --------- -- | /O(min(m,n))/ Unzip a vector of pairs. unzip :: (Vector v a, Vector v b, Vector v (a,b)) => v (a, b) -> (v a, v b) {-# INLINE unzip #-} unzip xs = (map fst xs, map snd xs) unzip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v (a, b, c) -> (v a, v b, v c) {-# INLINE unzip3 #-} unzip3 xs = (map (\(a, b, c) -> a) xs, map (\(a, b, c) -> b) xs, map (\(a, b, c) -> c) xs) unzip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v (a, b, c, d) -> (v a, v b, v c, v d) {-# INLINE unzip4 #-} unzip4 xs = (map (\(a, b, c, d) -> a) xs, map (\(a, b, c, d) -> b) xs, map (\(a, b, c, d) -> c) xs, map (\(a, b, c, d) -> d) xs) unzip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v (a, b, c, d, e) -> (v a, v b, v c, v d, v e) {-# INLINE unzip5 #-} unzip5 xs = (map (\(a, b, c, d, e) -> a) xs, map (\(a, b, c, d, e) -> b) xs, map (\(a, b, c, d, e) -> c) xs, map (\(a, b, c, d, e) -> d) xs, map (\(a, b, c, d, e) -> e) xs) unzip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v (a, b, c, d, e, f) -> (v a, v b, v c, v d, v e, v f) {-# INLINE unzip6 #-} unzip6 xs = (map (\(a, b, c, d, e, f) -> a) xs, map (\(a, b, c, d, e, f) -> b) xs, map (\(a, b, c, d, e, f) -> c) xs, map (\(a, b, c, d, e, f) -> d) xs, map (\(a, b, c, d, e, f) -> e) xs, map (\(a, b, c, d, e, f) -> f) xs) -- Filtering -- --------- -- | /O(n)/ Drop elements that do not satisfy the predicate filter :: Vector v a => (a -> Bool) -> v a -> v a {-# INLINE filter #-} filter f = unstream . inplace (MStream.filter f) . stream -- | /O(n)/ Drop elements that do not satisfy the predicate which is applied to -- values and their indices ifilter :: Vector v a => (Int -> a -> Bool) -> v a -> v a {-# INLINE ifilter #-} ifilter f = unstream . inplace (MStream.map snd . MStream.filter (uncurry f) . MStream.indexed) . stream -- | /O(n)/ Drop elements that do not satisfy the monadic predicate filterM :: (Monad m, Vector v a) => (a -> m Bool) -> v a -> m (v a) {-# INLINE filterM #-} filterM f = unstreamM . Stream.filterM f . stream -- | /O(n)/ Yield the longest prefix of elements satisfying the predicate -- without copying. takeWhile :: Vector v a => (a -> Bool) -> v a -> v a {-# INLINE takeWhile #-} takeWhile f = unstream . Stream.takeWhile f . stream -- | /O(n)/ Drop the longest prefix of elements that satisfy the predicate -- without copying. dropWhile :: Vector v a => (a -> Bool) -> v a -> v a {-# INLINE dropWhile #-} dropWhile f = unstream . Stream.dropWhile f . stream -- Parititioning -- ------------- -- | /O(n)/ Split the vector in two parts, the first one containing those -- elements that satisfy the predicate and the second one those that don't. The -- relative order of the elements is preserved at the cost of a sometimes -- reduced performance compared to 'unstablePartition'. partition :: Vector v a => (a -> Bool) -> v a -> (v a, v a) {-# INLINE partition #-} partition f = partition_stream f . stream -- FIXME: Make this inplace-fusible (look at how stable_partition is -- implemented in C++) partition_stream :: Vector v a => (a -> Bool) -> Stream a -> (v a, v a) {-# INLINE_STREAM partition_stream #-} partition_stream f s = s `seq` runST ( do (mv1,mv2) <- M.partitionStream f s v1 <- unsafeFreeze mv1 v2 <- unsafeFreeze mv2 return (v1,v2)) -- | /O(n)/ Split the vector in two parts, the first one containing those -- elements that satisfy the predicate and the second one those that don't. -- The order of the elements is not preserved but the operation is often -- faster than 'partition'. unstablePartition :: Vector v a => (a -> Bool) -> v a -> (v a, v a) {-# INLINE unstablePartition #-} unstablePartition f = unstablePartition_stream f . stream unstablePartition_stream :: Vector v a => (a -> Bool) -> Stream a -> (v a, v a) {-# INLINE_STREAM unstablePartition_stream #-} unstablePartition_stream f s = s `seq` runST ( do (mv1,mv2) <- M.unstablePartitionStream f s v1 <- unsafeFreeze mv1 v2 <- unsafeFreeze mv2 return (v1,v2)) unstablePartition_new :: Vector v a => (a -> Bool) -> New v a -> (v a, v a) {-# INLINE_STREAM unstablePartition_new #-} unstablePartition_new f (New.New p) = runST ( do mv <- p i <- M.unstablePartition f mv v <- unsafeFreeze mv return (unsafeTake i v, unsafeDrop i v)) {-# RULES "unstablePartition" forall f p. unstablePartition_stream f (stream (new p)) = unstablePartition_new f p #-} -- FIXME: make span and break fusible -- | /O(n)/ Split the vector into the longest prefix of elements that satisfy -- the predicate and the rest without copying. span :: Vector v a => (a -> Bool) -> v a -> (v a, v a) {-# INLINE span #-} span f = break (not . f) -- | /O(n)/ Split the vector into the longest prefix of elements that do not -- satisfy the predicate and the rest without copying. break :: Vector v a => (a -> Bool) -> v a -> (v a, v a) {-# INLINE break #-} break f xs = case findIndex f xs of Just i -> (unsafeSlice 0 i xs, unsafeSlice i (length xs - i) xs) Nothing -> (xs, empty) -- Searching -- --------- infix 4 `elem` -- | /O(n)/ Check if the vector contains an element elem :: (Vector v a, Eq a) => a -> v a -> Bool {-# INLINE elem #-} elem x = Stream.elem x . stream infix 4 `notElem` -- | /O(n)/ Check if the vector does not contain an element (inverse of 'elem') notElem :: (Vector v a, Eq a) => a -> v a -> Bool {-# INLINE notElem #-} notElem x = Stream.notElem x . stream -- | /O(n)/ Yield 'Just' the first element matching the predicate or 'Nothing' -- if no such element exists. find :: Vector v a => (a -> Bool) -> v a -> Maybe a {-# INLINE find #-} find f = Stream.find f . stream -- | /O(n)/ Yield 'Just' the index of the first element matching the predicate -- or 'Nothing' if no such element exists. findIndex :: Vector v a => (a -> Bool) -> v a -> Maybe Int {-# INLINE findIndex #-} findIndex f = Stream.findIndex f . stream -- | /O(n)/ Yield the indices of elements satisfying the predicate in ascending -- order. findIndices :: (Vector v a, Vector v Int) => (a -> Bool) -> v a -> v Int {-# INLINE findIndices #-} findIndices f = unstream . inplace (MStream.map fst . MStream.filter (f . snd) . MStream.indexed) . stream -- | /O(n)/ Yield 'Just' the index of the first occurence of the given element or -- 'Nothing' if the vector does not contain the element. This is a specialised -- version of 'findIndex'. elemIndex :: (Vector v a, Eq a) => a -> v a -> Maybe Int {-# INLINE elemIndex #-} elemIndex x = findIndex (x==) -- | /O(n)/ Yield the indices of all occurences of the given element in -- ascending order. This is a specialised version of 'findIndices'. elemIndices :: (Vector v a, Vector v Int, Eq a) => a -> v a -> v Int {-# INLINE elemIndices #-} elemIndices x = findIndices (x==) -- Folding -- ------- -- | /O(n)/ Left fold foldl :: Vector v b => (a -> b -> a) -> a -> v b -> a {-# INLINE foldl #-} foldl f z = Stream.foldl f z . stream -- | /O(n)/ Left fold on non-empty vectors foldl1 :: Vector v a => (a -> a -> a) -> v a -> a {-# INLINE foldl1 #-} foldl1 f = Stream.foldl1 f . stream -- | /O(n)/ Left fold with strict accumulator foldl' :: Vector v b => (a -> b -> a) -> a -> v b -> a {-# INLINE foldl' #-} foldl' f z = Stream.foldl' f z . stream -- | /O(n)/ Left fold on non-empty vectors with strict accumulator foldl1' :: Vector v a => (a -> a -> a) -> v a -> a {-# INLINE foldl1' #-} foldl1' f = Stream.foldl1' f . stream -- | /O(n)/ Right fold foldr :: Vector v a => (a -> b -> b) -> b -> v a -> b {-# INLINE foldr #-} foldr f z = Stream.foldr f z . stream -- | /O(n)/ Right fold on non-empty vectors foldr1 :: Vector v a => (a -> a -> a) -> v a -> a {-# INLINE foldr1 #-} foldr1 f = Stream.foldr1 f . stream -- | /O(n)/ Right fold with a strict accumulator foldr' :: Vector v a => (a -> b -> b) -> b -> v a -> b {-# INLINE foldr' #-} foldr' f z = Stream.foldl' (flip f) z . streamR -- | /O(n)/ Right fold on non-empty vectors with strict accumulator foldr1' :: Vector v a => (a -> a -> a) -> v a -> a {-# INLINE foldr1' #-} foldr1' f = Stream.foldl1' (flip f) . streamR -- | /O(n)/ Left fold (function applied to each element and its index) ifoldl :: Vector v b => (a -> Int -> b -> a) -> a -> v b -> a {-# INLINE ifoldl #-} ifoldl f z = Stream.foldl (uncurry . f) z . Stream.indexed . stream -- | /O(n)/ Left fold with strict accumulator (function applied to each element -- and its index) ifoldl' :: Vector v b => (a -> Int -> b -> a) -> a -> v b -> a {-# INLINE ifoldl' #-} ifoldl' f z = Stream.foldl' (uncurry . f) z . Stream.indexed . stream -- | /O(n)/ Right fold (function applied to each element and its index) ifoldr :: Vector v a => (Int -> a -> b -> b) -> b -> v a -> b {-# INLINE ifoldr #-} ifoldr f z = Stream.foldr (uncurry f) z . Stream.indexed . stream -- | /O(n)/ Right fold with strict accumulator (function applied to each -- element and its index) ifoldr' :: Vector v a => (Int -> a -> b -> b) -> b -> v a -> b {-# INLINE ifoldr' #-} ifoldr' f z xs = Stream.foldl' (flip (uncurry f)) z $ Stream.indexedR (length xs) $ streamR xs -- Specialised folds -- ----------------- -- | /O(n)/ Check if all elements satisfy the predicate. all :: Vector v a => (a -> Bool) -> v a -> Bool {-# INLINE all #-} all f = Stream.and . Stream.map f . stream -- | /O(n)/ Check if any element satisfies the predicate. any :: Vector v a => (a -> Bool) -> v a -> Bool {-# INLINE any #-} any f = Stream.or . Stream.map f . stream -- | /O(n)/ Check if all elements are 'True' and :: Vector v Bool => v Bool -> Bool {-# INLINE and #-} and = Stream.and . stream -- | /O(n)/ Check if any element is 'True' or :: Vector v Bool => v Bool -> Bool {-# INLINE or #-} or = Stream.or . stream -- | /O(n)/ Compute the sum of the elements sum :: (Vector v a, Num a) => v a -> a {-# INLINE sum #-} sum = Stream.foldl' (+) 0 . stream -- | /O(n)/ Compute the produce of the elements product :: (Vector v a, Num a) => v a -> a {-# INLINE product #-} product = Stream.foldl' (*) 1 . stream -- | /O(n)/ Yield the maximum element of the vector. The vector may not be -- empty. maximum :: (Vector v a, Ord a) => v a -> a {-# INLINE maximum #-} maximum = Stream.foldl1' max . stream -- | /O(n)/ Yield the maximum element of the vector according to the given -- comparison function. The vector may not be empty. maximumBy :: Vector v a => (a -> a -> Ordering) -> v a -> a {-# INLINE maximumBy #-} maximumBy cmp = Stream.foldl1' maxBy . stream where {-# INLINE maxBy #-} maxBy x y = case cmp x y of LT -> y _ -> x -- | /O(n)/ Yield the minimum element of the vector. The vector may not be -- empty. minimum :: (Vector v a, Ord a) => v a -> a {-# INLINE minimum #-} minimum = Stream.foldl1' min . stream -- | /O(n)/ Yield the minimum element of the vector according to the given -- comparison function. The vector may not be empty. minimumBy :: Vector v a => (a -> a -> Ordering) -> v a -> a {-# INLINE minimumBy #-} minimumBy cmp = Stream.foldl1' minBy . stream where {-# INLINE minBy #-} minBy x y = case cmp x y of GT -> y _ -> x -- | /O(n)/ Yield the index of the maximum element of the vector. The vector -- may not be empty. maxIndex :: (Vector v a, Ord a) => v a -> Int {-# INLINE maxIndex #-} maxIndex = maxIndexBy compare -- | /O(n)/ Yield the index of the maximum element of the vector according to -- the given comparison function. The vector may not be empty. maxIndexBy :: Vector v a => (a -> a -> Ordering) -> v a -> Int {-# INLINE maxIndexBy #-} maxIndexBy cmp = fst . Stream.foldl1' imax . Stream.indexed . stream where imax (i,x) (j,y) = i `seq` j `seq` case cmp x y of LT -> (j,y) _ -> (i,x) -- | /O(n)/ Yield the index of the minimum element of the vector. The vector -- may not be empty. minIndex :: (Vector v a, Ord a) => v a -> Int {-# INLINE minIndex #-} minIndex = minIndexBy compare -- | /O(n)/ Yield the index of the minimum element of the vector according to -- the given comparison function. The vector may not be empty. minIndexBy :: Vector v a => (a -> a -> Ordering) -> v a -> Int {-# INLINE minIndexBy #-} minIndexBy cmp = fst . Stream.foldl1' imin . Stream.indexed . stream where imin (i,x) (j,y) = i `seq` j `seq` case cmp x y of GT -> (j,y) _ -> (i,x) -- Monadic folds -- ------------- -- | /O(n)/ Monadic fold foldM :: (Monad m, Vector v b) => (a -> b -> m a) -> a -> v b -> m a {-# INLINE foldM #-} foldM m z = Stream.foldM m z . stream -- | /O(n)/ Monadic fold over non-empty vectors fold1M :: (Monad m, Vector v a) => (a -> a -> m a) -> v a -> m a {-# INLINE fold1M #-} fold1M m = Stream.fold1M m . stream -- | /O(n)/ Monadic fold with strict accumulator foldM' :: (Monad m, Vector v b) => (a -> b -> m a) -> a -> v b -> m a {-# INLINE foldM' #-} foldM' m z = Stream.foldM' m z . stream -- | /O(n)/ Monadic fold over non-empty vectors with strict accumulator fold1M' :: (Monad m, Vector v a) => (a -> a -> m a) -> v a -> m a {-# INLINE fold1M' #-} fold1M' m = Stream.fold1M' m . stream discard :: Monad m => m a -> m () {-# INLINE discard #-} discard m = m >> return () -- | /O(n)/ Monadic fold that discards the result foldM_ :: (Monad m, Vector v b) => (a -> b -> m a) -> a -> v b -> m () {-# INLINE foldM_ #-} foldM_ m z = discard . Stream.foldM m z . stream -- | /O(n)/ Monadic fold over non-empty vectors that discards the result fold1M_ :: (Monad m, Vector v a) => (a -> a -> m a) -> v a -> m () {-# INLINE fold1M_ #-} fold1M_ m = discard . Stream.fold1M m . stream -- | /O(n)/ Monadic fold with strict accumulator that discards the result foldM'_ :: (Monad m, Vector v b) => (a -> b -> m a) -> a -> v b -> m () {-# INLINE foldM'_ #-} foldM'_ m z = discard . Stream.foldM' m z . stream -- | /O(n)/ Monad fold over non-empty vectors with strict accumulator -- that discards the result fold1M'_ :: (Monad m, Vector v a) => (a -> a -> m a) -> v a -> m () {-# INLINE fold1M'_ #-} fold1M'_ m = discard . Stream.fold1M' m . stream -- Monadic sequencing -- ------------------ -- | Evaluate each action and collect the results sequence :: (Monad m, Vector v a, Vector v (m a)) => v (m a) -> m (v a) {-# INLINE sequence #-} sequence = mapM id -- | Evaluate each action and discard the results sequence_ :: (Monad m, Vector v (m a)) => v (m a) -> m () {-# INLINE sequence_ #-} sequence_ = mapM_ id -- Prefix sums (scans) -- ------------------- -- | /O(n)/ Prescan -- -- @ -- prescanl f z = 'init' . 'scanl' f z -- @ -- -- Example: @prescanl (+) 0 \<1,2,3,4\> = \<0,1,3,6\>@ -- prescanl :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE prescanl #-} prescanl f z = unstream . inplace (MStream.prescanl f z) . stream -- | /O(n)/ Prescan with strict accumulator prescanl' :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE prescanl' #-} prescanl' f z = unstream . inplace (MStream.prescanl' f z) . stream -- | /O(n)/ Scan -- -- @ -- postscanl f z = 'tail' . 'scanl' f z -- @ -- -- Example: @postscanl (+) 0 \<1,2,3,4\> = \<1,3,6,10\>@ -- postscanl :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE postscanl #-} postscanl f z = unstream . inplace (MStream.postscanl f z) . stream -- | /O(n)/ Scan with strict accumulator postscanl' :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE postscanl' #-} postscanl' f z = unstream . inplace (MStream.postscanl' f z) . stream -- | /O(n)/ Haskell-style scan -- -- > scanl f z <x1,...,xn> = <y1,...,y(n+1)> -- > where y1 = z -- > yi = f y(i-1) x(i-1) -- -- Example: @scanl (+) 0 \<1,2,3,4\> = \<0,1,3,6,10\>@ -- scanl :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE scanl #-} scanl f z = unstream . Stream.scanl f z . stream -- | /O(n)/ Haskell-style scan with strict accumulator scanl' :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a {-# INLINE scanl' #-} scanl' f z = unstream . Stream.scanl' f z . stream -- | /O(n)/ Scan over a non-empty vector -- -- > scanl f <x1,...,xn> = <y1,...,yn> -- > where y1 = x1 -- > yi = f y(i-1) xi -- scanl1 :: Vector v a => (a -> a -> a) -> v a -> v a {-# INLINE scanl1 #-} scanl1 f = unstream . inplace (MStream.scanl1 f) . stream -- | /O(n)/ Scan over a non-empty vector with a strict accumulator scanl1' :: Vector v a => (a -> a -> a) -> v a -> v a {-# INLINE scanl1' #-} scanl1' f = unstream . inplace (MStream.scanl1' f) . stream -- | /O(n)/ Right-to-left prescan -- -- @ -- prescanr f z = 'reverse' . 'prescanl' (flip f) z . 'reverse' -- @ -- prescanr :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE prescanr #-} prescanr f z = unstreamR . inplace (MStream.prescanl (flip f) z) . streamR -- | /O(n)/ Right-to-left prescan with strict accumulator prescanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE prescanr' #-} prescanr' f z = unstreamR . inplace (MStream.prescanl' (flip f) z) . streamR -- | /O(n)/ Right-to-left scan postscanr :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE postscanr #-} postscanr f z = unstreamR . inplace (MStream.postscanl (flip f) z) . streamR -- | /O(n)/ Right-to-left scan with strict accumulator postscanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE postscanr' #-} postscanr' f z = unstreamR . inplace (MStream.postscanl' (flip f) z) . streamR -- | /O(n)/ Right-to-left Haskell-style scan scanr :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE scanr #-} scanr f z = unstreamR . Stream.scanl (flip f) z . streamR -- | /O(n)/ Right-to-left Haskell-style scan with strict accumulator scanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b {-# INLINE scanr' #-} scanr' f z = unstreamR . Stream.scanl' (flip f) z . streamR -- | /O(n)/ Right-to-left scan over a non-empty vector scanr1 :: Vector v a => (a -> a -> a) -> v a -> v a {-# INLINE scanr1 #-} scanr1 f = unstreamR . inplace (MStream.scanl1 (flip f)) . streamR -- | /O(n)/ Right-to-left scan over a non-empty vector with a strict -- accumulator scanr1' :: Vector v a => (a -> a -> a) -> v a -> v a {-# INLINE scanr1' #-} scanr1' f = unstreamR . inplace (MStream.scanl1' (flip f)) . streamR -- Conversions - Lists -- ------------------------ -- | /O(n)/ Convert a vector to a list toList :: Vector v a => v a -> [a] {-# INLINE toList #-} toList = Stream.toList . stream -- | /O(n)/ Convert a list to a vector fromList :: Vector v a => [a] -> v a {-# INLINE fromList #-} fromList = unstream . Stream.fromList -- | /O(n)/ Convert the first @n@ elements of a list to a vector -- -- @ -- fromListN n xs = 'fromList' ('take' n xs) -- @ fromListN :: Vector v a => Int -> [a] -> v a {-# INLINE fromListN #-} fromListN n = unstream . Stream.fromListN n -- Conversions - Immutable vectors -- ------------------------------- -- | /O(n)/ Convert different vector types convert :: (Vector v a, Vector w a) => v a -> w a {-# INLINE convert #-} convert = unstream . stream -- Conversions - Mutable vectors -- ----------------------------- -- | /O(1)/ Unsafe convert a mutable vector to an immutable one without -- copying. The mutable vector may not be used after this operation. unsafeFreeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a -> m (v a) {-# INLINE unsafeFreeze #-} unsafeFreeze = basicUnsafeFreeze -- | /O(n)/ Yield an immutable copy of the mutable vector. freeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a -> m (v a) {-# INLINE freeze #-} freeze mv = unsafeFreeze =<< M.clone mv -- | /O(1)/ Unsafely convert an immutable vector to a mutable one without -- copying. The immutable vector may not be used after this operation. unsafeThaw :: (PrimMonad m, Vector v a) => v a -> m (Mutable v (PrimState m) a) {-# INLINE_STREAM unsafeThaw #-} unsafeThaw = basicUnsafeThaw -- | /O(n)/ Yield a mutable copy of the immutable vector. thaw :: (PrimMonad m, Vector v a) => v a -> m (Mutable v (PrimState m) a) {-# INLINE_STREAM thaw #-} thaw v = do mv <- M.unsafeNew (length v) unsafeCopy mv v return mv {-# RULES "unsafeThaw/new [Vector]" forall p. unsafeThaw (new p) = New.runPrim p "thaw/new [Vector]" forall p. thaw (new p) = New.runPrim p #-} {- -- | /O(n)/ Yield a mutable vector containing copies of each vector in the -- list. thawMany :: (PrimMonad m, Vector v a) => [v a] -> m (Mutable v (PrimState m) a) {-# INLINE_STREAM thawMany #-} -- FIXME: add rule for (stream (new (New.create (thawMany vs)))) -- NOTE: We don't try to consume the list lazily as this wouldn't significantly -- change the space requirements anyway. thawMany vs = do mv <- M.new n thaw_loop mv vs return mv where n = List.foldl' (\k v -> k + length v) 0 vs thaw_loop mv [] = mv `seq` return () thaw_loop mv (v:vs) = do let n = length v unsafeCopy (M.unsafeTake n mv) v thaw_loop (M.unsafeDrop n mv) vs -} -- | /O(n)/ Copy an immutable vector into a mutable one. The two vectors must -- have the same length. copy :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a -> v a -> m () {-# INLINE copy #-} copy dst src = BOUNDS_CHECK(check) "copy" "length mismatch" (M.length dst == length src) $ unsafeCopy dst src -- | /O(n)/ Copy an immutable vector into a mutable one. The two vectors must -- have the same length. This is not checked. unsafeCopy :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a -> v a -> m () {-# INLINE unsafeCopy #-} unsafeCopy dst src = UNSAFE_CHECK(check) "unsafeCopy" "length mismatch" (M.length dst == length src) $ (dst `seq` src `seq` basicUnsafeCopy dst src) -- Conversions to/from Streams -- --------------------------- -- | /O(1)/ Convert a vector to a 'Stream' stream :: Vector v a => v a -> Stream a {-# INLINE_STREAM stream #-} stream v = v `seq` n `seq` (Stream.unfoldr get 0 `Stream.sized` Exact n) where n = length v -- NOTE: the False case comes first in Core so making it the recursive one -- makes the code easier to read {-# INLINE get #-} get i | i >= n = Nothing | otherwise = case basicUnsafeIndexM v i of Box x -> Just (x, i+1) -- | /O(n)/ Construct a vector from a 'Stream' unstream :: Vector v a => Stream a -> v a {-# INLINE unstream #-} unstream s = new (New.unstream s) {-# RULES "stream/unstream [Vector]" forall s. stream (new (New.unstream s)) = s "New.unstream/stream [Vector]" forall v. New.unstream (stream v) = clone v "clone/new [Vector]" forall p. clone (new p) = p "inplace [Vector]" forall (f :: forall m. Monad m => MStream m a -> MStream m a) m. New.unstream (inplace f (stream (new m))) = New.transform f m "uninplace [Vector]" forall (f :: forall m. Monad m => MStream m a -> MStream m a) m. stream (new (New.transform f m)) = inplace f (stream (new m)) #-} -- | /O(1)/ Convert a vector to a 'Stream', proceeding from right to left streamR :: Vector v a => v a -> Stream a {-# INLINE_STREAM streamR #-} streamR v = v `seq` n `seq` (Stream.unfoldr get n `Stream.sized` Exact n) where n = length v {-# INLINE get #-} get 0 = Nothing get i = let i' = i-1 in case basicUnsafeIndexM v i' of Box x -> Just (x, i') -- | /O(n)/ Construct a vector from a 'Stream', proceeding from right to left unstreamR :: Vector v a => Stream a -> v a {-# INLINE unstreamR #-} unstreamR s = new (New.unstreamR s) {-# RULES "streamR/unstreamR [Vector]" forall s. streamR (new (New.unstreamR s)) = s "New.unstreamR/streamR/new [Vector]" forall p. New.unstreamR (streamR (new p)) = p "New.unstream/streamR/new [Vector]" forall p. New.unstream (streamR (new p)) = New.modify M.reverse p "New.unstreamR/stream/new [Vector]" forall p. New.unstreamR (stream (new p)) = New.modify M.reverse p "inplace right [Vector]" forall (f :: forall m. Monad m => MStream m a -> MStream m a) m. New.unstreamR (inplace f (streamR (new m))) = New.transformR f m "uninplace right [Vector]" forall (f :: forall m. Monad m => MStream m a -> MStream m a) m. streamR (new (New.transformR f m)) = inplace f (streamR (new m)) #-} unstreamM :: (Monad m, Vector v a) => MStream m a -> m (v a) {-# INLINE_STREAM unstreamM #-} unstreamM s = do xs <- MStream.toList s return $ unstream $ Stream.unsafeFromList (MStream.size s) xs unstreamPrimM :: (PrimMonad m, Vector v a) => MStream m a -> m (v a) {-# INLINE_STREAM unstreamPrimM #-} unstreamPrimM s = M.munstream s >>= unsafeFreeze -- FIXME: the next two functions are only necessary for the specialisations unstreamPrimM_IO :: Vector v a => MStream IO a -> IO (v a) {-# INLINE unstreamPrimM_IO #-} unstreamPrimM_IO = unstreamPrimM unstreamPrimM_ST :: Vector v a => MStream (ST s) a -> ST s (v a) {-# INLINE unstreamPrimM_ST #-} unstreamPrimM_ST = unstreamPrimM {-# RULES "unstreamM[IO]" unstreamM = unstreamPrimM_IO "unstreamM[ST]" unstreamM = unstreamPrimM_ST #-} -- Recycling support -- ----------------- -- | Construct a vector from a monadic initialiser. new :: Vector v a => New v a -> v a {-# INLINE_STREAM new #-} new m = m `seq` runST (unsafeFreeze =<< New.run m) -- | Convert a vector to an initialiser which, when run, produces a copy of -- the vector. clone :: Vector v a => v a -> New v a {-# INLINE_STREAM clone #-} clone v = v `seq` New.create ( do mv <- M.new (length v) unsafeCopy mv v return mv) -- Comparisons -- ----------- -- | /O(n)/ Check if two vectors are equal. All 'Vector' instances are also -- instances of 'Eq' and it is usually more appropriate to use those. This -- function is primarily intended for implementing 'Eq' instances for new -- vector types. eq :: (Vector v a, Eq a) => v a -> v a -> Bool {-# INLINE eq #-} xs `eq` ys = stream xs == stream ys -- | /O(n)/ Compare two vectors lexicographically. All 'Vector' instances are -- also instances of 'Ord' and it is usually more appropriate to use those. This -- function is primarily intended for implementing 'Ord' instances for new -- vector types. cmp :: (Vector v a, Ord a) => v a -> v a -> Ordering {-# INLINE cmp #-} cmp xs ys = compare (stream xs) (stream ys) -- Show -- ---- -- | Generic definition of 'Prelude.showsPrec' showsPrec :: (Vector v a, Show a) => Int -> v a -> ShowS {-# INLINE showsPrec #-} showsPrec p v = showParen (p > 10) $ showString "fromList " . shows (toList v) -- | Generic definition of 'Text.Read.readPrec' readPrec :: (Vector v a, Read a) => Read.ReadPrec (v a) {-# INLINE readPrec #-} readPrec = Read.parens $ Read.prec 10 $ do Read.Ident "fromList" <- Read.lexP xs <- Read.readPrec return (fromList xs) -- Data and Typeable -- ----------------- -- | Generic definion of 'Data.Data.gfoldl' that views a 'Vector' as a -- list. gfoldl :: (Vector v a, Data a) => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> v a -> c (v a) {-# INLINE gfoldl #-} gfoldl f z v = z fromList `f` toList v mkType :: String -> DataType {-# INLINE mkType #-} mkType = mkNoRepType dataCast :: (Vector v a, Data a, Typeable1 v, Typeable1 t) => (forall d. Data d => c (t d)) -> Maybe (c (v a)) {-# INLINE dataCast #-} dataCast f = gcast1 f