#line 1 "Arr.lhs" {-# OPTIONS_GHC -fno-implicit-prelude -fno-bang-patterns #-} ----------------------------------------------------------------------------- -- | -- Module : GHC.Arr -- Copyright : (c) The University of Glasgow, 1994-2000 -- License : see libraries/base/LICENSE -- -- Maintainer : cvs-ghc@haskell.org -- Stability : internal -- Portability : non-portable (GHC extensions) -- -- GHC\'s array implementation. -- ----------------------------------------------------------------------------- -- #hide module GHC.Arr where import {-# SOURCE #-} GHC.Err ( error ) import GHC.Enum import GHC.Num import GHC.ST import GHC.Base import GHC.List import GHC.Show infixl 9 !, // default () -- | The 'Ix' class is used to map a contiguous subrange of values in -- a type onto integers. It is used primarily for array indexing -- (see "Data.Array", "Data.Array.IArray" and "Data.Array.MArray"). -- -- The first argument @(l,u)@ of each of these operations is a pair -- specifying the lower and upper bounds of a contiguous subrange of values. -- -- An implementation is entitled to assume the following laws about these -- operations: -- -- * @'inRange' (l,u) i == 'elem' i ('range' (l,u))@ -- -- * @'range' (l,u) '!!' 'index' (l,u) i == i@, when @'inRange' (l,u) i@ -- -- * @'map' ('index' (l,u)) ('range' (l,u))) == [0..'rangeSize' (l,u)-1]@ -- -- * @'rangeSize' (l,u) == 'length' ('range' (l,u))@ -- -- Minimal complete instance: 'range', 'index' and 'inRange'. -- class (Ord a) => Ix a where -- | The list of values in the subrange defined by a bounding pair. range :: (a,a) -> [a] -- | The position of a subscript in the subrange. index :: (a,a) -> a -> Int -- | Like 'index', but without checking that the value is in range. unsafeIndex :: (a,a) -> a -> Int -- | Returns 'True' the given subscript lies in the range defined -- the bounding pair. inRange :: (a,a) -> a -> Bool -- | The size of the subrange defined by a bounding pair. rangeSize :: (a,a) -> Int -- | like 'rangeSize', but without checking that the upper bound is -- in range. unsafeRangeSize :: (a,a) -> Int -- Must specify one of index, unsafeIndex index b i | inRange b i = unsafeIndex b i | otherwise = error "Error in array index" unsafeIndex b i = index b i rangeSize b@(_l,h) | inRange b h = unsafeIndex b h + 1 | otherwise = 0 -- This case is only here to -- check for an empty range -- NB: replacing (inRange b h) by (l <= h) fails for -- tuples. E.g. (1,2) <= (2,1) but the range is empty unsafeRangeSize b@(_l,h) = unsafeIndex b h + 1 -- abstract these errors from the relevant index functions so that -- the guts of the function will be small enough to inline. {-# NOINLINE indexError #-} indexError :: Show a => (a,a) -> a -> String -> b indexError rng i tp = error (showString "Ix{" . showString tp . showString "}.index: Index " . showParen True (showsPrec 0 i) . showString " out of range " $ showParen True (showsPrec 0 rng) "") ---------------------------------------------------------------------- instance Ix Char where {-# INLINE range #-} range (m,n) = [m..n] {-# INLINE unsafeIndex #-} unsafeIndex (m,_n) i = fromEnum i - fromEnum m index b i | inRange b i = unsafeIndex b i | otherwise = indexError b i "Char" inRange (m,n) i = m <= i && i <= n ---------------------------------------------------------------------- instance Ix Int where {-# INLINE range #-} -- The INLINE stops the build in the RHS from getting inlined, -- so that callers can fuse with the result of range range (m,n) = [m..n] {-# INLINE unsafeIndex #-} unsafeIndex (m,_n) i = i - m index b i | inRange b i = unsafeIndex b i | otherwise = indexError b i "Int" {-# INLINE inRange #-} inRange (I# m,I# n) (I# i) = m <=# i && i <=# n ---------------------------------------------------------------------- instance Ix Integer where {-# INLINE range #-} range (m,n) = [m..n] {-# INLINE unsafeIndex #-} unsafeIndex (m,_n) i = fromInteger (i - m) index b i | inRange b i = unsafeIndex b i | otherwise = indexError b i "Integer" inRange (m,n) i = m <= i && i <= n ---------------------------------------------------------------------- instance Ix Bool where -- as derived {-# INLINE range #-} range (m,n) = [m..n] {-# INLINE unsafeIndex #-} unsafeIndex (l,_) i = fromEnum i - fromEnum l index b i | inRange b i = unsafeIndex b i | otherwise = indexError b i "Bool" inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u ---------------------------------------------------------------------- instance Ix Ordering where -- as derived {-# INLINE range #-} range (m,n) = [m..n] {-# INLINE unsafeIndex #-} unsafeIndex (l,_) i = fromEnum i - fromEnum l index b i | inRange b i = unsafeIndex b i | otherwise = indexError b i "Ordering" inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u ---------------------------------------------------------------------- instance Ix () where {-# INLINE range #-} range ((), ()) = [()] {-# INLINE unsafeIndex #-} unsafeIndex ((), ()) () = 0 {-# INLINE inRange #-} inRange ((), ()) () = True {-# INLINE index #-} index b i = unsafeIndex b i ---------------------------------------------------------------------- instance (Ix a, Ix b) => Ix (a, b) where -- as derived {-# SPECIALISE instance Ix (Int,Int) #-} {- INLINE range #-} range ((l1,l2),(u1,u2)) = [ (i1,i2) | i1 <- range (l1,u1), i2 <- range (l2,u2) ] {- INLINE unsafeIndex #-} unsafeIndex ((l1,l2),(u1,u2)) (i1,i2) = unsafeIndex (l1,u1) i1 * unsafeRangeSize (l2,u2) + unsafeIndex (l2,u2) i2 {- INLINE inRange #-} inRange ((l1,l2),(u1,u2)) (i1,i2) = inRange (l1,u1) i1 && inRange (l2,u2) i2 -- Default method for index ---------------------------------------------------------------------- instance (Ix a1, Ix a2, Ix a3) => Ix (a1,a2,a3) where {-# SPECIALISE instance Ix (Int,Int,Int) #-} range ((l1,l2,l3),(u1,u2,u3)) = [(i1,i2,i3) | i1 <- range (l1,u1), i2 <- range (l2,u2), i3 <- range (l3,u3)] unsafeIndex ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) = unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * ( unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * ( unsafeIndex (l1,u1) i1)) inRange ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) = inRange (l1,u1) i1 && inRange (l2,u2) i2 && inRange (l3,u3) i3 -- Default method for index ---------------------------------------------------------------------- instance (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1,a2,a3,a4) where range ((l1,l2,l3,l4),(u1,u2,u3,u4)) = [(i1,i2,i3,i4) | i1 <- range (l1,u1), i2 <- range (l2,u2), i3 <- range (l3,u3), i4 <- range (l4,u4)] unsafeIndex ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) = unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * ( unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * ( unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * ( unsafeIndex (l1,u1) i1))) inRange ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) = inRange (l1,u1) i1 && inRange (l2,u2) i2 && inRange (l3,u3) i3 && inRange (l4,u4) i4 -- Default method for index instance (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1,a2,a3,a4,a5) where range ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) = [(i1,i2,i3,i4,i5) | i1 <- range (l1,u1), i2 <- range (l2,u2), i3 <- range (l3,u3), i4 <- range (l4,u4), i5 <- range (l5,u5)] unsafeIndex ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) = unsafeIndex (l5,u5) i5 + unsafeRangeSize (l5,u5) * ( unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * ( unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * ( unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * ( unsafeIndex (l1,u1) i1)))) inRange ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) = inRange (l1,u1) i1 && inRange (l2,u2) i2 && inRange (l3,u3) i3 && inRange (l4,u4) i4 && inRange (l5,u5) i5 -- Default method for index type IPr = (Int, Int) -- | The type of immutable non-strict (boxed) arrays -- with indices in @i@ and elements in @e@. data Ix i => Array i e = Array !i !i (Array# e) -- | Mutable, boxed, non-strict arrays in the 'ST' monad. The type -- arguments are as follows: -- -- * @s@: the state variable argument for the 'ST' type -- -- * @i@: the index type of the array (should be an instance of 'Ix') -- -- * @e@: the element type of the array. -- data STArray s i e = STArray !i !i (MutableArray# s e) -- No Ix context for STArray. They are stupid, -- and force an Ix context on the equality instance. -- Just pointer equality on mutable arrays: instance Eq (STArray s i e) where STArray _ _ arr1# == STArray _ _ arr2# = sameMutableArray# arr1# arr2# {-# NOINLINE arrEleBottom #-} arrEleBottom :: a arrEleBottom = error "(Array.!): undefined array element" -- | Construct an array with the specified bounds and containing values -- for given indices within these bounds. -- -- The array is undefined (i.e. bottom) if any index in the list is -- out of bounds. The Haskell 98 Report further specifies that if any -- two associations in the list have the same index, the value at that -- index is undefined (i.e. bottom). However in GHC's implementation, -- the value at such an index is the value part of the last association -- with that index in the list. -- -- Because the indices must be checked for these errors, 'array' is -- strict in the bounds argument and in the indices of the association -- list, but nonstrict in the values. Thus, recurrences such as the -- following are possible: -- -- > a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i <- [2..100]]) -- -- Not every index within the bounds of the array need appear in the -- association list, but the values associated with indices that do not -- appear will be undefined (i.e. bottom). -- -- If, in any dimension, the lower bound is greater than the upper bound, -- then the array is legal, but empty. Indexing an empty array always -- gives an array-bounds error, but 'bounds' still yields the bounds -- with which the array was constructed. {-# INLINE array #-} array :: Ix i => (i,i) -- ^ a pair of /bounds/, each of the index type -- of the array. These bounds are the lowest and -- highest indices in the array, in that order. -- For example, a one-origin vector of length -- '10' has bounds '(1,10)', and a one-origin '10' -- by '10' matrix has bounds '((1,1),(10,10))'. -> [(i, e)] -- ^ a list of /associations/ of the form -- (/index/, /value/). Typically, this list will -- be expressed as a comprehension. An -- association '(i, x)' defines the value of -- the array at index 'i' to be 'x'. -> Array i e array (l,u) ies = unsafeArray (l,u) [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE unsafeArray #-} unsafeArray :: Ix i => (i,i) -> [(Int, e)] -> Array i e unsafeArray (l,u) ies = runST (ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# arrEleBottom s1# of { (# s2#, marr# #) -> foldr (fill marr#) (done l u marr#) ies s2# }}) {-# INLINE fill #-} fill :: MutableArray# s e -> (Int, e) -> STRep s a -> STRep s a fill marr# (I# i#, e) next s1# = case writeArray# marr# i# e s1# of { s2# -> next s2# } {-# INLINE done #-} done :: Ix i => i -> i -> MutableArray# s e -> STRep s (Array i e) done l u marr# s1# = case unsafeFreezeArray# marr# s1# of { (# s2#, arr# #) -> (# s2#, Array l u arr# #) } -- This is inefficient and I'm not sure why: -- listArray (l,u) es = unsafeArray (l,u) (zip [0 .. rangeSize (l,u) - 1] es) -- The code below is better. It still doesn't enable foldr/build -- transformation on the list of elements; I guess it's impossible -- using mechanisms currently available. -- | Construct an array from a pair of bounds and a list of values in -- index order. {-# INLINE listArray #-} listArray :: Ix i => (i,i) -> [e] -> Array i e listArray (l,u) es = runST (ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# arrEleBottom s1# of { (# s2#, marr# #) -> let fillFromList i# xs s3# | i# ==# n# = s3# | otherwise = case xs of [] -> s3# y:ys -> case writeArray# marr# i# y s3# of { s4# -> fillFromList (i# +# 1#) ys s4# } in case fillFromList 0# es s2# of { s3# -> done l u marr# s3# }}}) -- | The value at the given index in an array. {-# INLINE (!) #-} (!) :: Ix i => Array i e -> i -> e arr@(Array l u _) ! i = unsafeAt arr (index (l,u) i) {-# INLINE unsafeAt #-} unsafeAt :: Ix i => Array i e -> Int -> e unsafeAt (Array _ _ arr#) (I# i#) = case indexArray# arr# i# of (# e #) -> e -- | The bounds with which an array was constructed. {-# INLINE bounds #-} bounds :: Ix i => Array i e -> (i,i) bounds (Array l u _) = (l,u) -- | The list of indices of an array in ascending order. {-# INLINE indices #-} indices :: Ix i => Array i e -> [i] indices (Array l u _) = range (l,u) -- | The list of elements of an array in index order. {-# INLINE elems #-} elems :: Ix i => Array i e -> [e] elems arr@(Array l u _) = [unsafeAt arr i | i <- [0 .. rangeSize (l,u) - 1]] -- | The list of associations of an array in index order. {-# INLINE assocs #-} assocs :: Ix i => Array i e -> [(i, e)] assocs arr@(Array l u _) = [(i, unsafeAt arr (unsafeIndex (l,u) i)) | i <- range (l,u)] -- | The 'accumArray' deals with repeated indices in the association -- list using an /accumulating function/ which combines the values of -- associations with the same index. -- For example, given a list of values of some index type, @hist@ -- produces a histogram of the number of occurrences of each index within -- a specified range: -- -- > hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b -- > hist bnds is = accumArray (+) 0 bnds [(i, 1) | i<-is, inRange bnds i] -- -- If the accumulating function is strict, then 'accumArray' is strict in -- the values, as well as the indices, in the association list. Thus, -- unlike ordinary arrays built with 'array', accumulated arrays should -- not in general be recursive. {-# INLINE accumArray #-} accumArray :: Ix i => (e -> a -> e) -- ^ accumulating function -> e -- ^ initial value -> (i,i) -- ^ bounds of the array -> [(i, a)] -- ^ association list -> Array i e accumArray f init (l,u) ies = unsafeAccumArray f init (l,u) [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE unsafeAccumArray #-} unsafeAccumArray :: Ix i => (e -> a -> e) -> e -> (i,i) -> [(Int, a)] -> Array i e unsafeAccumArray f init (l,u) ies = runST (ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# init s1# of { (# s2#, marr# #) -> foldr (adjust f marr#) (done l u marr#) ies s2# }}) {-# INLINE adjust #-} adjust :: (e -> a -> e) -> MutableArray# s e -> (Int, a) -> STRep s b -> STRep s b adjust f marr# (I# i#, new) next s1# = case readArray# marr# i# s1# of { (# s2#, old #) -> case writeArray# marr# i# (f old new) s2# of { s3# -> next s3# }} -- | Constructs an array identical to the first argument except that it has -- been updated by the associations in the right argument. -- For example, if @m@ is a 1-origin, @n@ by @n@ matrix, then -- -- > m//[((i,i), 0) | i <- [1..n]] -- -- is the same matrix, except with the diagonal zeroed. -- -- Repeated indices in the association list are handled as for 'array': -- Haskell 98 specifies that the resulting array is undefined (i.e. bottom), -- but GHC's implementation uses the last association for each index. {-# INLINE (//) #-} (//) :: Ix i => Array i e -> [(i, e)] -> Array i e arr@(Array l u _) // ies = unsafeReplace arr [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE unsafeReplace #-} unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e unsafeReplace arr@(Array l u _) ies = runST (do STArray _ _ marr# <- thawSTArray arr ST (foldr (fill marr#) (done l u marr#) ies)) -- | @'accum' f@ takes an array and an association list and accumulates -- pairs from the list into the array with the accumulating function @f@. -- Thus 'accumArray' can be defined using 'accum': -- -- > accumArray f z b = accum f (array b [(i, z) | i <- range b]) -- {-# INLINE accum #-} accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e accum f arr@(Array l u _) ies = unsafeAccum f arr [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE unsafeAccum #-} unsafeAccum :: Ix i => (e -> a -> e) -> Array i e -> [(Int, a)] -> Array i e unsafeAccum f arr@(Array l u _) ies = runST (do STArray _ _ marr# <- thawSTArray arr ST (foldr (adjust f marr#) (done l u marr#) ies)) {-# INLINE amap #-} amap :: Ix i => (a -> b) -> Array i a -> Array i b amap f arr@(Array l u _) = unsafeArray (l,u) [(i, f (unsafeAt arr i)) | i <- [0 .. rangeSize (l,u) - 1]] -- | 'ixmap' allows for transformations on array indices. -- It may be thought of as providing function composition on the right -- with the mapping that the original array embodies. -- -- A similar transformation of array values may be achieved using 'fmap' -- from the 'Array' instance of the 'Functor' class. {-# INLINE ixmap #-} ixmap :: (Ix i, Ix j) => (i,i) -> (i -> j) -> Array j e -> Array i e ixmap (l,u) f arr = unsafeArray (l,u) [(unsafeIndex (l,u) i, arr ! f i) | i <- range (l,u)] {-# INLINE eqArray #-} eqArray :: (Ix i, Eq e) => Array i e -> Array i e -> Bool eqArray arr1@(Array l1 u1 _) arr2@(Array l2 u2 _) = if rangeSize (l1,u1) == 0 then rangeSize (l2,u2) == 0 else l1 == l2 && u1 == u2 && and [unsafeAt arr1 i == unsafeAt arr2 i | i <- [0 .. rangeSize (l1,u1) - 1]] {-# INLINE cmpArray #-} cmpArray :: (Ix i, Ord e) => Array i e -> Array i e -> Ordering cmpArray arr1 arr2 = compare (assocs arr1) (assocs arr2) {-# INLINE cmpIntArray #-} cmpIntArray :: Ord e => Array Int e -> Array Int e -> Ordering cmpIntArray arr1@(Array l1 u1 _) arr2@(Array l2 u2 _) = if rangeSize (l1,u1) == 0 then if rangeSize (l2,u2) == 0 then EQ else LT else if rangeSize (l2,u2) == 0 then GT else case compare l1 l2 of EQ -> foldr cmp (compare u1 u2) [0 .. rangeSize (l1, min u1 u2) - 1] other -> other where cmp i rest = case compare (unsafeAt arr1 i) (unsafeAt arr2 i) of EQ -> rest other -> other {-# RULES "cmpArray/Int" cmpArray = cmpIntArray #-} instance Ix i => Functor (Array i) where fmap = amap instance (Ix i, Eq e) => Eq (Array i e) where (==) = eqArray instance (Ix i, Ord e) => Ord (Array i e) where compare = cmpArray instance (Ix a, Show a, Show b) => Show (Array a b) where showsPrec p a = showParen (p > appPrec) $ showString "array " . showsPrec appPrec1 (bounds a) . showChar ' ' . showsPrec appPrec1 (assocs a) -- Precedence of 'array' is the precedence of application -- The Read instance is in GHC.Read {-# INLINE newSTArray #-} newSTArray :: Ix i => (i,i) -> e -> ST s (STArray s i e) newSTArray (l,u) init = ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# init s1# of { (# s2#, marr# #) -> (# s2#, STArray l u marr# #) }} {-# INLINE boundsSTArray #-} boundsSTArray :: STArray s i e -> (i,i) boundsSTArray (STArray l u _) = (l,u) {-# INLINE readSTArray #-} readSTArray :: Ix i => STArray s i e -> i -> ST s e readSTArray marr@(STArray l u _) i = unsafeReadSTArray marr (index (l,u) i) {-# INLINE unsafeReadSTArray #-} unsafeReadSTArray :: Ix i => STArray s i e -> Int -> ST s e unsafeReadSTArray (STArray _ _ marr#) (I# i#) = ST $ \s1# -> readArray# marr# i# s1# {-# INLINE writeSTArray #-} writeSTArray :: Ix i => STArray s i e -> i -> e -> ST s () writeSTArray marr@(STArray l u _) i e = unsafeWriteSTArray marr (index (l,u) i) e {-# INLINE unsafeWriteSTArray #-} unsafeWriteSTArray :: Ix i => STArray s i e -> Int -> e -> ST s () unsafeWriteSTArray (STArray _ _ marr#) (I# i#) e = ST $ \s1# -> case writeArray# marr# i# e s1# of { s2# -> (# s2#, () #) } freezeSTArray :: Ix i => STArray s i e -> ST s (Array i e) freezeSTArray (STArray l u marr#) = ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# arrEleBottom s1# of { (# s2#, marr'# #) -> let copy i# s3# | i# ==# n# = s3# | otherwise = case readArray# marr# i# s3# of { (# s4#, e #) -> case writeArray# marr'# i# e s4# of { s5# -> copy (i# +# 1#) s5# }} in case copy 0# s2# of { s3# -> case unsafeFreezeArray# marr'# s3# of { (# s4#, arr# #) -> (# s4#, Array l u arr# #) }}}} {-# INLINE unsafeFreezeSTArray #-} unsafeFreezeSTArray :: Ix i => STArray s i e -> ST s (Array i e) unsafeFreezeSTArray (STArray l u marr#) = ST $ \s1# -> case unsafeFreezeArray# marr# s1# of { (# s2#, arr# #) -> (# s2#, Array l u arr# #) } thawSTArray :: Ix i => Array i e -> ST s (STArray s i e) thawSTArray (Array l u arr#) = ST $ \s1# -> case rangeSize (l,u) of { I# n# -> case newArray# n# arrEleBottom s1# of { (# s2#, marr# #) -> let copy i# s3# | i# ==# n# = s3# | otherwise = case indexArray# arr# i# of { (# e #) -> case writeArray# marr# i# e s3# of { s4# -> copy (i# +# 1#) s4# }} in case copy 0# s2# of { s3# -> (# s3#, STArray l u marr# #) }}} {-# INLINE unsafeThawSTArray #-} unsafeThawSTArray :: Ix i => Array i e -> ST s (STArray s i e) unsafeThawSTArray (Array l u arr#) = ST $ \s1# -> case unsafeThawArray# arr# s1# of { (# s2#, marr# #) -> (# s2#, STArray l u marr# #) }