{-# LANGUAGE CPP, MultiParamTypeClasses #-} {- | Module : Data.ArrayBZ.Internals.IArray Copyright : (c) The University of Glasgow 2001 & (c) 2006 Bulat Ziganshin License : BSD3 Maintainer : Bulat Ziganshin <Bulat.Ziganshin@gmail.com> Stability : experimental Portability: GHC/Hugs Immutable arrays: class, general algorithms and Show/Ord/Eq implementations -} module Data.ArrayBZ.Internals.IArray where import Data.Ix #ifdef __GLASGOW_HASKELL__ import GHC.Arr ( unsafeIndex ) #endif #ifdef __HUGS__ import Hugs.Array ( unsafeIndex ) #endif ----------------------------------------------------------------------------- -- Class of immutable arrays -- | Class of array types with immutable bounds -- (even if the array elements are mutable). class HasBounds a where -- | Extracts the bounds of an array bounds :: Ix i => a i e -> (i,i) {- | Class of immutable array types. An array type has the form @(a i e)@ where @a@ is the array type constructor (kind @* -> * -> *@), @i@ is the index type (a member of the class 'Ix'), and @e@ is the element type. The @IArray@ class is parameterised over both @a@ and @e@, so that instances specialised to certain element types can be defined. -} class HasBounds a => IArray a e where unsafeArray :: Ix i => (i,i) -> [(Int, e)] -> a i e unsafeAt :: Ix i => a i e -> Int -> e unsafeReplace :: Ix i => a i e -> [(Int, e)] -> a i e unsafeAccum :: Ix i => (e -> e' -> e) -> a i e -> [(Int, e')] -> a i e unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i,i) -> [(Int, e')] -> a i e ----------------------------------------------------------------------------- -- Algorithms on immutable arrays {-# INLINE array #-} {-| Constructs an immutable array from a pair of bounds and a list of initial associations. The bounds are specified as a pair of the lowest and highest bounds in the array respectively. 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)). An association is a pair of the form @(i,x)@, which defines the value of the array at index @i@ to be @x@. The array is undefined if any index in the list is out of bounds. If any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for 'Array' the value at such indices is bottom.) Because the indices must be checked for these errors, 'array' is strict in the bounds argument and in the indices of the association list. Whether @array@ is strict or non-strict in the elements depends on the array type: 'Data.Array.Array' is a non-strict array type, but all of the 'Data.Array.Unboxed.UArray' arrays are strict. Thus in a non-strict array, 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. 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. -} array :: (IArray a e, Ix i) => (i,i) -- ^ bounds of the array: (lowest,highest) -> [(i, e)] -- ^ list of associations -> a i e array (l,u) ies = unsafeArray (l,u) [(index (l,u) i, e) | (i, e) <- ies] -- Since unsafeFreeze is not guaranteed to be only a cast, we will -- use unsafeArray and zip instead of a specialized loop to implement -- listArray, unlike Array.listArray, even though it generates some -- unnecessary heap allocation. Will use the loop only when we have -- fast unsafeFreeze, namely for Array and UArray (well, they cover -- almost all cases). {-# INLINE listArray #-} -- | Constructs an immutable array from a list of initial elements. -- The list gives the elements of the array in ascending order -- beginning with the lowest index. listArray :: (IArray a e, Ix i) => (i,i) -> [e] -> a i e listArray (l,u) es = unsafeArray (l,u) (zip [0 .. rangeSize (l,u) - 1] es) {-# INLINE (!) #-} -- | Returns the element of an immutable array at the specified index. (!) :: (IArray a e, Ix i) => a i e -> i -> e arr ! i = case bounds arr of (l,u) -> unsafeAt arr (index (l,u) i) {-# INLINE indices #-} -- | Returns a list of all the valid indices in an array. indices :: (HasBounds a, Ix i) => a i e -> [i] indices arr = case bounds arr of (l,u) -> range (l,u) {-# INLINE elems #-} -- | Returns a list of all the elements of an array, in the same order -- as their indices. elems :: (IArray a e, Ix i) => a i e -> [e] elems arr = case bounds arr of (l,u) -> [unsafeAt arr i | i <- [0 .. rangeSize (l,u) - 1]] {-# INLINE assocs #-} -- | Returns the contents of an array as a list of associations. assocs :: (IArray a e, Ix i) => a i e -> [(i, e)] assocs arr = case bounds arr of (l,u) -> [(i, unsafeAt arr (unsafeIndex (l,u) i)) | i <- range (l,u)] {-# INLINE accumArray #-} {-| Constructs an immutable array from a list of associations. Unlike 'array', the same index is allowed to occur multiple times in the list of associations; an /accumulating function/ is used to combine the values of elements 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] -} accumArray :: (IArray a e, Ix i) => (e -> e' -> e) -- ^ An accumulating function -> e -- ^ A default element -> (i,i) -- ^ The bounds of the array -> [(i, e')] -- ^ List of associations -> a i e -- ^ Returns: the array accumArray f initial (l,u) ies = unsafeAccumArray f initial (l,u) [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE (//) #-} {-| Takes an array and a list of pairs and returns an array identical to the left 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. As with the 'array' function, if any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for 'Array' the value at such indices is bottom.) For most array types, this operation is O(/n/) where /n/ is the size of the array. However, the 'Data.Array.Diff.DiffArray' type provides this operation with complexity linear in the number of updates. -} (//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e arr // ies = case bounds arr of (l,u) -> unsafeReplace arr [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE accum #-} {-| @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]) -} accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a i e accum f arr ies = case bounds arr of (l,u) -> unsafeAccum f arr [(index (l,u) i, e) | (i, e) <- ies] {-# INLINE amap #-} -- | Returns a new array derived from the original array by applying a -- function to each of the elements. amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e amap f arr = case bounds arr of (l,u) -> unsafeArray (l,u) [(i, f (unsafeAt arr i)) | i <- [0 .. rangeSize (l,u) - 1]] {-# INLINE ixmap #-} -- | Returns a new array derived from the original array by applying a -- function to each of the indices. ixmap :: (IArray a e, Ix i, Ix j) => (i,i) -> (i -> j) -> a j e -> a i e ixmap (l,u) f arr = unsafeArray (l,u) [(unsafeIndex (l,u) i, arr ! f i) | i <- range (l,u)] ----------------------------------------------------------------------------- -- Implementation of Show instance {-# SPECIALISE showsIArray :: (IArray a e, Ix i, Show i, Show e) => Int -> a i e -> ShowS #-} showsIArray :: (IArray a e, Ix i, Show i, Show e) => Int -> a i e -> ShowS showsIArray p a = showParen (p > 9) $ showString "array " . shows (bounds a) . showChar ' ' . shows (assocs a) ----------------------------------------------------------------------------- -- Implementation of Eq/Ord instances {-# INLINE eqIArray #-} eqIArray :: (IArray a e, Ix i, Eq e) => a i e -> a i e -> Bool eqIArray arr1 arr2 = case bounds arr1 of { (l1,u1) -> case bounds arr2 of { (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 cmpIArray #-} cmpIArray :: (IArray a e, Ix i, Ord e) => a i e -> a i e -> Ordering cmpIArray arr1 arr2 = compare (assocs arr1) (assocs arr2) {-# INLINE cmpIntIArray #-} cmpIntIArray :: (IArray a e, Ord e) => a Int e -> a Int e -> Ordering cmpIntIArray arr1 arr2 = case bounds arr1 of { (l1,u1) -> case bounds arr2 of { (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 "cmpIArray/Int" cmpIArray = cmpIntIArray #-}