content: {-# LANGUAGE BangPatterns, CPP, RankNTypes, MagicHash, UnboxedTuples, MultiParamTypeClasses, FlexibleInstances, FlexibleContexts, DeriveDataTypeable, UnliftedFFITypes #-}
  #if __GLASGOW_HASKELL__ >= 708
  {-# LANGUAGE RoleAnnotations #-}
  #endif
  {-# OPTIONS_HADDOCK hide #-}
  
  -----------------------------------------------------------------------------
  -- |
  -- Module      :  Data.Array.Base
  -- Copyright   :  (c) The University of Glasgow 2001
  -- License     :  BSD-style (see the file libraries/base/LICENSE)
  --
  -- Maintainer  :  libraries@haskell.org
  -- Stability   :  experimental
  -- Portability :  non-portable (MPTCs, uses Control.Monad.ST)
  --
  -- Basis for IArray and MArray.  Not intended for external consumption;
  -- use IArray or MArray instead.
  --
  -----------------------------------------------------------------------------
  
  module Data.Array.Base where
  
  import Control.Monad.ST.Lazy ( strictToLazyST )
  import qualified Control.Monad.ST.Lazy as Lazy (ST)
  import Data.Ix ( Ix, range, index, rangeSize )
  import Foreign.C.Types
  import Foreign.StablePtr
  
  import Data.Char
  import GHC.Arr          ( STArray )
  import qualified GHC.Arr as Arr
  import qualified GHC.Arr as ArrST
  import GHC.ST           ( ST(..), runST )
  import GHC.Base         ( IO(..) )
  import GHC.Exts
  import GHC.Ptr          ( nullPtr, nullFunPtr )
  import GHC.Stable       ( StablePtr(..) )
  #if !MIN_VERSION_base(4,6,0)
  import GHC.Exts         ( Word(..) )
  #endif
  import GHC.Int          ( Int8(..),  Int16(..),  Int32(..),  Int64(..) )
  import GHC.Word         ( Word8(..), Word16(..), Word32(..), Word64(..) )
  import GHC.IO           ( stToIO )
  import GHC.IOArray      ( IOArray(..),
                            newIOArray, unsafeReadIOArray, unsafeWriteIOArray )
  import Data.Typeable
  
  #include "MachDeps.h"
  
  -----------------------------------------------------------------------------
  -- Class of immutable arrays
  
  {- | 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 IArray a e where
      -- | Extracts the bounds of an immutable array
      bounds           :: Ix i => a i e -> (i,i)
      numElements      :: Ix i => a i e -> Int
      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
  
      unsafeReplace arr ies = runST (unsafeReplaceST arr ies >>= unsafeFreeze)
      unsafeAccum f arr ies = runST (unsafeAccumST f arr ies >>= unsafeFreeze)
      unsafeAccumArray f e lu ies = runST (unsafeAccumArrayST f e lu ies >>= unsafeFreeze)
  
  {-# INLINE safeRangeSize #-}
  safeRangeSize :: Ix i => (i, i) -> Int
  safeRangeSize (l,u) = let r = rangeSize (l, u)
                        in if r < 0 then error "Negative range size"
                                    else r
  
  {-# INLINE safeIndex #-}
  safeIndex :: Ix i => (i, i) -> Int -> i -> Int
  safeIndex (l,u) n i = let i' = index (l,u) i
                        in if (0 <= i') && (i' < n)
                           then i'
                           else error ("Error in array index; " ++ show i' ++
                                       " not in range [0.." ++ show n ++ ")")
  
  {-# INLINE unsafeReplaceST #-}
  unsafeReplaceST :: (IArray a e, Ix i) => a i e -> [(Int, e)] -> ST s (STArray s i e)
  unsafeReplaceST arr ies = do
      marr <- thaw arr
      sequence_ [unsafeWrite marr i e | (i, e) <- ies]
      return marr
  
  {-# INLINE unsafeAccumST #-}
  unsafeAccumST :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(Int, e')] -> ST s (STArray s i e)
  unsafeAccumST f arr ies = do
      marr <- thaw arr
      sequence_ [do old <- unsafeRead marr i
                    unsafeWrite marr i (f old new)
                | (i, new) <- ies]
      return marr
  
  {-# INLINE unsafeAccumArrayST #-}
  unsafeAccumArrayST :: Ix i => (e -> e' -> e) -> e -> (i,i) -> [(Int, e')] -> ST s (STArray s i e)
  unsafeAccumArrayST f e (l,u) ies = do
      marr <- newArray (l,u) e
      sequence_ [do old <- unsafeRead marr i
                    unsafeWrite marr i (f old new)
                | (i, new) <- ies]
      return marr
  
  
  {-# 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
      = let n = safeRangeSize (l,u)
        in unsafeArray (l,u)
                       [(safeIndex (l,u) n 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 [1] 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 =
      let n = safeRangeSize (l,u)
      in unsafeArray (l,u) (zip [0 .. n - 1] es)
  
  {-# INLINE listArrayST #-}
  listArrayST :: Ix i => (i,i) -> [e] -> ST s (STArray s i e)
  listArrayST (l,u) es = do
      marr <- newArray_ (l,u)
      let n = safeRangeSize (l,u)
      let fillFromList i xs | i == n    = return ()
                            | otherwise = case xs of
              []   -> return ()
              y:ys -> unsafeWrite marr i y >> fillFromList (i+1) ys
      fillFromList 0 es
      return marr
  
  {-# RULES
  "listArray/Array" listArray =
      \lu es -> runST (listArrayST lu es >>= ArrST.unsafeFreezeSTArray)
      #-}
  
  {-# INLINE listUArrayST #-}
  listUArrayST :: (MArray (STUArray s) e (ST s), Ix i)
               => (i,i) -> [e] -> ST s (STUArray s i e)
  listUArrayST (l,u) es = do
      marr <- newArray_ (l,u)
      let n = safeRangeSize (l,u)
      let fillFromList i xs | i == n    = return ()
                            | otherwise = case xs of
              []   -> return ()
              y:ys -> unsafeWrite marr i y >> fillFromList (i+1) ys
      fillFromList 0 es
      return marr
  
  -- I don't know how to write a single rule for listUArrayST, because
  -- the type looks like constrained over 's', which runST doesn't
  -- like. In fact all MArray (STUArray s) instances are polymorphic
  -- wrt. 's', but runST can't know that.
  --
  -- More precisely, we'd like to write this:
  --   listUArray :: (forall s. MArray (STUArray s) e (ST s), Ix i)
  --              => (i,i) -> [e] -> UArray i e
  --   listUArray lu = runST (listUArrayST lu es >>= unsafeFreezeSTUArray)
  --   {-# RULES listArray = listUArray
  -- Then we could call listUArray at any type 'e' that had a suitable
  -- MArray instance.  But sadly we can't, because we don't have quantified
  -- constraints.  Hence the mass of rules below.
  
  -- I would like also to write a rule for listUArrayST (or listArray or
  -- whatever) applied to unpackCString#. Unfortunately unpackCString#
  -- calls seem to be floated out, then floated back into the middle
  -- of listUArrayST, so I was not able to do this.
  
  type ListUArray e = forall i . Ix i => (i,i) -> [e] -> UArray i e
  
  {-# RULES
  "listArray/UArray/Bool"      listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Bool
  "listArray/UArray/Char"      listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Char
  "listArray/UArray/Int"       listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Int
  "listArray/UArray/Word"      listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Word
  "listArray/UArray/Ptr"       listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray (Ptr a)
  "listArray/UArray/FunPtr"    listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray (FunPtr a)
  "listArray/UArray/Float"     listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Float
  "listArray/UArray/Double"    listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Double
  "listArray/UArray/StablePtr" listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray (StablePtr a)
  "listArray/UArray/Int8"      listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Int8
  "listArray/UArray/Int16"     listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Int16
  "listArray/UArray/Int32"     listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Int32
  "listArray/UArray/Int64"     listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Int64
  "listArray/UArray/Word8"     listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Word8
  "listArray/UArray/Word16"    listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Word16
  "listArray/UArray/Word32"    listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Word32
  "listArray/UArray/Word64"    listArray
     = (\lu es -> runST (listUArrayST lu es >>= unsafeFreezeSTUArray)) :: ListUArray Word64
      #-}
  
  {-# 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 $ safeIndex (l,u) (numElements arr) i
  
  {-# INLINE indices #-}
  -- | Returns a list of all the valid indices in an array.
  indices :: (IArray a e, 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 .. numElements arr - 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, arr ! 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 initialValue (l,u) ies =
      let n = safeRangeSize (l, u)
      in unsafeAccumArray f initialValue (l,u)
                          [(safeIndex (l,u) n 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 diffarray package provides an array type
  for which this operation has 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 [ (safeIndex (l,u) (numElements arr) 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) -> let n = numElements arr
               in unsafeAccum f arr [(safeIndex (l,u) n 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) -> let n = numElements arr
               in unsafeArray (l,u) [ (i, f (unsafeAt arr i))
                                    | i <- [0 .. n - 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 =
      array (l,u) [(i, arr ! f i) | i <- range (l,u)]
  
  -----------------------------------------------------------------------------
  -- Normal polymorphic arrays
  
  instance IArray Arr.Array e where
      {-# INLINE bounds #-}
      bounds = Arr.bounds
      {-# INLINE numElements #-}
      numElements      = Arr.numElements
      {-# INLINE unsafeArray #-}
      unsafeArray      = Arr.unsafeArray
      {-# INLINE unsafeAt #-}
      unsafeAt         = Arr.unsafeAt
      {-# INLINE unsafeReplace #-}
      unsafeReplace    = Arr.unsafeReplace
      {-# INLINE unsafeAccum #-}
      unsafeAccum      = Arr.unsafeAccum
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray = Arr.unsafeAccumArray
  
  -----------------------------------------------------------------------------
  -- Flat unboxed arrays
  
  -- | Arrays with unboxed elements.  Instances of 'IArray' are provided
  -- for 'UArray' with certain element types ('Int', 'Float', 'Char',
  -- etc.; see the 'UArray' class for a full list).
  --
  -- A 'UArray' will generally be more efficient (in terms of both time
  -- and space) than the equivalent 'Data.Array.Array' with the same
  -- element type.  However, 'UArray' is strict in its elements - so
  -- don\'t use 'UArray' if you require the non-strictness that
  -- 'Data.Array.Array' provides.
  --
  -- Because the @IArray@ interface provides operations overloaded on
  -- the type of the array, it should be possible to just change the
  -- array type being used by a program from say @Array@ to @UArray@ to
  -- get the benefits of unboxed arrays (don\'t forget to import
  -- "Data.Array.Unboxed" instead of "Data.Array").
  --
  data UArray i e = UArray !i !i !Int ByteArray#
                    deriving Typeable
  #if __GLASGOW_HASKELL__ >= 708
  -- There are class-based invariants on both parameters. See also #9220.
  type role UArray nominal nominal
  #endif
  
  {-# INLINE unsafeArrayUArray #-}
  unsafeArrayUArray :: (MArray (STUArray s) e (ST s), Ix i)
                    => (i,i) -> [(Int, e)] -> e -> ST s (UArray i e)
  unsafeArrayUArray (l,u) ies default_elem = do
      marr <- newArray (l,u) default_elem
      sequence_ [unsafeWrite marr i e | (i, e) <- ies]
      unsafeFreezeSTUArray marr
  
  {-# INLINE unsafeFreezeSTUArray #-}
  unsafeFreezeSTUArray :: STUArray s i e -> ST s (UArray i e)
  unsafeFreezeSTUArray (STUArray l u n marr#) = ST $ \s1# ->
      case unsafeFreezeByteArray# marr# s1# of { (# s2#, arr# #) ->
      (# s2#, UArray l u n arr# #) }
  
  {-# INLINE unsafeReplaceUArray #-}
  unsafeReplaceUArray :: (MArray (STUArray s) e (ST s), Ix i)
                      => UArray i e -> [(Int, e)] -> ST s (UArray i e)
  unsafeReplaceUArray arr ies = do
      marr <- thawSTUArray arr
      sequence_ [unsafeWrite marr i e | (i, e) <- ies]
      unsafeFreezeSTUArray marr
  
  {-# INLINE unsafeAccumUArray #-}
  unsafeAccumUArray :: (MArray (STUArray s) e (ST s), Ix i)
                    => (e -> e' -> e) -> UArray i e -> [(Int, e')] -> ST s (UArray i e)
  unsafeAccumUArray f arr ies = do
      marr <- thawSTUArray arr
      sequence_ [do old <- unsafeRead marr i
                    unsafeWrite marr i (f old new)
                | (i, new) <- ies]
      unsafeFreezeSTUArray marr
  
  {-# INLINE unsafeAccumArrayUArray #-}
  unsafeAccumArrayUArray :: (MArray (STUArray s) e (ST s), Ix i)
                         => (e -> e' -> e) -> e -> (i,i) -> [(Int, e')] -> ST s (UArray i e)
  unsafeAccumArrayUArray f initialValue (l,u) ies = do
      marr <- newArray (l,u) initialValue
      sequence_ [do old <- unsafeRead marr i
                    unsafeWrite marr i (f old new)
                | (i, new) <- ies]
      unsafeFreezeSTUArray marr
  
  {-# INLINE eqUArray #-}
  eqUArray :: (IArray UArray e, Ix i, Eq e) => UArray i e -> UArray i e -> Bool
  eqUArray arr1@(UArray l1 u1 n1 _) arr2@(UArray l2 u2 n2 _) =
      if n1 == 0 then n2 == 0 else
      l1 == l2 && u1 == u2 &&
      and [unsafeAt arr1 i == unsafeAt arr2 i | i <- [0 .. n1 - 1]]
  
  {-# INLINE [1] cmpUArray #-}
  cmpUArray :: (IArray UArray e, Ix i, Ord e) => UArray i e -> UArray i e -> Ordering
  cmpUArray arr1 arr2 = compare (assocs arr1) (assocs arr2)
  
  {-# INLINE cmpIntUArray #-}
  cmpIntUArray :: (IArray UArray e, Ord e) => UArray Int e -> UArray Int e -> Ordering
  cmpIntUArray arr1@(UArray l1 u1 n1 _) arr2@(UArray l2 u2 n2 _) =
      if n1 == 0 then if n2 == 0 then EQ else LT else
      if n2 == 0 then GT else
      case compare l1 l2 of
          EQ    -> foldr cmp (compare u1 u2) [0 .. (n1 `min` n2) - 1]
          other -> other
      where
      cmp i rest = case compare (unsafeAt arr1 i) (unsafeAt arr2 i) of
          EQ    -> rest
          other -> other
  
  {-# RULES "cmpUArray/Int" cmpUArray = cmpIntUArray #-}
  
  -----------------------------------------------------------------------------
  -- Showing IArrays
  
  {-# SPECIALISE
      showsIArray :: (IArray UArray e, Ix i, Show i, Show e) =>
                     Int -> UArray 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)
  
  -----------------------------------------------------------------------------
  -- Flat unboxed arrays: instances
  
  instance IArray UArray Bool where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies False)
      {-# INLINE unsafeAt #-}
  #if __GLASGOW_HASKELL__ > 706
      unsafeAt (UArray _ _ _ arr#) (I# i#) = isTrue#
  #else
      unsafeAt (UArray _ _ _ arr#) (I# i#) =
  #endif
          ((indexWordArray# arr# (bOOL_INDEX i#) `and#` bOOL_BIT i#)
          `neWord#` int2Word# 0#)
  
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Char where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies '\0')
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = C# (indexWideCharArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Int where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = I# (indexIntArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Word where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = W# (indexWordArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray (Ptr a) where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies nullPtr)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = Ptr (indexAddrArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray (FunPtr a) where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies nullFunPtr)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = FunPtr (indexAddrArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Float where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = F# (indexFloatArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Double where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = D# (indexDoubleArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray (StablePtr a) where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies nullStablePtr)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = StablePtr (indexStablePtrArray# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  -- bogus StablePtr value for initialising a UArray of StablePtr.
  nullStablePtr :: StablePtr a
  nullStablePtr = StablePtr (unsafeCoerce# 0#)
  
  instance IArray UArray Int8 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = I8# (indexInt8Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Int16 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = I16# (indexInt16Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Int32 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = I32# (indexInt32Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Int64 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = I64# (unsafeCoerce# (indexInt64Array# arr# i#))
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Word8 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = W8# (indexWord8Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Word16 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = W16# (indexWord16Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Word32 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = W32# (indexWord32Array# arr# i#)
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance IArray UArray Word64 where
      {-# INLINE bounds #-}
      bounds (UArray l u _ _) = (l,u)
      {-# INLINE numElements #-}
      numElements (UArray _ _ n _) = n
      {-# INLINE unsafeArray #-}
      unsafeArray lu ies = runST (unsafeArrayUArray lu ies 0)
      {-# INLINE unsafeAt #-}
      unsafeAt (UArray _ _ _ arr#) (I# i#) = W64# (unsafeCoerce# (indexWord64Array# arr# i#))
      {-# INLINE unsafeReplace #-}
      unsafeReplace arr ies = runST (unsafeReplaceUArray arr ies)
      {-# INLINE unsafeAccum #-}
      unsafeAccum f arr ies = runST (unsafeAccumUArray f arr ies)
      {-# INLINE unsafeAccumArray #-}
      unsafeAccumArray f initialValue lu ies = runST (unsafeAccumArrayUArray f initialValue lu ies)
  
  instance (Ix ix, Eq e, IArray UArray e) => Eq (UArray ix e) where
      (==) = eqUArray
  
  instance (Ix ix, Ord e, IArray UArray e) => Ord (UArray ix e) where
      compare = cmpUArray
  
  instance (Ix ix, Show ix, Show e, IArray UArray e) => Show (UArray ix e) where
      showsPrec = showsIArray
  
  -----------------------------------------------------------------------------
  -- Mutable arrays
  
  {-# NOINLINE arrEleBottom #-}
  arrEleBottom :: a
  arrEleBottom = error "MArray: undefined array element"
  
  {-| Class of mutable 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 @MArray@ class is parameterised over both @a@ and @e@ (so that
  instances specialised to certain element types can be defined, in the
  same way as for 'IArray'), and also over the type of the monad, @m@,
  in which the mutable array will be manipulated.
  -}
  class (Monad m) => MArray a e m where
  
      -- | Returns the bounds of the array
      getBounds      :: Ix i => a i e -> m (i,i)
      -- | Returns the number of elements in the array
      getNumElements :: Ix i => a i e -> m Int
  
      -- | Builds a new array, with every element initialised to the supplied
      -- value.
      newArray    :: Ix i => (i,i) -> e -> m (a i e)
  
      -- | Builds a new array, with every element initialised to an
      -- undefined value. In a monadic context in which operations must
      -- be deterministic (e.g. the ST monad), the array elements are
      -- initialised to a fixed but undefined value, such as zero.
      newArray_ :: Ix i => (i,i) -> m (a i e)
  
      -- | Builds a new array, with every element initialised to an undefined
      -- value.
      unsafeNewArray_ :: Ix i => (i,i) -> m (a i e)
  
      unsafeRead  :: Ix i => a i e -> Int -> m e
      unsafeWrite :: Ix i => a i e -> Int -> e -> m ()
  
      {-# INLINE newArray #-}
          -- The INLINE is crucial, because until we know at least which monad
          -- we are in, the code below allocates like crazy.  So inline it,
          -- in the hope that the context will know the monad.
      newArray (l,u) initialValue = do
          let n = safeRangeSize (l,u)
          marr <- unsafeNewArray_ (l,u)
          sequence_ [unsafeWrite marr i initialValue | i <- [0 .. n - 1]]
          return marr
  
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = newArray (l,u) arrEleBottom
  
      {-# INLINE newArray_ #-}
      newArray_ (l,u) = newArray (l,u) arrEleBottom
  
      -- newArray takes an initialiser which all elements of
      -- the newly created array are initialised to.  unsafeNewArray_ takes
      -- no initialiser, it is assumed that the array is initialised with
      -- "undefined" values.
  
      -- why not omit unsafeNewArray_?  Because in the unboxed array
      -- case we would like to omit the initialisation altogether if
      -- possible.  We can't do this for boxed arrays, because the
      -- elements must all have valid values at all times in case of
      -- garbage collection.
  
      -- why not omit newArray?  Because in the boxed case, we can omit the
      -- default initialisation with undefined values if we *do* know the
      -- initial value and it is constant for all elements.
  
  instance MArray IOArray e IO where
      {-# INLINE getBounds #-}
      getBounds (IOArray marr) = stToIO $ getBounds marr
      {-# INLINE getNumElements #-}
      getNumElements (IOArray marr) = stToIO $ getNumElements marr
      newArray    = newIOArray
      unsafeRead  = unsafeReadIOArray
      unsafeWrite = unsafeWriteIOArray
  
  {-# INLINE newListArray #-}
  -- | Constructs a mutable array from a list of initial elements.
  -- The list gives the elements of the array in ascending order
  -- beginning with the lowest index.
  newListArray :: (MArray a e m, Ix i) => (i,i) -> [e] -> m (a i e)
  newListArray (l,u) es = do
      marr <- newArray_ (l,u)
      let n = safeRangeSize (l,u)
      let fillFromList i xs | i == n    = return ()
                            | otherwise = case xs of
              []   -> return ()
              y:ys -> unsafeWrite marr i y >> fillFromList (i+1) ys
      fillFromList 0 es
      return marr
  
  {-# INLINE readArray #-}
  -- | Read an element from a mutable array
  readArray :: (MArray a e m, Ix i) => a i e -> i -> m e
  readArray marr i = do
    (l,u) <- getBounds marr
    n <- getNumElements marr
    unsafeRead marr (safeIndex (l,u) n i)
  
  {-# INLINE writeArray #-}
  -- | Write an element in a mutable array
  writeArray :: (MArray a e m, Ix i) => a i e -> i -> e -> m ()
  writeArray marr i e = do
    (l,u) <- getBounds marr
    n <- getNumElements marr
    unsafeWrite marr (safeIndex (l,u) n i) e
  
  {-# INLINE getElems #-}
  -- | Return a list of all the elements of a mutable array
  getElems :: (MArray a e m, Ix i) => a i e -> m [e]
  getElems marr = do
    (_l, _u) <- getBounds marr
    n <- getNumElements marr
    sequence [unsafeRead marr i | i <- [0 .. n - 1]]
  
  {-# INLINE getAssocs #-}
  -- | Return a list of all the associations of a mutable array, in
  -- index order.
  getAssocs :: (MArray a e m, Ix i) => a i e -> m [(i, e)]
  getAssocs marr = do
    (l,u) <- getBounds marr
    n <- getNumElements marr
    sequence [ do e <- unsafeRead marr (safeIndex (l,u) n i); return (i,e)
             | i <- range (l,u)]
  
  {-# INLINE mapArray #-}
  -- | Constructs a new array derived from the original array by applying a
  -- function to each of the elements.
  mapArray :: (MArray a e' m, MArray a e m, Ix i) => (e' -> e) -> a i e' -> m (a i e)
  mapArray f marr = do
    (l,u) <- getBounds marr
    n <- getNumElements marr
    marr' <- newArray_ (l,u)
    sequence_ [do e <- unsafeRead marr i
                  unsafeWrite marr' i (f e)
              | i <- [0 .. n - 1]]
    return marr'
  
  {-# INLINE mapIndices #-}
  -- | Constructs a new array derived from the original array by applying a
  -- function to each of the indices.
  mapIndices :: (MArray a e m, Ix i, Ix j) => (i,i) -> (i -> j) -> a j e -> m (a i e)
  mapIndices (l',u') f marr = do
      marr' <- newArray_ (l',u')
      n' <- getNumElements marr'
      sequence_ [do e <- readArray marr (f i')
                    unsafeWrite marr' (safeIndex (l',u') n' i') e
                | i' <- range (l',u')]
      return marr'
  
  -----------------------------------------------------------------------------
  -- Polymorphic non-strict mutable arrays (ST monad)
  
  instance MArray (STArray s) e (ST s) where
      {-# INLINE getBounds #-}
      getBounds arr = return $! ArrST.boundsSTArray arr
      {-# INLINE getNumElements #-}
      getNumElements arr = return $! ArrST.numElementsSTArray arr
      {-# INLINE newArray #-}
      newArray    = ArrST.newSTArray
      {-# INLINE unsafeRead #-}
      unsafeRead  = ArrST.unsafeReadSTArray
      {-# INLINE unsafeWrite #-}
      unsafeWrite = ArrST.unsafeWriteSTArray
  
  instance MArray (STArray s) e (Lazy.ST s) where
      {-# INLINE getBounds #-}
      getBounds arr = strictToLazyST (return $! ArrST.boundsSTArray arr)
      {-# INLINE getNumElements #-}
      getNumElements arr = strictToLazyST (return $! ArrST.numElementsSTArray arr)
      {-# INLINE newArray #-}
      newArray (l,u) e    = strictToLazyST (ArrST.newSTArray (l,u) e)
      {-# INLINE unsafeRead #-}
      unsafeRead arr i    = strictToLazyST (ArrST.unsafeReadSTArray arr i)
      {-# INLINE unsafeWrite #-}
      unsafeWrite arr i e = strictToLazyST (ArrST.unsafeWriteSTArray arr i e)
  
  -----------------------------------------------------------------------------
  -- Flat unboxed mutable arrays (ST monad)
  
  -- | A mutable array with unboxed elements, that can be manipulated 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.  Only certain element types
  --    are supported.
  --
  -- An 'STUArray' will generally be more efficient (in terms of both time
  -- and space) than the equivalent boxed version ('STArray') with the same
  -- element type.  However, 'STUArray' is strict in its elements - so
  -- don\'t use 'STUArray' if you require the non-strictness that
  -- 'STArray' provides.
  data STUArray s i e = STUArray !i !i !Int (MutableByteArray# s)
                        deriving Typeable
  #if __GLASGOW_HASKELL__ >= 708
  -- The "ST" parameter must be nominal for the safety of the ST trick.
  -- The other parameters have class constraints. See also #9220.
  type role STUArray nominal nominal nominal
  #endif
  
  instance Eq (STUArray s i e) where
      STUArray _ _ _ arr1# == STUArray _ _ _ arr2# =
  #if __GLASGOW_HASKELL__ > 706
          isTrue# (sameMutableByteArray# arr1# arr2#)
  #else
          sameMutableByteArray# arr1# arr2#
  #endif
  
  {-# INLINE unsafeNewArraySTUArray_ #-}
  unsafeNewArraySTUArray_ :: Ix i
                          => (i,i) -> (Int# -> Int#) -> ST s (STUArray s i e)
  unsafeNewArraySTUArray_ (l,u) elemsToBytes
   = case rangeSize (l,u) of
         n@(I# n#) ->
             ST $ \s1# ->
                 case newByteArray# (elemsToBytes n#) s1# of
                     (# s2#, marr# #) ->
                         (# s2#, STUArray l u n marr# #)
  
  instance MArray (STUArray s) Bool (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE newArray #-}
      newArray (l,u) initialValue = ST $ \s1# ->
          case safeRangeSize (l,u)            of { n@(I# n#) ->
          case newByteArray# (bOOL_SCALE n#) s1# of { (# s2#, marr# #) ->
          case bOOL_WORD_SCALE n#         of { n'# ->
  #if __GLASGOW_HASKELL__ > 706
          let loop i# s3# | isTrue# (i# ==# n'#) = s3#
  #else
          let loop i# s3# | i# ==# n'#           = s3#
  #endif
                          | otherwise            =
                  case writeWordArray# marr# i# e# s3# of { s4# ->
                  loop (i# +# 1#) s4# } in
          case loop 0# s2#                of { s3# ->
          (# s3#, STUArray l u n marr# #) }}}}
        where
          !(W# e#) = if initialValue then maxBound else 0
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) bOOL_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds False
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWordArray# marr# (bOOL_INDEX i#) s1# of { (# s2#, e# #) ->
  #if __GLASGOW_HASKELL__ > 706
          (# s2#, isTrue# ((e# `and#` bOOL_BIT i#) `neWord#` int2Word# 0#) :: Bool #) }
  #else
          (# s2#, (e# `and#` bOOL_BIT i# `neWord#` int2Word# 0#) :: Bool #) }
  #endif
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) e = ST $ \s1# ->
          case bOOL_INDEX i#              of { j# ->
          case readWordArray# marr# j# s1# of { (# s2#, old# #) ->
          case if e then old# `or#` bOOL_BIT i#
               else old# `and#` bOOL_NOT_BIT i# of { e# ->
          case writeWordArray# marr# j# e# s2# of { s3# ->
          (# s3#, () #) }}}}
  
  instance MArray (STUArray s) Char (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 4#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds (chr 0)
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWideCharArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, C# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (C# e#) = ST $ \s1# ->
          case writeWideCharArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Int (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) wORD_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readIntArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, I# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (I# e#) = ST $ \s1# ->
          case writeIntArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Word (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) wORD_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWordArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, W# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (W# e#) = ST $ \s1# ->
          case writeWordArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) (Ptr a) (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) wORD_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds nullPtr
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readAddrArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, Ptr e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (Ptr e#) = ST $ \s1# ->
          case writeAddrArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) (FunPtr a) (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) wORD_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds nullFunPtr
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readAddrArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, FunPtr e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (FunPtr e#) = ST $ \s1# ->
          case writeAddrArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Float (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) fLOAT_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readFloatArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, F# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (F# e#) = ST $ \s1# ->
          case writeFloatArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Double (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) dOUBLE_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readDoubleArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, D# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (D# e#) = ST $ \s1# ->
          case writeDoubleArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) (StablePtr a) (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) wORD_SCALE
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds (castPtrToStablePtr nullPtr)
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readStablePtrArray# marr# i# s1# of { (# s2#, e# #) ->
          (# s2# , StablePtr e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (StablePtr e#) = ST $ \s1# ->
          case writeStablePtrArray# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Int8 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (\x -> x)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readInt8Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, I8# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (I8# e#) = ST $ \s1# ->
          case writeInt8Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Int16 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 2#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readInt16Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, I16# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (I16# e#) = ST $ \s1# ->
          case writeInt16Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Int32 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 4#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readInt32Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, I32# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (I32# e#) = ST $ \s1# ->
          case writeInt32Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Int64 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 8#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readInt64Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, I64# (unsafeCoerce# e#) #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (I64# e#) = ST $ \s1# ->
          case writeInt64Array# marr# i# (unsafeCoerce# e#) s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Word8 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (\x -> x)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWord8Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, W8# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (W8# e#) = ST $ \s1# ->
          case writeWord8Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Word16 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 2#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWord16Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, W16# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (W16# e#) = ST $ \s1# ->
          case writeWord16Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Word32 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 4#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWord32Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, W32# e# #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (W32# e#) = ST $ \s1# ->
          case writeWord32Array# marr# i# e# s1# of { s2# ->
          (# s2#, () #) }
  
  instance MArray (STUArray s) Word64 (ST s) where
      {-# INLINE getBounds #-}
      getBounds (STUArray l u _ _) = return (l,u)
      {-# INLINE getNumElements #-}
      getNumElements (STUArray _ _ n _) = return n
      {-# INLINE unsafeNewArray_ #-}
      unsafeNewArray_ (l,u) = unsafeNewArraySTUArray_ (l,u) (*# 8#)
      {-# INLINE newArray_ #-}
      newArray_ arrBounds = newArray arrBounds 0
      {-# INLINE unsafeRead #-}
      unsafeRead (STUArray _ _ _ marr#) (I# i#) = ST $ \s1# ->
          case readWord64Array# marr# i# s1# of { (# s2#, e# #) ->
          (# s2#, W64# (unsafeCoerce# e#) #) }
      {-# INLINE unsafeWrite #-}
      unsafeWrite (STUArray _ _ _ marr#) (I# i#) (W64# e#) = ST $ \s1# ->
          case writeWord64Array# marr# i# (unsafeCoerce# e#) s1# of { s2# ->
          (# s2#, () #) }
  
  -----------------------------------------------------------------------------
  -- Translation between elements and bytes
  
  bOOL_SCALE, bOOL_WORD_SCALE,
    wORD_SCALE, dOUBLE_SCALE, fLOAT_SCALE :: Int# -> Int#
  bOOL_SCALE n# = (n# +# last#) `uncheckedIShiftRA#` 3#
    where !(I# last#) = SIZEOF_HSWORD * 8 - 1
  bOOL_WORD_SCALE n# = bOOL_INDEX (n# +# last#)
    where !(I# last#) = SIZEOF_HSWORD * 8 - 1
  wORD_SCALE   n# = scale# *# n# where !(I# scale#) = SIZEOF_HSWORD
  dOUBLE_SCALE n# = scale# *# n# where !(I# scale#) = SIZEOF_HSDOUBLE
  fLOAT_SCALE  n# = scale# *# n# where !(I# scale#) = SIZEOF_HSFLOAT
  
  bOOL_INDEX :: Int# -> Int#
  #if SIZEOF_HSWORD == 4
  bOOL_INDEX i# = i# `uncheckedIShiftRA#` 5#
  #elif SIZEOF_HSWORD == 8
  bOOL_INDEX i# = i# `uncheckedIShiftRA#` 6#
  #endif
  
  bOOL_BIT, bOOL_NOT_BIT :: Int# -> Word#
  bOOL_BIT     n# = int2Word# 1# `uncheckedShiftL#` (word2Int# (int2Word# n# `and#` mask#))
      where !(W# mask#) = SIZEOF_HSWORD * 8 - 1
  bOOL_NOT_BIT n# = bOOL_BIT n# `xor#` mb#
      where !(W# mb#) = maxBound
  
  -----------------------------------------------------------------------------
  -- Freezing
  
  -- | Converts a mutable array (any instance of 'MArray') to an
  -- immutable array (any instance of 'IArray') by taking a complete
  -- copy of it.
  freeze :: (Ix i, MArray a e m, IArray b e) => a i e -> m (b i e)
  {-# NOINLINE [1] freeze #-}
  freeze marr = do
    (l,u) <- getBounds marr
    n <- getNumElements marr
    es <- mapM (unsafeRead marr) [0 .. n - 1]
    -- The old array and index might not be well-behaved, so we need to
    -- use the safe array creation function here.
    return (listArray (l,u) es)
  
  #if __GLASGOW_HASKELL__ >= 711
  freezeSTUArray :: STUArray s i e -> ST s (UArray i e)
  #else
  freezeSTUArray :: Ix i => STUArray s i e -> ST s (UArray i e)
  #endif
  freezeSTUArray (STUArray l u n marr#) = ST $ \s1# ->
      case sizeofMutableByteArray# marr#  of { n# ->
      case newByteArray# n# s1#           of { (# s2#, marr'# #) ->
      case memcpy_freeze marr'# marr# (fromIntegral (I# n#)) of { IO m ->
      case unsafeCoerce# m s2#            of { (# s3#, _ #) ->
      case unsafeFreezeByteArray# marr'# s3# of { (# s4#, arr# #) ->
      (# s4#, UArray l u n arr# #) }}}}}
  
  foreign import ccall unsafe "memcpy"
      memcpy_freeze :: MutableByteArray# s -> MutableByteArray# s -> CSize
             -> IO (Ptr a)
  
  {-# RULES
  "freeze/STArray"  freeze = ArrST.freezeSTArray
  "freeze/STUArray" freeze = freezeSTUArray
      #-}
  
  -- In-place conversion of mutable arrays to immutable ones places
  -- a proof obligation on the user: no other parts of your code can
  -- have a reference to the array at the point where you unsafely
  -- freeze it (and, subsequently mutate it, I suspect).
  
  {- |
     Converts an mutable array into an immutable array.  The
     implementation may either simply cast the array from
     one type to the other without copying the array, or it
     may take a full copy of the array.
  
     Note that because the array is possibly not copied, any subsequent
     modifications made to the mutable version of the array may be
     shared with the immutable version.  It is safe to use, therefore, if
     the mutable version is never modified after the freeze operation.
  
     The non-copying implementation is supported between certain pairs
     of array types only; one constraint is that the array types must
     have identical representations.  In GHC, The following pairs of
     array types have a non-copying O(1) implementation of
     'unsafeFreeze'.  Because the optimised versions are enabled by
     specialisations, you will need to compile with optimisation (-O) to
     get them.
  
       * 'Data.Array.IO.IOUArray' -> 'Data.Array.Unboxed.UArray'
  
       * 'Data.Array.ST.STUArray' -> 'Data.Array.Unboxed.UArray'
  
       * 'Data.Array.IO.IOArray' -> 'Data.Array.Array'
  
       * 'Data.Array.ST.STArray' -> 'Data.Array.Array'
  -}
  {-# INLINE [1] unsafeFreeze #-}
  unsafeFreeze :: (Ix i, MArray a e m, IArray b e) => a i e -> m (b i e)
  unsafeFreeze = freeze
  
  {-# RULES
  "unsafeFreeze/STArray"  unsafeFreeze = ArrST.unsafeFreezeSTArray
  "unsafeFreeze/STUArray" unsafeFreeze = unsafeFreezeSTUArray
      #-}
  
  -----------------------------------------------------------------------------
  -- Thawing
  
  -- | Converts an immutable array (any instance of 'IArray') into a
  -- mutable array (any instance of 'MArray') by taking a complete copy
  -- of it.
  thaw :: (Ix i, IArray a e, MArray b e m) => a i e -> m (b i e)
  {-# NOINLINE [1] thaw #-}
  thaw arr = case bounds arr of
    (l,u) -> do
      marr <- newArray_ (l,u)
      let n = safeRangeSize (l,u)
      sequence_ [ unsafeWrite marr i (unsafeAt arr i)
                | i <- [0 .. n - 1]]
      return marr
  
  #if __GLASGOW_HASKELL__ >= 711
  thawSTUArray :: UArray i e -> ST s (STUArray s i e)
  #else
  thawSTUArray :: Ix i => UArray i e -> ST s (STUArray s i e)
  #endif
  thawSTUArray (UArray l u n arr#) = ST $ \s1# ->
      case sizeofByteArray# arr#          of { n# ->
      case newByteArray# n# s1#           of { (# s2#, marr# #) ->
      case memcpy_thaw marr# arr# (fromIntegral (I# n#)) of { IO m ->
      case unsafeCoerce# m s2#            of { (# s3#, _ #) ->
      (# s3#, STUArray l u n marr# #) }}}}
  
  foreign import ccall unsafe "memcpy"
      memcpy_thaw :: MutableByteArray# s -> ByteArray# -> CSize
             -> IO (Ptr a)
  
  {-# RULES
  "thaw/STArray"  thaw = ArrST.thawSTArray
  "thaw/STUArray" thaw = thawSTUArray
      #-}
  
  -- In-place conversion of immutable arrays to mutable ones places
  -- a proof obligation on the user: no other parts of your code can
  -- have a reference to the array at the point where you unsafely
  -- thaw it (and, subsequently mutate it, I suspect).
  
  {- |
     Converts an immutable array into a mutable array.  The
     implementation may either simply cast the array from
     one type to the other without copying the array, or it
     may take a full copy of the array.
  
     Note that because the array is possibly not copied, any subsequent
     modifications made to the mutable version of the array may be
     shared with the immutable version.  It is only safe to use,
     therefore, if the immutable array is never referenced again in this
     thread, and there is no possibility that it can be also referenced
     in another thread.  If you use an unsafeThaw/write/unsafeFreeze
     sequence in a multi-threaded setting, then you must ensure that
     this sequence is atomic with respect to other threads, or a garbage
     collector crash may result (because the write may be writing to a
     frozen array).
  
     The non-copying implementation is supported between certain pairs
     of array types only; one constraint is that the array types must
     have identical representations.  In GHC, The following pairs of
     array types have a non-copying O(1) implementation of
     'unsafeThaw'.  Because the optimised versions are enabled by
     specialisations, you will need to compile with optimisation (-O) to
     get them.
  
       * 'Data.Array.Unboxed.UArray' -> 'Data.Array.IO.IOUArray'
  
       * 'Data.Array.Unboxed.UArray' -> 'Data.Array.ST.STUArray'
  
       * 'Data.Array.Array'  -> 'Data.Array.IO.IOArray'
  
       * 'Data.Array.Array'  -> 'Data.Array.ST.STArray'
  -}
  {-# INLINE [1] unsafeThaw #-}
  unsafeThaw :: (Ix i, IArray a e, MArray b e m) => a i e -> m (b i e)
  unsafeThaw = thaw
  
  {-# INLINE unsafeThawSTUArray #-}
  #if __GLASGOW_HASKELL__ >= 711
  unsafeThawSTUArray :: UArray i e -> ST s (STUArray s i e)
  #else
  unsafeThawSTUArray :: Ix i => UArray i e -> ST s (STUArray s i e)
  #endif
  unsafeThawSTUArray (UArray l u n marr#) =
      return (STUArray l u n (unsafeCoerce# marr#))
  
  {-# RULES
  "unsafeThaw/STArray"    unsafeThaw = ArrST.unsafeThawSTArray
  "unsafeThaw/STUArray"   unsafeThaw = unsafeThawSTUArray
      #-}
  
  {-# INLINE unsafeThawIOArray #-}
  #if __GLASGOW_HASKELL__ >= 711
  unsafeThawIOArray :: Arr.Array ix e -> IO (IOArray ix e)
  #else
  unsafeThawIOArray :: Ix ix => Arr.Array ix e -> IO (IOArray ix e)
  #endif
  unsafeThawIOArray arr = stToIO $ do
      marr <- ArrST.unsafeThawSTArray arr
      return (IOArray marr)
  
  {-# RULES
  "unsafeThaw/IOArray"  unsafeThaw = unsafeThawIOArray
      #-}
  
  #if __GLASGOW_HASKELL__ >= 711
  thawIOArray :: Arr.Array ix e -> IO (IOArray ix e)
  #else
  thawIOArray :: Ix ix => Arr.Array ix e -> IO (IOArray ix e)
  #endif
  thawIOArray arr = stToIO $ do
      marr <- ArrST.thawSTArray arr
      return (IOArray marr)
  
  {-# RULES
  "thaw/IOArray"  thaw = thawIOArray
      #-}
  
  #if __GLASGOW_HASKELL__ >= 711
  freezeIOArray :: IOArray ix e -> IO (Arr.Array ix e)
  #else
  freezeIOArray :: Ix ix => IOArray ix e -> IO (Arr.Array ix e)
  #endif
  freezeIOArray (IOArray marr) = stToIO (ArrST.freezeSTArray marr)
  
  {-# RULES
  "freeze/IOArray"  freeze = freezeIOArray
      #-}
  
  {-# INLINE unsafeFreezeIOArray #-}
  #if __GLASGOW_HASKELL__ >= 711
  unsafeFreezeIOArray :: IOArray ix e -> IO (Arr.Array ix e)
  #else
  unsafeFreezeIOArray :: Ix ix => IOArray ix e -> IO (Arr.Array ix e)
  #endif
  unsafeFreezeIOArray (IOArray marr) = stToIO (ArrST.unsafeFreezeSTArray marr)
  
  {-# RULES
  "unsafeFreeze/IOArray"  unsafeFreeze = unsafeFreezeIOArray
      #-}
  
  -- | Casts an 'STUArray' with one element type into one with a
  -- different element type.  All the elements of the resulting array
  -- are undefined (unless you know what you\'re doing...).
  
  castSTUArray :: STUArray s ix a -> ST s (STUArray s ix b)
  castSTUArray (STUArray l u n marr#) = return (STUArray l u n marr#)
  