2 {-# OPTIONS_GHC -funbox-strict-fields #-}
3 {-# LANGUAGE NoImplicitPrelude, NoBangPatterns #-}
4 {-# OPTIONS_HADDOCK hide #-}
5 -----------------------------------------------------------------------------
8 -- Copyright : (c) The University of Glasgow, 1994-2000
9 -- License : see libraries/base/LICENSE
11 -- Maintainer : cvs-ghc@haskell.org
12 -- Stability : internal
13 -- Portability : non-portable (GHC extensions)
15 -- GHC\'s array implementation.
17 -----------------------------------------------------------------------------
35 %*********************************************************
37 \subsection{The @Ix@ class}
39 %*********************************************************
42 -- | The 'Ix' class is used to map a contiguous subrange of values in
43 -- a type onto integers. It is used primarily for array indexing
44 -- (see the array package).
46 -- The first argument @(l,u)@ of each of these operations is a pair
47 -- specifying the lower and upper bounds of a contiguous subrange of values.
49 -- An implementation is entitled to assume the following laws about these
52 -- * @'inRange' (l,u) i == 'elem' i ('range' (l,u))@
54 -- * @'range' (l,u) '!!' 'index' (l,u) i == i@, when @'inRange' (l,u) i@
56 -- * @'map' ('index' (l,u)) ('range' (l,u))) == [0..'rangeSize' (l,u)-1]@
58 -- * @'rangeSize' (l,u) == 'length' ('range' (l,u))@
60 -- Minimal complete instance: 'range', 'index' and 'inRange'.
62 class (Ord a) => Ix a where
63 -- | The list of values in the subrange defined by a bounding pair.
65 -- | The position of a subscript in the subrange.
66 index :: (a,a) -> a -> Int
67 -- | Like 'index', but without checking that the value is in range.
68 unsafeIndex :: (a,a) -> a -> Int
69 -- | Returns 'True' the given subscript lies in the range defined
71 inRange :: (a,a) -> a -> Bool
72 -- | The size of the subrange defined by a bounding pair.
73 rangeSize :: (a,a) -> Int
74 -- | like 'rangeSize', but without checking that the upper bound is
76 unsafeRangeSize :: (a,a) -> Int
78 -- Must specify one of index, unsafeIndex
80 -- 'index' is typically over-ridden in instances, with essentially
81 -- the same code, but using indexError instead of hopelessIndexError
82 -- Reason: we have 'Show' at the instances
83 {-# INLINE index #-} -- See Note [Inlining index]
84 index b i | inRange b i = unsafeIndex b i
85 | otherwise = hopelessIndexError
87 unsafeIndex b i = index b i
89 rangeSize b@(_l,h) | inRange b h = unsafeIndex b h + 1
90 | otherwise = 0 -- This case is only here to
91 -- check for an empty range
92 -- NB: replacing (inRange b h) by (l <= h) fails for
93 -- tuples. E.g. (1,2) <= (2,1) but the range is empty
95 unsafeRangeSize b@(_l,h) = unsafeIndex b h + 1
98 Note that the following is NOT right
99 rangeSize (l,h) | l <= h = index b h + 1
102 Because it might be the case that l<h, but the range
103 is nevertheless empty. Consider
105 Here l<h, but the second index ranges from 2..1 and
108 %*********************************************************
110 \subsection{Instances of @Ix@}
112 %*********************************************************
114 Note [Inlining index]
115 ~~~~~~~~~~~~~~~~~~~~~
116 We inline the 'index' operation,
118 * Partly because it generates much faster code
119 (although bigger); see Trac #1216
121 * Partly because it exposes the bounds checks to the simplifier which
124 If you make a per-instance index method, you may consider inlining it.
126 Note [Double bounds-checking of index values]
127 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
128 When you index an array, a!x, there are two possible bounds checks we might make:
130 (A) Check that (inRange (bounds a) x) holds.
132 (A) is checked in the method for 'index'
134 (B) Check that (index (bounds a) x) lies in the range 0..n,
135 where n is the size of the underlying array
137 (B) is checked in the top-level function (!), in safeIndex.
139 Of course it *should* be the case that (A) holds iff (B) holds, but that
140 is a property of the particular instances of index, bounds, and inRange,
141 so GHC cannot guarantee it.
143 * If you do (A) and not (B), then you might get a seg-fault,
144 by indexing at some bizarre location. Trac #1610
146 * If you do (B) but not (A), you may get no complaint when you index
147 an array out of its semantic bounds. Trac #2120
149 At various times we have had (A) and not (B), or (B) and not (A); both
150 led to complaints. So now we implement *both* checks (Trac #2669).
152 For 1-d, 2-d, and 3-d arrays of Int we have specialised instances to avoid this.
154 Note [Out-of-bounds error messages]
155 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
156 The default method for 'index' generates hoplelessIndexError, because
157 Ix doesn't have Show as a superclass. For particular base types we
158 can do better, so we override the default method for index.
161 -- Abstract these errors from the relevant index functions so that
162 -- the guts of the function will be small enough to inline.
164 {-# NOINLINE indexError #-}
165 indexError :: Show a => (a,a) -> a -> String -> b
167 = error (showString "Ix{" . showString tp . showString "}.index: Index " .
168 showParen True (showsPrec 0 i) .
169 showString " out of range " $
170 showParen True (showsPrec 0 rng) "")
172 hopelessIndexError :: Int -- Try to use 'indexError' instead!
173 hopelessIndexError = error "Error in array index"
175 ----------------------------------------------------------------------
176 instance Ix Char where
180 {-# INLINE unsafeIndex #-}
181 unsafeIndex (m,_n) i = fromEnum i - fromEnum m
183 {-# INLINE index #-} -- See Note [Out-of-bounds error messages]
184 -- and Note [Inlining index]
185 index b i | inRange b i = unsafeIndex b i
186 | otherwise = indexError b i "Char"
188 inRange (m,n) i = m <= i && i <= n
190 ----------------------------------------------------------------------
191 instance Ix Int where
193 -- The INLINE stops the build in the RHS from getting inlined,
194 -- so that callers can fuse with the result of range
197 {-# INLINE unsafeIndex #-}
198 unsafeIndex (m,_n) i = i - m
200 {-# INLINE index #-} -- See Note [Out-of-bounds error messages]
201 -- and Note [Inlining index]
202 index b i | inRange b i = unsafeIndex b i
203 | otherwise = indexError b i "Int"
205 {-# INLINE inRange #-}
206 inRange (I# m,I# n) (I# i) = m <=# i && i <=# n
208 ----------------------------------------------------------------------
209 instance Ix Integer where
213 {-# INLINE unsafeIndex #-}
214 unsafeIndex (m,_n) i = fromInteger (i - m)
216 {-# INLINE index #-} -- See Note [Out-of-bounds error messages]
217 -- and Note [Inlining index]
218 index b i | inRange b i = unsafeIndex b i
219 | otherwise = indexError b i "Integer"
221 inRange (m,n) i = m <= i && i <= n
223 ----------------------------------------------------------------------
224 instance Ix Bool where -- as derived
228 {-# INLINE unsafeIndex #-}
229 unsafeIndex (l,_) i = fromEnum i - fromEnum l
231 {-# INLINE index #-} -- See Note [Out-of-bounds error messages]
232 -- and Note [Inlining index]
233 index b i | inRange b i = unsafeIndex b i
234 | otherwise = indexError b i "Bool"
236 inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
238 ----------------------------------------------------------------------
239 instance Ix Ordering where -- as derived
243 {-# INLINE unsafeIndex #-}
244 unsafeIndex (l,_) i = fromEnum i - fromEnum l
246 {-# INLINE index #-} -- See Note [Out-of-bounds error messages]
247 -- and Note [Inlining index]
248 index b i | inRange b i = unsafeIndex b i
249 | otherwise = indexError b i "Ordering"
251 inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
253 ----------------------------------------------------------------------
256 range ((), ()) = [()]
257 {-# INLINE unsafeIndex #-}
258 unsafeIndex ((), ()) () = 0
259 {-# INLINE inRange #-}
260 inRange ((), ()) () = True
262 {-# INLINE index #-} -- See Note [Inlining index]
263 index b i = unsafeIndex b i
265 ----------------------------------------------------------------------
266 instance (Ix a, Ix b) => Ix (a, b) where -- as derived
267 {-# SPECIALISE instance Ix (Int,Int) #-}
270 range ((l1,l2),(u1,u2)) =
271 [ (i1,i2) | i1 <- range (l1,u1), i2 <- range (l2,u2) ]
273 {-# INLINE unsafeIndex #-}
274 unsafeIndex ((l1,l2),(u1,u2)) (i1,i2) =
275 unsafeIndex (l1,u1) i1 * unsafeRangeSize (l2,u2) + unsafeIndex (l2,u2) i2
277 {-# INLINE inRange #-}
278 inRange ((l1,l2),(u1,u2)) (i1,i2) =
279 inRange (l1,u1) i1 && inRange (l2,u2) i2
281 -- Default method for index
283 ----------------------------------------------------------------------
284 instance (Ix a1, Ix a2, Ix a3) => Ix (a1,a2,a3) where
285 {-# SPECIALISE instance Ix (Int,Int,Int) #-}
287 range ((l1,l2,l3),(u1,u2,u3)) =
288 [(i1,i2,i3) | i1 <- range (l1,u1),
292 unsafeIndex ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
293 unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
294 unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
295 unsafeIndex (l1,u1) i1))
297 inRange ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
298 inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
301 -- Default method for index
303 ----------------------------------------------------------------------
304 instance (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1,a2,a3,a4) where
305 range ((l1,l2,l3,l4),(u1,u2,u3,u4)) =
306 [(i1,i2,i3,i4) | i1 <- range (l1,u1),
311 unsafeIndex ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
312 unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
313 unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
314 unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
315 unsafeIndex (l1,u1) i1)))
317 inRange ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
318 inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
319 inRange (l3,u3) i3 && inRange (l4,u4) i4
321 -- Default method for index
323 instance (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1,a2,a3,a4,a5) where
324 range ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) =
325 [(i1,i2,i3,i4,i5) | i1 <- range (l1,u1),
331 unsafeIndex ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
332 unsafeIndex (l5,u5) i5 + unsafeRangeSize (l5,u5) * (
333 unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
334 unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
335 unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
336 unsafeIndex (l1,u1) i1))))
338 inRange ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
339 inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
340 inRange (l3,u3) i3 && inRange (l4,u4) i4 &&
343 -- Default method for index
346 %*********************************************************
348 \subsection{The @Array@ types}
350 %*********************************************************
353 type IPr = (Int, Int)
355 -- | The type of immutable non-strict (boxed) arrays
356 -- with indices in @i@ and elements in @e@.
357 data Ix i => Array i e
358 = Array !i -- the lower bound, l
359 !i -- the upper bound, u
360 !Int -- a cache of (rangeSize (l,u))
361 -- used to make sure an index is
363 (Array# e) -- The actual elements
365 -- | Mutable, boxed, non-strict arrays in the 'ST' monad. The type
366 -- arguments are as follows:
368 -- * @s@: the state variable argument for the 'ST' type
370 -- * @i@: the index type of the array (should be an instance of 'Ix')
372 -- * @e@: the element type of the array.
375 = STArray !i -- the lower bound, l
376 !i -- the upper bound, u
377 !Int -- a cache of (rangeSize (l,u))
378 -- used to make sure an index is
380 (MutableArray# s e) -- The actual elements
381 -- No Ix context for STArray. They are stupid,
382 -- and force an Ix context on the equality instance.
384 -- Just pointer equality on mutable arrays:
385 instance Eq (STArray s i e) where
386 STArray _ _ _ arr1# == STArray _ _ _ arr2# =
387 sameMutableArray# arr1# arr2#
391 %*********************************************************
393 \subsection{Operations on immutable arrays}
395 %*********************************************************
398 {-# NOINLINE arrEleBottom #-}
400 arrEleBottom = error "(Array.!): undefined array element"
402 -- | Construct an array with the specified bounds and containing values
403 -- for given indices within these bounds.
405 -- The array is undefined (i.e. bottom) if any index in the list is
406 -- out of bounds. The Haskell 98 Report further specifies that if any
407 -- two associations in the list have the same index, the value at that
408 -- index is undefined (i.e. bottom). However in GHC's implementation,
409 -- the value at such an index is the value part of the last association
410 -- with that index in the list.
412 -- Because the indices must be checked for these errors, 'array' is
413 -- strict in the bounds argument and in the indices of the association
414 -- list, but nonstrict in the values. Thus, recurrences such as the
415 -- following are possible:
417 -- > a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i <- [2..100]])
419 -- Not every index within the bounds of the array need appear in the
420 -- association list, but the values associated with indices that do not
421 -- appear will be undefined (i.e. bottom).
423 -- If, in any dimension, the lower bound is greater than the upper bound,
424 -- then the array is legal, but empty. Indexing an empty array always
425 -- gives an array-bounds error, but 'bounds' still yields the bounds
426 -- with which the array was constructed.
429 => (i,i) -- ^ a pair of /bounds/, each of the index type
430 -- of the array. These bounds are the lowest and
431 -- highest indices in the array, in that order.
432 -- For example, a one-origin vector of length
433 -- '10' has bounds '(1,10)', and a one-origin '10'
434 -- by '10' matrix has bounds '((1,1),(10,10))'.
435 -> [(i, e)] -- ^ a list of /associations/ of the form
436 -- (/index/, /value/). Typically, this list will
437 -- be expressed as a comprehension. An
438 -- association '(i, x)' defines the value of
439 -- the array at index 'i' to be 'x'.
442 = let n = safeRangeSize (l,u)
443 in unsafeArray' (l,u) n
444 [(safeIndex (l,u) n i, e) | (i, e) <- ies]
446 {-# INLINE unsafeArray #-}
447 unsafeArray :: Ix i => (i,i) -> [(Int, e)] -> Array i e
448 unsafeArray b ies = unsafeArray' b (rangeSize b) ies
450 {-# INLINE unsafeArray' #-}
451 unsafeArray' :: Ix i => (i,i) -> Int -> [(Int, e)] -> Array i e
452 unsafeArray' (l,u) n@(I# n#) ies = runST (ST $ \s1# ->
453 case newArray# n# arrEleBottom s1# of
455 foldr (fill marr#) (done l u n marr#) ies s2#)
458 fill :: MutableArray# s e -> (Int, e) -> STRep s a -> STRep s a
459 fill marr# (I# i#, e) next s1# =
460 case writeArray# marr# i# e s1# of { s2# ->
464 done :: Ix i => i -> i -> Int -> MutableArray# s e -> STRep s (Array i e)
465 done l u n marr# s1# =
466 case unsafeFreezeArray# marr# s1# of
467 (# s2#, arr# #) -> (# s2#, Array l u n arr# #)
469 -- This is inefficient and I'm not sure why:
470 -- listArray (l,u) es = unsafeArray (l,u) (zip [0 .. rangeSize (l,u) - 1] es)
471 -- The code below is better. It still doesn't enable foldr/build
472 -- transformation on the list of elements; I guess it's impossible
473 -- using mechanisms currently available.
475 -- | Construct an array from a pair of bounds and a list of values in
477 {-# INLINE listArray #-}
478 listArray :: Ix i => (i,i) -> [e] -> Array i e
479 listArray (l,u) es = runST (ST $ \s1# ->
480 case safeRangeSize (l,u) of { n@(I# n#) ->
481 case newArray# n# arrEleBottom s1# of { (# s2#, marr# #) ->
482 let fillFromList i# xs s3# | i# ==# n# = s3#
483 | otherwise = case xs of
485 y:ys -> case writeArray# marr# i# y s3# of { s4# ->
486 fillFromList (i# +# 1#) ys s4# } in
487 case fillFromList 0# es s2# of { s3# ->
488 done l u n marr# s3# }}})
490 -- | The value at the given index in an array.
492 (!) :: Ix i => Array i e -> i -> e
493 arr@(Array l u n _) ! i = unsafeAt arr $ safeIndex (l,u) n i
495 {-# INLINE safeRangeSize #-}
496 safeRangeSize :: Ix i => (i, i) -> Int
497 safeRangeSize (l,u) = let r = rangeSize (l, u)
498 in if r < 0 then negRange
501 -- Don't inline this error message everywhere!!
502 negRange :: Int -- Uninformative, but Ix does not provide Show
503 negRange = error "Negative range size"
505 {-# INLINE[1] safeIndex #-}
506 -- See Note [Double bounds-checking of index values]
507 -- Inline *after* (!) so the rules can fire
508 safeIndex :: Ix i => (i, i) -> Int -> i -> Int
509 safeIndex (l,u) n i = let i' = index (l,u) i
510 in if (0 <= i') && (i' < n)
512 else badSafeIndex i' n
514 -- See Note [Double bounds-checking of index values]
516 "safeIndex/I" safeIndex = lessSafeIndex :: (Int,Int) -> Int -> Int -> Int
517 "safeIndex/(I,I)" safeIndex = lessSafeIndex :: ((Int,Int),(Int,Int)) -> Int -> (Int,Int) -> Int
518 "safeIndex/(I,I,I)" safeIndex = lessSafeIndex :: ((Int,Int,Int),(Int,Int,Int)) -> Int -> (Int,Int,Int) -> Int
521 lessSafeIndex :: Ix i => (i, i) -> Int -> i -> Int
522 -- See Note [Double bounds-checking of index values]
523 -- Do only (A), the semantic check
524 lessSafeIndex (l,u) _ i = index (l,u) i
526 -- Don't inline this long error message everywhere!!
527 badSafeIndex :: Int -> Int -> Int
528 badSafeIndex i' n = error ("Error in array index; " ++ show i' ++
529 " not in range [0.." ++ show n ++ ")")
531 {-# INLINE unsafeAt #-}
532 unsafeAt :: Ix i => Array i e -> Int -> e
533 unsafeAt (Array _ _ _ arr#) (I# i#) =
534 case indexArray# arr# i# of (# e #) -> e
536 -- | The bounds with which an array was constructed.
537 {-# INLINE bounds #-}
538 bounds :: Ix i => Array i e -> (i,i)
539 bounds (Array l u _ _) = (l,u)
541 -- | The number of elements in the array.
542 {-# INLINE numElements #-}
543 numElements :: Ix i => Array i e -> Int
544 numElements (Array _ _ n _) = n
546 -- | The list of indices of an array in ascending order.
547 {-# INLINE indices #-}
548 indices :: Ix i => Array i e -> [i]
549 indices (Array l u _ _) = range (l,u)
551 -- | The list of elements of an array in index order.
553 elems :: Ix i => Array i e -> [e]
554 elems arr@(Array _ _ n _) =
555 [unsafeAt arr i | i <- [0 .. n - 1]]
557 -- | The list of associations of an array in index order.
558 {-# INLINE assocs #-}
559 assocs :: Ix i => Array i e -> [(i, e)]
560 assocs arr@(Array l u _ _) =
561 [(i, arr ! i) | i <- range (l,u)]
563 -- | The 'accumArray' function deals with repeated indices in the association
564 -- list using an /accumulating function/ which combines the values of
565 -- associations with the same index.
566 -- For example, given a list of values of some index type, @hist@
567 -- produces a histogram of the number of occurrences of each index within
568 -- a specified range:
570 -- > hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b
571 -- > hist bnds is = accumArray (+) 0 bnds [(i, 1) | i<-is, inRange bnds i]
573 -- If the accumulating function is strict, then 'accumArray' is strict in
574 -- the values, as well as the indices, in the association list. Thus,
575 -- unlike ordinary arrays built with 'array', accumulated arrays should
576 -- not in general be recursive.
577 {-# INLINE accumArray #-}
579 => (e -> a -> e) -- ^ accumulating function
580 -> e -- ^ initial value
581 -> (i,i) -- ^ bounds of the array
582 -> [(i, a)] -- ^ association list
584 accumArray f initial (l,u) ies =
585 let n = safeRangeSize (l,u)
586 in unsafeAccumArray' f initial (l,u) n
587 [(safeIndex (l,u) n i, e) | (i, e) <- ies]
589 {-# INLINE unsafeAccumArray #-}
590 unsafeAccumArray :: Ix i => (e -> a -> e) -> e -> (i,i) -> [(Int, a)] -> Array i e
591 unsafeAccumArray f initial b ies = unsafeAccumArray' f initial b (rangeSize b) ies
593 {-# INLINE unsafeAccumArray' #-}
594 unsafeAccumArray' :: Ix i => (e -> a -> e) -> e -> (i,i) -> Int -> [(Int, a)] -> Array i e
595 unsafeAccumArray' f initial (l,u) n@(I# n#) ies = runST (ST $ \s1# ->
596 case newArray# n# initial s1# of { (# s2#, marr# #) ->
597 foldr (adjust f marr#) (done l u n marr#) ies s2# })
599 {-# INLINE adjust #-}
600 adjust :: (e -> a -> e) -> MutableArray# s e -> (Int, a) -> STRep s b -> STRep s b
601 adjust f marr# (I# i#, new) next s1# =
602 case readArray# marr# i# s1# of
604 case writeArray# marr# i# (f old new) s2# of
607 -- | Constructs an array identical to the first argument except that it has
608 -- been updated by the associations in the right argument.
609 -- For example, if @m@ is a 1-origin, @n@ by @n@ matrix, then
611 -- > m//[((i,i), 0) | i <- [1..n]]
613 -- is the same matrix, except with the diagonal zeroed.
615 -- Repeated indices in the association list are handled as for 'array':
616 -- Haskell 98 specifies that the resulting array is undefined (i.e. bottom),
617 -- but GHC's implementation uses the last association for each index.
619 (//) :: Ix i => Array i e -> [(i, e)] -> Array i e
620 arr@(Array l u n _) // ies =
621 unsafeReplace arr [(safeIndex (l,u) n i, e) | (i, e) <- ies]
623 {-# INLINE unsafeReplace #-}
624 unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e
625 unsafeReplace arr ies = runST (do
626 STArray l u n marr# <- thawSTArray arr
627 ST (foldr (fill marr#) (done l u n marr#) ies))
629 -- | @'accum' f@ takes an array and an association list and accumulates
630 -- pairs from the list into the array with the accumulating function @f@.
631 -- Thus 'accumArray' can be defined using 'accum':
633 -- > accumArray f z b = accum f (array b [(i, z) | i <- range b])
636 accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e
637 accum f arr@(Array l u n _) ies =
638 unsafeAccum f arr [(safeIndex (l,u) n i, e) | (i, e) <- ies]
640 {-# INLINE unsafeAccum #-}
641 unsafeAccum :: Ix i => (e -> a -> e) -> Array i e -> [(Int, a)] -> Array i e
642 unsafeAccum f arr ies = runST (do
643 STArray l u n marr# <- thawSTArray arr
644 ST (foldr (adjust f marr#) (done l u n marr#) ies))
647 amap :: Ix i => (a -> b) -> Array i a -> Array i b
648 amap f arr@(Array l u n _) =
649 unsafeArray' (l,u) n [(i, f (unsafeAt arr i)) | i <- [0 .. n - 1]]
651 -- | 'ixmap' allows for transformations on array indices.
652 -- It may be thought of as providing function composition on the right
653 -- with the mapping that the original array embodies.
655 -- A similar transformation of array values may be achieved using 'fmap'
656 -- from the 'Array' instance of the 'Functor' class.
658 ixmap :: (Ix i, Ix j) => (i,i) -> (i -> j) -> Array j e -> Array i e
660 array (l,u) [(i, arr ! f i) | i <- range (l,u)]
662 {-# INLINE eqArray #-}
663 eqArray :: (Ix i, Eq e) => Array i e -> Array i e -> Bool
664 eqArray arr1@(Array l1 u1 n1 _) arr2@(Array l2 u2 n2 _) =
665 if n1 == 0 then n2 == 0 else
666 l1 == l2 && u1 == u2 &&
667 and [unsafeAt arr1 i == unsafeAt arr2 i | i <- [0 .. n1 - 1]]
669 {-# INLINE cmpArray #-}
670 cmpArray :: (Ix i, Ord e) => Array i e -> Array i e -> Ordering
671 cmpArray arr1 arr2 = compare (assocs arr1) (assocs arr2)
673 {-# INLINE cmpIntArray #-}
674 cmpIntArray :: Ord e => Array Int e -> Array Int e -> Ordering
675 cmpIntArray arr1@(Array l1 u1 n1 _) arr2@(Array l2 u2 n2 _) =
677 if n2 == 0 then EQ else LT
678 else if n2 == 0 then GT
679 else case compare l1 l2 of
680 EQ -> foldr cmp (compare u1 u2) [0 .. (n1 `min` n2) - 1]
683 cmp i rest = case compare (unsafeAt arr1 i) (unsafeAt arr2 i) of
687 {-# RULES "cmpArray/Int" cmpArray = cmpIntArray #-}
691 %*********************************************************
693 \subsection{Array instances}
695 %*********************************************************
698 instance Ix i => Functor (Array i) where
701 instance (Ix i, Eq e) => Eq (Array i e) where
704 instance (Ix i, Ord e) => Ord (Array i e) where
707 instance (Ix a, Show a, Show b) => Show (Array a b) where
709 showParen (p > appPrec) $
710 showString "array " .
711 showsPrec appPrec1 (bounds a) .
713 showsPrec appPrec1 (assocs a)
714 -- Precedence of 'array' is the precedence of application
716 -- The Read instance is in GHC.Read
720 %*********************************************************
722 \subsection{Operations on mutable arrays}
724 %*********************************************************
726 Idle ADR question: What's the tradeoff here between flattening these
727 datatypes into @STArray ix ix (MutableArray# s elt)@ and using
728 it as is? As I see it, the former uses slightly less heap and
729 provides faster access to the individual parts of the bounds while the
730 code used has the benefit of providing a ready-made @(lo, hi)@ pair as
731 required by many array-related functions. Which wins? Is the
732 difference significant (probably not).
734 Idle AJG answer: When I looked at the outputted code (though it was 2
735 years ago) it seems like you often needed the tuple, and we build
736 it frequently. Now we've got the overloading specialiser things
737 might be different, though.
740 {-# INLINE newSTArray #-}
741 newSTArray :: Ix i => (i,i) -> e -> ST s (STArray s i e)
742 newSTArray (l,u) initial = ST $ \s1# ->
743 case safeRangeSize (l,u) of { n@(I# n#) ->
744 case newArray# n# initial s1# of { (# s2#, marr# #) ->
745 (# s2#, STArray l u n marr# #) }}
747 {-# INLINE boundsSTArray #-}
748 boundsSTArray :: STArray s i e -> (i,i)
749 boundsSTArray (STArray l u _ _) = (l,u)
751 {-# INLINE numElementsSTArray #-}
752 numElementsSTArray :: STArray s i e -> Int
753 numElementsSTArray (STArray _ _ n _) = n
755 {-# INLINE readSTArray #-}
756 readSTArray :: Ix i => STArray s i e -> i -> ST s e
757 readSTArray marr@(STArray l u n _) i =
758 unsafeReadSTArray marr (safeIndex (l,u) n i)
760 {-# INLINE unsafeReadSTArray #-}
761 unsafeReadSTArray :: Ix i => STArray s i e -> Int -> ST s e
762 unsafeReadSTArray (STArray _ _ _ marr#) (I# i#)
763 = ST $ \s1# -> readArray# marr# i# s1#
765 {-# INLINE writeSTArray #-}
766 writeSTArray :: Ix i => STArray s i e -> i -> e -> ST s ()
767 writeSTArray marr@(STArray l u n _) i e =
768 unsafeWriteSTArray marr (safeIndex (l,u) n i) e
770 {-# INLINE unsafeWriteSTArray #-}
771 unsafeWriteSTArray :: Ix i => STArray s i e -> Int -> e -> ST s ()
772 unsafeWriteSTArray (STArray _ _ _ marr#) (I# i#) e = ST $ \s1# ->
773 case writeArray# marr# i# e s1# of
778 %*********************************************************
780 \subsection{Moving between mutable and immutable}
782 %*********************************************************
785 freezeSTArray :: Ix i => STArray s i e -> ST s (Array i e)
786 freezeSTArray (STArray l u n@(I# n#) marr#) = ST $ \s1# ->
787 case newArray# n# arrEleBottom s1# of { (# s2#, marr'# #) ->
788 let copy i# s3# | i# ==# n# = s3#
790 case readArray# marr# i# s3# of { (# s4#, e #) ->
791 case writeArray# marr'# i# e s4# of { s5# ->
792 copy (i# +# 1#) s5# }} in
793 case copy 0# s2# of { s3# ->
794 case unsafeFreezeArray# marr'# s3# of { (# s4#, arr# #) ->
795 (# s4#, Array l u n arr# #) }}}
797 {-# INLINE unsafeFreezeSTArray #-}
798 unsafeFreezeSTArray :: Ix i => STArray s i e -> ST s (Array i e)
799 unsafeFreezeSTArray (STArray l u n marr#) = ST $ \s1# ->
800 case unsafeFreezeArray# marr# s1# of { (# s2#, arr# #) ->
801 (# s2#, Array l u n arr# #) }
803 thawSTArray :: Ix i => Array i e -> ST s (STArray s i e)
804 thawSTArray (Array l u n@(I# n#) arr#) = ST $ \s1# ->
805 case newArray# n# arrEleBottom s1# of { (# s2#, marr# #) ->
806 let copy i# s3# | i# ==# n# = s3#
808 case indexArray# arr# i# of { (# e #) ->
809 case writeArray# marr# i# e s3# of { s4# ->
810 copy (i# +# 1#) s4# }} in
811 case copy 0# s2# of { s3# ->
812 (# s3#, STArray l u n marr# #) }}
814 {-# INLINE unsafeThawSTArray #-}
815 unsafeThawSTArray :: Ix i => Array i e -> ST s (STArray s i e)
816 unsafeThawSTArray (Array l u n arr#) = ST $ \s1# ->
817 case unsafeThawArray# arr# s1# of { (# s2#, marr# #) ->
818 (# s2#, STArray l u n marr# #) }