1 {-# OPTIONS_GHC -fparr #-}
3 -----------------------------------------------------------------------------
6 -- Copyright : (c) 2001-2002 Manuel M T Chakravarty & Gabriele Keller
7 -- License : see libraries/base/LICENSE
9 -- Maintainer : Manuel M. T. Chakravarty <chak@cse.unsw.edu.au>
10 -- Stability : internal
11 -- Portability : non-portable (GHC Extensions)
13 -- Basic implementation of Parallel Arrays.
15 -- This module has two functions: (1) It defines the interface to the
16 -- parallel array extension of the Prelude and (2) it provides a vanilla
17 -- implementation of parallel arrays that does not require to flatten the
18 -- array code. The implementation is not very optimised.
20 --- DOCU ----------------------------------------------------------------------
22 -- Language: Haskell 98 plus unboxed values and parallel arrays
24 -- The semantic difference between standard Haskell arrays (aka "lazy
25 -- arrays") and parallel arrays (aka "strict arrays") is that the evaluation
26 -- of two different elements of a lazy array is independent, whereas in a
27 -- strict array either non or all elements are evaluated. In other words,
28 -- when a parallel array is evaluated to WHNF, all its elements will be
29 -- evaluated to WHNF. The name parallel array indicates that all array
30 -- elements may, in general, be evaluated to WHNF in parallel without any
31 -- need to resort to speculative evaluation. This parallel evaluation
32 -- semantics is also beneficial in the sequential case, as it facilitates
33 -- loop-based array processing as known from classic array-based languages,
36 -- The interface of this module is essentially a variant of the list
37 -- component of the Prelude, but also includes some functions (such as
38 -- permutations) that are not provided for lists. The following list
39 -- operations are not supported on parallel arrays, as they would require the
40 -- availability of infinite parallel arrays: `iterate', `repeat', and `cycle'.
42 -- The current implementation is quite simple and entirely based on boxed
43 -- arrays. One disadvantage of boxed arrays is that they require to
44 -- immediately initialise all newly allocated arrays with an error thunk to
45 -- keep the garbage collector happy, even if it is guaranteed that the array
46 -- is fully initialised with different values before passing over the
47 -- user-visible interface boundary. Currently, no effort is made to use
48 -- raw memory copy operations to speed things up.
50 --- TODO ----------------------------------------------------------------------
52 -- * We probably want a standard library `PArray' in addition to the prelude
53 -- extension in the same way as the standard library `List' complements the
54 -- list functions from the prelude.
56 -- * Currently, functions that emphasis the constructor-based definition of
57 -- lists (such as, head, last, tail, and init) are not supported.
59 -- Is it worthwhile to support the string processing functions lines,
60 -- words, unlines, and unwords? (Currently, they are not implemented.)
62 -- It can, however, be argued that it would be worthwhile to include them
63 -- for completeness' sake; maybe only in the standard library `PArray'.
65 -- * Prescans are often more useful for array programming than scans. Shall
66 -- we include them into the Prelude or the library?
68 -- * Due to the use of the iterator `loop', we could define some fusion rules
71 -- * We might want to add bounds checks that can be deactivated.
76 -- [::], -- Built-in syntax
78 mapP, -- :: (a -> b) -> [:a:] -> [:b:]
79 (+:+), -- :: [:a:] -> [:a:] -> [:a:]
80 filterP, -- :: (a -> Bool) -> [:a:] -> [:a:]
81 concatP, -- :: [:[:a:]:] -> [:a:]
82 concatMapP, -- :: (a -> [:b:]) -> [:a:] -> [:b:]
83 -- head, last, tail, init, -- it's not wise to use them on arrays
84 nullP, -- :: [:a:] -> Bool
85 lengthP, -- :: [:a:] -> Int
86 (!:), -- :: [:a:] -> Int -> a
87 foldlP, -- :: (a -> b -> a) -> a -> [:b:] -> a
88 foldl1P, -- :: (a -> a -> a) -> [:a:] -> a
89 scanlP, -- :: (a -> b -> a) -> a -> [:b:] -> [:a:]
90 scanl1P, -- :: (a -> a -> a) -> [:a:] -> [:a:]
91 foldrP, -- :: (a -> b -> b) -> b -> [:a:] -> b
92 foldr1P, -- :: (a -> a -> a) -> [:a:] -> a
93 scanrP, -- :: (a -> b -> b) -> b -> [:a:] -> [:b:]
94 scanr1P, -- :: (a -> a -> a) -> [:a:] -> [:a:]
95 -- iterate, repeat, -- parallel arrays must be finite
96 replicateP, -- :: Int -> a -> [:a:]
97 -- cycle, -- parallel arrays must be finite
98 takeP, -- :: Int -> [:a:] -> [:a:]
99 dropP, -- :: Int -> [:a:] -> [:a:]
100 splitAtP, -- :: Int -> [:a:] -> ([:a:],[:a:])
101 takeWhileP, -- :: (a -> Bool) -> [:a:] -> [:a:]
102 dropWhileP, -- :: (a -> Bool) -> [:a:] -> [:a:]
103 spanP, -- :: (a -> Bool) -> [:a:] -> ([:a:], [:a:])
104 breakP, -- :: (a -> Bool) -> [:a:] -> ([:a:], [:a:])
105 -- lines, words, unlines, unwords, -- is string processing really needed
106 reverseP, -- :: [:a:] -> [:a:]
107 andP, -- :: [:Bool:] -> Bool
108 orP, -- :: [:Bool:] -> Bool
109 anyP, -- :: (a -> Bool) -> [:a:] -> Bool
110 allP, -- :: (a -> Bool) -> [:a:] -> Bool
111 elemP, -- :: (Eq a) => a -> [:a:] -> Bool
112 notElemP, -- :: (Eq a) => a -> [:a:] -> Bool
113 lookupP, -- :: (Eq a) => a -> [:(a, b):] -> Maybe b
114 sumP, -- :: (Num a) => [:a:] -> a
115 productP, -- :: (Num a) => [:a:] -> a
116 maximumP, -- :: (Ord a) => [:a:] -> a
117 minimumP, -- :: (Ord a) => [:a:] -> a
118 zipP, -- :: [:a:] -> [:b:] -> [:(a, b) :]
119 zip3P, -- :: [:a:] -> [:b:] -> [:c:] -> [:(a, b, c):]
120 zipWithP, -- :: (a -> b -> c) -> [:a:] -> [:b:] -> [:c:]
121 zipWith3P, -- :: (a -> b -> c -> d) -> [:a:]->[:b:]->[:c:]->[:d:]
122 unzipP, -- :: [:(a, b) :] -> ([:a:], [:b:])
123 unzip3P, -- :: [:(a, b, c):] -> ([:a:], [:b:], [:c:])
125 -- overloaded functions
127 enumFromToP, -- :: Enum a => a -> a -> [:a:]
128 enumFromThenToP, -- :: Enum a => a -> a -> a -> [:a:]
130 -- the following functions are not available on lists
132 toP, -- :: [a] -> [:a:]
133 fromP, -- :: [:a:] -> [a]
134 sliceP, -- :: Int -> Int -> [:e:] -> [:e:]
135 foldP, -- :: (e -> e -> e) -> e -> [:e:] -> e
136 fold1P, -- :: (e -> e -> e) -> [:e:] -> e
137 permuteP, -- :: [:Int:] -> [:e:] -> [:e:]
138 bpermuteP, -- :: [:Int:] -> [:e:] -> [:e:]
139 bpermuteDftP, -- :: [:Int:] -> [:e:] -> [:e:] -> [:e:]
140 crossP, -- :: [:a:] -> [:b:] -> [:(a, b):]
141 indexOfP -- :: (a -> Bool) -> [:a:] -> [:Int:]
146 import GHC.ST ( ST(..), STRep, runST )
147 import GHC.Exts ( Int#, Array#, Int(I#), MutableArray#, newArray#,
148 unsafeFreezeArray#, indexArray#, writeArray# )
152 infix 4 `elemP`, `notElemP`
155 -- representation of parallel arrays
156 -- ---------------------------------
158 -- this rather straight forward implementation maps parallel arrays to the
159 -- internal representation used for standard Haskell arrays in GHC's Prelude
160 -- (EXPORTED ABSTRACTLY)
162 -- * This definition *must* be kept in sync with `TysWiredIn.parrTyCon'!
164 data [::] e = PArr Int# (Array# e)
167 -- exported operations on parallel arrays
168 -- --------------------------------------
170 -- operations corresponding to list operations
173 mapP :: (a -> b) -> [:a:] -> [:b:]
174 mapP f = fst . loop (mapEFL f) noAL
176 (+:+) :: [:a:] -> [:a:] -> [:a:]
177 a1 +:+ a2 = fst $ loop (mapEFL sel) noAL (enumFromToP 0 (len1 + len2 - 1))
178 -- we can't use the [:x..y:] form here for tedious
179 -- reasons to do with the typechecker and the fact that
180 -- `enumFromToP' is defined in the same module
185 sel i | i < len1 = a1!:i
186 | otherwise = a2!:(i - len1)
188 filterP :: (a -> Bool) -> [:a:] -> [:a:]
189 filterP p = fst . loop (filterEFL p) noAL
191 concatP :: [:[:a:]:] -> [:a:]
192 concatP xss = foldlP (+:+) [::] xss
194 concatMapP :: (a -> [:b:]) -> [:a:] -> [:b:]
195 concatMapP f = concatP . mapP f
197 -- head, last, tail, init, -- it's not wise to use them on arrays
199 nullP :: [:a:] -> Bool
203 lengthP :: [:a:] -> Int
204 lengthP (PArr n# _) = I# n#
206 (!:) :: [:a:] -> Int -> a
209 foldlP :: (a -> b -> a) -> a -> [:b:] -> a
210 foldlP f z = snd . loop (foldEFL (flip f)) z
212 foldl1P :: (a -> a -> a) -> [:a:] -> a
213 foldl1P f [::] = error "Prelude.foldl1P: empty array"
214 foldl1P f a = snd $ loopFromTo 1 (lengthP a - 1) (foldEFL f) (a!:0) a
216 scanlP :: (a -> b -> a) -> a -> [:b:] -> [:a:]
217 scanlP f z = fst . loop (scanEFL (flip f)) z
219 scanl1P :: (a -> a -> a) -> [:a:] -> [:a:]
220 acanl1P f [::] = error "Prelude.scanl1P: empty array"
221 scanl1P f a = fst $ loopFromTo 1 (lengthP a - 1) (scanEFL f) (a!:0) a
223 foldrP :: (a -> b -> b) -> b -> [:a:] -> b
224 foldrP = error "Prelude.foldrP: not implemented yet" -- FIXME
226 foldr1P :: (a -> a -> a) -> [:a:] -> a
227 foldr1P = error "Prelude.foldr1P: not implemented yet" -- FIXME
229 scanrP :: (a -> b -> b) -> b -> [:a:] -> [:b:]
230 scanrP = error "Prelude.scanrP: not implemented yet" -- FIXME
232 scanr1P :: (a -> a -> a) -> [:a:] -> [:a:]
233 scanr1P = error "Prelude.scanr1P: not implemented yet" -- FIXME
235 -- iterate, repeat -- parallel arrays must be finite
237 replicateP :: Int -> a -> [:a:]
238 {-# INLINE replicateP #-}
239 replicateP n e = runST (do
240 marr# <- newArray n e
243 -- cycle -- parallel arrays must be finite
245 takeP :: Int -> [:a:] -> [:a:]
246 takeP n = sliceP 0 (n - 1)
248 dropP :: Int -> [:a:] -> [:a:]
249 dropP n a = sliceP (n - 1) (lengthP a - 1) a
251 splitAtP :: Int -> [:a:] -> ([:a:],[:a:])
252 splitAtP n xs = (takeP n xs, dropP n xs)
254 takeWhileP :: (a -> Bool) -> [:a:] -> [:a:]
255 takeWhileP = error "Prelude.takeWhileP: not implemented yet" -- FIXME
257 dropWhileP :: (a -> Bool) -> [:a:] -> [:a:]
258 dropWhileP = error "Prelude.dropWhileP: not implemented yet" -- FIXME
260 spanP :: (a -> Bool) -> [:a:] -> ([:a:], [:a:])
261 spanP = error "Prelude.spanP: not implemented yet" -- FIXME
263 breakP :: (a -> Bool) -> [:a:] -> ([:a:], [:a:])
264 breakP p = spanP (not . p)
266 -- lines, words, unlines, unwords, -- is string processing really needed
268 reverseP :: [:a:] -> [:a:]
269 reverseP a = permuteP (enumFromThenToP (len - 1) (len - 2) 0) a
270 -- we can't use the [:x, y..z:] form here for tedious
271 -- reasons to do with the typechecker and the fact that
272 -- `enumFromThenToP' is defined in the same module
276 andP :: [:Bool:] -> Bool
277 andP = foldP (&&) True
279 orP :: [:Bool:] -> Bool
280 orP = foldP (||) True
282 anyP :: (a -> Bool) -> [:a:] -> Bool
283 anyP p = orP . mapP p
285 allP :: (a -> Bool) -> [:a:] -> Bool
286 allP p = andP . mapP p
288 elemP :: (Eq a) => a -> [:a:] -> Bool
289 elemP x = anyP (== x)
291 notElemP :: (Eq a) => a -> [:a:] -> Bool
292 notElemP x = allP (/= x)
294 lookupP :: (Eq a) => a -> [:(a, b):] -> Maybe b
295 lookupP = error "Prelude.lookupP: not implemented yet" -- FIXME
297 sumP :: (Num a) => [:a:] -> a
300 productP :: (Num a) => [:a:] -> a
301 productP = foldP (*) 0
303 maximumP :: (Ord a) => [:a:] -> a
304 maximumP [::] = error "Prelude.maximumP: empty parallel array"
305 maximumP xs = fold1P max xs
307 minimumP :: (Ord a) => [:a:] -> a
308 minimumP [::] = error "Prelude.minimumP: empty parallel array"
309 minimumP xs = fold1P min xs
311 zipP :: [:a:] -> [:b:] -> [:(a, b):]
314 zip3P :: [:a:] -> [:b:] -> [:c:] -> [:(a, b, c):]
315 zip3P = zipWith3P (,,)
317 zipWithP :: (a -> b -> c) -> [:a:] -> [:b:] -> [:c:]
318 zipWithP f a1 a2 = let
321 len = len1 `min` len2
323 fst $ loopFromTo 0 (len - 1) combine 0 a1
325 combine e1 i = (Just $ f e1 (a2!:i), i + 1)
327 zipWith3P :: (a -> b -> c -> d) -> [:a:]->[:b:]->[:c:]->[:d:]
328 zipWith3P f a1 a2 a3 = let
332 len = len1 `min` len2 `min` len3
334 fst $ loopFromTo 0 (len - 1) combine 0 a1
336 combine e1 i = (Just $ f e1 (a2!:i) (a3!:i), i + 1)
338 unzipP :: [:(a, b):] -> ([:a:], [:b:])
339 unzipP a = (fst $ loop (mapEFL fst) noAL a, fst $ loop (mapEFL snd) noAL a)
340 -- FIXME: these two functions should be optimised using a tupled custom loop
341 unzip3P :: [:(a, b, c):] -> ([:a:], [:b:], [:c:])
342 unzip3P a = (fst $ loop (mapEFL fst3) noAL a,
343 fst $ loop (mapEFL snd3) noAL a,
344 fst $ loop (mapEFL trd3) noAL a)
353 instance Eq a => Eq [:a:] where
354 a1 == a2 | lengthP a1 == lengthP a2 = andP (zipWithP (==) a1 a2)
357 instance Ord a => Ord [:a:] where
358 compare a1 a2 = case foldlP combineOrdering EQ (zipWithP compare a1 a2) of
359 EQ | lengthP a1 == lengthP a2 -> EQ
360 | lengthP a1 < lengthP a2 -> LT
363 combineOrdering EQ EQ = EQ
364 combineOrdering EQ other = other
365 combineOrdering other _ = other
367 instance Functor [::] where
370 instance Monad [::] where
371 m >>= k = foldrP ((+:+) . k ) [::] m
372 m >> k = foldrP ((+:+) . const k) [::] m
376 instance Show a => Show [:a:] where
377 showsPrec _ = showPArr . fromP
379 showPArr [] s = "[::]" ++ s
380 showPArr (x:xs) s = "[:" ++ shows x (showPArr' xs s)
382 showPArr' [] s = ":]" ++ s
383 showPArr' (y:ys) s = ',' : shows y (showPArr' ys s)
385 instance Read a => Read [:a:] where
386 readsPrec _ a = [(toP v, rest) | (v, rest) <- readPArr a]
388 readPArr = readParen False (\r -> do
392 (do { (":]", t) <- lex s; return ([], t) }) ++
393 (do { (x, t) <- reads s; (xs, u) <- readPArr2 t; return (x:xs, u) })
396 (do { (":]", t) <- lex s; return ([], t) }) ++
397 (do { (",", t) <- lex s; (x, u) <- reads t; (xs, v) <- readPArr2 u;
400 -- overloaded functions
403 -- Ideally, we would like `enumFromToP' and `enumFromThenToP' to be members of
404 -- `Enum'. On the other hand, we really do not want to change `Enum'. Thus,
405 -- for the moment, we hope that the compiler is sufficiently clever to
406 -- properly fuse the following definition.
408 enumFromToP :: Enum a => a -> a -> [:a:]
409 enumFromToP x y = mapP toEnum (eftInt (fromEnum x) (fromEnum y))
411 eftInt x y = scanlP (+) x $ replicateP (y - x + 1) 1
413 enumFromThenToP :: Enum a => a -> a -> a -> [:a:]
414 enumFromThenToP x y z =
415 mapP toEnum (efttInt (fromEnum x) (fromEnum y) (fromEnum z))
417 efttInt x y z = scanlP (+) x $
418 replicateP ((z - x + 1) `div` delta - 1) delta
422 -- the following functions are not available on lists
425 -- create an array from a list (EXPORTED)
428 toP l = fst $ loop store l (replicateP (length l) ())
430 store _ (x:xs) = (Just x, xs)
432 -- convert an array to a list (EXPORTED)
434 fromP :: [:a:] -> [a]
435 fromP a = [a!:i | i <- [0..lengthP a - 1]]
437 -- cut a subarray out of an array (EXPORTED)
439 sliceP :: Int -> Int -> [:e:] -> [:e:]
441 fst $ loopFromTo (0 `max` from) (to `min` (lengthP a - 1)) (mapEFL id) noAL a
443 -- parallel folding (EXPORTED)
445 -- * the first argument must be associative; otherwise, the result is undefined
447 foldP :: (e -> e -> e) -> e -> [:e:] -> e
450 -- parallel folding without explicit neutral (EXPORTED)
452 -- * the first argument must be associative; otherwise, the result is undefined
454 fold1P :: (e -> e -> e) -> [:e:] -> e
457 -- permute an array according to the permutation vector in the first argument
460 permuteP :: [:Int:] -> [:e:] -> [:e:]
461 permuteP is es = fst $ loop (mapEFL (es!:)) noAL is
463 -- permute an array according to the back-permutation vector in the first
464 -- argument (EXPORTED)
466 -- * the permutation vector must represent a surjective function; otherwise,
467 -- the result is undefined
469 bpermuteP :: [:Int:] -> [:e:] -> [:e:]
470 bpermuteP is es = error "Prelude.bpermuteP: not implemented yet" -- FIXME
472 -- permute an array according to the back-permutation vector in the first
473 -- argument, which need not be surjective (EXPORTED)
475 -- * any elements in the result that are not covered by the back-permutation
476 -- vector assume the value of the corresponding position of the third
479 bpermuteDftP :: [:Int:] -> [:e:] -> [:e:] -> [:e:]
480 bpermuteDftP is es = error "Prelude.bpermuteDftP: not implemented yet"-- FIXME
482 -- computes the cross combination of two arrays (EXPORTED)
484 crossP :: [:a:] -> [:b:] -> [:(a, b):]
485 crossP a1 a2 = fst $ loop combine (0, 0) $ replicateP len ()
491 combine _ (i, j) = (Just $ (a1!:i, a2!:j), next)
493 next | (i + 1) == len1 = (0 , j + 1)
494 | otherwise = (i + 1, j)
496 {- An alternative implementation
497 * The one above is certainly better for flattened code, but here where we
498 are handling boxed arrays, the trade off is less clear. However, I
499 think, the above one is still better.
504 x1 = concatP $ mapP (replicateP len2) a1
505 x2 = concatP $ replicateP len1 a2
510 -- computes an index array for all elements of the second argument for which
511 -- the predicate yields `True' (EXPORTED)
513 indexOfP :: (a -> Bool) -> [:a:] -> [:Int:]
514 indexOfP p a = fst $ loop calcIdx 0 a
516 calcIdx e idx | p e = (Just idx, idx + 1)
517 | otherwise = (Nothing , idx )
520 -- auxiliary functions
521 -- -------------------
523 -- internally used mutable boxed arrays
525 data MPArr s e = MPArr Int# (MutableArray# s e)
527 -- allocate a new mutable array that is pre-initialised with a given value
529 newArray :: Int -> e -> ST s (MPArr s e)
530 {-# INLINE newArray #-}
531 newArray (I# n#) e = ST $ \s1# ->
532 case newArray# n# e s1# of { (# s2#, marr# #) ->
533 (# s2#, MPArr n# marr# #)}
535 -- convert a mutable array into the external parallel array representation
537 mkPArr :: Int -> MPArr s e -> ST s [:e:]
538 {-# INLINE mkPArr #-}
539 mkPArr (I# n#) (MPArr _ marr#) = ST $ \s1# ->
540 case unsafeFreezeArray# marr# s1# of { (# s2#, arr# #) ->
541 (# s2#, PArr n# arr# #) }
543 -- general array iterator
545 -- * corresponds to `loopA' from ``Functional Array Fusion'', Chakravarty &
548 loop :: (e -> acc -> (Maybe e', acc)) -- mapping & folding, once per element
549 -> acc -- initial acc value
550 -> [:e:] -- input array
553 loop mf acc arr = loopFromTo 0 (lengthP arr - 1) mf acc arr
555 -- general array iterator with bounds
557 loopFromTo :: Int -- from index
559 -> (e -> acc -> (Maybe e', acc))
563 {-# INLINE loopFromTo #-}
564 loopFromTo from to mf start arr = runST (do
565 marr <- newArray (to - from + 1) noElem
566 (n', acc) <- trans from to marr arr mf start
567 arr <- mkPArr n' marr
570 noElem = error "PrelPArr.loopFromTo: I do not exist!"
571 -- unlike standard Haskell arrays, this value represents an
574 -- actually loop body of `loop'
576 -- * for this to be really efficient, it has to be translated with the
577 -- constructor specialisation phase "SpecConstr" switched on; as of GHC 5.03
578 -- this requires an optimisation level of at least -O2
580 trans :: Int -- index of first elem to process
581 -> Int -- index of last elem to process
582 -> MPArr s e' -- destination array
583 -> [:e:] -- source array
584 -> (e -> acc -> (Maybe e', acc)) -- mutator
585 -> acc -- initial accumulator
586 -> ST s (Int, acc) -- final destination length/final acc
588 trans from to marr arr mf start = trans' from 0 start
590 trans' arrOff marrOff acc
591 | arrOff > to = return (marrOff, acc)
593 let (oe', acc') = mf (arr `indexPArr` arrOff) acc
594 marrOff' <- case oe' of
595 Nothing -> return marrOff
597 writeMPArr marr marrOff e'
599 trans' (arrOff + 1) marrOff' acc'
602 -- common patterns for using `loop'
605 -- initial value for the accumulator when the accumulator is not needed
610 -- `loop' mutator maps a function over array elements
612 mapEFL :: (e -> e') -> (e -> () -> (Maybe e', ()))
613 {-# INLINE mapEFL #-}
614 mapEFL f = \e a -> (Just $ f e, ())
616 -- `loop' mutator that filter elements according to a predicate
618 filterEFL :: (e -> Bool) -> (e -> () -> (Maybe e, ()))
619 {-# INLINE filterEFL #-}
620 filterEFL p = \e a -> if p e then (Just e, ()) else (Nothing, ())
622 -- `loop' mutator for array folding
624 foldEFL :: (e -> acc -> acc) -> (e -> acc -> (Maybe (), acc))
625 {-# INLINE foldEFL #-}
626 foldEFL f = \e a -> (Nothing, f e a)
628 -- `loop' mutator for array scanning
630 scanEFL :: (e -> acc -> acc) -> (e -> acc -> (Maybe acc, acc))
631 {-# INLINE scanEFL #-}
632 scanEFL f = \e a -> (Just a, f e a)
634 -- elementary array operations
637 -- unlifted array indexing
639 indexPArr :: [:e:] -> Int -> e
640 {-# INLINE indexPArr #-}
641 indexPArr (PArr _ arr#) (I# i#) =
642 case indexArray# arr# i# of (# e #) -> e
644 -- encapsulate writing into a mutable array into the `ST' monad
646 writeMPArr :: MPArr s e -> Int -> e -> ST s ()
647 {-# INLINE writeMPArr #-}
648 writeMPArr (MPArr _ marr#) (I# i#) e = ST $ \s# ->
649 case writeArray# marr# i# e s# of s'# -> (# s'#, () #)