1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
module PreludeArray ( Array, Assoc((:=)), array, listArray, (!), bounds,
indices, elems, assocs, accumArray, (//), accum, amap,
ixmap
) where
{-#Prelude#-} -- Indicates definitions of compiler prelude symbols
-- This module uses some simple techniques with updatable vectors to
-- avoid vector copying in loops where single threading is obvious.
-- This is rather fragile and depends on the way the compiler handles
-- strictness.
import PreludeBltinArray
infixl 9 !
infixl 9 //
infix 1 :=
data Assoc a b = a := b deriving (Eq, Ord, Ix, Text, Binary)
data (Ix a) => Array a b = MkArray (a,a) {-#STRICT#-}
(Vector (Box b)) {-#STRICT#-}
deriving ()
array :: (Ix a) => (a,a) -> [Assoc a b] -> Array a b
listArray :: (Ix a) => (a,a) -> [b] -> Array a b
(!) :: (Ix a) => Array a b -> a -> b
bounds :: (Ix a) => Array a b -> (a,a)
indices :: (Ix a) => Array a b -> [a]
elems :: (Ix a) => Array a b -> [b]
assocs :: (Ix a) => Array a b -> [Assoc a b]
accumArray :: (Ix a) => (b -> c -> b) -> b -> (a,a) -> [Assoc a c]
-> Array a b
(//) :: (Ix a) => Array a b -> [Assoc a b] -> Array a b
accum :: (Ix a) => (b -> c -> b) -> Array a b -> [Assoc a c]
-> Array a b
amap :: (Ix a) => (b -> c) -> Array a b -> Array a c
ixmap :: (Ix a, Ix b) => (a,a) -> (a -> b) -> Array b c
-> Array a c
-- Arrays are a datatype containing a bounds pair and a vector of values.
-- Uninitialized array elements contain an error value.
-- Primitive vectors now contain only unboxed values. This permits us to
-- treat array indexing as an atomic operation without forcing the element
-- being accessed. The boxing and unboxing of array elements happens
-- explicitly using these operations:
data Box a = MkBox a
unBox (MkBox x) = x
{-# unBox :: Inline #-}
-- Array construction and update using index/value associations share
-- the same helper function.
array b@(bmin, bmax) ivs =
let size = (index b bmax) + 1
v = primMakeVector size uninitializedArrayError
in (MkArray b (updateArrayIvs b v ivs))
{-# array :: Inline #-}
a@(MkArray b v) // ivs =
let v' = primCopyVector v
in (MkArray b (updateArrayIvs b v' ivs))
{-# (//) :: Inline #-}
updateArrayIvs b v ivs =
let g (i := x) next = strict1 (primVectorUpdate v (index b i) (MkBox x))
next
in foldr g v ivs
{-# updateArrayIvs :: Inline #-}
uninitializedArrayError =
MkBox (error "(!){PreludeArray}: uninitialized array element.")
-- when mapping a list onto an array, be smart and don't do full index
-- computation
listArray b@(bmin, bmax) vs =
let size = (index b bmax) + 1
v = primMakeVector size uninitializedArrayError
in (MkArray b (updateArrayVs size v vs))
{-# listArray :: Inline #-}
updateArrayVs size v vs =
let g x next j = if (j == size)
then v
else strict1 (primVectorUpdate v j (MkBox x))
(next (j + 1))
in foldr g (\ _ -> v) vs 0
{-# updateArrayVs :: Inline #-}
-- Array access
a@(MkArray b v) ! i = unBox (primVectorSel v (index b i))
{-# (!) :: Inline #-}
bounds (MkArray b _) = b
indices = range . bounds
-- Again, when mapping array elements into a list, be smart and don't do
-- the full index computation for every element.
elems a@(MkArray b@(bmin, bmax) v) =
build (\ c n ->
let size = (index b bmax) + 1
g j = if (j == size)
then n
else c (unBox (primVectorSel v j)) (g (j + 1))
-- This strict1 is so size doesn't get inlined and recomputed
-- at every iteration. It should also force the array argument
-- to be strict.
in strict1 size (g 0))
{-# elems :: Inline #-}
assocs a@(MkArray b@(bmin, bmax) v) =
build (\ c n ->
let g i next j = let y = unBox (primVectorSel v j)
in c (i := y) (next (j + 1))
in foldr g (\ _ -> n) (range b) 0)
{-# assocs :: Inline #-}
-- accum and accumArray share the same helper function. The difference is
-- that accum makes a copy of an existing array and accumArray creates
-- a new one with all elements initialized to the given value.
accum f a@(MkArray b v) ivs =
let v' = primCopyVector v
in (MkArray b (accumArrayIvs f b v' ivs))
{-# accum :: Inline #-}
accumArray f z b@(bmin, bmax) ivs =
let size = (index b bmax) + 1
v = primMakeVector size (MkBox z)
in (MkArray b (accumArrayIvs f b v ivs))
{-# accumArray :: Inline #-}
-- This is a bit tricky. We need to force the access to the array element
-- before the update, but not force the thunk that is the value of the
-- array element unless f is strict.
accumArrayIvs f b v ivs =
let g (i := x) next =
let j = index b i
y = primVectorSel v j
in strict1
y
(strict1 (primVectorUpdate v j (MkBox (f (unBox y) x)))
next)
in foldr g v ivs
{-# accumArrayIvs :: Inline #-}
-- again, be smart and bypass full array indexing on array mapping
amap f a@(MkArray b@(bmin, bmax) v) =
let size = (index b bmax) + 1
v' = primMakeVector size uninitializedArrayError
g j = if (j == size)
then v'
else let y = primVectorSel v j
in strict1 (primVectorUpdate v' j (MkBox (f (unBox y))))
(g (j + 1))
in (MkArray b (g 0))
{-# amap :: Inline #-}
-- can't bypass the index computation here since f needs it as an argument
ixmap b f a = array b [i := a ! f i | i <- range b]
{-# ixmap :: Inline #-}
-- random other stuff
instance (Ix a, Eq b) => Eq (Array a b) where
a == a' = assocs a == assocs a'
instance (Ix a, Ord b) => Ord (Array a b) where
a <= a' = assocs a <= assocs a'
instance (Ix a, Text a, Text b) => Text (Array a b) where
showsPrec p a = showParen (p > 9) (
showString "array " .
shows (bounds a) . showChar ' ' .
shows (assocs a) )
readsPrec p = readParen (p > 9)
(\r -> [(array b as, u) | ("array",s) <- lex r,
(b,t) <- reads s,
(as,u) <- reads t ]
++
[(listArray b xs, u) | ("listArray",s) <- lex r,
(b,t) <- reads s,
(xs,u) <- reads t ])
|
