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
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
|
from rpython.rlib.rarithmetic import ovfcheck, LONG_BIT, maxint, is_valid_int
from rpython.rlib.objectmodel import we_are_translated
from rpython.jit.metainterp.resoperation import rop, ResOperation
from rpython.jit.metainterp.history import BoxInt, ConstInt
MAXINT = maxint
MININT = -maxint - 1
class IntBound(object):
_attrs_ = ('has_upper', 'has_lower', 'upper', 'lower')
def __init__(self, lower, upper):
self.has_upper = True
self.has_lower = True
self.upper = upper
self.lower = lower
# check for unexpected overflows:
if not we_are_translated():
assert type(upper) is not long or is_valid_int(upper)
assert type(lower) is not long or is_valid_int(lower)
# Returns True if the bound was updated
def make_le(self, other):
if other.has_upper:
if not self.has_upper or other.upper < self.upper:
self.has_upper = True
self.upper = other.upper
return True
return False
def make_lt(self, other):
return self.make_le(other.add(-1))
def make_ge(self, other):
if other.has_lower:
if not self.has_lower or other.lower > self.lower:
self.has_lower = True
self.lower = other.lower
return True
return False
def make_gt(self, other):
return self.make_ge(other.add(1))
def make_constant(self, value):
self.has_lower = True
self.has_upper = True
self.lower = value
self.upper = value
def make_unbounded(self):
self.has_lower = False
self.has_upper = False
def bounded(self):
return self.has_lower and self.has_upper
def known_lt(self, other):
if self.has_upper and other.has_lower and self.upper < other.lower:
return True
return False
def known_le(self, other):
if self.has_upper and other.has_lower and self.upper <= other.lower:
return True
return False
def known_gt(self, other):
return other.known_lt(self)
def known_ge(self, other):
return other.known_le(self)
def intersect(self, other):
r = False
if other.has_lower:
if other.lower > self.lower or not self.has_lower:
self.lower = other.lower
self.has_lower = True
r = True
if other.has_upper:
if other.upper < self.upper or not self.has_upper:
self.upper = other.upper
self.has_upper = True
r = True
return r
def add(self, offset):
res = self.clone()
try:
res.lower = ovfcheck(res.lower + offset)
except OverflowError:
res.has_lower = False
try:
res.upper = ovfcheck(res.upper + offset)
except OverflowError:
res.has_upper = False
return res
def mul(self, value):
return self.mul_bound(IntBound(value, value))
def add_bound(self, other):
res = self.clone()
if other.has_upper:
try:
res.upper = ovfcheck(res.upper + other.upper)
except OverflowError:
res.has_upper = False
else:
res.has_upper = False
if other.has_lower:
try:
res.lower = ovfcheck(res.lower + other.lower)
except OverflowError:
res.has_lower = False
else:
res.has_lower = False
return res
def sub_bound(self, other):
res = self.clone()
if other.has_lower:
try:
res.upper = ovfcheck(res.upper - other.lower)
except OverflowError:
res.has_upper = False
else:
res.has_upper = False
if other.has_upper:
try:
res.lower = ovfcheck(res.lower - other.upper)
except OverflowError:
res.has_lower = False
else:
res.has_lower = False
return res
def mul_bound(self, other):
if self.has_upper and self.has_lower and \
other.has_upper and other.has_lower:
try:
vals = (ovfcheck(self.upper * other.upper),
ovfcheck(self.upper * other.lower),
ovfcheck(self.lower * other.upper),
ovfcheck(self.lower * other.lower))
return IntBound(min4(vals), max4(vals))
except OverflowError:
return IntUnbounded()
else:
return IntUnbounded()
def div_bound(self, other):
if self.has_upper and self.has_lower and \
other.has_upper and other.has_lower and \
not other.contains(0):
try:
vals = (ovfcheck(self.upper / other.upper),
ovfcheck(self.upper / other.lower),
ovfcheck(self.lower / other.upper),
ovfcheck(self.lower / other.lower))
return IntBound(min4(vals), max4(vals))
except OverflowError:
return IntUnbounded()
else:
return IntUnbounded()
def lshift_bound(self, other):
if self.has_upper and self.has_lower and \
other.has_upper and other.has_lower and \
other.known_ge(IntBound(0, 0)) and \
other.known_lt(IntBound(LONG_BIT, LONG_BIT)):
try:
vals = (ovfcheck(self.upper << other.upper),
ovfcheck(self.upper << other.lower),
ovfcheck(self.lower << other.upper),
ovfcheck(self.lower << other.lower))
return IntBound(min4(vals), max4(vals))
except (OverflowError, ValueError):
return IntUnbounded()
else:
return IntUnbounded()
def rshift_bound(self, other):
if self.has_upper and self.has_lower and \
other.has_upper and other.has_lower and \
other.known_ge(IntBound(0, 0)) and \
other.known_lt(IntBound(LONG_BIT, LONG_BIT)):
vals = (self.upper >> other.upper,
self.upper >> other.lower,
self.lower >> other.upper,
self.lower >> other.lower)
return IntBound(min4(vals), max4(vals))
else:
return IntUnbounded()
def contains(self, val):
if self.has_lower and val < self.lower:
return False
if self.has_upper and val > self.upper:
return False
return True
def contains_bound(self, other):
if other.has_lower:
if not self.contains(other.lower):
return False
elif self.has_lower:
return False
if other.has_upper:
if not self.contains(other.upper):
return False
elif self.has_upper:
return False
return True
def __repr__(self):
if self.has_lower:
l = '%d' % self.lower
else:
l = '-Inf'
if self.has_upper:
u = '%d' % self.upper
else:
u = 'Inf'
return '%s <= x <= %s' % (l, u)
def clone(self):
res = IntBound(self.lower, self.upper)
res.has_lower = self.has_lower
res.has_upper = self.has_upper
return res
def make_guards(self, box, guards):
if self.has_lower and self.lower > MININT:
bound = self.lower
res = BoxInt()
op = ResOperation(rop.INT_GE, [box, ConstInt(bound)], res)
guards.append(op)
op = ResOperation(rop.GUARD_TRUE, [res], None)
guards.append(op)
if self.has_upper and self.upper < MAXINT:
bound = self.upper
res = BoxInt()
op = ResOperation(rop.INT_LE, [box, ConstInt(bound)], res)
guards.append(op)
op = ResOperation(rop.GUARD_TRUE, [res], None)
guards.append(op)
class IntUpperBound(IntBound):
def __init__(self, upper):
self.has_upper = True
self.has_lower = False
self.upper = upper
self.lower = 0
class IntLowerBound(IntBound):
def __init__(self, lower):
self.has_upper = False
self.has_lower = True
self.upper = 0
self.lower = lower
class IntUnbounded(IntBound):
def __init__(self):
self.has_upper = False
self.has_lower = False
self.upper = 0
self.lower = 0
class ImmutableIntUnbounded(IntUnbounded):
def _raise(self):
raise TypeError('ImmutableIntUnbounded is immutable')
def make_le(self, other):
self._raise()
def make_lt(self, other):
self._raise()
def make_ge(self, other):
self._raise()
def make_gt(self, other):
self._raise()
def make_constant(self, value):
self._raise()
def intersect(self, other):
self._raise()
def min4(t):
return min(min(t[0], t[1]), min(t[2], t[3]))
def max4(t):
return max(max(t[0], t[1]), max(t[2], t[3]))
|
