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
|
from miasm2.core.graph import *
g = DiGraph()
g.add_node('a')
g.add_node('b')
g.add_edge('a', 'b')
g.add_edge('a', 'c')
g.add_edge('a', 'c')
g.add_edge('c', 'c')
print g
print [x for x in g.successors('a')]
print [x for x in g.predecessors('a')]
print [x for x in g.predecessors('b')]
print [x for x in g.predecessors('c')]
print [x for x in g.successors('c')]
"""
Test from: https://en.wikipedia.org/wiki/Dominator_(graph_theory)
"""
g1 = DiGraph()
g1.add_edge(1, 2)
g1.add_edge(2, 3)
g1.add_edge(2, 4)
g1.add_edge(3, 5)
g1.add_edge(4, 5)
g1.add_edge(5, 2)
g1.add_edge(2, 6)
dominators = g1.compute_dominators(1)
assert(dominators == {1: set([1]),
2: set([1, 2]),
3: set([1, 2, 3]),
4: set([1, 2, 4]),
5: set([1, 2, 5]),
6: set([1, 2, 6])})
assert(list(g1.walk_dominators(1, dominators)) == [])
assert(list(g1.walk_dominators(2, dominators)) == [1])
assert(list(g1.walk_dominators(3, dominators)) == [2, 1])
assert(list(g1.walk_dominators(4, dominators)) == [2, 1])
assert(list(g1.walk_dominators(5, dominators)) == [2, 1])
assert(list(g1.walk_dominators(6, dominators)) == [2, 1])
# Regression test with multiple heads
g2 = DiGraph()
g2.add_edge(1, 2)
g2.add_edge(2, 3)
g2.add_edge(3, 4)
g2.add_edge(5, 6)
g2.add_edge(6, 3)
g2.add_edge(4, 7)
g2.add_edge(4, 8)
g2.add_edge(7, 9)
g2.add_edge(8, 9)
dominators = g2.compute_dominators(5)
assert(dominators == {3: set([3, 5, 6]),
4: set([3, 4, 5, 6]),
5: set([5]),
6: set([5, 6]),
7: set([3, 4, 5, 6, 7]),
8: set([3, 4, 5, 6, 8]),
9: set([3, 4, 5, 6, 9])})
assert(list(g2.walk_dominators(1, dominators)) == [])
assert(list(g2.walk_dominators(2, dominators)) == [])
assert(list(g2.walk_dominators(3, dominators)) == [6, 5])
assert(list(g2.walk_dominators(4, dominators)) == [3, 6, 5])
assert(list(g2.walk_dominators(5, dominators)) == [])
assert(list(g2.walk_dominators(6, dominators)) == [5])
assert(list(g2.walk_dominators(7, dominators)) == [4, 3, 6, 5])
assert(list(g2.walk_dominators(8, dominators)) == [4, 3, 6, 5])
assert(list(g2.walk_dominators(9, dominators)) == [4, 3, 6, 5])
postdominators = g1.compute_postdominators(6)
assert(postdominators == {1: set([1, 2, 6]),
2: set([2, 6]),
3: set([2, 3, 5, 6]),
4: set([2, 4, 5, 6]),
5: set([2, 5, 6]),
6: set([6])})
assert(list(g1.walk_postdominators(1, postdominators)) == [2, 6])
assert(list(g1.walk_postdominators(2, postdominators)) == [6])
assert(list(g1.walk_postdominators(3, postdominators)) == [5, 2, 6])
assert(list(g1.walk_postdominators(4, postdominators)) == [5, 2, 6])
assert(list(g1.walk_postdominators(5, postdominators)) == [2, 6])
assert(list(g1.walk_postdominators(6, postdominators)) == [])
postdominators = g1.compute_postdominators(5)
assert(postdominators == {1: set([1, 2, 5]),
2: set([2, 5]),
3: set([3, 5]),
4: set([4, 5]),
5: set([5])})
assert(list(g1.walk_postdominators(1, postdominators)) == [2, 5])
assert(list(g1.walk_postdominators(2, postdominators)) == [5])
assert(list(g1.walk_postdominators(3, postdominators)) == [5])
assert(list(g1.walk_postdominators(4, postdominators)) == [5])
assert(list(g1.walk_postdominators(5, postdominators)) == [])
assert(list(g1.walk_postdominators(6, postdominators)) == [])
postdominators = g2.compute_postdominators(4)
assert(postdominators == {1: set([1, 2, 3, 4]),
2: set([2, 3, 4]),
3: set([3, 4]),
4: set([4]),
5: set([3, 4, 5, 6]),
6: set([3, 4, 6])})
assert(list(g2.walk_postdominators(1, postdominators)) == [2, 3, 4])
assert(list(g2.walk_postdominators(2, postdominators)) == [3, 4])
assert(list(g2.walk_postdominators(3, postdominators)) == [4])
assert(list(g2.walk_postdominators(4, postdominators)) == [])
assert(list(g2.walk_postdominators(5, postdominators)) == [6, 3, 4])
assert(list(g2.walk_postdominators(6, postdominators)) == [3, 4])
assert(list(g2.walk_postdominators(7, postdominators)) == [])
assert(list(g2.walk_postdominators(8, postdominators)) == [])
assert(list(g2.walk_postdominators(9, postdominators)) == [])
idoms = g1.compute_immediate_dominators(1)
assert(idoms == {2: 1,
3: 2,
4: 2,
5: 2,
6: 2})
idoms = g2.compute_immediate_dominators(1)
assert(idoms == {2: 1,
3: 2,
4: 3,
7: 4,
8: 4,
9: 4})
idoms = g2.compute_immediate_dominators(5)
assert(idoms == {3: 6,
4: 3,
6: 5,
7: 4,
8: 4,
9: 4})
frontier = g1.compute_dominance_frontier(1)
assert(frontier == {2: set([2]),
3: set([5]),
4: set([5]),
5: set([2])})
frontier = g2.compute_dominance_frontier(1)
assert(frontier == {7: set([9]),
8: set([9])})
frontier = g2.compute_dominance_frontier(5)
assert(frontier == {7: set([9]),
8: set([9])})
# Regression test with natural loops and irreducible loops
g3 = DiGraph()
g3.add_edge(1, 2)
g3.add_edge(1, 3)
g3.add_edge(2, 4)
g3.add_edge(2, 5)
g3.add_edge(3, 7)
g3.add_edge(3, 8)
g3.add_edge(4, 9)
g3.add_edge(5, 9)
g3.add_edge(7, 6)
g3.add_edge(8, 6)
g3.add_edge(9, 6)
g3.add_edge(9, 2)
g3.add_edge(9, 1)
g3.add_edge(7, 8)
g3.add_edge(8, 7)
loops = set([(backedge, frozenset(body)) for backedge, body in g3.compute_natural_loops(1)])
assert(loops == {((1, 9), frozenset({1, 2, 4, 5, 9})),
((2, 9), frozenset({2, 4, 5, 9}))})
sccs = set([frozenset(scc) for scc in g3.compute_strongly_connected_components()])
assert(sccs == {frozenset({6}),
frozenset({7, 8}),
frozenset({3}),
frozenset({1, 2, 4, 5, 9})})
# Equality
graph = DiGraph()
graph.add_edge(1, 2)
graph.add_edge(2, 3)
graph2 = DiGraph()
graph2.add_edge(2, 3)
graph2.add_edge(1, 2)
assert graph == graph2
# Copy
graph4 = graph.copy()
assert graph == graph4
# Merge
graph3 = DiGraph()
graph3.add_edge(3, 1)
graph3.add_edge(1, 4)
graph4 += graph3
for node in graph3.nodes():
assert node in graph4.nodes()
for edge in graph3.edges():
assert edge in graph4.edges()
assert graph4.nodes() == graph.nodes().union(graph3.nodes())
assert sorted(graph4.edges()) == sorted(graph.edges() + graph3.edges())
|