def test_boost_example(self):
# Graph taken from Figure 1 of
# http://www.boost.org/doc/libs/1_56_0/libs/graph/doc/lengauer_tarjan_dominator.htm
edges = [(0, 1), (1, 2), (1, 3), (2, 7), (3, 4), (4, 5), (4, 6),
(5, 7), (6, 4)]
G = nx.DiGraph(edges)
assert (nx.immediate_dominators(G, 0) == {
0: 0,
1: 0,
2: 1,
3: 1,
4: 3,
5: 4,
6: 4,
7: 1
})
# Test postdominance.
with nx.utils.reversed(G):
assert (nx.immediate_dominators(G, 7) == {
0: 1,
1: 7,
2: 7,
3: 4,
4: 5,
5: 7,
6: 4,
7: 7
})
def test_domrel_png(self):
# Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
G = nx.DiGraph(edges)
result = nx.immediate_dominators(G, 1)
assert result == {1: 1, 2: 1, 3: 2, 4: 2, 5: 2, 6: 2}
# Test postdominance.
result = nx.immediate_dominators(G.reverse(copy=False), 6)
assert result == {1: 2, 2: 6, 3: 5, 4: 5, 5: 2, 6: 6}
def test_domrel_png(self):
# Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
G = nx.DiGraph(edges)
assert_equal(nx.immediate_dominators(G, 1),
{1: 1, 2: 1, 3: 2, 4: 2, 5: 2, 6: 2})
# Test postdominance.
with nx.utils.reversed(G):
assert_equal(nx.immediate_dominators(G, 6),
{1: 2, 2: 6, 3: 5, 4: 5, 5: 2, 6: 6})
def create_graph_from(self, starting_ep):
visited = set()
to_visit = [starting_ep]
graph = nx.DiGraph()
g = Digraph('G', filename='CFG.gv')
count = 0
while len(to_visit) > 0:
count += 1
current_ep = to_visit.pop(0)
current_instr = self.program.get_instruction_at_execution_point(
current_ep)
for succ_ep in current_instr.get_successors_checked():
graph.add_edge(current_ep, succ_ep)
g.edge(str(hex(current_instr.address)),
str(
hex(
self.program.get_instruction_at_execution_point(
succ_ep).address)),
label=None)
#g.edge(current_instr, self.program.get_instruction_at_execution_point(succ_ep),label=None)
if succ_ep not in visited:
visited.add(succ_ep)
to_visit.append(succ_ep)
g.view()
self.program.possible_exit_points = [
ep for ep in graph if graph.out_degree(ep) == 0
]
if len(self.program.possible_exit_points
) > 0 and self.program.exit_point is None:
self.program.exit_point = self.program.possible_exit_points[-1]
imm_doms = nx.immediate_dominators(graph, starting_ep)
graph_reverse = graph.reverse()
post_doms = [
nx.immediate_dominators(graph_reverse, exit_ep)
for exit_ep in self.program.possible_exit_points
]
for ep in graph:
instr = self.program.get_instruction_at_execution_point(ep)
possible_post_dominators = {pd.get(ep, None) for pd in post_doms}
if len(possible_post_dominators) == 1:
instr.immediate_post_dominator = possible_post_dominators.pop()
instr.predecessors = graph.predecessors(ep)
instr.immediate_dominator = imm_doms[ep]
return graph
def test_boost_example(self):
# Graph taken from Figure 1 of
# http://www.boost.org/doc/libs/1_56_0/libs/graph/doc/lengauer_tarjan_dominator.htm
edges = [(0, 1), (1, 2), (1, 3), (2, 7), (3, 4), (4, 5), (4, 6),
(5, 7), (6, 4)]
G = nx.DiGraph(edges)
assert_equal(nx.immediate_dominators(G, 0),
{0: 0, 1: 0, 2: 1, 3: 1, 4: 3, 5: 4, 6: 4, 7: 1})
# Test postdominance.
with nx.utils.reversed(G):
assert_equal(nx.immediate_dominators(G, 7),
{0: 1, 1: 7, 2: 7, 3: 4, 4: 5, 5: 7, 6: 4, 7: 7})
def _execute_graph(data):
log("executing graph")
controlflow = _get_required_controlflow_graph(data)
splits = []
for n, idom in nx.immediate_dominators(controlflow, root_op).items():
if n == idom:
continue
if n in controlflow.successors(idom):
continue
splits.append((idom, n))
# Graph mode
order = list(nx.topological_sort(controlflow))
iteration = 0
max_threads = 4
while iteration < len(order):
ops = []
for i in range(max_threads):
if iteration >= len(order):
break
next_op = order[iteration]
if sum([op in nx.ancestors(controlflow, next_op)
for op in ops]) > 0:
break
ops.append(order[iteration])
iteration += 1
_run_ops_in_parallel(ops)
def test_unreachable(self):
n = 5
assert n > 1
G = nx.path_graph(n, create_using=nx.DiGraph())
assert (nx.immediate_dominators(
G, n // 2) == {i: max(i - 1, n // 2)
for i in range(n // 2, n)})
def acyclic_dominance_frontier(sdfg: SDFG, idom=None) -> Dict[SDFGState, Set[SDFGState]]:
"""
Finds the dominance frontier for an SDFG while ignoring any back edges.
This is a modified version of the dominance frontiers algorithm as
implemented by networkx.
:param sdfg: The SDFG for which to compute the acyclic dominance frontier.
:param idom: Optional precomputed immediate dominators.
:return: A dictionary keyed by states, containing the dominance frontier
for each SDFG state.
"""
idom = idom or nx.immediate_dominators(sdfg.nx, sdfg.start_state)
dom_frontiers = {state: set() for state in sdfg.nodes()}
for u in idom:
if len(sdfg.nx.pred[u]) >= 2:
for v in sdfg.nx.pred[u]:
if v in idom:
df_candidates = set()
while v != idom[u]:
if v == u:
df_candidates = None
break
df_candidates.add(v)
v = idom[v]
if df_candidates is not None:
for candidate in df_candidates:
dom_frontiers[candidate].add(u)
return dom_frontiers
def buildPdomTree(entryID, exitID, funName, CFGsR):
'''build post domains tree
Construct the postdominator tree for AugCFG
:param entryID:
:param exitID:
:param funName:
:param CFGsR:
:return:
'''
# Augment the CFG by adding a node Start with edge (Start, entry)
# labeled “T” and edge (Start, exit) labeled “F”;call this AugCFG
CFGsR.add_edges_from([(entryID, funName), (exitID, funName)])
nxPdomDict = nx.immediate_dominators(CFGsR, exitID)
# PdomEdgeDict = dict()
PdomEdges = list()
for i in nxPdomDict:
# if getNodeIDNo(nxPdomDict[i],CFGsR) not in PdomEdgeDict:
# PdomEdgeDict[getNodeIDNo(nxPdomDict[i],CFGsR)] = list()
if (nxPdomDict[i] != i):
# PdomEdgeDict[getNodeIDNo(nxPdomDict[i],CFGsR)].append(getNodeIDNo(i,CFGsR))
PdomEdges.append((nxPdomDict[i], i))
# print(PdomEdgeDict)
PdomTree = nx.DiGraph()
PdomTree.add_edges_from(PdomEdges)
return PdomTree
def dominate(name):
for (n, _) in find_nodes(name):
lst = dict((nx.immediate_dominators(G, n).items()))
out.write(str(lst))
print(len(lst))
for (t, _) in targets:
domination = []
temp = [t]
while not (temp.__contains__(n)):
list_p = []
for tt in temp:
shortest = nx.dijkstra_path_length(G, lst[tt], tt)
print("shortest:" + str(shortest))
if shortest > 3:
parent = list(G.predecessors(tt))
print(parent)
for p in parent:
if p in lst.keys():
# shortest = nx.dijkstra_path_length(G, lst[p], tt)
# print("shortest:" + str(shortest))
if nx.dijkstra_path_length(G, lst[p], tt) <= 3:
list_p.append(lst[p])
else:
list_p.append(lst[tt])
list_p = list(set(list_p))
temp = list_p
list_n = []
for l in list_p:
node = G.nodes[l]['label']
node = re.sub(r'[^\w\s]', '', node)
print(node)
list_n.append(node)
domination.append(list_n)
print(domination)
def _build_dom_sets(self, graph: nx.DiGraph, gname=''):
v_entry = 'virtual_entry'
graph.add_edges_from(
((v_entry, node) for node, i in tuple(graph.in_degree) if i == 0))
if v_entry not in graph:
err_msg = f'Failed to find an entry to build dominance tree for {gname}'
logging.error(err_msg)
raise NoEntryForDomTreeError(err_msg)
dom_tree = nx.DiGraph()
dom_tree.add_nodes_from(graph.nodes)
for node, dominator in nx.immediate_dominators(graph, v_entry).items():
dom_tree.add_edge(dominator, node)
dom_tree.remove_node(v_entry)
dominances = {
node: set.union(nx.descendants(dom_tree, node), {
node,
})
for node in dom_tree.nodes
}
frontier = nx.dominance_frontiers(graph, v_entry)
frontier.pop(v_entry)
graph.remove_node(v_entry)
return dom_tree, dominances, frontier
def test_irreducible1(self):
# Graph taken from Figure 2 of
# K. D. Cooper, T. J. Harvey, and K. Kennedy.
# A simple, fast dominance algorithm.
# Software Practice & Experience, 4:110, 2001.
edges = [(1, 2), (2, 1), (3, 2), (4, 1), (5, 3), (5, 4)]
G = nx.DiGraph(edges)
assert (nx.immediate_dominators(G, 5) == {i: 5 for i in range(1, 6)})
def get_fixed_strings(r):
# convert regex to graph
G = nx.MultiDiGraph()
cmd = ["./src/tools/util/regex2dfa", "-r", r]
s = subprocess.run(cmd,
stdout=subprocess.PIPE,
stderr=subprocess.PIPE,
check=True).stdout.decode("utf-8")
end = None
for l in s.splitlines():
items = l.split("\t")
if len(items) == 4:
a, b, i, o = map(int, items)
G.add_edge(a, b, label=(i).to_bytes(length=1, byteorder="big"))
else:
assert len(items) == 1
end = int(items[0])
break
assert end is not None
# convenciente function
def get_edges(u):
ret = []
for v in G[u]:
for i in G[u][v]:
ret.append((u, v, G[u][v][i]["label"]))
return ret
# get relevant nodes
start = 0
dom = nx.immediate_dominators(G, start)
relevant = [end]
node = end
while node != start:
node = dom[node]
relevant.append(node)
relevant = relevant[::-1]
# get fixed strings starting from relevant nodes
# idea: check if a node has only one edge, collect the label and continue
# until a branch is discovered
strs = {}
seen = set()
for node in relevant:
strs[node] = []
edges = get_edges(node)
while len(edges) == 1:
u, v, l = edges[0]
if u in seen or u == end:
break
seen.add(u)
strs[node].append(l)
edges = get_edges(v)
return list(
set([
b"".join(l) for l in sorted(strs.values(), key=len, reverse=True)
if len(l) > 0
]))
def dominator_forest(self):
if self._dominator_forest is not None:
return self._dominator_forest
self._dominator_forest = DAG()
for root in self.roots:
for node, dominated_by in nx.immediate_dominators(self, root).items():
if node != dominated_by:
self._dominator_forest.add_edge(dominated_by, node)
return self._dominator_forest
def test_irreducible1(self):
# Graph taken from Figure 2 of
# K. D. Cooper, T. J. Harvey, and K. Kennedy.
# A simple, fast dominance algorithm.
# Software Practice & Experience, 4:110, 2001.
edges = [(1, 2), (2, 1), (3, 2), (4, 1), (5, 3), (5, 4)]
G = nx.DiGraph(edges)
assert_equal(nx.immediate_dominators(G, 5),
{i: 5 for i in range(1, 6)})
def _build_dom_tree(self, digraph, entry):
if len(digraph.nodes) == 1:
self._domTree.add_node(entry)
return
# Code below assumes digraph has more then one node
idom_list = nx.immediate_dominators(digraph, entry).items()
for tup in idom_list:
if tup[0] == entry:
continue
self._domTree.add_edge(tup[1], tup[0])
def test_irreducible2(self):
# Graph taken from Figure 4 of
# K. D. Cooper, T. J. Harvey, and K. Kennedy.
# A simple, fast dominance algorithm.
# Software Practice & Experience, 4:110, 2001.
edges = [(1, 2), (2, 1), (2, 3), (3, 2), (4, 2), (4, 3), (5, 1),
(6, 4), (6, 5)]
G = nx.DiGraph(edges)
assert_equal(nx.immediate_dominators(G, 6),
dict((i, 6) for i in range(1, 7)))
def _compute_dominators(self):
import networkx
g = networkx.DiGraph()
for bb in self.bbs:
for succ in bb.succ:
g.add_edge(bb.start, succ.start)
self._dominators = {
self._bb_at[k]: self._bb_at[v]
for k, v in networkx.immediate_dominators(g, 0).items()
}
def dependencies(g, entry):
dominators = nx.immediate_dominators(g, entry)
deps = []
for n in g.nodes():
for m in g.nodes():
ifdom = dominators[m]
if any([ifdom not in path for path in nx.all_simple_paths(g, n, m)]):
deps.append((m, n))
return deps
def dominance_frontiers(G, start):
"""Returns the dominance frontiers of all nodes of a directed graph.
Parameters
----------
G : a DiGraph or MultiDiGraph
The graph where dominance is to be computed.
start : node
The start node of dominance computation.
Returns
-------
df : dict keyed by nodes
A dict containing the dominance frontiers of each node reachable from
``start`` as lists.
Raises
------
NetworkXNotImplemented
If ``G`` is undirected.
NetworkXError
If ``start`` is not in ``G``.
Examples
--------
>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
>>> sorted((u, sorted(df)) for u, df in nx.dominance_frontiers(G, 1).items())
[(1, []), (2, [5]), (3, [5]), (4, [5]), (5, [])]
References
----------
.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
A simple, fast dominance algorithm.
Software Practice & Experience, 4:110, 2001.
"""
idom = nx.immediate_dominators(G, start)
df = {u: [] for u in idom}
for u in idom:
if len(G.pred[u]) - int(u in G.pred[u]) >= 2:
p = set()
for v in G.pred[u]:
while v != idom[u] and v not in p:
p.add(v)
v = idom[v]
p.discard(u)
for v in p:
df[v].append(u)
return df
def dominance_frontiers(G, start):
"""Returns the dominance frontiers of all nodes of a directed graph.
Parameters
----------
G : a DiGraph or MultiDiGraph
The graph where dominance is to be computed.
start : node
The start node of dominance computation.
Returns
-------
df : dict keyed by nodes
A dict containing the dominance frontiers of each node reachable from
`start` as lists.
Raises
------
NetworkXNotImplemented
If `G` is undirected.
NetworkXError
If `start` is not in `G`.
Examples
--------
>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
>>> sorted((u, sorted(df)) for u, df in nx.dominance_frontiers(G, 1).items())
[(1, []), (2, [5]), (3, [5]), (4, [5]), (5, [])]
References
----------
.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
A simple, fast dominance algorithm.
Software Practice & Experience, 4:110, 2001.
"""
idom = nx.immediate_dominators(G, start)
df = {u: [] for u in idom}
for u in idom:
if len(G.pred[u]) - int(u in G.pred[u]) >= 2:
p = set()
for v in G.pred[u]:
while v != idom[u] and v not in p:
p.add(v)
v = idom[v]
p.discard(u)
for v in p:
df[v].append(u)
return df
def _post_dominate(reversed_graph, n1, n2):
"""
Checks whether `n1` post-dominates `n2` in the *original* (not reversed) graph.
:param networkx.DiGraph reversed_graph: The reversed networkx.DiGraph instance.
:param networkx.Node n1: Node 1.
:param networkx.Node n2: Node 2.
:returns bool: True/False.
"""
ds = networkx.immediate_dominators(reversed_graph, n1)
return n2 in ds
def _post_dominate(reversed_graph, n1, n2):
"""
Checks whether `n1` post-dominates `n2` in the *original* (not reversed) graph.
:param networkx.DiGraph reversed_graph: The reversed networkx.DiGraph instance.
:param networkx.Node n1: Node 1.
:param networkx.Node n2: Node 2.
:returns bool: True/False.
"""
ds = networkx.immediate_dominators(reversed_graph, n1)
return n2 in ds
def test_domrel_png(self):
# Graph taken from https://commons.wikipedia.org/wiki/File:Domrel.png
edges = [(1, 2), (2, 3), (2, 4), (2, 6), (3, 5), (4, 5), (5, 2)]
G = nx.DiGraph(edges)
assert (nx.immediate_dominators(G, 1) == {
1: 1,
2: 1,
3: 2,
4: 2,
5: 2,
6: 2
})
# Test postdominance.
with nx.utils.reversed(G):
assert (nx.immediate_dominators(G, 6) == {
1: 2,
2: 6,
3: 5,
4: 5,
5: 2,
6: 6
})
def nx_dominators(G, node_target, node_start='b0'):
# get dominator tree, parent is immediate dominator
lookup = nx.immediate_dominators(G, node_start)
assert node_target in lookup
# walk up the tree
result = []
current = node_target
while True:
result.append(current)
if current == node_start:
break
current = lookup[current]
return result
def all_dominators(sdfg: SDFG, idom: Dict[SDFGState, SDFGState] = None) -> Dict[SDFGState, Set[SDFGState]]:
""" Returns a mapping between each state and all its dominators. """
idom = idom or nx.immediate_dominators(sdfg.nx, sdfg.start_state)
# Create a dictionary of all dominators of each node by using the
# transitive closure of the DAG induced by the idoms
g = nx.DiGraph()
for node, dom in idom.items():
if node is dom: # Skip root
continue
g.add_edge(node, dom)
tc = nx.transitive_closure_dag(g)
alldoms: Dict[SDFGState, Set[SDFGState]] = {sdfg.start_state: set()}
for node in tc:
alldoms[node] = set(dst for _, dst in tc.out_edges(node))
return alldoms
def dom(p):
g = nx.DiGraph(p.cfg_edges)
d = nx.immediate_dominators(g, p.entry)
roots = [node for node, idom in d.items() if node == idom]
gd = nx.DiGraph((idom, node) for node, idom in d.items()
if node != idom)
r, s = [], []
for root in roots:
r.extend(nx.dfs_preorder_nodes(gd, root))
s.extend(nx.dfs_postorder_nodes(gd, root))
p = {b: i for i, b in enumerate(r)}
q = {b: i for i, b in enumerate(s)}
return TreeQueries(p, q), d
def _refine_loop(self, graph, head, initial_loop_nodes, initial_exit_nodes):
refined_loop_nodes = initial_loop_nodes.copy()
refined_exit_nodes = initial_exit_nodes.copy()
idom = networkx.immediate_dominators(graph, self._start_node)
n_new = refined_exit_nodes
while len(refined_exit_nodes) > 1 and len(n_new) != 0:
n_new = set()
for n in list(refined_exit_nodes):
if len(set(graph.predecessors(n)) - refined_loop_nodes) == 0:
refined_loop_nodes.add(n)
refined_exit_nodes.remove(n)
for u in (set(graph.successors(n)) - refined_loop_nodes):
if self._dominates(idom, head, n):
n_new.add(u)
refined_exit_nodes |= n_new
return refined_loop_nodes, refined_exit_nodes
def _refine_loop(self, graph, head, initial_loop_nodes, initial_exit_nodes):
refined_loop_nodes = initial_loop_nodes.copy()
refined_exit_nodes = initial_exit_nodes.copy()
idom = networkx.immediate_dominators(graph, self._start_node)
n_new = refined_exit_nodes
while len(refined_exit_nodes) > 1 and len(n_new) != 0:
n_new = set()
for n in list(refined_exit_nodes):
if len(set(graph.predecessors(n)) - refined_loop_nodes) == 0:
refined_loop_nodes.add(n)
refined_exit_nodes.remove(n)
for u in (set(graph.successors(n)) - refined_loop_nodes):
if self._dominates(idom, head, n):
n_new.add(u)
refined_exit_nodes |= n_new
return refined_loop_nodes, refined_exit_nodes
def build_dominators(self, root: str):
"""
This builds the requisite dominator structures:
dominator tree, immediate dominators, and dominance frontier
for each function present in the program.
:param root: Name of function to build for.
:return: None
"""
self.frontier[root] = nx.dominance_frontiers(
self.program.bb_graph, self.program.functions[root]['entry'])
self.idoms[root] = nx.immediate_dominators(
self.program.bb_graph, self.program.functions[root]['entry'])
self.dominator_tree[root] = defaultdict(lambda: set())
for key, value in self.idoms[root].items():
# Ensure a self dominated node isn't added
# This guarantees no infinite iteration
if key != value:
self.dominator_tree[root][value].add(key)
def compare_immediate_dominators(self, start, end, edges):
G = nx.DiGraph(edges)
idom_nx = sorted(nx.immediate_dominators(G, start).items())
cfg = ControlFlowGraph.fromEdgeList(start, end, edges)
dom = dominators(cfg)
idom_hw = immediateDominator(dom)
# print(idom_nx)
# print(idom_hw)
for node, idom in idom_nx:
if node == start:
self.assertEqual(idom_hw[node], '')
else:
self.assertEqual(
idom_hw[node], idom,
"nx: {}, homework: {}".format(idom_nx, idom_hw))
def _refine_loop(self, graph, head, initial_loop_nodes, initial_exit_nodes):
refined_loop_nodes = initial_loop_nodes.copy()
refined_exit_nodes = initial_exit_nodes.copy()
idom = networkx.immediate_dominators(graph, self._start_node)
new_exit_nodes = refined_exit_nodes
while len(refined_exit_nodes) > 1 and new_exit_nodes:
new_exit_nodes = set()
for n in list(refined_exit_nodes):
if all(pred in refined_loop_nodes for pred in graph.predecessors(n)) and dominates(idom, head, n):
refined_loop_nodes.add(n)
refined_exit_nodes.remove(n)
for u in (set(graph.successors(n)) - refined_loop_nodes):
new_exit_nodes.add(u)
refined_exit_nodes |= new_exit_nodes
refined_loop_nodes = refined_loop_nodes - refined_exit_nodes
return refined_loop_nodes, refined_exit_nodes
def _update_stable(self):
# compute stable vertices
self.log("""== Computing the stable vertices ==""")
# compute immediate dominators
self.dominators = networkx.immediate_dominators(self.N, self.root)
# for each vertex, assign a leaf that they are stable on
self.stability = dict((u, u) for u in self.leaves)
X = list(self.leaves.copy())
while X:
u = X.pop()
v = self.dominators[u]
if v not in self.stability:
self.stability[v] = u
X.append(v)
if self.verbose:
self.log('immediate dominators:')
for u in self.stability:
if self.is_stable(u):
self.log(str(u) + ': ' + str(self.stability[u]))
def get_dominator_graphs(self):
assert self.forwarding_graphs, "Forwarding Graph needs to be built before the Dominator Graphs"
for subnet, forwarding_graph in self.forwarding_graphs.items():
rev_graph = forwarding_graph.reverse(copy=True)
try:
dominators = set(
nx.immediate_dominators(rev_graph, 'sink').items())
except nx.NetworkXError as e:
self.logger.error(
"Sink node is not in the forwarding graph for {subnet}. "
"Official error message: {error}".format(subnet=subnet,
error=e))
# sys.exit(1)
else:
if ("sink", "sink") in dominators:
dominators.remove(("sink", "sink"))
tmp_dominator_graph = nx.DiGraph(list(dominators))
self.dominator_graphs[subnet] = tmp_dominator_graph
return self.dominator_graphs
edges = []
with open('edges.txt') as fedges:
for line in fedges:
e = line.split()
edges.append((int(e[0]),int(e[1])))
# creating the graph from edges.txt
graph=nx.DiGraph()
graph.add_nodes_from(IDs)
graph.add_edges_from(edges)
dftree = nx.dfs_tree(graph,0)
#tree = nx.dfs_edges(graph)
imdom = sorted(nx.immediate_dominators(graph, 0).items()) # immediante dominance
dom_tree = nx.DiGraph()
#dom_tree.add_nodes_from(IDs)
dom_tree.add_edges_from(imdom)
fdomtree = open("domtree.txt",'w')
fdomtree.write('\n'.join('%s %s' % (str(x[0]), str(x[1])) for x in dftree.edges()))
fdomtree.close()
#nx.draw_graphviz(dftree, with_labels = True)
# drawings
# nx.draw_networkx(dom_tree, with_labels = True)
#nx.draw(graph)
def recover_reaching_conditions(self,
region,
with_successors=False,
jump_tables=None):
def _strictly_postdominates(inv_idoms, node_a, node_b):
"""
Does node A strictly post-dominate node B on the graph?
"""
return dominates(inv_idoms, node_a, node_b)
edge_conditions = {}
predicate_mapping = {}
# traverse the graph to recover the condition for each edge
for src in region.graph.nodes():
nodes = list(region.graph[src])
if len(nodes) >= 1:
for dst in nodes:
edge = src, dst
edge_data = region.graph.get_edge_data(*edge)
edge_type = edge_data.get('type', 'transition')
try:
predicate = self._extract_predicate(
src, dst, edge_type)
except EmptyBlockNotice:
# catch empty block notice - although this should not really happen
predicate = claripy.true
edge_conditions[edge] = predicate
predicate_mapping[predicate] = dst
if jump_tables:
self.recover_reaching_conditions_for_jumptables(
region, jump_tables, edge_conditions)
if with_successors and region.graph_with_successors is not None:
_g = region.graph_with_successors
else:
_g = region.graph
end_nodes = {n for n in _g.nodes() if _g.out_degree(n) == 0}
inverted_graph = shallow_reverse(_g)
if end_nodes:
if len(end_nodes) > 1:
# make sure there is only one end node
dummy_node = "DUMMY_NODE"
for end_node in end_nodes:
inverted_graph.add_edge(dummy_node, end_node)
endnode = dummy_node
else:
endnode = next(iter(end_nodes)) # pick the end node
idoms = networkx.immediate_dominators(inverted_graph, endnode)
else:
idoms = None
reaching_conditions = {}
# recover the reaching condition for each node
sorted_nodes = CFGUtils.quasi_topological_sort_nodes(_g)
terminating_nodes = []
for node in sorted_nodes:
preds = _g.predecessors(node)
reaching_condition = None
out_degree = _g.out_degree(node)
if out_degree == 0:
terminating_nodes.append(node)
if node is region.head:
# the head is always reachable
reaching_condition = claripy.true
elif idoms is not None and _strictly_postdominates(
idoms, node, region.head):
# the node that post dominates the head is always reachable
reaching_conditions[node] = claripy.true
else:
for pred in preds:
edge = (pred, node)
pred_condition = reaching_conditions.get(
pred, claripy.true)
edge_condition = edge_conditions.get(edge, claripy.true)
if reaching_condition is None:
reaching_condition = claripy.And(
pred_condition, edge_condition)
else:
reaching_condition = claripy.Or(
claripy.And(pred_condition, edge_condition),
reaching_condition)
if reaching_condition is not None:
reaching_conditions[node] = self.simplify_condition(
reaching_condition)
# My hypothesis to be proved: in any regioned graph, there must be a node with a 0 out-degree whose reaching
# conditions can be marked as True. In other words, if all 0 out-degree nodes have non-trivial reaching
# conditions, we can always pick one of them and change its reaching condition to True, without changing the
# semantics of the regioned graph.
if terminating_nodes and all(not reaching_conditions[node].is_true()
for node in terminating_nodes
if node in reaching_conditions):
# pick the node with the greatest in-degree
terminating_nodes = sorted(terminating_nodes, key=_g.in_degree)
node_with_greatest_indegree = terminating_nodes[-1]
if _g.in_degree(node_with_greatest_indegree) > 1:
# forcing the in-degree to be greater than 1 allows us to skip the case blocks in switch-cases
# otherwise structurer will fail to structure the control flow
reaching_conditions[node_with_greatest_indegree] = claripy.true
l.warning(
"Marking node %r as trivially reachable. Disable this optimization in condition_processor.py "
"if it leads to incorrect decompilation result.",
node_with_greatest_indegree)
# Another hypothesis: for nodes where two paths come together *and* those that cannot be further structured into
# another if-else construct (we take the short-cut by testing if the operator is an "Or" after running our
# condition simplifiers previously), we are better off using their "guarding conditions" instead of their
# reaching conditions for if-else. see my super long chatlog with rhelmot on 5/14/2021.
guarding_conditions = {}
for the_node in sorted_nodes:
preds = list(_g.predecessors(the_node))
if len(preds) != 2:
continue
# generate a graph slice that goes from the region head to this node
slice_nodes = list(networkx.dfs_tree(inverted_graph, the_node))
subgraph = networkx.subgraph(_g, slice_nodes)
# figure out which paths cause the divergence from this node
nodes_do_not_reach_the_node = set()
for node_ in subgraph:
if node_ is the_node:
continue
for succ in _g.successors(node_):
if not networkx.has_path(_g, succ, the_node):
nodes_do_not_reach_the_node.add(succ)
diverging_conditions = []
for node_ in nodes_do_not_reach_the_node:
preds_ = list(_g.predecessors(node_))
for pred_ in preds_:
if pred_ in nodes_do_not_reach_the_node:
continue
# this predecessor is the diverging node!
edge_ = pred_, node_
edge_condition = edge_conditions.get(edge_, None)
if edge_condition is not None:
diverging_conditions.append(edge_condition)
if diverging_conditions:
# the negation of the union of diverging conditions is the guarding condition for this node
cond = claripy.Or(*map(claripy.Not, diverging_conditions))
guarding_conditions[the_node] = cond
self.reaching_conditions = reaching_conditions
self.guarding_conditions = guarding_conditions
def test_cycle(self):
n = 5
G = nx.cycle_graph(n, create_using=nx.DiGraph())
assert_equal(nx.immediate_dominators(G, 0),
{i: max(i - 1, 0) for i in range(n)})
def test_unreachable(self):
n = 5
assert_greater(n, 1)
G = nx.path_graph(n, create_using=nx.DiGraph())
assert_equal(nx.immediate_dominators(G, n // 2),
{i: max(i - 1, n // 2) for i in range(n // 2, n)})
def recover_reaching_conditions(self, region, with_successors=False, jump_tables=None):
def _strictly_postdominates(inv_idoms, node_a, node_b):
"""
Does node A strictly post-dominate node B on the graph?
"""
return dominates(inv_idoms, node_a, node_b)
edge_conditions = {}
predicate_mapping = {}
# traverse the graph to recover the condition for each edge
for src in region.graph.nodes():
nodes = list(region.graph[src])
if len(nodes) >= 1:
for dst in nodes:
edge = src, dst
edge_data = region.graph.get_edge_data(*edge)
edge_type = edge_data.get('type', 'transition')
try:
predicate = self._extract_predicate(src, dst, edge_type)
except EmptyBlockNotice:
# catch empty block notice - although this should not really happen
predicate = claripy.true
edge_conditions[edge] = predicate
predicate_mapping[predicate] = dst
if jump_tables:
self.recover_reaching_conditions_for_jumptables(region, jump_tables, edge_conditions)
if with_successors and region.graph_with_successors is not None:
_g = region.graph_with_successors
else:
_g = region.graph
end_nodes = {n for n in _g.nodes() if _g.out_degree(n) == 0}
if end_nodes:
inverted_graph = shallow_reverse(_g)
if len(end_nodes) > 1:
# make sure there is only one end node
dummy_node = "DUMMY_NODE"
for end_node in end_nodes:
inverted_graph.add_edge(dummy_node, end_node)
endnode = dummy_node
else:
endnode = next(iter(end_nodes)) # pick the end node
idoms = networkx.immediate_dominators(inverted_graph, endnode)
else:
idoms = None
reaching_conditions = {}
# recover the reaching condition for each node
sorted_nodes = CFGUtils.quasi_topological_sort_nodes(_g)
terminating_nodes = [ ]
for node in sorted_nodes:
preds = _g.predecessors(node)
reaching_condition = None
out_degree = _g.out_degree(node)
if out_degree == 0:
terminating_nodes.append(node)
if node is region.head:
# the head is always reachable
reaching_condition = claripy.true
elif idoms is not None and _strictly_postdominates(idoms, node, region.head):
# the node that post dominates the head is always reachable
reaching_conditions[node] = claripy.true
else:
for pred in preds:
edge = (pred, node)
pred_condition = reaching_conditions.get(pred, claripy.true)
edge_condition = edge_conditions.get(edge, claripy.true)
if reaching_condition is None:
reaching_condition = claripy.And(pred_condition, edge_condition)
else:
reaching_condition = claripy.Or(claripy.And(pred_condition, edge_condition), reaching_condition)
if reaching_condition is not None:
reaching_conditions[node] = self.simplify_condition(reaching_condition)
# My hypothesis to be proved: in any regioned graph, there must be a node with a 0 out-degree whose reaching
# conditions can be marked as True. In other words, if all 0 out-degree nodes have non-trivial reaching
# conditions, we can always pick one of them and change its reaching condition to True, without changing the
# semantics of the regioned graph.
if terminating_nodes and all(not reaching_conditions[node].is_true() for node in terminating_nodes
if node in reaching_conditions):
# pick the node with the greatest in-degree
terminating_nodes = sorted(terminating_nodes, key=_g.in_degree)
node_with_greatest_indegree = terminating_nodes[-1]
if _g.in_degree(node_with_greatest_indegree) > 1:
# forcing the in-degree to be greater than 1 allows us to skip the case blocks in switch-cases
# otherwise structurer will fail to structure the control flow
reaching_conditions[node_with_greatest_indegree] = claripy.true
l.warning("Marking node %r as trivially reachable. Disable this optimization in condition_processor.py "
"if it leads to incorrect decompilation result.", node_with_greatest_indegree)
self.reaching_conditions = reaching_conditions
def test_singleton(self):
G = nx.DiGraph()
G.add_node(0)
assert_equal(nx.immediate_dominators(G, 0), {0: 0})
G.add_edge(0, 0)
assert_equal(nx.immediate_dominators(G, 0), {0: 0})