from __future__ import print_function, division, absolute_import
import collections
import functools
import sys
from numba import utils
# List of bytecodes creating a new block in the control flow graph
# (in addition to explicit jump labels).
NEW_BLOCKERS = frozenset(['SETUP_LOOP', 'FOR_ITER', 'SETUP_WITH'])
class CFBlock(object):
def __init__(self, offset):
self.offset = offset
self.body = []
# A map of jumps to outgoing blocks (successors):
# { offset of outgoing block -> number of stack pops }
self.outgoing_jumps = {}
# A map of jumps to incoming blocks (predecessors):
# { offset of incoming block -> number of stack pops }
self.incoming_jumps = {}
self.terminating = False
def __repr__(self):
args = self.offset, sorted(self.outgoing_jumps), sorted(self.incoming_jumps)
return "block(offset:%d, outgoing: %s, incoming: %s)" % args
def __iter__(self):
return iter(self.body)
class Loop(
collections.namedtuple("Loop", ("entries", "exits", "header", "body"))):
"""
A control flow loop, as detected by a CFGraph object.
"""
__slots__ = ()
# The loop header is enough to detect that two loops are really
# the same, assuming they belong to the same graph.
# (note: in practice, only one loop instance is created per graph
# loop, so identity would be fine)
def __eq__(self, other):
return isinstance(other, Loop) and other.header == self.header
def __hash__(self):
return hash(self.header)
class CFGraph(object):
"""
Generic (almost) implementation of a Control Flow Graph.
"""
def __init__(self):
self._nodes = set()
self._preds = collections.defaultdict(set)
self._succs = collections.defaultdict(set)
self._edge_data = {}
self._entry_point = None
def add_node(self, node):
"""
Add *node* to the graph. This is necessary before adding any
edges from/to the node. *node* can be any hashable object.
"""
self._nodes.add(node)
def add_edge(self, src, dest, data=None):
"""
Add an edge from node *src* to node *dest*, with optional
per-edge *data*.
If such an edge already exists, it is replaced (duplicate edges
are not possible).
"""
assert src in self._nodes
assert dest in self._nodes
self._add_edge(src, dest, data)
def successors(self, src):
"""
Yield (node, data) pairs representing the successors of node *src*.
(*data* will be None if no data was specified when adding the edge)
"""
for dest in self._succs[src]:
yield dest, self._edge_data[src, dest]
def predecessors(self, dest):
"""
Yield (node, data) pairs representing the predecessors of node *dest*.
(*data* will be None if no data was specified when adding the edge)
"""
for src in self._preds[dest]:
yield src, self._edge_data[src, dest]
def set_entry_point(self, node):
"""
Set the entry point of the graph to *node*.
"""
assert node in self._nodes
self._entry_point = node
def process(self):
"""
Compute various properties of the control flow graph. The graph
must have been fully populated, and its entry point specified.
"""
if self._entry_point is None:
raise RuntimeError("no entry point defined!")
self._eliminate_dead_blocks()
self._find_exit_points()
self._find_dominators()
self._find_back_edges()
self._find_topo_order()
self._find_descendents()
self._find_loops()
self._find_post_dominators()
def dominators(self):
"""
Return a dictionary of {node -> set(nodes)} mapping each node to
the nodes dominating it.
A node D dominates a node N when any path leading to N must go through D.
"""
return self._doms
def post_dominators(self):
"""
Return a dictionary of {node -> set(nodes)} mapping each node to
the nodes post-dominating it.
A node P post-dominates a node N when any path starting from N must go
through P.
"""
return self._post_doms
def descendents(self, node):
"""
Return the set of descendents of the given *node*, in topological
order (ignoring back edges).
"""
return self._descs[node]
def entry_point(self):
"""
Return the entry point node.
"""
assert self._entry_point is not None
return self._entry_point
def exit_points(self):
"""
Return the computed set of exit nodes (may be empty).
"""
return self._exit_points
def backbone(self):
"""
Return the set of nodes constituting the graph's backbone.
(i.e. the nodes that every path starting from the entry point
must go through). By construction, it is non-empty: it contains
at least the entry point.
"""
return self._post_doms[self._entry_point]
def loops(self):
"""
Return a dictionary of {node -> loop} mapping each loop header
to the loop (a Loop instance) starting with it.
"""
return self._loops
def in_loops(self, node):
"""
Return the list of Loop objects the *node* belongs to,
from innermost to outermost.
"""
return [self._loops[x] for x in self._in_loops[node]]
def dead_nodes(self):
"""
Return the set of dead nodes (eliminated from the graph).
"""
return self._dead_nodes
def nodes(self):
"""
Return the set of live nodes.
"""
return self._nodes
def topo_order(self):
"""
Return the sequence of nodes in topological order (ignoring back
edges).
"""
return self._topo_order
def topo_sort(self, nodes, reverse=False):
"""
Iterate over the *nodes* in topological order (ignoring back edges).
The sort isn't guaranteed to be stable.
"""
nodes = set(nodes)
it = self._topo_order
if reverse:
it = reversed(it)
for n in it:
if n in nodes:
yield n
def dump(self, file=None):
"""
Dump extensive debug information.
"""
import pprint
file = file or sys.stdout
if 1:
print("CFG adjacency lists:", file=file)
self._dump_adj_lists(file)
print("CFG dominators:", file=file)
pprint.pprint(self._doms, stream=file)
print("CFG post-dominators:", file=file)
pprint.pprint(self._post_doms, stream=file)
print("CFG back edges:", sorted(self._back_edges), file=file)
print("CFG loops:", file=file)
pprint.pprint(self._loops, stream=file)
print("CFG node-to-loops:", file=file)
pprint.pprint(self._in_loops, stream=file)
# Internal APIs
def _add_edge(self, from_, to, data=None):
# This internal version allows adding edges to/from unregistered
# (ghost) nodes.
self._preds[to].add(from_)
self._succs[from_].add(to)
self._edge_data[from_, to] = data
def _remove_node_edges(self, node):
for succ in self._succs.pop(node, ()):
self._preds[succ].remove(node)
del self._edge_data[node, succ]
for pred in self._preds.pop(node, ()):
self._succs[pred].remove(node)
del self._edge_data[pred, node]
def _dfs(self, entries=None):
if entries is None:
entries = (self._entry_point,)
seen = set()
stack = list(entries)
while stack:
node = stack.pop()
if node not in seen:
yield node
seen.add(node)
for succ in self._succs[node]:
stack.append(succ)
def _eliminate_dead_blocks(self):
"""
Eliminate all blocks not reachable from the entry point, and
stash them into self._dead_nodes.
"""
live = set()
for node in self._dfs():
live.add(node)
self._dead_nodes = self._nodes - live
self._nodes = live
# Remove all edges leading from dead nodes
for dead in self._dead_nodes:
self._remove_node_edges(dead)
def _find_exit_points(self):
"""
Compute the graph's exit points.
"""
exit_points = set()
for n in self._nodes:
if not self._succs.get(n):
exit_points.add(n)
self._exit_points = exit_points
def _find_dominators_internal(self, post=False):
# See theoretical description in
# http://en.wikipedia.org/wiki/Dominator_%28graph_theory%29
# The algorithm implemented here uses a todo-list as described
# in http://pages.cs.wisc.edu/~fischer/cs701.f08/finding.loops.html
if post:
entries = set(self._exit_points)
preds_table = self._succs
succs_table = self._preds
else:
entries = set([self._entry_point])
preds_table = self._preds
succs_table = self._succs
if not entries:
raise RuntimeError("no entry points: dominator algorithm "
"cannot be seeded")
doms = {}
for e in entries:
doms[e] = set([e])
todo = []
for n in self._nodes:
if n not in entries:
doms[n] = set(self._nodes)
todo.append(n)
while todo:
n = todo.pop()
if n in entries:
continue
new_doms = set([n])
preds = preds_table[n]
if preds:
new_doms |= functools.reduce(set.intersection,
[doms[p] for p in preds])
if new_doms != doms[n]:
assert len(new_doms) < len(doms[n])
doms[n] = new_doms
todo.extend(succs_table[n])
return doms
def _find_dominators(self):
self._doms = self._find_dominators_internal(post=False)
def _find_post_dominators(self):
# To handle infinite loops correctly, we need to add a dummy
# exit point, and link members of infinite loops to it.
dummy_exit = object()
self._exit_points.add(dummy_exit)
for loop in self._loops.values():
if not loop.exits:
for b in loop.body:
self._add_edge(b, dummy_exit)
self._post_doms = self._find_dominators_internal(post=True)
# Fix the _post_doms table to make no reference to the dummy exit
del self._post_doms[dummy_exit]
for doms in self._post_doms.values():
doms.discard(dummy_exit)
self._remove_node_edges(dummy_exit)
self._exit_points.remove(dummy_exit)
# Finding loops and back edges: see
# http://pages.cs.wisc.edu/~fischer/cs701.f08/finding.loops.html
def _find_back_edges(self):
"""
Find back edges. An edge (src, dest) is a back edge if and
only if *dest* dominates *src*.
"""
back_edges = set()
for src, succs in self._succs.items():
back = self._doms[src] & succs
# In CPython bytecode, at most one back edge can flow from a
# given block.
assert len(back) <= 1
back_edges.update((src, dest) for dest in back)
self._back_edges = back_edges
def _find_topo_order(self):
succs = self._succs
back_edges = self._back_edges
post_order = []
seen = set()
def _dfs_rec(node):
if node not in seen:
seen.add(node)
for dest in succs[node]:
if (node, dest) not in back_edges:
_dfs_rec(dest)
post_order.append(node)
_dfs_rec(self._entry_point)
post_order.reverse()
self._topo_order = post_order
def _find_descendents(self):
descs = {}
for node in reversed(self._topo_order):
descs[node] = node_descs = set()
for succ in self._succs[node]:
if (node, succ) not in self._back_edges:
node_descs.add(succ)
node_descs.update(descs[succ])
self._descs = descs
def _find_loops(self):
"""
Find the loops defined by the graph's back edges.
"""
bodies = {}
for src, dest in self._back_edges:
# The destination of the back edge is the loop header
header = dest
# Build up the loop body from the back edge's source node,
# up to the source header.
body = set([header])
queue = [src]
while queue:
n = queue.pop()
if n not in body:
body.add(n)
queue.extend(self._preds[n])
# There can be several back edges to a given loop header;
# if so, merge the resulting body fragments.
if header in bodies:
bodies[header].update(body)
else:
bodies[header] = body
# Create a Loop object for each header.
loops = {}
for header, body in bodies.items():
entries = set()
exits = set()
for n in body:
entries.update(self._preds[n] - body)
exits.update(self._succs[n] - body)
loop = Loop(header=header, body=body, entries=entries, exits=exits)
loops[header] = loop
self._loops = loops
# Compute the loops to which each node belongs.
in_loops = dict((n, []) for n in self._nodes)
# Sort loops from longest to shortest
# This ensures that outer loops will come before inner loops
for loop in sorted(loops.values(), key=lambda loop: len(loop.body)):
for n in loop.body:
in_loops[n].append(loop.header)
self._in_loops = in_loops
def _dump_adj_lists(self, file):
adj_lists = dict((src, list(dests))
for src, dests in self._succs.items())
import pprint
pprint.pprint(adj_lists, stream=file)
class ControlFlowAnalysis(object):
"""
Attributes
----------
- bytecode
- blocks
- blockseq
- doms: dict of set
Dominators
- backbone: set of block offsets
The set of block that is common to all possible code path.
"""
def __init__(self, bytecode):
self.bytecode = bytecode
self.blocks = {}
self.liveblocks = {}
self.blockseq = []
self.doms = None
self.backbone = None
# Internal temp states
self._force_new_block = True
self._curblock = None
self._blockstack = []
self._loops = []
self._withs = []
def iterblocks(self):
"""
Return all blocks in sequence of occurrence
"""
for i in self.blockseq:
yield self.blocks[i]
def iterliveblocks(self):
"""
Return all live blocks in sequence of occurrence
"""
for i in self.blockseq:
if i in self.liveblocks:
yield self.blocks[i]
def incoming_blocks(self, block):
"""
Yield (incoming block, number of stack pops) pairs for *block*.
"""
for i, pops in block.incoming_jumps.items():
if i in self.liveblocks:
yield self.blocks[i], pops
def dump(self, file=None):
self.graph.dump(file=None)
def run(self):
for inst in self._iter_inst():
fname = "op_%s" % inst.opname
fn = getattr(self, fname, None)
if fn is not None:
fn(inst)
else:
assert not inst.is_jump, inst
# Close all blocks
for cur, nxt in zip(self.blockseq, self.blockseq[1:]):
blk = self.blocks[cur]
if not blk.outgoing_jumps and not blk.terminating:
blk.outgoing_jumps[nxt] = 0
graph = CFGraph()
for b in self.blocks:
graph.add_node(b)
for b in self.blocks.values():
for out, pops in b.outgoing_jumps.items():
graph.add_edge(b.offset, out, pops)
graph.set_entry_point(min(self.blocks))
graph.process()
self.graph = graph
# Fill incoming
for b in utils.itervalues(self.blocks):
for out, pops in b.outgoing_jumps.items():
self.blocks[out].incoming_jumps[b.offset] = pops
# Find liveblocks
self.liveblocks = dict((i, self.blocks[i])
for i in self.graph.nodes())
for lastblk in reversed(self.blockseq):
if lastblk in self.liveblocks:
break
else:
raise AssertionError("No live block that exits!?")
# Find backbone
backbone = self.graph.backbone()
# Filter out in loop blocks (Assuming no other cyclic control blocks)
# This is to unavoid variable defined in loops to be considered as
# function scope.
inloopblocks = set()
for b in self.blocks.keys():
for s, e in self._loops:
if s <= b < e:
inloopblocks.add(b)
self.backbone = backbone - inloopblocks
def jump(self, target, pops=0):
"""
Register a jump (conditional or not) to *target* offset.
*pops* is the number of stack pops implied by the jump (default 0).
"""
self._curblock.outgoing_jumps[target] = pops
def _iter_inst(self):
for inst in self.bytecode:
if self._use_new_block(inst):
self._start_new_block(inst)
self._curblock.body.append(inst.offset)
yield inst
def _use_new_block(self, inst):
if inst.offset in self.bytecode.labels:
res = True
elif inst.opname in NEW_BLOCKERS:
res = True
else:
res = self._force_new_block
self._force_new_block = False
return res
def _start_new_block(self, inst):
self._curblock = CFBlock(inst.offset)
self.blocks[inst.offset] = self._curblock
self.blockseq.append(inst.offset)
def op_SETUP_LOOP(self, inst):
end = inst.get_jump_target()
self._blockstack.append(end)
self._loops.append((inst.offset, end))
# TODO: Looplifting requires the loop entry be its own block.
# Forcing a new block here is the simplest solution for now.
# But, we should consider other less ad-hoc ways.
self.jump(inst.next)
self._force_new_block = True
def op_SETUP_WITH(self, inst):
end = inst.get_jump_target()
self._blockstack.append(end)
self._withs.append((inst.offset, end))
# TODO: WithLifting requires the loop entry be its own block.
# Forcing a new block here is the simplest solution for now.
# But, we should consider other less ad-hoc ways.
self.jump(inst.next)
self._force_new_block = True
def op_POP_BLOCK(self, inst):
self._blockstack.pop()
def op_FOR_ITER(self, inst):
self.jump(inst.get_jump_target())
self.jump(inst.next)
self._force_new_block = True
def _op_ABSOLUTE_JUMP_IF(self, inst):
self.jump(inst.get_jump_target())
self.jump(inst.next)
self._force_new_block = True
op_POP_JUMP_IF_FALSE = _op_ABSOLUTE_JUMP_IF
op_POP_JUMP_IF_TRUE = _op_ABSOLUTE_JUMP_IF
op_JUMP_IF_FALSE = _op_ABSOLUTE_JUMP_IF
op_JUMP_IF_TRUE = _op_ABSOLUTE_JUMP_IF
def _op_ABSOLUTE_JUMP_OR_POP(self, inst):
self.jump(inst.get_jump_target())
self.jump(inst.next, pops=1)
self._force_new_block = True
op_JUMP_IF_FALSE_OR_POP = _op_ABSOLUTE_JUMP_OR_POP
op_JUMP_IF_TRUE_OR_POP = _op_ABSOLUTE_JUMP_OR_POP
def op_JUMP_ABSOLUTE(self, inst):
self.jump(inst.get_jump_target())
self._force_new_block = True
def op_JUMP_FORWARD(self, inst):
self.jump(inst.get_jump_target())
self._force_new_block = True
def op_RETURN_VALUE(self, inst):
self._curblock.terminating = True
self._force_new_block = True
def op_RAISE_VARARGS(self, inst):
self._curblock.terminating = True
self._force_new_block = True
def op_BREAK_LOOP(self, inst):
self.jump(self._blockstack[-1])
self._force_new_block = True