Files
2019-01-16 11:48:58 +00:00

725 lines
25 KiB
Python

class SmallSet(list):
__slots__ = []
def update(self, other):
filtered = [x for x in other if x not in self]
self.extend(filtered)
def add(self, item):
if item not in self:
self.append(item)
class DiGraph(object):
'''A simple directed graph class (not necessarily a DAG).
Nodes must be hashable'''
def __init__(self, name = ""):
self.name = name
self.pred = {}
self.succ = {}
self.all_nodes = []
self.node_annotations = {}
self.edge_annotations = {}
def add_node(self, n):
'Add a node to the graph'
if n not in self.succ:
self.pred[n] = SmallSet()
self.succ[n] = SmallSet()
self.all_nodes.append(n)
def add_edge(self, x, y):
'''Add an edge (x -> y) to the graph. Return true if x, y was
previously in graph'''
if x in self.succ:
if y in self.succ[x]:
return True
else:
self.add_node(x)
self.add_node(y)
self.pred[y].add(x)
self.succ[x].add(y)
return False
def remove_node(self, x):
if x not in self.succ:
raise ValueError("Node %s does not exist." % x)
preds = self.pred[x]
succs = self.succ[x]
for p in preds:
self.succ[p].remove(x)
for s in succs:
self.pred[s].remove(x)
del self.succ[x]
del self.pred[x]
def remove_edge(self, x, y):
self.pred[y].remove(x)
self.succ[x].remove(y)
def annotate_edge(self, x, y, note):
'''Set the annotation on the edge (x -> y) to note.
'''
if x not in self.succ or y not in self.succ[x]:
raise ValueError("Edge %s -> %s does not exist." % (x, y))
self.edge_annotations[(x,y)] = note
def annotate_node(self, x, note):
'''Set the annotation on the node x to note.
'''
if x not in self.succ:
raise ValueError("Node %s does not exist." % x)
self.node_annotations[x] = note
def nodes(self):
'''Return an iterator for all nodes, in the form (node, note) pairs.
Do not modify the graph while using this iterator'''
for node in self.all_nodes:
yield node, self.node_annotations.get(node)
def edges(self):
'''Return an iterator for all edges, in the form of (pred, succ, note) triple.
Do not modify the graph while using this iterator'''
index = dict((n, i) for i, n in enumerate(self.all_nodes))
for n in self.all_nodes:
n_succs = self.succ[n]
for succ in sorted(n_succs, key = lambda n : index[n]):
yield n, succ, self.edge_annotations.get((n,succ))
def sources(self):
'''Return an iterator for all nodes with no predecessors.
Do not modify the graph while using this iterator'''
for n, p in self.pred.items():
if not p:
yield n
def __contains__(self, node):
return node in self.succ
class FlowGraph(DiGraph):
'''A DiGraph that supports the concept of definitions and variables.
Used to compute dominance and SSA form.
For more explanation of the algorithms used see
'Modern Compiler Implementation by Andrew W. Appel.
'''
def __init__(self, root, name):
DiGraph.__init__(self, name)
self.definitions = {}
self.deletions = {}
self.uses = {}
self.use_all_nodes = set()
self.root = root
def clear_computed(self):
to_be_deleted = [attr for attr in self.__dict__ if attr[0] == '_']
for attr in to_be_deleted:
delattr(self, attr)
def _require(self, what):
'''Ensures that 'what' has been computed (computing if needed).'''
if hasattr(self, "_" + what):
return
setattr(self, "_" + what, getattr(self, "_compute_" + what)())
def add_deletion(self, node, var):
assert node in self.succ
self.deletions[node] = var
def add_definition(self, node, var):
assert node in self.succ
self.definitions[node] = var
def add_use(self, node, var):
assert node in self.succ, node
self.uses[node] = var
def use_all_defined_variables(self, node):
assert node in self.succ
self.use_all_nodes.add(node)
def _compute_depth_first_pre_order(self):
self._require("depth_first_pre_order_labels")
reachable = [ f for f in self.all_nodes if f in self._depth_first_pre_order_labels ]
return sorted(reachable, key = lambda f : -self._depth_first_pre_order_labels[f])
def _compute_reachable(self):
self._require("depth_first_pre_order")
return frozenset(self._depth_first_pre_order)
def reachable_nodes(self):
self._require("reachable")
return self._reachable
def _compute_reversed_depth_first_pre_order(self):
self._require("depth_first_pre_order")
return reversed(self._depth_first_pre_order)
def _compute_bb_depth_first_pre_order(self):
self._require('depth_first_pre_order')
self._require('bb_heads')
bbs = []
for n in self._depth_first_pre_order:
if n in self._bb_heads:
bbs.append(n)
return bbs
def _compute_bb_reversed_depth_first_pre_order(self):
self._require("bb_depth_first_pre_order")
return reversed(self._bb_depth_first_pre_order)
def _compute_depth_first_pre_order_labels(self):
'Compute order with depth first search.'
orders = {}
order = 0
nodes_to_visit = [ self.root ]
while nodes_to_visit:
node = nodes_to_visit[-1]
orders[node] = 0
if node in self.succ:
for succ in self.succ[node]:
if succ not in orders:
nodes_to_visit.append(succ)
else:
order += 1
orders[node] = order
if node is nodes_to_visit[-1]:
nodes_to_visit.pop()
order += 1
orders[node] = order
return orders
def _compute_idoms(self):
self._require("depth_first_pre_order")
idoms = {}
def idom_intersection(n1, n2):
'Determine the last common idom of n1, n2'
orders = self._depth_first_pre_order_labels
while n1 is not n2:
while orders[n1] < orders[n2]:
n1 = idoms[n1]
while orders[n2] < orders[n1]:
n2 = idoms[n2]
return n1
for node in self._depth_first_pre_order:
if len(self.pred[node]) == 1:
idoms[node] = next(iter(self.pred[node]))
else:
idom = None
for p in self.pred[node]:
if p == self.root:
idom = p
elif p in idoms:
if idom is None:
idom = p
else:
idom = idom_intersection(idom, p)
if idom is not None:
idoms[node] = idom
return idoms
def idoms(self):
'''Returns an iterable of node pairs: node, idom(node)'''
self._require('idoms')
idoms = self._idoms
for n in self.all_nodes:
if n in idoms:
yield n, idoms[n]
def _compute_dominance_frontier(self):
'''Compute the dominance frontier:
DF[n] = DF_local[n] Union over C in children DF_up[c]'''
def dominates(dom, node):
while node in idoms:
next_node = idoms[node]
if dom == next_node:
return True
node = next_node
return False
self._require('idoms')
idoms = self._idoms
dominance_frontier = {}
df_up = {}
dom_tree = _reverse_map(idoms)
self._require('reversed_depth_first_pre_order')
for node in self._reversed_depth_first_pre_order:
df_local_n = set(n for n in self.succ[node] if node != idoms[n])
dfn = df_local_n
if node in dom_tree:
for child in dom_tree[node]:
dfn.update(df_up[child])
dominance_frontier[node] = dfn
if node in idoms:
imm_dom = idoms[node]
df_up[node] = set(n for n in dfn if not dominates(imm_dom, n))
else:
df_up[node] = dfn
return dominance_frontier
def _compute_phi_nodes(self):
'''Compute the phi nodes for this graph.
A minimal set of phi-nodes are computed;
No phi-nodes are added unless the variable is live.
'''
self._require('dominance_frontier')
self._require('liveness')
dominance_frontier = self._dominance_frontier
definitions = dict(self.definitions)
# We must count deletions as definitions here. Otherwise, we can have
# uses of a deleted variable whose SSA definition is an actual definition,
# rather than a deletion.
definitions.update(self.deletions)
phi_nodes = {}
defsites = {}
for a in definitions.values():
defsites[a] = set()
for n in definitions:
a = definitions[n]
defsites[a].add(n)
for a in defsites:
W = set(defsites[a])
while W:
n = W.pop()
if n not in dominance_frontier:
continue
for y in dominance_frontier[n]:
if y not in phi_nodes:
phi_nodes[y] = set()
if a not in phi_nodes[y]:
phi_nodes[y].add(a)
if y not in definitions or a != definitions[y]:
W.add(y)
trimmed = {}
for node in phi_nodes:
assert node in self._bb_heads
if node not in self._liveness:
continue
new_phi_vars = set()
phi_vars = phi_nodes[node]
for v in phi_vars:
if v in self._liveness[node]:
new_phi_vars.add(v)
if new_phi_vars:
trimmed[node] = new_phi_vars
return trimmed
def _compute_ssa_data(self):
''' Compute the SSA variables, definitions, uses and phi-inputs.
'''
self._require('basic_blocks')
self._require('phi_nodes')
self._require('bb_depth_first_pre_order')
self._require('use_all')
phi_nodes = self._phi_nodes
reaching_ssa_vars = {}
work_set = set()
work_set.add(self.root)
ssa_defns = {}
ssa_uses = {}
ssa_phis = {}
ssa_vars = set()
ssa_var_cache = {}
def make_ssa_var(variable, node):
'''Ensure that there is no more than one SSA variable for each (variable, node) pair.'''
uid = (variable, node)
if uid in ssa_var_cache:
return ssa_var_cache[uid]
var = SSA_Var(variable, node)
ssa_var_cache[uid] = var
return var
for bb in self._bb_depth_first_pre_order:
#Track SSA variables in each BB.
reaching_ssa_vars[bb] = {}
for bb in self._bb_depth_first_pre_order:
live_vars = reaching_ssa_vars[bb].copy()
#Add an SSA definition for each phi-node.
if bb in phi_nodes:
variables = phi_nodes[bb]
for v in variables:
var = make_ssa_var(v, bb)
ssa_defns[var] = bb
live_vars[v] = var
for node in self.nodes_in_bb(bb):
#Add an SSA use for each use.
if node in self.uses:
a = self.uses[node]
if a not in live_vars:
#Treat a use as adding a reaching variable,
#since a second use, if it can be reached,
#will always find the variable defined.
var = make_ssa_var(a, node)
live_vars[a] = var
else:
var = live_vars[a]
ssa_vars.add(var)
ssa_uses[node] = [ var ]
#Add an SSA use for all live SSA variables for
#each use_all (end of module/class scope).
if node in self._use_all:
all_live = [ var for var in live_vars.values() if var.variable in self._use_all[node]]
ssa_uses[node] = all_live
ssa_vars.update(all_live)
#Add an SSA definition for each definition.
if node in self.definitions:
a = self.definitions[node]
var = make_ssa_var(a, node)
ssa_defns[var] = node
live_vars[a] = var
#Although deletions are not definitions, we treat them as such.
#SSA form has no concept of deletion, so we have to treat `del x`
#as `x = Undefined`.
if node in self.deletions:
a = self.deletions[node]
if a in live_vars:
var = live_vars[a]
ssa_vars.add(var)
ssa_uses[node] = [ var ]
else:
#If no var is defined here we don't need to create one
#as a new one will be immediately be defined by the deletion.
pass
var = make_ssa_var(a, node)
ssa_defns[var] = node
live_vars[a] = var
#Propagate set of reaching variables to
#successor blocks.
for n in self.succ[node]:
reaching_ssa_vars[n].update(live_vars)
if n in phi_nodes:
for v in phi_nodes[n]:
if v in live_vars:
var = make_ssa_var(v, n)
if var not in ssa_phis:
ssa_phis[var] = set()
ssa_vars.add(live_vars[v])
ssa_phis[var].add(live_vars[v])
#Prune unused definitions.
used_ssa_defns = {}
for var in ssa_defns:
if var in ssa_vars:
used_ssa_defns[var] = ssa_defns[var]
ssa_defns = used_ssa_defns
sorted_vars = list(self._sort_ssa_variables(ssa_vars))
assert set(sorted_vars) == ssa_vars
assert len(sorted_vars) == len(ssa_vars)
ssa_vars = sorted_vars
return ssa_vars, ssa_defns, ssa_uses, ssa_phis
def ssa_variables(self):
'''Returns all the SSA variables for this graph'''
self._require('ssa_data')
return self._ssa_data[0]
def _sort_ssa_variables(self, ssa_vars):
node_to_var = {}
for v in ssa_vars:
node = v.node
if node in node_to_var:
vset = node_to_var[node]
else:
vset = set()
node_to_var[node] = vset
vset.add(v)
for n in self.all_nodes:
if n in node_to_var:
variables = node_to_var[n]
for v in sorted(variables, key=lambda v:v.variable.id):
yield v
def ssa_definitions(self):
'''Returns all the SSA definition as an iterator of (node, variable) pairs.'''
self._require('ssa_data')
ssa_defns = self._ssa_data[1]
reversed_defns = _reverse_map(ssa_defns)
for n in self.all_nodes:
if n in reversed_defns:
variables = reversed_defns[n]
for v in sorted(variables, key=lambda v:v.variable.id):
yield n, v
def get_ssa_definition(self, var):
'''Returns the definition node of var. Returns None if there is no definition.'''
self._require('ssa_data')
ssa_defns = self._ssa_data[1]
return ssa_defns.get(var)
def ssa_uses(self):
'''Returns all the SSA uses as an iterator of (node, variable) pairs.'''
self._require('ssa_data')
ssa_uses = self._ssa_data[2]
for n in self.all_nodes:
if n in ssa_uses:
variables = ssa_uses[n]
for v in sorted(variables, key=lambda v:v.variable.id):
yield n, v
def get_ssa_variables_used(self, node):
'''Returns all the SSA variables used at this node'''
self._require('ssa_data')
ssa_uses = self._ssa_data[2]
return ssa_uses.get(node, ())
def ssa_phis(self):
'''Return all SSA phi inputs as an iterator of (variable, input-variable) pairs.'''
self._require('ssa_data')
ssa_phis = self._ssa_data[3]
ssa_vars = self._ssa_data[0]
indexed = dict((v, index) for index, v in enumerate(ssa_vars))
for v in ssa_vars:
if v not in ssa_phis:
continue
phis = ssa_phis[v]
for phi in sorted(phis, key=lambda v:indexed[v]):
yield v, phi
def _compute_bb_heads(self):
'''Compute all flow nodes that are the first node in a basic block.'''
bb_heads = set()
for node in self.all_nodes:
preds = self.pred[node]
if len(preds) != 1 or len(self.succ[preds[0]]) != 1:
bb_heads.add(node)
return bb_heads
def _compute_basic_blocks(self):
'''Compute Basic blocks membership'''
self._require('bb_heads')
basic_blocks = {}
bb_tails = {}
for bb in self._bb_heads:
for index, node in enumerate(self.nodes_in_bb(bb)):
basic_blocks[node] = bb, index
bb_tails[bb] = node
self._bb_tails = bb_tails
return basic_blocks
def get_basic_blocks(self):
self._require('basic_blocks')
return self._basic_blocks
def _compute_bb_succ(self):
self._require('basic_blocks')
bb_succs = {}
for bb in self._bb_heads:
bb_succs[bb] = self.succ[self._bb_tails[bb]]
return bb_succs
def _compute_bb_pred(self):
self._require('basic_blocks')
bb_preds = {}
for bb in self._bb_heads:
preds_of_bb = self.pred[bb]
bb_preds[bb] = SmallSet(self._basic_blocks[p][0] for p in preds_of_bb)
return bb_preds
def nodes_in_bb(self, bb):
'''Return an iterator over all node in basic block 'bb.'''
node = bb
while True:
yield node
succs = self.succ[node]
if not succs:
return
node = succs[0]
if node in self._bb_heads:
return
def _compute_use_all(self):
'''Compute which variables have been defined.
A variable is defined at node n, if there is a path to n which
passes through a definition, but not through a subsequent deletion.
'''
self._require('bb_heads')
self._require('bb_succ')
self._require('bb_pred')
use_all = {}
def defined_in_block(bb):
defined = defined_at_start[bb].copy()
for node in self.nodes_in_bb(bb):
if node in self.definitions:
var = self.definitions[node]
defined.add(var)
if node in self.deletions:
var = self.deletions[node]
defined.discard(var)
if node in self.use_all_nodes:
use_all[node] = frozenset(defined)
return defined
defined_at_start = {}
work_set = set()
for bb in self._bb_heads:
if not self._bb_pred[bb]:
work_set.add(bb)
defined_at_start[bb] = set()
work_list = list(work_set)
while work_list:
bb = work_list.pop()
work_set.remove(bb)
defined_at_bb_end = defined_in_block(bb)
for succ in self._bb_succ[bb]:
if succ not in defined_at_start:
defined_at_start[succ] = set()
elif defined_at_start[succ] >= defined_at_bb_end:
continue
defined_at_start[succ].update(defined_at_bb_end)
if succ not in work_set:
work_list.append(succ)
work_set.add(succ)
return use_all
def _compute_liveness(self):
'''Compute liveness of all variables in this flow-graph.
Return a mapping of basic blocks to the set of variables
that are live at the start of that basic block.
See http://en.wikipedia.org/wiki/Live_variable_analysis.'''
self._require('bb_pred')
self._require('use_all')
def gen_and_kill_for_block(bb):
gen = set()
kill = set()
for node in reversed(list(self.nodes_in_bb(bb))):
if node in self.uses:
var = self.uses[node]
gen.add(var)
kill.discard(var)
if node in self.deletions:
var = self.deletions[node]
gen.add(var)
kill.discard(var)
if node in self.definitions:
var = self.definitions[node]
gen.discard(var)
kill.add(var)
if node in self._use_all:
for var in self._use_all[node]:
gen.add(var)
kill.discard(var)
return gen, kill
def liveness_for_block(bb, live_out):
return gens[bb].union(live_out.difference(kills[bb]))
live_at_end = {}
live_at_start = {}
gens = {}
kills = {}
work_set = set()
#Initialise
for bb in self._bb_heads:
gens[bb], kills[bb] = gen_and_kill_for_block(bb)
live_at_end[bb] = set()
live_at_start[bb] = set()
work_set.add(bb)
#Find fixed point
while work_set:
bb = work_set.pop()
live_in = liveness_for_block(bb, live_at_end[bb])
if live_in != live_at_start[bb]:
assert len(live_in) > len(live_at_start[bb])
live_at_start[bb] = live_in
for pred in self._bb_pred[bb]:
work_set.add(pred)
live_at_end[pred] = live_at_end[pred].union(live_in)
return live_at_start
def delete_unreachable_nodes(self):
self._require("reachable")
unreachable = [u for u in self.all_nodes if u not in self._reachable]
if not unreachable:
return
for mapping in (self.definitions, self.deletions, self.uses):
for u in unreachable:
if u in mapping:
del mapping[u]
for u in unreachable:
self.use_all_nodes.discard(u)
self.remove_node(u)
#Make sure we retain the order of all_nodes.
self.all_nodes = [r for r in self.all_nodes if r in self._reachable]
self.clear_computed()
def dominated_by(self, node):
self._require('idoms')
assert node in self, str(node) + " is not in graph"
dominated = set([node])
todo = set(self.succ[node])
while todo:
n = todo.pop()
if n in dominated:
continue
#Unreachable nodes will not be in self._idoms
if n in self._idoms and self._idoms[n] in dominated:
dominated.add(n)
todo.update(self.succ[n])
return dominated
def strictly_dominates(self, pre, post):
self._require('idoms')
while post in self._idoms:
post = self._idoms[post]
if pre == post:
return True
return False
def reaches_while_dominated(self, pre, post, control):
''' Holds if `pre` reaches `post` while remaining in the
region dominated by `control`.'''
self._require('dominance_frontier')
dominance_frontier = self._dominance_frontier[control]
todo = { pre }
reached = set()
while todo:
node = todo.pop()
if node in dominance_frontier:
continue
if node == post:
return True
if node in reached:
continue
reached.add(node)
todo.update(self.succ[node])
return False
class SSA_Var(object):
'A single static assignment variable'
__slots__ = [ 'variable', 'node' ]
def __init__(self, variable, node):
self.variable = variable
self.node = node
def __repr__(self):
return 'SSA_Var(%r, %r)' % (self.variable.id, self.node)
def _reverse_map(mapping):
'Reverse a mapping of keys -> values to value->set(keys)'
inv_map = {}
for k, v in mapping.items():
if v not in inv_map:
inv_map[v] = SmallSet()
inv_map[v].add(k)
return inv_map