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compiler.analyses.domination: implement new dominator tree algorithm.

This commit is contained in:
whitequark 2015-11-09 11:51:54 +03:00
parent 73c22b0b1e
commit 19fae9181c
3 changed files with 253 additions and 49 deletions

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@ -2,65 +2,154 @@
:class:`DominatorTree` computes the dominance relation over
control flow graphs.
See http://www.cs.colostate.edu/~mstrout/CS553/slides/lecture04.pdf.
See http://www.cs.rice.edu/~keith/EMBED/dom.pdf.
"""
from functools import reduce, cmp_to_key
class GenericDominatorTree:
def __init__(self):
self._assign_names()
self._compute()
# Key Idea
# If a node dominates all
# predecessors of node n, then it
# also dominates node n
class DominatorTree:
def __init__(self, func):
entry = func.entry()
def _start_blocks(self):
"""
Returns a starting collection of basic blocks (entry block
for dominator tree and exit blocks for postdominator tree).
"""
raise NotImplementedError
self.dominated_by = { entry: {entry} }
for block in func.basic_blocks:
if block != entry:
self.dominated_by[block] = set(func.basic_blocks)
def _next_blocks(self, block):
"""
Returns the collection of blocks to be traversed after `block`
(successors for dominator tree and predecessors for postdominator
tree).
"""
raise NotImplementedError
def _prev_blocks(self, block):
"""
Returns the collection of blocks to be traversed before `block`
(predecessors for dominator tree and successors for postdominator
tree).
"""
raise NotImplementedError
def _assign_names(self):
"""Assigns names to basic blocks in postorder."""
visited = set()
postorder = []
def visit(block):
visited.add(block)
for next_block in self._next_blocks(block):
if next_block not in visited:
visit(next_block)
postorder.append(block)
for block in self._start_blocks():
visit(block)
self._last_name = len(postorder)
self._block_of_name = postorder
self._name_of_block = {}
for block_name, block in enumerate(postorder):
# print("name", block_name + 1, block.name)
self._name_of_block[block] = block_name
def _start_block_names(self):
for block in self._start_blocks():
yield self._name_of_block[block]
def _next_block_names(self, block_name):
for block in self._next_blocks(self._block_of_name[block_name]):
yield self._name_of_block[block]
def _prev_block_names(self, block_name):
for block in self._prev_blocks(self._block_of_name[block_name]):
yield self._name_of_block[block]
def _intersect(self, block_name_1, block_name_2):
finger_1, finger_2 = block_name_1, block_name_2
while finger_1 != finger_2:
while finger_1 < finger_2:
finger_1 = self._doms[finger_1]
while finger_2 < finger_1:
finger_2 = self._doms[finger_2]
return finger_1
def _compute(self):
self._doms = {}
for block_name in range(self._last_name):
self._doms[block_name] = None
start_block_names = set()
for block_name in self._start_block_names():
self._doms[block_name] = block_name
start_block_names.add(block_name)
changed = True
while changed:
# print("doms", {k+1: self._doms[k]+1 if self._doms[k] is not None else None for k in self._doms})
predecessors = {block: block.predecessors() for block in func.basic_blocks}
while True:
changed = False
for block in func.basic_blocks:
if block == entry:
for block_name in reversed(range(self._last_name)):
if block_name in start_block_names:
continue
new_dominated_by = {block}.union(
reduce(lambda a, b: a.intersection(b),
(self.dominated_by[pred] for pred in predecessors[block])))
if new_dominated_by != self.dominated_by[block]:
self.dominated_by[block] = new_dominated_by
new_idom, prev_block_names = None, []
for prev_block_name in self._prev_block_names(block_name):
if new_idom is None and self._doms[prev_block_name] is not None:
new_idom = prev_block_name
else:
prev_block_names.append(prev_block_name)
# print("block_name", block_name + 1, "new_idom", new_idom + 1)
for prev_block_name in prev_block_names:
# print("prev_block_name", prev_block_name + 1)
if self._doms[prev_block_name] is not None:
new_idom = self._intersect(prev_block_name, new_idom)
# print("new_idom+", new_idom + 1)
if self._doms[block_name] != new_idom:
self._doms[block_name] = new_idom
changed = True
if not changed:
break
def immediate_dominator(self, block):
return self._block_of_name[self._doms[self._name_of_block[block]]]
class PostDominatorTree:
def __init__(self, func):
exits = [block for block in func.basic_blocks if none(block.successors())]
def dominators(self, block):
yield block
self.dominated_by = { exit: {exit} for exit in exits }
for block in func.basic_blocks:
if block != entry:
self.dominated_by[block] = set(func.basic_blocks)
block_name = self._name_of_block[block]
while block_name != self._doms[block_name]:
block_name = self._doms[block_name]
yield self._block_of_name[block_name]
successors = {block: block.successors() for block in func.basic_blocks}
while True:
changed = False
class DominatorTree(GenericDominatorTree):
def __init__(self, function):
self.function = function
super().__init__()
for block in func.basic_blocks:
if block in exits:
continue
def _start_blocks(self):
return [self.function.entry()]
new_dominated_by = {block}.union(
reduce(lambda a, b: a.intersection(b),
(self.dominated_by[pred] for pred in successors[block])))
if new_dominated_by != self.dominated_by[block]:
self.dominated_by[block] = new_dominated_by
changed = True
def _next_blocks(self, block):
return block.successors()
if not changed:
break
def _prev_blocks(self, block):
return block.predecessors()
class PostDominatorTree(GenericDominatorTree):
def __init__(self, function):
self.function = function
super().__init__()
def _start_blocks(self):
return [block for block in self.function.basic_blocks
if none(block.successors())]
def _next_blocks(self, block):
return block.predecessors()
def _prev_blocks(self, block):
return block.successors()

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@ -38,7 +38,7 @@ class LocalAccessValidator:
# Traverse the acyclic graph made of basic blocks and forward edges only,
# while updating the environment state.
dom = analyses.DominatorTree(func)
domtree = analyses.DominatorTree(func)
state = {}
def traverse(block):
# Have we computed the state of this block already?
@ -48,7 +48,7 @@ class LocalAccessValidator:
# No! Which forward edges lead to this block?
# If we dominate a predecessor, it's a back edge instead.
forward_edge_preds = [pred for pred in block.predecessors()
if block not in dom.dominated_by[pred]]
if block not in domtree.dominators(pred)]
# Figure out what the state is before the leader
# instruction of this block.

View File

@ -0,0 +1,115 @@
import unittest
from artiq.compiler.analyses.domination import DominatorTree, PostDominatorTree
class MockBasicBlock:
def __init__(self, name):
self.name = name
self._successors = []
self._predecessors = []
def successors(self):
return self._successors
def predecessors(self):
return self._predecessors
def set_successors(self, successors):
self._successors = list(successors)
for block in self._successors:
block._predecessors.append(self)
class MockFunction:
def __init__(self, entry, basic_blocks):
self._entry = entry
self.basic_blocks = basic_blocks
def entry(self):
return self._entry
def makefn(entry_name, graph):
blocks = {}
for block_name in graph:
blocks[block_name] = MockBasicBlock(block_name)
for block_name in graph:
successors = list(map(lambda name: blocks[name], graph[block_name]))
blocks[block_name].set_successors(successors)
return MockFunction(blocks[entry_name], blocks.values())
def dom(function, domtree):
dom = {}
for block in function.basic_blocks:
dom[block.name] = [dom_block.name for dom_block in domtree.dominators(block)]
return dom
def idom(function, domtree):
idom = {}
for block in function.basic_blocks:
idom[block.name] = domtree.immediate_dominator(block).name
return idom
class TestDominatorTree(unittest.TestCase):
def test_linear(self):
func = makefn('A', {
'A': ['B'],
'B': ['C'],
'C': []
})
domtree = DominatorTree(func)
self.assertEqual({
'C': 'B', 'B': 'A', 'A': 'A'
}, idom(func, domtree))
self.assertEqual({
'C': ['C', 'B', 'A'], 'B': ['B', 'A'], 'A': ['A']
}, dom(func, domtree))
def test_diamond(self):
func = makefn('A', {
'A': ['C', 'B'],
'B': ['D'],
'C': ['D'],
'D': []
})
domtree = DominatorTree(func)
self.assertEqual({
'D': 'A', 'C': 'A', 'B': 'A', 'A': 'A'
}, idom(func, domtree))
def test_combined(self):
func = makefn('A', {
'A': ['B', 'D'],
'B': ['C'],
'C': ['E'],
'D': ['E'],
'E': []
})
domtree = DominatorTree(func)
self.assertEqual({
'A': 'A', 'B': 'A', 'C': 'B', 'D': 'A', 'E': 'A'
}, idom(func, domtree))
def test_figure_2(self):
func = makefn(5, {
5: [3, 4],
4: [1],
3: [2],
2: [1],
1: [2]
})
domtree = DominatorTree(func)
self.assertEqual({
1: 5, 2: 5, 3: 5, 4: 5, 5: 5
}, idom(func, domtree))
def test_figure_4(self):
func = makefn(6, {
6: [4, 5],
5: [1],
4: [3, 2],
3: [2],
2: [1, 3],
1: [2]
})
domtree = DominatorTree(func)
self.assertEqual({
1: 6, 2: 6, 3: 6, 4: 6, 5: 6, 6: 6
}, idom(func, domtree))