forked from M-Labs/artiq
compiler.analyses.domination: implement new dominator tree algorithm.
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whitequark
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73c22b0b1e
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19fae9181c
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@ -2,65 +2,154 @@
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:class:`DominatorTree` computes the dominance relation over
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control flow graphs.
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See http://www.cs.colostate.edu/~mstrout/CS553/slides/lecture04.pdf.
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See http://www.cs.rice.edu/~keith/EMBED/dom.pdf.
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"""
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from functools import reduce, cmp_to_key
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class GenericDominatorTree:
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def __init__(self):
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self._assign_names()
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self._compute()
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# Key Idea
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# If a node dominates all
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# predecessors of node n, then it
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# also dominates node n
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class DominatorTree:
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def __init__(self, func):
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entry = func.entry()
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def _start_blocks(self):
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"""
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Returns a starting collection of basic blocks (entry block
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for dominator tree and exit blocks for postdominator tree).
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"""
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raise NotImplementedError
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self.dominated_by = { entry: {entry} }
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for block in func.basic_blocks:
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if block != entry:
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self.dominated_by[block] = set(func.basic_blocks)
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def _next_blocks(self, block):
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"""
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Returns the collection of blocks to be traversed after `block`
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(successors for dominator tree and predecessors for postdominator
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tree).
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"""
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raise NotImplementedError
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def _prev_blocks(self, block):
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"""
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Returns the collection of blocks to be traversed before `block`
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(predecessors for dominator tree and successors for postdominator
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tree).
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"""
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raise NotImplementedError
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def _assign_names(self):
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"""Assigns names to basic blocks in postorder."""
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visited = set()
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postorder = []
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def visit(block):
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visited.add(block)
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for next_block in self._next_blocks(block):
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if next_block not in visited:
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visit(next_block)
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postorder.append(block)
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for block in self._start_blocks():
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visit(block)
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self._last_name = len(postorder)
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self._block_of_name = postorder
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self._name_of_block = {}
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for block_name, block in enumerate(postorder):
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# print("name", block_name + 1, block.name)
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self._name_of_block[block] = block_name
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def _start_block_names(self):
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for block in self._start_blocks():
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yield self._name_of_block[block]
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def _next_block_names(self, block_name):
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for block in self._next_blocks(self._block_of_name[block_name]):
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yield self._name_of_block[block]
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def _prev_block_names(self, block_name):
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for block in self._prev_blocks(self._block_of_name[block_name]):
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yield self._name_of_block[block]
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def _intersect(self, block_name_1, block_name_2):
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finger_1, finger_2 = block_name_1, block_name_2
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while finger_1 != finger_2:
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while finger_1 < finger_2:
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finger_1 = self._doms[finger_1]
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while finger_2 < finger_1:
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finger_2 = self._doms[finger_2]
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return finger_1
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def _compute(self):
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self._doms = {}
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for block_name in range(self._last_name):
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self._doms[block_name] = None
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start_block_names = set()
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for block_name in self._start_block_names():
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self._doms[block_name] = block_name
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start_block_names.add(block_name)
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changed = True
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while changed:
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# print("doms", {k+1: self._doms[k]+1 if self._doms[k] is not None else None for k in self._doms})
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predecessors = {block: block.predecessors() for block in func.basic_blocks}
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while True:
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changed = False
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for block in func.basic_blocks:
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if block == entry:
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for block_name in reversed(range(self._last_name)):
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if block_name in start_block_names:
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continue
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new_dominated_by = {block}.union(
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reduce(lambda a, b: a.intersection(b),
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(self.dominated_by[pred] for pred in predecessors[block])))
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if new_dominated_by != self.dominated_by[block]:
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self.dominated_by[block] = new_dominated_by
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new_idom, prev_block_names = None, []
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for prev_block_name in self._prev_block_names(block_name):
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if new_idom is None and self._doms[prev_block_name] is not None:
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new_idom = prev_block_name
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else:
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prev_block_names.append(prev_block_name)
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# print("block_name", block_name + 1, "new_idom", new_idom + 1)
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for prev_block_name in prev_block_names:
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# print("prev_block_name", prev_block_name + 1)
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if self._doms[prev_block_name] is not None:
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new_idom = self._intersect(prev_block_name, new_idom)
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# print("new_idom+", new_idom + 1)
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if self._doms[block_name] != new_idom:
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self._doms[block_name] = new_idom
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changed = True
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if not changed:
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break
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def immediate_dominator(self, block):
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return self._block_of_name[self._doms[self._name_of_block[block]]]
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class PostDominatorTree:
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def __init__(self, func):
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exits = [block for block in func.basic_blocks if none(block.successors())]
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def dominators(self, block):
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yield block
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self.dominated_by = { exit: {exit} for exit in exits }
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for block in func.basic_blocks:
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if block != entry:
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self.dominated_by[block] = set(func.basic_blocks)
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block_name = self._name_of_block[block]
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while block_name != self._doms[block_name]:
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block_name = self._doms[block_name]
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yield self._block_of_name[block_name]
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successors = {block: block.successors() for block in func.basic_blocks}
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while True:
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changed = False
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class DominatorTree(GenericDominatorTree):
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def __init__(self, function):
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self.function = function
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super().__init__()
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for block in func.basic_blocks:
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if block in exits:
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continue
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def _start_blocks(self):
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return [self.function.entry()]
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new_dominated_by = {block}.union(
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reduce(lambda a, b: a.intersection(b),
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(self.dominated_by[pred] for pred in successors[block])))
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if new_dominated_by != self.dominated_by[block]:
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self.dominated_by[block] = new_dominated_by
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changed = True
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def _next_blocks(self, block):
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return block.successors()
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if not changed:
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break
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def _prev_blocks(self, block):
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return block.predecessors()
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class PostDominatorTree(GenericDominatorTree):
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def __init__(self, function):
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self.function = function
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super().__init__()
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def _start_blocks(self):
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return [block for block in self.function.basic_blocks
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if none(block.successors())]
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def _next_blocks(self, block):
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return block.predecessors()
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def _prev_blocks(self, block):
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return block.successors()
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@ -38,7 +38,7 @@ class LocalAccessValidator:
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# Traverse the acyclic graph made of basic blocks and forward edges only,
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# while updating the environment state.
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dom = analyses.DominatorTree(func)
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domtree = analyses.DominatorTree(func)
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state = {}
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def traverse(block):
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# Have we computed the state of this block already?
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@ -48,7 +48,7 @@ class LocalAccessValidator:
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# No! Which forward edges lead to this block?
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# If we dominate a predecessor, it's a back edge instead.
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forward_edge_preds = [pred for pred in block.predecessors()
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if block not in dom.dominated_by[pred]]
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if block not in domtree.dominators(pred)]
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# Figure out what the state is before the leader
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# instruction of this block.
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@ -0,0 +1,115 @@
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import unittest
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from artiq.compiler.analyses.domination import DominatorTree, PostDominatorTree
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class MockBasicBlock:
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def __init__(self, name):
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self.name = name
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self._successors = []
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self._predecessors = []
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def successors(self):
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return self._successors
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def predecessors(self):
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return self._predecessors
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def set_successors(self, successors):
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self._successors = list(successors)
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for block in self._successors:
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block._predecessors.append(self)
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class MockFunction:
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def __init__(self, entry, basic_blocks):
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self._entry = entry
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self.basic_blocks = basic_blocks
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def entry(self):
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return self._entry
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def makefn(entry_name, graph):
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blocks = {}
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for block_name in graph:
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blocks[block_name] = MockBasicBlock(block_name)
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for block_name in graph:
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successors = list(map(lambda name: blocks[name], graph[block_name]))
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blocks[block_name].set_successors(successors)
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return MockFunction(blocks[entry_name], blocks.values())
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def dom(function, domtree):
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dom = {}
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for block in function.basic_blocks:
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dom[block.name] = [dom_block.name for dom_block in domtree.dominators(block)]
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return dom
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def idom(function, domtree):
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idom = {}
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for block in function.basic_blocks:
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idom[block.name] = domtree.immediate_dominator(block).name
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return idom
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class TestDominatorTree(unittest.TestCase):
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def test_linear(self):
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func = makefn('A', {
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'A': ['B'],
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'B': ['C'],
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'C': []
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})
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domtree = DominatorTree(func)
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self.assertEqual({
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'C': 'B', 'B': 'A', 'A': 'A'
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}, idom(func, domtree))
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self.assertEqual({
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'C': ['C', 'B', 'A'], 'B': ['B', 'A'], 'A': ['A']
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}, dom(func, domtree))
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def test_diamond(self):
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func = makefn('A', {
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'A': ['C', 'B'],
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'B': ['D'],
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'C': ['D'],
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'D': []
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})
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domtree = DominatorTree(func)
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self.assertEqual({
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'D': 'A', 'C': 'A', 'B': 'A', 'A': 'A'
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}, idom(func, domtree))
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def test_combined(self):
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func = makefn('A', {
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'A': ['B', 'D'],
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'B': ['C'],
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'C': ['E'],
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'D': ['E'],
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'E': []
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})
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domtree = DominatorTree(func)
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self.assertEqual({
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'A': 'A', 'B': 'A', 'C': 'B', 'D': 'A', 'E': 'A'
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}, idom(func, domtree))
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def test_figure_2(self):
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func = makefn(5, {
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5: [3, 4],
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4: [1],
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3: [2],
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2: [1],
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1: [2]
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})
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domtree = DominatorTree(func)
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self.assertEqual({
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1: 5, 2: 5, 3: 5, 4: 5, 5: 5
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}, idom(func, domtree))
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def test_figure_4(self):
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func = makefn(6, {
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6: [4, 5],
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5: [1],
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4: [3, 2],
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3: [2],
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2: [1, 3],
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1: [2]
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})
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domtree = DominatorTree(func)
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self.assertEqual({
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1: 6, 2: 6, 3: 6, 4: 6, 5: 6, 6: 6
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}, idom(func, domtree))
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