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

artiq/compiler/analyses/domination.py

@@ -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()

artiq/compiler/validators/local_access.py

@@ -38,8 +38,8 @@ class LocalAccessValidator:
 
         # Traverse the acyclic graph made of basic blocks and forward edges only,
         # while updating the environment state.
-        dom   = analyses.DominatorTree(func)
-        state = {}
+        domtree = analyses.DominatorTree(func)
+        state   = {}
         def traverse(block):
             # Have we computed the state of this block already?
             if block in state:
@@ -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.

artiq/test/compiler/domination.py

@@ -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))