/* * Copyright (C) 2011, 2014-2016 Apple Inc. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #ifndef WTFDominators_h #define WTFDominators_h #include #include namespace WTF { // This is a utility for finding the dominators of a graph. Dominators are almost universally used // for control flow graph analysis, so this code will refer to the graph's "nodes" as "blocks". In // that regard this code is kind of specialized for the various JSC compilers, but you could use it // for non-compiler things if you are OK with referring to your "nodes" as "blocks". template class Dominators { public: Dominators(Graph& graph, bool selfCheck = false) : m_graph(graph) , m_data(graph.template newMap()) { LengauerTarjan lengauerTarjan(m_graph); lengauerTarjan.compute(); m_data = m_graph.template newMap(); // From here we want to build a spanning tree with both upward and downward links and we want // to do a search over this tree to compute pre and post numbers that can be used for dominance // tests. for (unsigned blockIndex = m_graph.numNodes(); blockIndex--;) { typename Graph::Node block = m_graph.node(blockIndex); if (!block) continue; typename Graph::Node idomBlock = lengauerTarjan.immediateDominator(block); m_data[block].idomParent = idomBlock; if (idomBlock) m_data[idomBlock].idomKids.append(block); } unsigned nextPreNumber = 0; unsigned nextPostNumber = 0; // Plain stack-based worklist because we are guaranteed to see each block exactly once anyway. Vector> worklist; worklist.append(GraphNodeWithOrder(m_graph.root(), GraphVisitOrder::Pre)); while (!worklist.isEmpty()) { GraphNodeWithOrder item = worklist.takeLast(); switch (item.order) { case GraphVisitOrder::Pre: m_data[item.node].preNumber = nextPreNumber++; worklist.append(GraphNodeWithOrder(item.node, GraphVisitOrder::Post)); for (typename Graph::Node kid : m_data[item.node].idomKids) worklist.append(GraphNodeWithOrder(kid, GraphVisitOrder::Pre)); break; case GraphVisitOrder::Post: m_data[item.node].postNumber = nextPostNumber++; break; } } if (selfCheck) { // Check our dominator calculation: // 1) Check that our range-based ancestry test is the same as a naive ancestry test. // 2) Check that our notion of who dominates whom is identical to a naive (not // Lengauer-Tarjan) dominator calculation. ValidationContext context(m_graph, *this); for (unsigned fromBlockIndex = m_graph.numNodes(); fromBlockIndex--;) { typename Graph::Node fromBlock = m_graph.node(fromBlockIndex); if (!fromBlock || m_data[fromBlock].preNumber == UINT_MAX) continue; for (unsigned toBlockIndex = m_graph.numNodes(); toBlockIndex--;) { typename Graph::Node toBlock = m_graph.node(toBlockIndex); if (!toBlock || m_data[toBlock].preNumber == UINT_MAX) continue; if (dominates(fromBlock, toBlock) != naiveDominates(fromBlock, toBlock)) context.reportError(fromBlock, toBlock, "Range-based domination check is broken"); if (dominates(fromBlock, toBlock) != context.naiveDominators.dominates(fromBlock, toBlock)) context.reportError(fromBlock, toBlock, "Lengauer-Tarjan domination is broken"); } } context.handleErrors(); } } bool strictlyDominates(typename Graph::Node from, typename Graph::Node to) const { return m_data[to].preNumber > m_data[from].preNumber && m_data[to].postNumber < m_data[from].postNumber; } bool dominates(typename Graph::Node from, typename Graph::Node to) const { return from == to || strictlyDominates(from, to); } // Returns the immediate dominator of this block. Returns null for the root block. typename Graph::Node idom(typename Graph::Node block) const { return m_data[block].idomParent; } template void forAllStrictDominatorsOf(typename Graph::Node to, const Functor& functor) const { for (typename Graph::Node block = m_data[to].idomParent; block; block = m_data[block].idomParent) functor(block); } template void forAllDominatorsOf(typename Graph::Node to, const Functor& functor) const { for (typename Graph::Node block = to; block; block = m_data[block].idomParent) functor(block); } template void forAllBlocksStrictlyDominatedBy(typename Graph::Node from, const Functor& functor) const { Vector worklist; worklist.appendVector(m_data[from].idomKids); while (!worklist.isEmpty()) { typename Graph::Node block = worklist.takeLast(); functor(block); worklist.appendVector(m_data[block].idomKids); } } template void forAllBlocksDominatedBy(typename Graph::Node from, const Functor& functor) const { Vector worklist; worklist.append(from); while (!worklist.isEmpty()) { typename Graph::Node block = worklist.takeLast(); functor(block); worklist.appendVector(m_data[block].idomKids); } } typename Graph::Set strictDominatorsOf(typename Graph::Node to) const { typename Graph::Set result; forAllStrictDominatorsOf( to, [&] (typename Graph::Node node) { result.add(node); }); return result; } typename Graph::Set dominatorsOf(typename Graph::Node to) const { typename Graph::Set result; forAllDominatorsOf( to, [&] (typename Graph::Node node) { result.add(node); }); return result; } typename Graph::Set blocksStrictlyDominatedBy(typename Graph::Node from) const { typename Graph::Set result; forAllBlocksStrictlyDominatedBy( from, [&] (typename Graph::Node node) { result.add(node); }); return result; } typename Graph::Set blocksDominatedBy(typename Graph::Node from) const { typename Graph::Set result; forAllBlocksDominatedBy( from, [&] (typename Graph::Node node) { result.add(node); }); return result; } template void forAllBlocksInDominanceFrontierOf( typename Graph::Node from, const Functor& functor) const { typename Graph::Set set; forAllBlocksInDominanceFrontierOfImpl( from, [&] (typename Graph::Node block) { if (set.add(block)) functor(block); }); } typename Graph::Set dominanceFrontierOf(typename Graph::Node from) const { typename Graph::Set result; forAllBlocksInDominanceFrontierOf( from, [&] (typename Graph::Node node) { result.add(node); }); return result; } template void forAllBlocksInIteratedDominanceFrontierOf(const typename Graph::List& from, const Functor& functor) { forAllBlocksInPrunedIteratedDominanceFrontierOf( from, [&] (typename Graph::Node block) -> bool { functor(block); return true; }); } // This is a close relative of forAllBlocksInIteratedDominanceFrontierOf(), which allows the // given functor to return false to indicate that we don't wish to consider the given block. // Useful for computing pruned SSA form. template void forAllBlocksInPrunedIteratedDominanceFrontierOf( const typename Graph::List& from, const Functor& functor) { typename Graph::Set set; forAllBlocksInIteratedDominanceFrontierOfImpl( from, [&] (typename Graph::Node block) -> bool { if (!set.add(block)) return false; return functor(block); }); } typename Graph::Set iteratedDominanceFrontierOf(const typename Graph::List& from) const { typename Graph::Set result; forAllBlocksInIteratedDominanceFrontierOfImpl( from, [&] (typename Graph::Node node) -> bool { return result.add(node); }); return result; } void dump(PrintStream& out) const { for (unsigned blockIndex = 0; blockIndex < m_data.size(); ++blockIndex) { if (m_data[blockIndex].preNumber == UINT_MAX) continue; out.print(" Block #", blockIndex, ": idom = ", m_graph.dump(m_data[blockIndex].idomParent), ", idomKids = ["); CommaPrinter comma; for (unsigned i = 0; i < m_data[blockIndex].idomKids.size(); ++i) out.print(comma, m_graph.dump(m_data[blockIndex].idomKids[i])); out.print("], pre/post = ", m_data[blockIndex].preNumber, "/", m_data[blockIndex].postNumber, "\n"); } } private: // This implements Lengauer and Tarjan's "A Fast Algorithm for Finding Dominators in a Flowgraph" // (TOPLAS 1979). It uses the "simple" implementation of LINK and EVAL, which yields an O(n log n) // solution. The full paper is linked below; this code attempts to closely follow the algorithm as // it is presented in the paper; in particular sections 3 and 4 as well as appendix B. // https://www.cs.princeton.edu/courses/archive/fall03/cs528/handouts/a%20fast%20algorithm%20for%20finding.pdf // // This code is very subtle. The Lengauer-Tarjan algorithm is incredibly deep to begin with. The // goal of this code is to follow the code in the paper, however our implementation must deviate // from the paper when it comes to recursion. The authors had used recursion to implement DFS, and // also to implement the "simple" EVAL. We convert both of those into worklist-based solutions. // Finally, once the algorithm gives us immediate dominators, we implement dominance tests by // walking the dominator tree and computing pre and post numbers. We then use the range inclusion // check trick that was first discovered by Paul F. Dietz in 1982 in "Maintaining order in a linked // list" (see http://dl.acm.org/citation.cfm?id=802184). class LengauerTarjan { public: LengauerTarjan(Graph& graph) : m_graph(graph) , m_data(graph.template newMap()) { for (unsigned blockIndex = m_graph.numNodes(); blockIndex--;) { typename Graph::Node block = m_graph.node(blockIndex); if (!block) continue; m_data[block].label = block; } } void compute() { computeDepthFirstPreNumbering(); // Step 1. computeSemiDominatorsAndImplicitImmediateDominators(); // Steps 2 and 3. computeExplicitImmediateDominators(); // Step 4. } typename Graph::Node immediateDominator(typename Graph::Node block) { return m_data[block].dom; } private: void computeDepthFirstPreNumbering() { // Use a block worklist that also tracks the index inside the successor list. This is // necessary for ensuring that we don't attempt to visit a successor until the previous // successors that we had visited are fully processed. This ends up being revealed in the // output of this method because the first time we see an edge to a block, we set the // block's parent. So, if we have: // // A -> B // A -> C // B -> C // // And we're processing A, then we want to ensure that if we see A->B first (and hence set // B's prenumber before we set C's) then we also end up setting C's parent to B by virtue // of not noticing A->C until we're done processing B. ExtendedGraphNodeWorklist worklist; worklist.push(m_graph.root(), 0); while (GraphNodeWith item = worklist.pop()) { typename Graph::Node block = item.node; unsigned successorIndex = item.data; // We initially push with successorIndex = 0 regardless of whether or not we have any // successors. This is so that we can assign our prenumber. Subsequently we get pushed // with higher successorIndex values, but only if they are in range. ASSERT(!successorIndex || successorIndex < m_graph.successors(block).size()); if (!successorIndex) { m_data[block].semiNumber = m_blockByPreNumber.size(); m_blockByPreNumber.append(block); } if (successorIndex < m_graph.successors(block).size()) { unsigned nextSuccessorIndex = successorIndex + 1; if (nextSuccessorIndex < m_graph.successors(block).size()) worklist.forcePush(block, nextSuccessorIndex); typename Graph::Node successorBlock = m_graph.successors(block)[successorIndex]; if (worklist.push(successorBlock, 0)) m_data[successorBlock].parent = block; } } } void computeSemiDominatorsAndImplicitImmediateDominators() { for (unsigned currentPreNumber = m_blockByPreNumber.size(); currentPreNumber-- > 1;) { typename Graph::Node block = m_blockByPreNumber[currentPreNumber]; BlockData& blockData = m_data[block]; // Step 2: for (typename Graph::Node predecessorBlock : m_graph.predecessors(block)) { typename Graph::Node intermediateBlock = eval(predecessorBlock); blockData.semiNumber = std::min( m_data[intermediateBlock].semiNumber, blockData.semiNumber); } unsigned bucketPreNumber = blockData.semiNumber; ASSERT(bucketPreNumber <= currentPreNumber); m_data[m_blockByPreNumber[bucketPreNumber]].bucket.append(block); link(blockData.parent, block); // Step 3: for (typename Graph::Node semiDominee : m_data[blockData.parent].bucket) { typename Graph::Node possibleDominator = eval(semiDominee); BlockData& semiDomineeData = m_data[semiDominee]; ASSERT(m_blockByPreNumber[semiDomineeData.semiNumber] == blockData.parent); BlockData& possibleDominatorData = m_data[possibleDominator]; if (possibleDominatorData.semiNumber < semiDomineeData.semiNumber) semiDomineeData.dom = possibleDominator; else semiDomineeData.dom = blockData.parent; } m_data[blockData.parent].bucket.clear(); } } void computeExplicitImmediateDominators() { for (unsigned currentPreNumber = 1; currentPreNumber < m_blockByPreNumber.size(); ++currentPreNumber) { typename Graph::Node block = m_blockByPreNumber[currentPreNumber]; BlockData& blockData = m_data[block]; if (blockData.dom != m_blockByPreNumber[blockData.semiNumber]) blockData.dom = m_data[blockData.dom].dom; } } void link(typename Graph::Node from, typename Graph::Node to) { m_data[to].ancestor = from; } typename Graph::Node eval(typename Graph::Node block) { if (!m_data[block].ancestor) return block; compress(block); return m_data[block].label; } void compress(typename Graph::Node initialBlock) { // This was meant to be a recursive function, but we don't like recursion because we don't // want to blow the stack. The original function will call compress() recursively on the // ancestor of anything that has an ancestor. So, we populate our worklist with the // recursive ancestors of initialBlock. Then we process the list starting from the block // that is furthest up the ancestor chain. typename Graph::Node ancestor = m_data[initialBlock].ancestor; ASSERT(ancestor); if (!m_data[ancestor].ancestor) return; Vector stack; for (typename Graph::Node block = initialBlock; block; block = m_data[block].ancestor) stack.append(block); // We only care about blocks that have an ancestor that has an ancestor. The last two // elements in the stack won't satisfy this property. ASSERT(stack.size() >= 2); ASSERT(!m_data[stack[stack.size() - 1]].ancestor); ASSERT(!m_data[m_data[stack[stack.size() - 2]].ancestor].ancestor); for (unsigned i = stack.size() - 2; i--;) { typename Graph::Node block = stack[i]; typename Graph::Node& labelOfBlock = m_data[block].label; typename Graph::Node& ancestorOfBlock = m_data[block].ancestor; ASSERT(ancestorOfBlock); ASSERT(m_data[ancestorOfBlock].ancestor); typename Graph::Node labelOfAncestorOfBlock = m_data[ancestorOfBlock].label; if (m_data[labelOfAncestorOfBlock].semiNumber < m_data[labelOfBlock].semiNumber) labelOfBlock = labelOfAncestorOfBlock; ancestorOfBlock = m_data[ancestorOfBlock].ancestor; } } struct BlockData { BlockData() : parent(nullptr) , preNumber(UINT_MAX) , semiNumber(UINT_MAX) , ancestor(nullptr) , label(nullptr) , dom(nullptr) { } typename Graph::Node parent; unsigned preNumber; unsigned semiNumber; typename Graph::Node ancestor; typename Graph::Node label; Vector bucket; typename Graph::Node dom; }; Graph& m_graph; typename Graph::template Map m_data; Vector m_blockByPreNumber; }; class NaiveDominators { public: NaiveDominators(Graph& graph) : m_graph(graph) { // This implements a naive dominator solver. ASSERT(!graph.predecessors(graph.root()).size()); unsigned numBlocks = graph.numNodes(); // Allocate storage for the dense dominance matrix. m_results.grow(numBlocks); for (unsigned i = numBlocks; i--;) m_results[i].resize(numBlocks); m_scratch.resize(numBlocks); // We know that the entry block is only dominated by itself. m_results[0].clearAll(); m_results[0].set(0); // Find all of the valid blocks. m_scratch.clearAll(); for (unsigned i = numBlocks; i--;) { if (!graph.node(i)) continue; m_scratch.set(i); } // Mark all nodes as dominated by everything. for (unsigned i = numBlocks; i-- > 1;) { if (!graph.node(i) || !graph.predecessors(graph.node(i)).size()) m_results[i].clearAll(); else m_results[i].set(m_scratch); } // Iteratively eliminate nodes that are not dominator. bool changed; do { changed = false; // Prune dominators in all non entry blocks: forward scan. for (unsigned i = 1; i < numBlocks; ++i) changed |= pruneDominators(i); if (!changed) break; // Prune dominators in all non entry blocks: backward scan. changed = false; for (unsigned i = numBlocks; i-- > 1;) changed |= pruneDominators(i); } while (changed); } bool dominates(unsigned from, unsigned to) const { return m_results[to].get(from); } bool dominates(typename Graph::Node from, typename Graph::Node to) const { return dominates(m_graph.index(from), m_graph.index(to)); } void dump(PrintStream& out) const { for (unsigned blockIndex = 0; blockIndex < m_graph.numNodes(); ++blockIndex) { typename Graph::Node block = m_graph.node(blockIndex); if (!block) continue; out.print(" Block ", m_graph.dump(block), ":"); for (unsigned otherIndex = 0; otherIndex < m_graph.numNodes(); ++otherIndex) { if (!dominates(m_graph.index(block), otherIndex)) continue; out.print(" ", m_graph.dump(m_graph.node(otherIndex))); } out.print("\n"); } } private: bool pruneDominators(unsigned idx) { typename Graph::Node block = m_graph.node(idx); if (!block || !m_graph.predecessors(block).size()) return false; // Find the intersection of dom(preds). m_scratch.set(m_results[m_graph.index(m_graph.predecessors(block)[0])]); for (unsigned j = m_graph.predecessors(block).size(); j-- > 1;) m_scratch.filter(m_results[m_graph.index(m_graph.predecessors(block)[j])]); // The block is also dominated by itself. m_scratch.set(idx); return m_results[idx].setAndCheck(m_scratch); } Graph& m_graph; Vector m_results; // For each block, the bitvector of blocks that dominate it. FastBitVector m_scratch; // A temporary bitvector with bit for each block. We recycle this to save new/deletes. }; struct ValidationContext { ValidationContext(Graph& graph, Dominators& dominators) : graph(graph) , dominators(dominators) , naiveDominators(graph) { } void reportError(typename Graph::Node from, typename Graph::Node to, const char* message) { Error error; error.from = from; error.to = to; error.message = message; errors.append(error); } void handleErrors() { if (errors.isEmpty()) return; dataLog("DFG DOMINATOR VALIDATION FAILED:\n"); dataLog("\n"); dataLog("For block domination relationships:\n"); for (unsigned i = 0; i < errors.size(); ++i) { dataLog( " ", graph.dump(errors[i].from), " -> ", graph.dump(errors[i].to), " (", errors[i].message, ")\n"); } dataLog("\n"); dataLog("Control flow graph:\n"); for (unsigned blockIndex = 0; blockIndex < graph.numNodes(); ++blockIndex) { typename Graph::Node block = graph.node(blockIndex); if (!block) continue; dataLog(" Block ", graph.dump(graph.node(blockIndex)), ": successors = ["); CommaPrinter comma; for (auto successor : graph.successors(block)) dataLog(comma, graph.dump(successor)); dataLog("], predecessors = ["); comma = CommaPrinter(); for (auto predecessor : graph.predecessors(block)) dataLog(comma, graph.dump(predecessor)); dataLog("]\n"); } dataLog("\n"); dataLog("Lengauer-Tarjan Dominators:\n"); dataLog(dominators); dataLog("\n"); dataLog("Naive Dominators:\n"); naiveDominators.dump(WTF::dataFile()); dataLog("\n"); dataLog("Graph at time of failure:\n"); dataLog(graph); dataLog("\n"); dataLog("DFG DOMINATOR VALIDATION FAILIED!\n"); CRASH(); } Graph& graph; Dominators& dominators; NaiveDominators naiveDominators; struct Error { typename Graph::Node from; typename Graph::Node to; const char* message; }; Vector errors; }; bool naiveDominates(typename Graph::Node from, typename Graph::Node to) const { for (typename Graph::Node block = to; block; block = m_data[block].idomParent) { if (block == from) return true; } return false; } template void forAllBlocksInDominanceFrontierOfImpl( typename Graph::Node from, const Functor& functor) const { // Paraphrasing from http://en.wikipedia.org/wiki/Dominator_(graph_theory): // "The dominance frontier of a block 'from' is the set of all blocks 'to' such that // 'from' dominates an immediate predecessor of 'to', but 'from' does not strictly // dominate 'to'." // // A useful corner case to remember: a block may be in its own dominance frontier if it has // a loop edge to itself, since it dominates itself and so it dominates its own immediate // predecessor, and a block never strictly dominates itself. forAllBlocksDominatedBy( from, [&] (typename Graph::Node block) { for (typename Graph::Node to : m_graph.successors(block)) { if (!strictlyDominates(from, to)) functor(to); } }); } template void forAllBlocksInIteratedDominanceFrontierOfImpl( const typename Graph::List& from, const Functor& functor) const { typename Graph::List worklist = from; while (!worklist.isEmpty()) { typename Graph::Node block = worklist.takeLast(); forAllBlocksInDominanceFrontierOfImpl( block, [&] (typename Graph::Node otherBlock) { if (functor(otherBlock)) worklist.append(otherBlock); }); } } struct BlockData { BlockData() : idomParent(nullptr) , preNumber(UINT_MAX) , postNumber(UINT_MAX) { } Vector idomKids; typename Graph::Node idomParent; unsigned preNumber; unsigned postNumber; }; Graph& m_graph; typename Graph::template Map m_data; }; } // namespace WTF using WTF::Dominators; #endif // WTFDominators_h