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+/*
+ * Copyright (C) 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 WTF_BackwardsGraph_h
+#define WTF_BackwardsGraph_h
+
+#include <wtf/FastMalloc.h>
+#include <wtf/GraphNodeWorklist.h>
+#include <wtf/Noncopyable.h>
+#include <wtf/StdLibExtras.h>
+
+namespace WTF {
+
+template<typename Graph>
+class BackwardsGraph {
+    WTF_MAKE_NONCOPYABLE(BackwardsGraph);
+    WTF_MAKE_FAST_ALLOCATED;
+public:
+    // We use "#end" to refer to the synthetic root we have created.
+    static const char* rootName() { return "#end"; };
+
+    class Node {
+    public:
+        Node(typename Graph::Node node = typename Graph::Node())
+            : m_node(node)
+        {
+        }
+
+        static Node root()
+        {
+            Node result;
+            result.m_node = 0;
+            result.m_isRoot = true;
+            return result;
+        }
+
+        bool operator==(const Node& other) const
+        {
+            return m_node == other.m_node
+                && m_isRoot == other.m_isRoot;
+        }
+
+        bool operator!=(const Node& other) const
+        {
+            return !(*this == other);
+        }
+
+        explicit operator bool() const { return *this != Node(); }
+
+        bool isRoot() const
+        {
+            return m_isRoot;
+        }
+
+        typename Graph::Node node() const { return m_node; }
+
+    private:
+        typename Graph::Node m_node;
+        bool m_isRoot { false };
+    };
+
+    class Set {
+    public:
+        Set()
+        {
+        }
+        
+        bool add(const Node& node)
+        {
+            if (node.isRoot())
+                return checkAndSet(m_hasRoot, true);
+            return m_set.add(node.node());
+        }
+
+        bool remove(const Node& node)
+        {
+            if (node.isRoot())
+                return checkAndSet(m_hasRoot, false);
+            return m_set.remove(node.node());
+        }
+
+        bool contains(const Node& node)
+        {
+            if (node.isRoot())
+                return m_hasRoot;
+            return m_set.contains(node.node());
+        }
+
+        void dump(PrintStream& out) const
+        {
+            if (m_hasRoot)
+                out.print(rootName(), " ");
+            out.print(m_set);
+        }
+        
+    private:
+        typename Graph::Set m_set;
+        bool m_hasRoot { false };
+    };
+
+    template<typename T>
+    class Map {
+    public:
+        Map(Graph& graph)
+            : m_map(graph.template newMap<T>())
+        {
+        }
+
+        void clear()
+        {
+            m_map.clear();
+            m_root = T();
+        }
+
+        size_t size() const { return m_map.size() + 1; }
+
+        T& operator[](size_t index)
+        {
+            if (!index)
+                return m_root;
+            return m_map[index - 1];
+        }
+
+        const T& operator[](size_t index) const
+        {
+            return (*const_cast<Map*>(this))[index];
+        }
+
+        T& operator[](const Node& node)
+        {
+            if (node.isRoot())
+                return m_root;
+            return m_map[node.node()];
+        }
+
+        const T& operator[](const Node& node) const
+        {
+            return (*const_cast<Map*>(this))[node];
+        }
+        
+    private:
+        typename Graph::template Map<T> m_map;
+        T m_root;
+    };
+
+    typedef Vector<Node, 4> List;
+
+    BackwardsGraph(Graph& graph)
+        : m_graph(graph)
+    {
+        GraphNodeWorklist<typename Graph::Node, typename Graph::Set> worklist;
+
+        auto addRootSuccessor = [&] (typename Graph::Node node) {
+            if (worklist.push(node)) {
+                m_rootSuccessorList.append(node);
+                m_rootSuccessorSet.add(node);
+                while (typename Graph::Node node = worklist.pop())
+                    worklist.pushAll(graph.predecessors(node));
+            }
+        };
+
+        for (unsigned i = 0; i < graph.numNodes(); ++i) {
+            if (typename Graph::Node node = graph.node(i)) {
+                if (!graph.successors(node).size())
+                    addRootSuccessor(node);
+            }
+        }
+
+        // At this point there will be some nodes in the graph that aren't known to the worklist. We
+        // could add any or all of them to the root successors list. Adding all of them would be a bad
+        // pessimisation. Ideally we would pick the ones that have backward edges but no forward
+        // edges. That would require thinking, so we just use a rough heuristic: add the highest
+        // numbered nodes first, which is totally fine if the input program is already sorted nicely.
+        for (unsigned i = graph.numNodes(); i--;) {
+            if (typename Graph::Node node = graph.node(i))
+                addRootSuccessor(node);
+        }
+    }
+
+    Node root() { return Node::root(); }
+
+    template<typename T>
+    Map<T> newMap() { return Map<T>(m_graph); }
+
+    List successors(const Node& node) const
+    {
+        if (node.isRoot())
+            return m_rootSuccessorList;
+        List result;
+        for (typename Graph::Node predecessor : m_graph.predecessors(node.node()))
+            result.append(predecessor);
+        return result;
+    }
+
+    List predecessors(const Node& node) const
+    {
+        if (node.isRoot())
+            return { };
+
+        List result;
+        
+        if (m_rootSuccessorSet.contains(node.node()))
+            result.append(Node::root());
+
+        for (typename Graph::Node successor : m_graph.successors(node.node()))
+            result.append(successor);
+
+        return result;
+    }
+
+    unsigned index(const Node& node) const
+    {
+        if (node.isRoot())
+            return 0;
+        return m_graph.index(node.node()) + 1;
+    }
+
+    Node node(unsigned index) const
+    {
+        if (!index)
+            return Node::root();
+        return m_graph.node(index - 1);
+    }
+
+    unsigned numNodes() const
+    {
+        return m_graph.numNodes() + 1;
+    }
+
+    CString dump(Node node) const
+    {
+        StringPrintStream out;
+        if (!node)
+            out.print("<null>");
+        else if (node.isRoot())
+            out.print(rootName());
+        else
+            out.print(m_graph.dump(node.node()));
+        return out.toCString();
+    }
+
+    void dump(PrintStream& out) const
+    {
+        for (unsigned i = 0; i < numNodes(); ++i) {
+            Node node = this->node(i);
+            if (!node)
+                continue;
+            out.print(dump(node), ":\n");
+            out.print("    Preds: ");
+            CommaPrinter comma;
+            for (Node predecessor : predecessors(node))
+                out.print(comma, dump(predecessor));
+            out.print("\n");
+            out.print("    Succs: ");
+            comma = CommaPrinter();
+            for (Node successor : successors(node))
+                out.print(comma, dump(successor));
+            out.print("\n");
+        }
+    }
+
+private:
+    Graph& m_graph;
+    List m_rootSuccessorList;
+    typename Graph::Set m_rootSuccessorSet;
+};
+
+} // namespace WTF
+
+using WTF::BackwardsGraph;
+
+#endif // WTF_BackwardsGraph_h
+