lib/Target/X86/ImmutableGraph.h - llvm-project/llvm - Git at Google

 //==========-- ImmutableGraph.h - A fast DAG implementation ---------=========//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 /// \file
 /// Description: ImmutableGraph is a fast DAG implementation that cannot be
 /// modified, except by creating a new ImmutableGraph. ImmutableGraph is
 /// implemented as two arrays: one containing nodes, and one containing edges.
 /// The advantages to this implementation are two-fold:
 /// 1. Iteration and traversal operations benefit from cache locality.
 /// 2. Operations on sets of nodes/edges are efficient, and representations of
 ///    those sets in memory are compact. For instance, a set of edges is
 ///    implemented as a bit vector, wherein each bit corresponds to one edge in
 ///    the edge array. This implies a lower bound of 64x spatial improvement
 ///    over, e.g., an llvm::DenseSet or llvm::SmallSet. It also means that
 ///    insert/erase/contains operations complete in negligible constant time:
 ///    insert and erase require one load and one store, and contains requires
 ///    just one load.
 ///
 //===----------------------------------------------------------------------===//

 #ifndef LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H
 #define LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H

 #include "llvm/ADT/BitVector.h"
 #include "llvm/ADT/GraphTraits.h"
 #include "llvm/ADT/STLExtras.h"
 #include <algorithm>
 #include <iterator>
 #include <utility>
 #include <vector>

 namespace llvm {

 template <typename NodeValueT, typename EdgeValueT> class ImmutableGraph {
   using Traits = GraphTraits<ImmutableGraph<NodeValueT, EdgeValueT> *>;
   template <typename> friend class ImmutableGraphBuilder;

 public:
   using node_value_type = NodeValueT;
   using edge_value_type = EdgeValueT;
   using size_type = int;
   class Node;
   class Edge {
     friend class ImmutableGraph;
     template <typename> friend class ImmutableGraphBuilder;

     const Node *Dest;
     edge_value_type Value;

   public:
     const Node *getDest() const { return Dest; };
     const edge_value_type &getValue() const { return Value; }
   };
   class Node {
     friend class ImmutableGraph;
     template <typename> friend class ImmutableGraphBuilder;

     const Edge *Edges;
     node_value_type Value;

   public:
     const node_value_type &getValue() const { return Value; }

     const Edge *edges_begin() const { return Edges; }
     // Nodes are allocated sequentially. Edges for a node are stored together.
     // The end of this Node's edges is the beginning of the next node's edges.
     // An extra node was allocated to hold the end pointer for the last real
     // node.
     const Edge *edges_end() const { return (this + 1)->Edges; }
     ArrayRef<Edge> edges() const {
       return makeArrayRef(edges_begin(), edges_end());
     }
   };

 protected:
   ImmutableGraph(std::unique_ptr<Node[]> Nodes, std::unique_ptr<Edge[]> Edges,
                  size_type NodesSize, size_type EdgesSize)
       : Nodes(std::move(Nodes)), Edges(std::move(Edges)), NodesSize(NodesSize),
         EdgesSize(EdgesSize) {}
   ImmutableGraph(const ImmutableGraph &) = delete;
   ImmutableGraph(ImmutableGraph &&) = delete;
   ImmutableGraph &operator=(const ImmutableGraph &) = delete;
   ImmutableGraph &operator=(ImmutableGraph &&) = delete;

 public:
   ArrayRef<Node> nodes() const { return makeArrayRef(Nodes.get(), NodesSize); }
   const Node *nodes_begin() const { return nodes().begin(); }
   const Node *nodes_end() const { return nodes().end(); }

   ArrayRef<Edge> edges() const { return makeArrayRef(Edges.get(), EdgesSize); }
   const Edge *edges_begin() const { return edges().begin(); }
   const Edge *edges_end() const { return edges().end(); }

   size_type nodes_size() const { return NodesSize; }
   size_type edges_size() const { return EdgesSize; }

   // Node N must belong to this ImmutableGraph.
   size_type getNodeIndex(const Node &N) const {
     return std::distance(nodes_begin(), &N);
   }
   // Edge E must belong to this ImmutableGraph.
   size_type getEdgeIndex(const Edge &E) const {
     return std::distance(edges_begin(), &E);
   }

   // FIXME: Could NodeSet and EdgeSet be templated to share code?
   class NodeSet {
     const ImmutableGraph &G;
     BitVector V;

   public:
     NodeSet(const ImmutableGraph &G, bool ContainsAll = false)
         : G{G}, V{static_cast<unsigned>(G.nodes_size()), ContainsAll} {}
     bool insert(const Node &N) {
       size_type Idx = G.getNodeIndex(N);
       bool AlreadyExists = V.test(Idx);
       V.set(Idx);
       return !AlreadyExists;
     }
     void erase(const Node &N) {
       size_type Idx = G.getNodeIndex(N);
       V.reset(Idx);
     }
     bool contains(const Node &N) const {
       size_type Idx = G.getNodeIndex(N);
       return V.test(Idx);
     }
     void clear() { V.reset(); }
     size_type empty() const { return V.none(); }
     /// Return the number of elements in the set
     size_type count() const { return V.count(); }
     /// Return the size of the set's domain
     size_type size() const { return V.size(); }
     /// Set union
     NodeSet &operator|=(const NodeSet &RHS) {
       assert(&this->G == &RHS.G);
       V |= RHS.V;
       return *this;
     }
     /// Set intersection
     NodeSet &operator&=(const NodeSet &RHS) {
       assert(&this->G == &RHS.G);
       V &= RHS.V;
       return *this;
     }
     /// Set disjoint union
     NodeSet &operator^=(const NodeSet &RHS) {
       assert(&this->G == &RHS.G);
       V ^= RHS.V;
       return *this;
     }

     using index_iterator = typename BitVector::const_set_bits_iterator;
     index_iterator index_begin() const { return V.set_bits_begin(); }
     index_iterator index_end() const { return V.set_bits_end(); }
     void set(size_type Idx) { V.set(Idx); }
     void reset(size_type Idx) { V.reset(Idx); }

     class iterator {
       const NodeSet &Set;
       size_type Current;

       void advance() {
         assert(Current != -1);
         Current = Set.V.find_next(Current);
       }

     public:
       iterator(const NodeSet &Set, size_type Begin)
           : Set{Set}, Current{Begin} {}
       iterator operator++(int) {
         iterator Tmp = *this;
         advance();
         return Tmp;
       }
       iterator &operator++() {
         advance();
         return *this;
       }
       Node *operator*() const {
         assert(Current != -1);
         return Set.G.nodes_begin() + Current;
       }
       bool operator==(const iterator &other) const {
         assert(&this->Set == &other.Set);
         return this->Current == other.Current;
       }
       bool operator!=(const iterator &other) const { return !(*this == other); }
     };

     iterator begin() const { return iterator{*this, V.find_first()}; }
     iterator end() const { return iterator{*this, -1}; }
   };

   class EdgeSet {
     const ImmutableGraph &G;
     BitVector V;

   public:
     EdgeSet(const ImmutableGraph &G, bool ContainsAll = false)
         : G{G}, V{static_cast<unsigned>(G.edges_size()), ContainsAll} {}
     bool insert(const Edge &E) {
       size_type Idx = G.getEdgeIndex(E);
       bool AlreadyExists = V.test(Idx);
       V.set(Idx);
       return !AlreadyExists;
     }
     void erase(const Edge &E) {
       size_type Idx = G.getEdgeIndex(E);
       V.reset(Idx);
     }
     bool contains(const Edge &E) const {
       size_type Idx = G.getEdgeIndex(E);
       return V.test(Idx);
     }
     void clear() { V.reset(); }
     bool empty() const { return V.none(); }
     /// Return the number of elements in the set
     size_type count() const { return V.count(); }
     /// Return the size of the set's domain
     size_type size() const { return V.size(); }
     /// Set union
     EdgeSet &operator|=(const EdgeSet &RHS) {
       assert(&this->G == &RHS.G);
       V |= RHS.V;
       return *this;
     }
     /// Set intersection
     EdgeSet &operator&=(const EdgeSet &RHS) {
       assert(&this->G == &RHS.G);
       V &= RHS.V;
       return *this;
     }
     /// Set disjoint union
     EdgeSet &operator^=(const EdgeSet &RHS) {
       assert(&this->G == &RHS.G);
       V ^= RHS.V;
       return *this;
     }

     using index_iterator = typename BitVector::const_set_bits_iterator;
     index_iterator index_begin() const { return V.set_bits_begin(); }
     index_iterator index_end() const { return V.set_bits_end(); }
     void set(size_type Idx) { V.set(Idx); }
     void reset(size_type Idx) { V.reset(Idx); }

     class iterator {
       const EdgeSet &Set;
       size_type Current;

       void advance() {
         assert(Current != -1);
         Current = Set.V.find_next(Current);
       }

     public:
       iterator(const EdgeSet &Set, size_type Begin)
           : Set{Set}, Current{Begin} {}
       iterator operator++(int) {
         iterator Tmp = *this;
         advance();
         return Tmp;
       }
       iterator &operator++() {
         advance();
         return *this;
       }
       Edge *operator*() const {
         assert(Current != -1);
         return Set.G.edges_begin() + Current;
       }
       bool operator==(const iterator &other) const {
         assert(&this->Set == &other.Set);
         return this->Current == other.Current;
       }
       bool operator!=(const iterator &other) const { return !(*this == other); }
     };

     iterator begin() const { return iterator{*this, V.find_first()}; }
     iterator end() const { return iterator{*this, -1}; }
   };

 private:
   std::unique_ptr<Node[]> Nodes;
   std::unique_ptr<Edge[]> Edges;
   size_type NodesSize;
   size_type EdgesSize;
 };

 template <typename GraphT> class ImmutableGraphBuilder {
   using node_value_type = typename GraphT::node_value_type;
   using edge_value_type = typename GraphT::edge_value_type;
   static_assert(
       std::is_base_of<ImmutableGraph<node_value_type, edge_value_type>,
                       GraphT>::value,
       "Template argument to ImmutableGraphBuilder must derive from "
       "ImmutableGraph<>");
   using size_type = typename GraphT::size_type;
   using NodeSet = typename GraphT::NodeSet;
   using Node = typename GraphT::Node;
   using EdgeSet = typename GraphT::EdgeSet;
   using Edge = typename GraphT::Edge;
   using BuilderEdge = std::pair<edge_value_type, size_type>;
   using EdgeList = std::vector<BuilderEdge>;
   using BuilderVertex = std::pair<node_value_type, EdgeList>;
   using VertexVec = std::vector<BuilderVertex>;

 public:
   using BuilderNodeRef = size_type;

   BuilderNodeRef addVertex(const node_value_type &V) {
     auto I = AdjList.emplace(AdjList.end(), V, EdgeList{});
     return std::distance(AdjList.begin(), I);
   }

   void addEdge(const edge_value_type &E, BuilderNodeRef From,
                BuilderNodeRef To) {
     AdjList[From].second.emplace_back(E, To);
   }

   bool empty() const { return AdjList.empty(); }

   template <typename... ArgT> std::unique_ptr<GraphT> get(ArgT &&... Args) {
     size_type VertexSize = AdjList.size(), EdgeSize = 0;
     for (const auto &V : AdjList) {
       EdgeSize += V.second.size();
     }
     auto VertexArray =
         std::make_unique<Node[]>(VertexSize + 1 /* terminator node */);
     auto EdgeArray = std::make_unique<Edge[]>(EdgeSize);
     size_type VI = 0, EI = 0;
     for (; VI < VertexSize; ++VI) {
       VertexArray[VI].Value = std::move(AdjList[VI].first);
       VertexArray[VI].Edges = &EdgeArray[EI];
       auto NumEdges = static_cast<size_type>(AdjList[VI].second.size());
       for (size_type VEI = 0; VEI < NumEdges; ++VEI, ++EI) {
         auto &E = AdjList[VI].second[VEI];
         EdgeArray[EI].Value = std::move(E.first);
         EdgeArray[EI].Dest = &VertexArray[E.second];
       }
     }
     assert(VI == VertexSize && EI == EdgeSize && "ImmutableGraph malformed");
     VertexArray[VI].Edges = &EdgeArray[EdgeSize]; // terminator node
     return std::make_unique<GraphT>(std::move(VertexArray),
                                     std::move(EdgeArray), VertexSize, EdgeSize,
                                     std::forward<ArgT>(Args)...);
   }

   template <typename... ArgT>
   static std::unique_ptr<GraphT> trim(const GraphT &G, const NodeSet &TrimNodes,
                                       const EdgeSet &TrimEdges,
                                       ArgT &&... Args) {
     size_type NewVertexSize = G.nodes_size() - TrimNodes.count();
     size_type NewEdgeSize = G.edges_size() - TrimEdges.count();
     auto NewVertexArray =
         std::make_unique<Node[]>(NewVertexSize + 1 /* terminator node */);
     auto NewEdgeArray = std::make_unique<Edge[]>(NewEdgeSize);

     // Walk the nodes and determine the new index for each node.
     size_type NewNodeIndex = 0;
     std::vector<size_type> RemappedNodeIndex(G.nodes_size());
     for (const Node &N : G.nodes()) {
       if (TrimNodes.contains(N))
         continue;
       RemappedNodeIndex[G.getNodeIndex(N)] = NewNodeIndex++;
     }
     assert(NewNodeIndex == NewVertexSize &&
            "Should have assigned NewVertexSize indices");

     size_type VertexI = 0, EdgeI = 0;
     for (const Node &N : G.nodes()) {
       if (TrimNodes.contains(N))
         continue;
       NewVertexArray[VertexI].Value = N.getValue();
       NewVertexArray[VertexI].Edges = &NewEdgeArray[EdgeI];
       for (const Edge &E : N.edges()) {
         if (TrimEdges.contains(E))
           continue;
         NewEdgeArray[EdgeI].Value = E.getValue();
         size_type DestIdx = G.getNodeIndex(*E.getDest());
         size_type NewIdx = RemappedNodeIndex[DestIdx];
         assert(NewIdx < NewVertexSize);
         NewEdgeArray[EdgeI].Dest = &NewVertexArray[NewIdx];
         ++EdgeI;
       }
       ++VertexI;
     }
     assert(VertexI == NewVertexSize && EdgeI == NewEdgeSize &&
            "Gadget graph malformed");
     NewVertexArray[VertexI].Edges = &NewEdgeArray[NewEdgeSize]; // terminator
     return std::make_unique<GraphT>(std::move(NewVertexArray),
                                     std::move(NewEdgeArray), NewVertexSize,
                                     NewEdgeSize, std::forward<ArgT>(Args)...);
   }

 private:
   VertexVec AdjList;
 };

 template <typename NodeValueT, typename EdgeValueT>
 struct GraphTraits<ImmutableGraph<NodeValueT, EdgeValueT> *> {
   using GraphT = ImmutableGraph<NodeValueT, EdgeValueT>;
   using NodeRef = typename GraphT::Node const *;
   using EdgeRef = typename GraphT::Edge const &;

   static NodeRef edge_dest(EdgeRef E) { return E.getDest(); }
   using ChildIteratorType =
       mapped_iterator<typename GraphT::Edge const *, decltype(&edge_dest)>;

   static NodeRef getEntryNode(GraphT *G) { return G->nodes_begin(); }
   static ChildIteratorType child_begin(NodeRef N) {
     return {N->edges_begin(), &edge_dest};
   }
   static ChildIteratorType child_end(NodeRef N) {
     return {N->edges_end(), &edge_dest};
   }

   static NodeRef getNode(typename GraphT::Node const &N) { return NodeRef{&N}; }
   using nodes_iterator =
       mapped_iterator<typename GraphT::Node const *, decltype(&getNode)>;
   static nodes_iterator nodes_begin(GraphT *G) {
     return {G->nodes_begin(), &getNode};
   }
   static nodes_iterator nodes_end(GraphT *G) {
     return {G->nodes_end(), &getNode};
   }

   using ChildEdgeIteratorType = typename GraphT::Edge const *;

   static ChildEdgeIteratorType child_edge_begin(NodeRef N) {
     return N->edges_begin();
   }
   static ChildEdgeIteratorType child_edge_end(NodeRef N) {
     return N->edges_end();
   }
   static typename GraphT::size_type size(GraphT *G) { return G->nodes_size(); }
 };

 } // end namespace llvm

 #endif // LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H
	//==========-- ImmutableGraph.h - A fast DAG implementation ---------=========//
	//
	// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
	// See https://llvm.org/LICENSE.txt for license information.
	// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
	//
	//===----------------------------------------------------------------------===//
	/// \file
	/// Description: ImmutableGraph is a fast DAG implementation that cannot be
	/// modified, except by creating a new ImmutableGraph. ImmutableGraph is
	/// implemented as two arrays: one containing nodes, and one containing edges.
	/// The advantages to this implementation are two-fold:
	/// 1. Iteration and traversal operations benefit from cache locality.
	/// 2. Operations on sets of nodes/edges are efficient, and representations of
	/// those sets in memory are compact. For instance, a set of edges is
	/// implemented as a bit vector, wherein each bit corresponds to one edge in
	/// the edge array. This implies a lower bound of 64x spatial improvement
	/// over, e.g., an llvm::DenseSet or llvm::SmallSet. It also means that
	/// insert/erase/contains operations complete in negligible constant time:
	/// insert and erase require one load and one store, and contains requires
	/// just one load.
	///
	//===----------------------------------------------------------------------===//

	#ifndef LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H
	#define LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H

	#include "llvm/ADT/BitVector.h"
	#include "llvm/ADT/GraphTraits.h"
	#include "llvm/ADT/STLExtras.h"
	#include <algorithm>
	#include <iterator>
	#include <utility>
	#include <vector>

	namespace llvm {

	template <typename NodeValueT, typename EdgeValueT> class ImmutableGraph {
	using Traits = GraphTraits<ImmutableGraph<NodeValueT, EdgeValueT> *>;
	template <typename> friend class ImmutableGraphBuilder;

	public:
	using node_value_type = NodeValueT;
	using edge_value_type = EdgeValueT;
	using size_type = int;
	class Node;
	class Edge {
	friend class ImmutableGraph;
	template <typename> friend class ImmutableGraphBuilder;

	const Node *Dest;
	edge_value_type Value;

	public:
	const Node *getDest() const { return Dest; };
	const edge_value_type &getValue() const { return Value; }
	};
	class Node {
	friend class ImmutableGraph;
	template <typename> friend class ImmutableGraphBuilder;

	const Edge *Edges;
	node_value_type Value;

	public:
	const node_value_type &getValue() const { return Value; }

	const Edge *edges_begin() const { return Edges; }
	// Nodes are allocated sequentially. Edges for a node are stored together.
	// The end of this Node's edges is the beginning of the next node's edges.
	// An extra node was allocated to hold the end pointer for the last real
	// node.
	const Edge *edges_end() const { return (this + 1)->Edges; }
	ArrayRef<Edge> edges() const {
	return makeArrayRef(edges_begin(), edges_end());
	}
	};

	protected:
	ImmutableGraph(std::unique_ptr<Node[]> Nodes, std::unique_ptr<Edge[]> Edges,
	size_type NodesSize, size_type EdgesSize)
	: Nodes(std::move(Nodes)), Edges(std::move(Edges)), NodesSize(NodesSize),
	EdgesSize(EdgesSize) {}
	ImmutableGraph(const ImmutableGraph &) = delete;
	ImmutableGraph(ImmutableGraph &&) = delete;
	ImmutableGraph &operator=(const ImmutableGraph &) = delete;
	ImmutableGraph &operator=(ImmutableGraph &&) = delete;

	public:
	ArrayRef<Node> nodes() const { return makeArrayRef(Nodes.get(), NodesSize); }
	const Node *nodes_begin() const { return nodes().begin(); }
	const Node *nodes_end() const { return nodes().end(); }

	ArrayRef<Edge> edges() const { return makeArrayRef(Edges.get(), EdgesSize); }
	const Edge *edges_begin() const { return edges().begin(); }
	const Edge *edges_end() const { return edges().end(); }

	size_type nodes_size() const { return NodesSize; }
	size_type edges_size() const { return EdgesSize; }

	// Node N must belong to this ImmutableGraph.
	size_type getNodeIndex(const Node &N) const {
	return std::distance(nodes_begin(), &N);
	}
	// Edge E must belong to this ImmutableGraph.
	size_type getEdgeIndex(const Edge &E) const {
	return std::distance(edges_begin(), &E);
	}

	// FIXME: Could NodeSet and EdgeSet be templated to share code?
	class NodeSet {
	const ImmutableGraph &G;
	BitVector V;

	public:
	NodeSet(const ImmutableGraph &G, bool ContainsAll = false)
	: G{G}, V{static_cast<unsigned>(G.nodes_size()), ContainsAll} {}
	bool insert(const Node &N) {
	size_type Idx = G.getNodeIndex(N);
	bool AlreadyExists = V.test(Idx);
	V.set(Idx);
	return !AlreadyExists;
	}
	void erase(const Node &N) {
	size_type Idx = G.getNodeIndex(N);
	V.reset(Idx);
	}
	bool contains(const Node &N) const {
	size_type Idx = G.getNodeIndex(N);
	return V.test(Idx);
	}
	void clear() { V.reset(); }
	size_type empty() const { return V.none(); }
	/// Return the number of elements in the set
	size_type count() const { return V.count(); }
	/// Return the size of the set's domain
	size_type size() const { return V.size(); }
	/// Set union
	NodeSet &operator\|=(const NodeSet &RHS) {
	assert(&this->G == &RHS.G);
	V \|= RHS.V;
	return *this;
	}
	/// Set intersection
	NodeSet &operator&=(const NodeSet &RHS) {
	assert(&this->G == &RHS.G);
	V &= RHS.V;
	return *this;
	}
	/// Set disjoint union
	NodeSet &operator^=(const NodeSet &RHS) {
	assert(&this->G == &RHS.G);
	V ^= RHS.V;
	return *this;
	}

	using index_iterator = typename BitVector::const_set_bits_iterator;
	index_iterator index_begin() const { return V.set_bits_begin(); }
	index_iterator index_end() const { return V.set_bits_end(); }
	void set(size_type Idx) { V.set(Idx); }
	void reset(size_type Idx) { V.reset(Idx); }

	class iterator {
	const NodeSet &Set;
	size_type Current;

	void advance() {
	assert(Current != -1);
	Current = Set.V.find_next(Current);
	}

	public:
	iterator(const NodeSet &Set, size_type Begin)
	: Set{Set}, Current{Begin} {}
	iterator operator++(int) {
	iterator Tmp = *this;
	advance();
	return Tmp;
	}
	iterator &operator++() {
	advance();
	return *this;
	}
	Node operator() const {
	assert(Current != -1);
	return Set.G.nodes_begin() + Current;
	}
	bool operator==(const iterator &other) const {
	assert(&this->Set == &other.Set);
	return this->Current == other.Current;
	}
	bool operator!=(const iterator &other) const { return !(*this == other); }
	};

	iterator begin() const { return iterator{*this, V.find_first()}; }
	iterator end() const { return iterator{*this, -1}; }
	};

	class EdgeSet {
	const ImmutableGraph &G;
	BitVector V;

	public:
	EdgeSet(const ImmutableGraph &G, bool ContainsAll = false)
	: G{G}, V{static_cast<unsigned>(G.edges_size()), ContainsAll} {}
	bool insert(const Edge &E) {
	size_type Idx = G.getEdgeIndex(E);
	bool AlreadyExists = V.test(Idx);
	V.set(Idx);
	return !AlreadyExists;
	}
	void erase(const Edge &E) {
	size_type Idx = G.getEdgeIndex(E);
	V.reset(Idx);
	}
	bool contains(const Edge &E) const {
	size_type Idx = G.getEdgeIndex(E);
	return V.test(Idx);
	}
	void clear() { V.reset(); }
	bool empty() const { return V.none(); }
	/// Return the number of elements in the set
	size_type count() const { return V.count(); }
	/// Return the size of the set's domain
	size_type size() const { return V.size(); }
	/// Set union
	EdgeSet &operator\|=(const EdgeSet &RHS) {
	assert(&this->G == &RHS.G);
	V \|= RHS.V;
	return *this;
	}
	/// Set intersection
	EdgeSet &operator&=(const EdgeSet &RHS) {
	assert(&this->G == &RHS.G);
	V &= RHS.V;
	return *this;
	}
	/// Set disjoint union
	EdgeSet &operator^=(const EdgeSet &RHS) {
	assert(&this->G == &RHS.G);
	V ^= RHS.V;
	return *this;
	}

	using index_iterator = typename BitVector::const_set_bits_iterator;
	index_iterator index_begin() const { return V.set_bits_begin(); }
	index_iterator index_end() const { return V.set_bits_end(); }
	void set(size_type Idx) { V.set(Idx); }
	void reset(size_type Idx) { V.reset(Idx); }

	class iterator {
	const EdgeSet &Set;
	size_type Current;

	void advance() {
	assert(Current != -1);
	Current = Set.V.find_next(Current);
	}

	public:
	iterator(const EdgeSet &Set, size_type Begin)
	: Set{Set}, Current{Begin} {}
	iterator operator++(int) {
	iterator Tmp = *this;
	advance();
	return Tmp;
	}
	iterator &operator++() {
	advance();
	return *this;
	}
	Edge operator() const {
	assert(Current != -1);
	return Set.G.edges_begin() + Current;
	}
	bool operator==(const iterator &other) const {
	assert(&this->Set == &other.Set);
	return this->Current == other.Current;
	}
	bool operator!=(const iterator &other) const { return !(*this == other); }
	};

	iterator begin() const { return iterator{*this, V.find_first()}; }
	iterator end() const { return iterator{*this, -1}; }
	};

	private:
	std::unique_ptr<Node[]> Nodes;
	std::unique_ptr<Edge[]> Edges;
	size_type NodesSize;
	size_type EdgesSize;
	};

	template <typename GraphT> class ImmutableGraphBuilder {
	using node_value_type = typename GraphT::node_value_type;
	using edge_value_type = typename GraphT::edge_value_type;
	static_assert(
	std::is_base_of<ImmutableGraph<node_value_type, edge_value_type>,
	GraphT>::value,
	"Template argument to ImmutableGraphBuilder must derive from "
	"ImmutableGraph<>");
	using size_type = typename GraphT::size_type;
	using NodeSet = typename GraphT::NodeSet;
	using Node = typename GraphT::Node;
	using EdgeSet = typename GraphT::EdgeSet;
	using Edge = typename GraphT::Edge;
	using BuilderEdge = std::pair<edge_value_type, size_type>;
	using EdgeList = std::vector<BuilderEdge>;
	using BuilderVertex = std::pair<node_value_type, EdgeList>;
	using VertexVec = std::vector<BuilderVertex>;

	public:
	using BuilderNodeRef = size_type;

	BuilderNodeRef addVertex(const node_value_type &V) {
	auto I = AdjList.emplace(AdjList.end(), V, EdgeList{});
	return std::distance(AdjList.begin(), I);
	}

	void addEdge(const edge_value_type &E, BuilderNodeRef From,
	BuilderNodeRef To) {
	AdjList[From].second.emplace_back(E, To);
	}

	bool empty() const { return AdjList.empty(); }

	template <typename... ArgT> std::unique_ptr<GraphT> get(ArgT &&... Args) {
	size_type VertexSize = AdjList.size(), EdgeSize = 0;
	for (const auto &V : AdjList) {
	EdgeSize += V.second.size();
	}
	auto VertexArray =
	std::make_unique<Node[]>(VertexSize + 1 /* terminator node */);
	auto EdgeArray = std::make_unique<Edge[]>(EdgeSize);
	size_type VI = 0, EI = 0;
	for (; VI < VertexSize; ++VI) {
	VertexArray[VI].Value = std::move(AdjList[VI].first);
	VertexArray[VI].Edges = &EdgeArray[EI];
	auto NumEdges = static_cast<size_type>(AdjList[VI].second.size());
	for (size_type VEI = 0; VEI < NumEdges; ++VEI, ++EI) {
	auto &E = AdjList[VI].second[VEI];
	EdgeArray[EI].Value = std::move(E.first);
	EdgeArray[EI].Dest = &VertexArray[E.second];
	}
	}
	assert(VI == VertexSize && EI == EdgeSize && "ImmutableGraph malformed");
	VertexArray[VI].Edges = &EdgeArray[EdgeSize]; // terminator node
	return std::make_unique<GraphT>(std::move(VertexArray),
	std::move(EdgeArray), VertexSize, EdgeSize,
	std::forward<ArgT>(Args)...);
	}

	template <typename... ArgT>
	static std::unique_ptr<GraphT> trim(const GraphT &G, const NodeSet &TrimNodes,
	const EdgeSet &TrimEdges,
	ArgT &&... Args) {
	size_type NewVertexSize = G.nodes_size() - TrimNodes.count();
	size_type NewEdgeSize = G.edges_size() - TrimEdges.count();
	auto NewVertexArray =
	std::make_unique<Node[]>(NewVertexSize + 1 /* terminator node */);
	auto NewEdgeArray = std::make_unique<Edge[]>(NewEdgeSize);

	// Walk the nodes and determine the new index for each node.
	size_type NewNodeIndex = 0;
	std::vector<size_type> RemappedNodeIndex(G.nodes_size());
	for (const Node &N : G.nodes()) {
	if (TrimNodes.contains(N))
	continue;
	RemappedNodeIndex[G.getNodeIndex(N)] = NewNodeIndex++;
	}
	assert(NewNodeIndex == NewVertexSize &&
	"Should have assigned NewVertexSize indices");

	size_type VertexI = 0, EdgeI = 0;
	for (const Node &N : G.nodes()) {
	if (TrimNodes.contains(N))
	continue;
	NewVertexArray[VertexI].Value = N.getValue();
	NewVertexArray[VertexI].Edges = &NewEdgeArray[EdgeI];
	for (const Edge &E : N.edges()) {
	if (TrimEdges.contains(E))
	continue;
	NewEdgeArray[EdgeI].Value = E.getValue();
	size_type DestIdx = G.getNodeIndex(*E.getDest());
	size_type NewIdx = RemappedNodeIndex[DestIdx];
	assert(NewIdx < NewVertexSize);
	NewEdgeArray[EdgeI].Dest = &NewVertexArray[NewIdx];
	++EdgeI;
	}
	++VertexI;
	}
	assert(VertexI == NewVertexSize && EdgeI == NewEdgeSize &&
	"Gadget graph malformed");
	NewVertexArray[VertexI].Edges = &NewEdgeArray[NewEdgeSize]; // terminator
	return std::make_unique<GraphT>(std::move(NewVertexArray),
	std::move(NewEdgeArray), NewVertexSize,
	NewEdgeSize, std::forward<ArgT>(Args)...);
	}

	private:
	VertexVec AdjList;
	};

	template <typename NodeValueT, typename EdgeValueT>
	struct GraphTraits<ImmutableGraph<NodeValueT, EdgeValueT> *> {
	using GraphT = ImmutableGraph<NodeValueT, EdgeValueT>;
	using NodeRef = typename GraphT::Node const *;
	using EdgeRef = typename GraphT::Edge const &;

	static NodeRef edge_dest(EdgeRef E) { return E.getDest(); }
	using ChildIteratorType =
	mapped_iterator<typename GraphT::Edge const *, decltype(&edge_dest)>;

	static NodeRef getEntryNode(GraphT *G) { return G->nodes_begin(); }
	static ChildIteratorType child_begin(NodeRef N) {
	return {N->edges_begin(), &edge_dest};
	}
	static ChildIteratorType child_end(NodeRef N) {
	return {N->edges_end(), &edge_dest};
	}

	static NodeRef getNode(typename GraphT::Node const &N) { return NodeRef{&N}; }
	using nodes_iterator =
	mapped_iterator<typename GraphT::Node const *, decltype(&getNode)>;
	static nodes_iterator nodes_begin(GraphT *G) {
	return {G->nodes_begin(), &getNode};
	}
	static nodes_iterator nodes_end(GraphT *G) {
	return {G->nodes_end(), &getNode};
	}

	using ChildEdgeIteratorType = typename GraphT::Edge const *;

	static ChildEdgeIteratorType child_edge_begin(NodeRef N) {
	return N->edges_begin();
	}
	static ChildEdgeIteratorType child_edge_end(NodeRef N) {
	return N->edges_end();
	}
	static typename GraphT::size_type size(GraphT *G) { return G->nodes_size(); }
	};

	} // end namespace llvm

	#endif // LLVM_LIB_TARGET_X86_IMMUTABLEGRAPH_H