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Closure Compiler is a JavaScript optimizing compiler. It parses your JavaScript, analyzes it, removes dead code and rewrites and minimizes what's left. It also checks syntax, variable references, and types, and warns about common JavaScript pitfalls. It is used in many of Google's JavaScript apps, including Gmail, Google Web Search, Google Maps, and Google Docs.
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/*
 * Copyright 2008 The Closure Compiler Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.google.javascript.jscomp.graph;

import static com.google.common.base.Preconditions.checkState;
import static java.lang.Math.max;
import static java.lang.Math.min;

import com.google.javascript.jscomp.graph.DiGraph.DiGraphEdge;
import com.google.javascript.jscomp.graph.DiGraph.DiGraphNode;
import java.util.LinkedHashSet;
import java.util.Set;

/**
 * A utility class for doing fixed-point computations. We traverse
 * the edges over the given directed graph until the graph reaches
 * a steady state.
 *
 *
 * @param  Value type that the graph node stores.
 * @param  Value type that the graph edge stores.
 */
public final class FixedPointGraphTraversal {
  // TODO(nicksantos): Generalize the algorithm for undirected graphs, if we
  // need it.

  private final EdgeCallback callback;

  private enum TraversalDirection {
    INWARDS, // from a node to its incoming edges
    OUTWARDS // from a node to its outgoing edges
  }

  private final TraversalDirection traversalDirection;

  public static final String NON_HALTING_ERROR_MSG =
    "Fixed point computation not halting";

  /**
   * Create a new traversal.
   *
   * @param callback A callback for updating the state of the graph each time an edge is traversed.
   */
  private FixedPointGraphTraversal(
      EdgeCallback callback, TraversalDirection traversalDirection) {
    this.callback = callback;
    this.traversalDirection = traversalDirection;
  }

  /** Helper method for creating new traversals that traverse from parent to child. */
  public static  FixedPointGraphTraversal newTraversal(
      EdgeCallback callback) {
    return new FixedPointGraphTraversal<>(callback, TraversalDirection.OUTWARDS);
  }

  /** Helper method for creating new traversals that traverse from child to parent. */
  public static  FixedPointGraphTraversal newReverseTraversal(
      EdgeCallback callback) {
    return new FixedPointGraphTraversal<>(callback, TraversalDirection.INWARDS);
  }

  /**
   * Compute a fixed point for the given graph.
   *
   * @param graph The graph to traverse.
   */
  public void computeFixedPoint(DiGraph graph) {
    Set nodes = new LinkedHashSet<>();
    for (DiGraphNode node : graph.getNodes()) {
      nodes.add(node.getValue());
    }
    computeFixedPoint(graph, nodes);
  }

  /**
   * Compute a fixed point for the given graph, entering from the given node.
   * @param graph The graph to traverse.
   * @param entry The node to begin traversing from.
   */
  public void computeFixedPoint(DiGraph graph, N entry) {
    Set entrySet = new LinkedHashSet<>();
    entrySet.add(entry);
    computeFixedPoint(graph, entrySet);
  }

  // We cube the number of nodes to estimate the largest number of iterations we should allow before
  // deciding that we aren't reaching a fixed point.
  // We have to make sure that we don't hit integer overflow when calculating this value.
  // We also don't want to wait longer than a full minute for any fixed point calculation.
  // We'll be generous and assume each iteration takes only a nanosecond.
  // That's 60*10^9 iterations, so we must cap the node count we use for calculation at the
  // cube root of that number.
  private static final long MAX_NODE_COUNT_FOR_ITERATION_LIMIT = (long) Math.floor(Math.cbrt(60e9));

  /**
   * Compute a fixed point for the given graph, entering from the given nodes.
   * @param graph The graph to traverse.
   * @param entrySet The nodes to begin traversing from.
   */
  public void computeFixedPoint(DiGraph graph, Set entrySet) {
    long cycleCount = 0;
    long nodeCount = min(graph.getNodeCount(), MAX_NODE_COUNT_FOR_ITERATION_LIMIT);

    // Choose a bail-out heuristically in case the computation
    // doesn't converge.
    long maxIterations = max(nodeCount * nodeCount * nodeCount, 100L);

    // Use a LinkedHashSet, so that the traversal is deterministic.
    LinkedHashSet> workSet = new LinkedHashSet<>();
    for (N n : entrySet) {
      workSet.add(graph.getNode(n));
    }
    for (; !workSet.isEmpty() && cycleCount < maxIterations; cycleCount++) {
      visitNode(workSet.iterator().next(), workSet);
    }

    checkState(cycleCount != maxIterations, NON_HALTING_ERROR_MSG);
  }

  private void visitNode(DiGraphNode node, LinkedHashSet> workSet) {
    // For every out edge in the workSet, traverse that edge. If that
    // edge updates the state of the graph, then add the destination
    // node to the resultSet, so that we can update all of its out edges
    // on the next iteration.
    workSet.remove(node);
    switch (traversalDirection) {
      case OUTWARDS:
        N sourceValue = node.getValue();
        for (DiGraphEdge edge : node.getOutEdges()) {
          N destValue = edge.getDestination().getValue();
          if (callback.traverseEdge(sourceValue, edge.getValue(), destValue)) {
            workSet.add(edge.getDestination());
          }
        }
        return;
      case INWARDS:
        N revSourceValue = node.getValue();
        for (DiGraphEdge edge : node.getInEdges()) {
          N revDestValue = edge.getSource().getValue();
          if (callback.traverseEdge(revSourceValue, edge.getValue(), revDestValue)) {
            workSet.add(edge.getSource());
          }
        }
        return;
    }
    throw new AssertionError("Unrecognized direction " + traversalDirection);
  }

  /** Edge callback */
  public interface EdgeCallback {
    /**
     * Update the state of the destination node when the given edge is traversed.
     *
     * Recall that depending on the direction of the traversal, {@code source} and {@code
     * destination} may be swapped compared to the orientation of the edge in the graph. In either
     * case, only the {@code destination} parameter may be mutated.
     *
     * @param source The start node.
     * @param e The edge.
     * @param destination The end node.
     * @return Whether the state of the destination node changed.
     */
    boolean traverseEdge(NodeT source, EdgeT e, NodeT destination);
  }
}