kc3-lang/harfbuzz/src/graph/graph.hh

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• Hash : 29e3b246
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  Date : 2022-08-18T01:19:54
  

  [repacker] optimzie remove_real_links as it's a hot method.
  

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• src/graph/graph.hh

• /*
   * Copyright © 2022  Google, Inc.
   *
   *  This is part of HarfBuzz, a text shaping library.
   *
   * Permission is hereby granted, without written agreement and without
   * license or royalty fees, to use, copy, modify, and distribute this
   * software and its documentation for any purpose, provided that the
   * above copyright notice and the following two paragraphs appear in
   * all copies of this software.
   *
   * IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
   * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
   * ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
   * IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
   * DAMAGE.
   *
   * THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
   * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
   * FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS
   * ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
   * PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
   *
   * Google Author(s): Garret Rieger
   */
  
  #include "../hb-set.hh"
  #include "../hb-priority-queue.hh"
  #include "../hb-serialize.hh"
  
  #ifndef GRAPH_GRAPH_HH
  #define GRAPH_GRAPH_HH
  
  namespace graph {
  
  /**
   * Represents a serialized table in the form of a graph.
   * Provides methods for modifying and reordering the graph.
   */
  struct graph_t
  {
    struct vertex_t
    {
      hb_serialize_context_t::object_t obj;
      int64_t distance = 0 ;
      int64_t space = 0 ;
      hb_vector_t<unsigned> parents;
      unsigned start = 0;
      unsigned end = 0;
      unsigned priority = 0;
  
      void normalize ()
      {
        obj.real_links.qsort ();
        for (auto& l : obj.real_links)
        {
          for (unsigned i = 0; i < l.width; i++)
          {
            obj.head[l.position + i] = 0;
          }
        }
      }
  
      bool equals (const vertex_t& other,
                   const graph_t& graph,
                   const graph_t& other_graph,
                   unsigned depth) const
      {
        if (!(as_bytes () == other.as_bytes ()))
        {
          DEBUG_MSG (SUBSET_REPACK, nullptr,
                     "vertex [%lu] bytes != [%lu] bytes, depth = %u",
                     table_size (),
                     other.table_size (),
                     depth);
  
          auto a = as_bytes ();
          auto b = other.as_bytes ();
          while (a || b)
          {
            DEBUG_MSG (SUBSET_REPACK, nullptr,
                       "  0x%x %s 0x%x", *a, (*a == *b) ? "==" : "!=", *b);
            a++;
            b++;
          }
          return false;
        }
  
        return links_equal (obj.real_links, other.obj.real_links, graph, other_graph, depth);
      }
  
      hb_bytes_t as_bytes () const
      {
        return hb_bytes_t (obj.head, table_size ());
      }
  
      friend void swap (vertex_t& a, vertex_t& b)
      {
        hb_swap (a.obj, b.obj);
        hb_swap (a.distance, b.distance);
        hb_swap (a.space, b.space);
        hb_swap (a.parents, b.parents);
        hb_swap (a.start, b.start);
        hb_swap (a.end, b.end);
        hb_swap (a.priority, b.priority);
      }
  
      hb_hashmap_t<unsigned, unsigned>
      position_to_index_map () const
      {
        hb_hashmap_t<unsigned, unsigned> result;
  
        for (const auto& l : obj.real_links) {
          result.set (l.position, l.objidx);
        }
  
        return result;
      }
  
      bool is_shared () const
      {
        return parents.length > 1;
      }
  
      unsigned incoming_edges () const
      {
        return parents.length;
      }
  
      void remove_parent (unsigned parent_index)
      {
        for (unsigned i = 0; i < parents.length; i++)
        {
          if (parents[i] != parent_index) continue;
          parents.remove (i);
          break;
        }
      }
  
      void remove_real_link (unsigned child_index, const void* offset)
      {
        for (unsigned i = 0; i < obj.real_links.length; i++)
        {
          auto& link = obj.real_links.arrayZ[i];
          if (link.objidx != child_index)
            continue;
  
          if ((obj.head + link.position) != offset)
            continue;
  
          obj.real_links.remove (i);
          return;
        }
      }
  
      void remap_parents (const hb_vector_t<unsigned>& id_map)
      {
        for (unsigned i = 0; i < parents.length; i++)
          parents[i] = id_map[parents[i]];
      }
  
      void remap_parent (unsigned old_index, unsigned new_index)
      {
        for (unsigned i = 0; i < parents.length; i++)
        {
          if (parents[i] == old_index)
            parents[i] = new_index;
        }
      }
  
      bool is_leaf () const
      {
        return !obj.real_links.length && !obj.virtual_links.length;
      }
  
      bool raise_priority ()
      {
        if (has_max_priority ()) return false;
        priority++;
        return true;
      }
  
      bool has_max_priority () const {
        return priority >= 3;
      }
  
      size_t table_size () const {
        return obj.tail - obj.head;
      }
  
      int64_t modified_distance (unsigned order) const
      {
        // TODO(garretrieger): once priority is high enough, should try
        // setting distance = 0 which will force to sort immediately after
        // it's parent where possible.
  
        int64_t modified_distance =
            hb_min (hb_max(distance + distance_modifier (), 0), 0x7FFFFFFFFFF);
        if (has_max_priority ()) {
          modified_distance = 0;
        }
        return (modified_distance << 18) | (0x003FFFF & order);
      }
  
      int64_t distance_modifier () const
      {
        if (!priority) return 0;
        int64_t table_size = obj.tail - obj.head;
  
        if (priority == 1)
          return -table_size / 2;
  
        return -table_size;
      }
  
     private:
      bool links_equal (const hb_vector_t<hb_serialize_context_t::object_t::link_t>& this_links,
                        const hb_vector_t<hb_serialize_context_t::object_t::link_t>& other_links,
                        const graph_t& graph,
                        const graph_t& other_graph,
                        unsigned depth) const
      {
        auto a = this_links.iter ();
        auto b = other_links.iter ();
  
        while (a && b)
        {
          const auto& link_a = *a;
          const auto& link_b = *b;
  
          if (link_a.width != link_b.width ||
              link_a.is_signed != link_b.is_signed ||
              link_a.whence != link_b.whence ||
              link_a.position != link_b.position ||
              link_a.bias != link_b.bias)
            return false;
  
          if (!graph.vertices_[link_a.objidx].equals (
                  other_graph.vertices_[link_b.objidx], graph, other_graph, depth + 1))
            return false;
  
          a++;
          b++;
        }
  
        if (bool (a) != bool (b))
          return false;
  
        return true;
      }
    };
  
    template <typename T>
    struct vertex_and_table_t
    {
      vertex_and_table_t () : index (0), vertex (nullptr), table (nullptr)
      {}
  
      unsigned index;
      vertex_t* vertex;
      T* table;
  
      operator bool () {
         return table && vertex;
      }
    };
  
    /*
     * A topological sorting of an object graph. Ordered
     * in reverse serialization order (first object in the
     * serialization is at the end of the list). This matches
     * the 'packed' object stack used internally in the
     * serializer
     */
    template<typename T>
    graph_t (const T& objects)
        : parents_invalid (true),
          distance_invalid (true),
          positions_invalid (true),
          successful (true),
          buffers ()
    {
      num_roots_for_space_.push (1);
      bool removed_nil = false;
      vertices_.alloc (objects.length);
      vertices_scratch_.alloc (objects.length);
      for (unsigned i = 0; i < objects.length; i++)
      {
        // TODO(grieger): check all links point to valid objects.
  
        // If this graph came from a serialization buffer object 0 is the
        // nil object. We don't need it for our purposes here so drop it.
        if (i == 0 && !objects[i])
        {
          removed_nil = true;
          continue;
        }
  
        vertex_t* v = vertices_.push ();
        if (check_success (!vertices_.in_error ()))
          v->obj = *objects[i];
        if (!removed_nil) continue;
        // Fix indices to account for removed nil object.
        for (auto& l : v->obj.all_links_writer ()) {
          l.objidx--;
        }
      }
    }
  
    ~graph_t ()
    {
      vertices_.fini ();
      for (char* b : buffers)
        hb_free (b);
    }
  
    bool operator== (const graph_t& other) const
    {
      return root ().equals (other.root (), *this, other, 0);
    }
  
    // Sorts links of all objects in a consistent manner and zeroes all offsets.
    void normalize ()
    {
      for (auto& v : vertices_.writer ())
        v.normalize ();
    }
  
    bool in_error () const
    {
      return !successful ||
          vertices_.in_error () ||
          num_roots_for_space_.in_error ();
    }
  
    const vertex_t& root () const
    {
      return vertices_[root_idx ()];
    }
  
    unsigned root_idx () const
    {
      // Object graphs are in reverse order, the first object is at the end
      // of the vector. Since the graph is topologically sorted it's safe to
      // assume the first object has no incoming edges.
      return vertices_.length - 1;
    }
  
    const hb_serialize_context_t::object_t& object (unsigned i) const
    {
      return vertices_[i].obj;
    }
  
    void add_buffer (char* buffer)
    {
      buffers.push (buffer);
    }
  
    /*
     * Adds a 16 bit link from parent_id to child_id
     */
    template<typename T>
    void add_link (T* offset,
                   unsigned parent_id,
                   unsigned child_id)
    {
      auto& v = vertices_[parent_id];
      auto* link = v.obj.real_links.push ();
      link->width = 2;
      link->objidx = child_id;
      link->position = (char*) offset - (char*) v.obj.head;
      vertices_[child_id].parents.push (parent_id);
    }
  
    /*
     * Generates a new topological sorting of graph ordered by the shortest
     * distance to each node if positions are marked as invalid.
     */
    void sort_shortest_distance_if_needed ()
    {
      if (!positions_invalid) return;
      sort_shortest_distance ();
    }
  
  
    /*
     * Generates a new topological sorting of graph ordered by the shortest
     * distance to each node.
     */
    void sort_shortest_distance ()
    {
      positions_invalid = true;
  
      if (vertices_.length <= 1) {
        // Graph of 1 or less doesn't need sorting.
        return;
      }
  
      update_distances ();
  
      hb_priority_queue_t queue;
      hb_vector_t<vertex_t> &sorted_graph = vertices_scratch_;
      if (unlikely (!check_success (sorted_graph.resize (vertices_.length)))) return;
      hb_vector_t<unsigned> id_map;
      if (unlikely (!check_success (id_map.resize (vertices_.length)))) return;
  
      hb_vector_t<unsigned> removed_edges;
      if (unlikely (!check_success (removed_edges.resize (vertices_.length)))) return;
      update_parents ();
  
      queue.insert (root ().modified_distance (0), root_idx ());
      int new_id = root_idx ();
      unsigned order = 1;
      while (!queue.in_error () && !queue.is_empty ())
      {
        unsigned next_id = queue.pop_minimum().second;
  
        hb_swap (sorted_graph[new_id], vertices_[next_id]);
        const vertex_t& next = sorted_graph[new_id];
  
        id_map[next_id] = new_id--;
  
        for (const auto& link : next.obj.all_links ()) {
          removed_edges[link.objidx]++;
          if (!(vertices_[link.objidx].incoming_edges () - removed_edges[link.objidx]))
            // Add the order that the links were encountered to the priority.
            // This ensures that ties between priorities objects are broken in a consistent
            // way. More specifically this is set up so that if a set of objects have the same
            // distance they'll be added to the topological order in the order that they are
            // referenced from the parent object.
            queue.insert (vertices_[link.objidx].modified_distance (order++),
                          link.objidx);
        }
      }
  
      check_success (!queue.in_error ());
      check_success (!sorted_graph.in_error ());
  
      remap_all_obj_indices (id_map, &sorted_graph);
      hb_swap (vertices_, sorted_graph);
  
      if (!check_success (new_id == -1))
        print_orphaned_nodes ();
    }
  
    /*
     * Finds the set of nodes (placed into roots) that should be assigned unique spaces.
     * More specifically this looks for the top most 24 bit or 32 bit links in the graph.
     * Some special casing is done that is specific to the layout of GSUB/GPOS tables.
     */
    void find_space_roots (hb_set_t& visited, hb_set_t& roots)
    {
      int root_index = (int) root_idx ();
      for (int i = root_index; i >= 0; i--)
      {
        if (visited.has (i)) continue;
  
        // Only real links can form 32 bit spaces
        for (auto& l : vertices_[i].obj.real_links)
        {
          if (l.is_signed || l.width < 3)
            continue;
  
          if (i == root_index && l.width == 3)
            // Ignore 24bit links from the root node, this skips past the single 24bit
            // pointer to the lookup list.
            continue;
  
          if (l.width == 3)
          {
            // A 24bit offset forms a root, unless there is 32bit offsets somewhere
            // in it's subgraph, then those become the roots instead. This is to make sure
            // that extension subtables beneath a 24bit lookup become the spaces instead
            // of the offset to the lookup.
            hb_set_t sub_roots;
            find_32bit_roots (l.objidx, sub_roots);
            if (sub_roots) {
              for (unsigned sub_root_idx : sub_roots) {
                roots.add (sub_root_idx);
                find_subgraph (sub_root_idx, visited);
              }
              continue;
            }
          }
  
          roots.add (l.objidx);
          find_subgraph (l.objidx, visited);
        }
      }
    }
  
    template <typename T, typename ...Ts>
    vertex_and_table_t<T> as_table (unsigned parent, const void* offset, Ts... ds)
    {
      return as_table_from_index<T> (index_for_offset (parent, offset), std::forward<Ts>(ds)...);
    }
  
    template <typename T, typename ...Ts>
    vertex_and_table_t<T> as_table_from_index (unsigned index, Ts... ds)
    {
      if (index >= vertices_.length)
        return vertex_and_table_t<T> ();
  
      vertex_and_table_t<T> r;
      r.vertex = &vertices_[index];
      r.table = (T*) r.vertex->obj.head;
      r.index = index;
      if (!r.table)
        return vertex_and_table_t<T> ();
  
      if (!r.table->sanitize (*(r.vertex), std::forward<Ts>(ds)...))
        return vertex_and_table_t<T> ();
  
      return r;
    }
  
    // Finds the object id of the object pointed to by the offset at 'offset'
    // within object[node_idx].
    unsigned index_for_offset (unsigned node_idx, const void* offset) const
    {
      const auto& node = object (node_idx);
      if (offset < node.head || offset >= node.tail) return -1;
  
      unsigned length = node.real_links.length;
      for (unsigned i = 0; i < length; i++)
      {
        // Use direct access for increased performance, this is a hot method.
        const auto& link = node.real_links.arrayZ[i];
        if (offset != node.head + link.position)
          continue;
        return link.objidx;
      }
  
      return -1;
    }
  
    // Finds the object id of the object pointed to by the offset at 'offset'
    // within object[node_idx]. Ensures that the returned object is safe to mutate.
    // That is, if the original child object is shared by parents other than node_idx
    // it will be duplicated and the duplicate will be returned instead.
    unsigned mutable_index_for_offset (unsigned node_idx, const void* offset)
    {
      unsigned child_idx = index_for_offset (node_idx, offset);
      auto& child = vertices_[child_idx];
      for (unsigned p : child.parents)
      {
        if (p != node_idx) {
          return duplicate (node_idx, child_idx);
        }
      }
  
      return child_idx;
    }
  
  
    /*
     * Assign unique space numbers to each connected subgraph of 24 bit and/or 32 bit offset(s).
     * Currently, this is implemented specifically tailored to the structure of a GPOS/GSUB
     * (including with 24bit offsets) table.
     */
    bool assign_spaces ()
    {
      update_parents ();
  
      hb_set_t visited;
      hb_set_t roots;
      find_space_roots (visited, roots);
  
      // Mark everything not in the subgraphs of the roots as visited. This prevents
      // subgraphs from being connected via nodes not in those subgraphs.
      visited.invert ();
  
      if (!roots) return false;
  
      while (roots)
      {
        unsigned next = HB_SET_VALUE_INVALID;
        if (unlikely (!check_success (!roots.in_error ()))) break;
        if (!roots.next (&next)) break;
  
        hb_set_t connected_roots;
        find_connected_nodes (next, roots, visited, connected_roots);
        if (unlikely (!check_success (!connected_roots.in_error ()))) break;
  
        isolate_subgraph (connected_roots);
        if (unlikely (!check_success (!connected_roots.in_error ()))) break;
  
        unsigned next_space = this->next_space ();
        num_roots_for_space_.push (0);
        for (unsigned root : connected_roots)
        {
          DEBUG_MSG (SUBSET_REPACK, nullptr, "Subgraph %u gets space %u", root, next_space);
          vertices_[root].space = next_space;
          num_roots_for_space_[next_space] = num_roots_for_space_[next_space] + 1;
          distance_invalid = true;
          positions_invalid = true;
        }
  
        // TODO(grieger): special case for GSUB/GPOS use extension promotions to move 16 bit space
        //                into the 32 bit space as needed, instead of using isolation.
      }
  
  
  
      return true;
    }
  
    /*
     * Isolates the subgraph of nodes reachable from root. Any links to nodes in the subgraph
     * that originate from outside of the subgraph will be removed by duplicating the linked to
     * object.
     *
     * Indices stored in roots will be updated if any of the roots are duplicated to new indices.
     */
    bool isolate_subgraph (hb_set_t& roots)
    {
      update_parents ();
      hb_map_t subgraph;
  
      // incoming edges to root_idx should be all 32 bit in length so we don't need to de-dup these
      // set the subgraph incoming edge count to match all of root_idx's incoming edges
      hb_set_t parents;
      for (unsigned root_idx : roots)
      {
        subgraph.set (root_idx, wide_parents (root_idx, parents));
        find_subgraph (root_idx, subgraph);
      }
  
      unsigned original_root_idx = root_idx ();
      hb_map_t index_map;
      bool made_changes = false;
      for (auto entry : subgraph.iter ())
      {
        const auto& node = vertices_[entry.first];
        unsigned subgraph_incoming_edges = entry.second;
  
        if (subgraph_incoming_edges < node.incoming_edges ())
        {
          // Only  de-dup objects with incoming links from outside the subgraph.
          made_changes = true;
          duplicate_subgraph (entry.first, index_map);
        }
      }
  
      if (!made_changes)
        return false;
  
      if (original_root_idx != root_idx ()
          && parents.has (original_root_idx))
      {
        // If the root idx has changed since parents was determined, update root idx in parents
        parents.add (root_idx ());
        parents.del (original_root_idx);
      }
  
      auto new_subgraph =
          + subgraph.keys ()
          | hb_map([&] (unsigned node_idx) {
            const unsigned *v;
            if (index_map.has (node_idx, &v)) return *v;
            return node_idx;
          })
          ;
  
      remap_obj_indices (index_map, new_subgraph);
      remap_obj_indices (index_map, parents.iter (), true);
  
      // Update roots set with new indices as needed.
      unsigned next = HB_SET_VALUE_INVALID;
      while (roots.next (&next))
      {
        const unsigned *v;
        if (index_map.has (next, &v))
        {
          roots.del (next);
          roots.add (*v);
        }
      }
  
      return true;
    }
  
    void find_subgraph (unsigned node_idx, hb_map_t& subgraph)
    {
      for (const auto& link : vertices_[node_idx].obj.all_links ())
      {
        const unsigned *v;
        if (subgraph.has (link.objidx, &v))
        {
          subgraph.set (link.objidx, *v + 1);
          continue;
        }
        subgraph.set (link.objidx, 1);
        find_subgraph (link.objidx, subgraph);
      }
    }
  
    void find_subgraph (unsigned node_idx, hb_set_t& subgraph)
    {
      if (subgraph.has (node_idx)) return;
      subgraph.add (node_idx);
      for (const auto& link : vertices_[node_idx].obj.all_links ())
        find_subgraph (link.objidx, subgraph);
    }
  
    size_t find_subgraph_size (unsigned node_idx, hb_set_t& subgraph, unsigned max_depth = -1)
    {
      if (subgraph.has (node_idx)) return 0;
      subgraph.add (node_idx);
  
      const auto& o = vertices_[node_idx].obj;
      size_t size = o.tail - o.head;
      if (max_depth == 0)
        return size;
  
      for (const auto& link : o.all_links ())
        size += find_subgraph_size (link.objidx, subgraph, max_depth - 1);
      return size;
    }
  
    /*
     * Finds the topmost children of 32bit offsets in the subgraph starting
     * at node_idx. Found indices are placed into 'found'.
     */
    void find_32bit_roots (unsigned node_idx, hb_set_t& found)
    {
      for (const auto& link : vertices_[node_idx].obj.all_links ())
      {
        if (!link.is_signed && link.width == 4) {
          found.add (link.objidx);
          continue;
        }
        find_32bit_roots (link.objidx, found);
      }
    }
  
    /*
     * Moves the child of old_parent_idx pointed to by old_offset to a new
     * vertex at the new_offset.
     */
    template<typename O>
    void move_child (unsigned old_parent_idx,
                     const O* old_offset,
                     unsigned new_parent_idx,
                     const O* new_offset)
    {
      distance_invalid = true;
      positions_invalid = true;
  
      auto& old_v = vertices_[old_parent_idx];
      auto& new_v = vertices_[new_parent_idx];
  
      unsigned child_id = index_for_offset (old_parent_idx,
                                            old_offset);
  
      auto* new_link = new_v.obj.real_links.push ();
      new_link->width = O::static_size;
      new_link->objidx = child_id;
      new_link->position = (const char*) new_offset - (const char*) new_v.obj.head;
  
      auto& child = vertices_[child_id];
      child.parents.push (new_parent_idx);
  
      old_v.remove_real_link (child_id, old_offset);
      child.remove_parent (old_parent_idx);
    }
  
    /*
     * duplicates all nodes in the subgraph reachable from node_idx. Does not re-assign
     * links. index_map is updated with mappings from old id to new id. If a duplication has already
     * been performed for a given index, then it will be skipped.
     */
    void duplicate_subgraph (unsigned node_idx, hb_map_t& index_map)
    {
      if (index_map.has (node_idx))
        return;
  
      index_map.set (node_idx, duplicate (node_idx));
      for (const auto& l : object (node_idx).all_links ()) {
        duplicate_subgraph (l.objidx, index_map);
      }
    }
  
    /*
     * Creates a copy of node_idx and returns it's new index.
     */
    unsigned duplicate (unsigned node_idx)
    {
      positions_invalid = true;
      distance_invalid = true;
  
      auto* clone = vertices_.push ();
      auto& child = vertices_[node_idx];
      if (vertices_.in_error ()) {
        return -1;
      }
  
      clone->obj.head = child.obj.head;
      clone->obj.tail = child.obj.tail;
      clone->distance = child.distance;
      clone->space = child.space;
      clone->parents.reset ();
  
      unsigned clone_idx = vertices_.length - 2;
      for (const auto& l : child.obj.real_links)
      {
        clone->obj.real_links.push (l);
        vertices_[l.objidx].parents.push (clone_idx);
      }
      for (const auto& l : child.obj.virtual_links)
      {
        clone->obj.virtual_links.push (l);
        vertices_[l.objidx].parents.push (clone_idx);
      }
  
      check_success (!clone->obj.real_links.in_error ());
      check_success (!clone->obj.virtual_links.in_error ());
  
      // The last object is the root of the graph, so swap back the root to the end.
      // The root's obj idx does change, however since it's root nothing else refers to it.
      // all other obj idx's will be unaffected.
      hb_swap (vertices_[vertices_.length - 2], *clone);
  
      // Since the root moved, update the parents arrays of all children on the root.
      for (const auto& l : root ().obj.all_links ())
        vertices_[l.objidx].remap_parent (root_idx () - 1, root_idx ());
  
      return clone_idx;
    }
  
    /*
     * Creates a copy of child and re-assigns the link from
     * parent to the clone. The copy is a shallow copy, objects
     * linked from child are not duplicated.
     */
    bool duplicate (unsigned parent_idx, unsigned child_idx)
    {
      update_parents ();
  
      unsigned links_to_child = 0;
      for (const auto& l : vertices_[parent_idx].obj.all_links ())
      {
        if (l.objidx == child_idx) links_to_child++;
      }
  
      if (vertices_[child_idx].incoming_edges () <= links_to_child)
      {
        // Can't duplicate this node, doing so would orphan the original one as all remaining links
        // to child are from parent.
        DEBUG_MSG (SUBSET_REPACK, nullptr, "  Not duplicating %d => %d",
                   parent_idx, child_idx);
        return false;
      }
  
      DEBUG_MSG (SUBSET_REPACK, nullptr, "  Duplicating %d => %d",
                 parent_idx, child_idx);
  
      unsigned clone_idx = duplicate (child_idx);
      if (clone_idx == (unsigned) -1) return false;
      // duplicate shifts the root node idx, so if parent_idx was root update it.
      if (parent_idx == clone_idx) parent_idx++;
  
      auto& parent = vertices_[parent_idx];
      for (auto& l : parent.obj.all_links_writer ())
      {
        if (l.objidx != child_idx)
          continue;
  
        reassign_link (l, parent_idx, clone_idx);
      }
  
      return true;
    }
  
  
    /*
     * Adds a new node to the graph, not connected to anything.
     */
    unsigned new_node (char* head, char* tail)
    {
      positions_invalid = true;
      distance_invalid = true;
  
      auto* clone = vertices_.push ();
      if (vertices_.in_error ()) {
        return -1;
      }
  
      clone->obj.head = head;
      clone->obj.tail = tail;
      clone->distance = 0;
      clone->space = 0;
  
      unsigned clone_idx = vertices_.length - 2;
  
      // The last object is the root of the graph, so swap back the root to the end.
      // The root's obj idx does change, however since it's root nothing else refers to it.
      // all other obj idx's will be unaffected.
      hb_swap (vertices_[vertices_.length - 2], *clone);
  
      // Since the root moved, update the parents arrays of all children on the root.
      for (const auto& l : root ().obj.all_links ())
        vertices_[l.objidx].remap_parent (root_idx () - 1, root_idx ());
  
      return clone_idx;
    }
  
    /*
     * Raises the sorting priority of all children.
     */
    bool raise_childrens_priority (unsigned parent_idx)
    {
      DEBUG_MSG (SUBSET_REPACK, nullptr, "  Raising priority of all children of %d",
                 parent_idx);
      // This operation doesn't change ordering until a sort is run, so no need
      // to invalidate positions. It does not change graph structure so no need
      // to update distances or edge counts.
      auto& parent = vertices_[parent_idx].obj;
      bool made_change = false;
      for (auto& l : parent.all_links_writer ())
        made_change |= vertices_[l.objidx].raise_priority ();
      return made_change;
    }
  
    void print_orphaned_nodes ()
    {
      if (!DEBUG_ENABLED(SUBSET_REPACK)) return;
  
      DEBUG_MSG (SUBSET_REPACK, nullptr, "Graph is not fully connected.");
      parents_invalid = true;
      update_parents();
  
      for (unsigned i = 0; i < root_idx (); i++)
      {
        const auto& v = vertices_[i];
        if (!v.parents)
          DEBUG_MSG (SUBSET_REPACK, nullptr, "Node %u is orphaned.", i);
      }
    }
  
    unsigned num_roots_for_space (unsigned space) const
    {
      return num_roots_for_space_[space];
    }
  
    unsigned next_space () const
    {
      return num_roots_for_space_.length;
    }
  
    void move_to_new_space (const hb_set_t& indices)
    {
      num_roots_for_space_.push (0);
      unsigned new_space = num_roots_for_space_.length - 1;
  
      for (unsigned index : indices) {
        auto& node = vertices_[index];
        num_roots_for_space_[node.space] = num_roots_for_space_[node.space] - 1;
        num_roots_for_space_[new_space] = num_roots_for_space_[new_space] + 1;
        node.space = new_space;
        distance_invalid = true;
        positions_invalid = true;
      }
    }
  
    unsigned space_for (unsigned index, unsigned* root = nullptr) const
    {
      const auto& node = vertices_[index];
      if (node.space)
      {
        if (root != nullptr)
          *root = index;
        return node.space;
      }
  
      if (!node.parents)
      {
        if (root)
          *root = index;
        return 0;
      }
  
      return space_for (node.parents[0], root);
    }
  
    void err_other_error () { this->successful = false; }
  
    size_t total_size_in_bytes () const {
      size_t total_size = 0;
      for (unsigned i = 0; i < vertices_.length; i++) {
        size_t size = vertices_[i].obj.tail - vertices_[i].obj.head;
        total_size += size;
      }
      return total_size;
    }
  
  
   private:
  
    /*
     * Returns the numbers of incoming edges that are 24 or 32 bits wide.
     */
    unsigned wide_parents (unsigned node_idx, hb_set_t& parents) const
    {
      unsigned count = 0;
      hb_set_t visited;
      for (unsigned p : vertices_[node_idx].parents)
      {
        if (visited.has (p)) continue;
        visited.add (p);
  
        // Only real links can be wide
        for (const auto& l : vertices_[p].obj.real_links)
        {
          if (l.objidx == node_idx
              && (l.width == 3 || l.width == 4)
              && !l.is_signed)
          {
            count++;
            parents.add (p);
          }
        }
      }
      return count;
    }
  
    bool check_success (bool success)
    { return this->successful && (success || ((void) err_other_error (), false)); }
  
   public:
    /*
     * Creates a map from objid to # of incoming edges.
     */
    void update_parents ()
    {
      if (!parents_invalid) return;
  
      for (unsigned i = 0; i < vertices_.length; i++)
        vertices_[i].parents.reset ();
  
      for (unsigned p = 0; p < vertices_.length; p++)
      {
        for (auto& l : vertices_[p].obj.all_links ())
        {
          vertices_[l.objidx].parents.push (p);
        }
      }
  
      parents_invalid = false;
    }
  
    /*
     * compute the serialized start and end positions for each vertex.
     */
    void update_positions ()
    {
      if (!positions_invalid) return;
  
      unsigned current_pos = 0;
      for (int i = root_idx (); i >= 0; i--)
      {
        auto& v = vertices_[i];
        v.start = current_pos;
        current_pos += v.obj.tail - v.obj.head;
        v.end = current_pos;
      }
  
      positions_invalid = false;
    }
  
    /*
     * Finds the distance to each object in the graph
     * from the initial node.
     */
    void update_distances ()
    {
      if (!distance_invalid) return;
  
      // Uses Dijkstra's algorithm to find all of the shortest distances.
      // https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
      //
      // Implementation Note:
      // Since our priority queue doesn't support fast priority decreases
      // we instead just add new entries into the queue when a priority changes.
      // Redundant ones are filtered out later on by the visited set.
      // According to https://www3.cs.stonybrook.edu/~rezaul/papers/TR-07-54.pdf
      // for practical performance this is faster then using a more advanced queue
      // (such as a fibonacci queue) with a fast decrease priority.
      for (unsigned i = 0; i < vertices_.length; i++)
      {
        if (i == vertices_.length - 1)
          vertices_[i].distance = 0;
        else
          vertices_[i].distance = hb_int_max (int64_t);
      }
  
      hb_priority_queue_t queue;
      queue.insert (0, vertices_.length - 1);
  
      hb_vector_t<bool> visited;
      visited.resize (vertices_.length);
  
      while (!queue.in_error () && !queue.is_empty ())
      {
        unsigned next_idx = queue.pop_minimum ().second;
        if (visited[next_idx]) continue;
        const auto& next = vertices_[next_idx];
        int64_t next_distance = vertices_[next_idx].distance;
        visited[next_idx] = true;
  
        for (const auto& link : next.obj.all_links ())
        {
          if (visited[link.objidx]) continue;
  
          const auto& child = vertices_[link.objidx].obj;
          unsigned link_width = link.width ? link.width : 4; // treat virtual offsets as 32 bits wide
          int64_t child_weight = (child.tail - child.head) +
                                 ((int64_t) 1 << (link_width * 8)) * (vertices_[link.objidx].space + 1);
          int64_t child_distance = next_distance + child_weight;
  
          if (child_distance < vertices_[link.objidx].distance)
          {
            vertices_[link.objidx].distance = child_distance;
            queue.insert (child_distance, link.objidx);
          }
        }
      }
  
      check_success (!queue.in_error ());
      if (!check_success (queue.is_empty ()))
      {
        print_orphaned_nodes ();
        return;
      }
  
      distance_invalid = false;
    }
  
   private:
    /*
     * Updates a link in the graph to point to a different object. Corrects the
     * parents vector on the previous and new child nodes.
     */
    void reassign_link (hb_serialize_context_t::object_t::link_t& link,
                        unsigned parent_idx,
                        unsigned new_idx)
    {
      unsigned old_idx = link.objidx;
      link.objidx = new_idx;
      vertices_[old_idx].remove_parent (parent_idx);
      vertices_[new_idx].parents.push (parent_idx);
    }
  
    /*
     * Updates all objidx's in all links using the provided mapping. Corrects incoming edge counts.
     */
    template<typename Iterator, hb_requires (hb_is_iterator (Iterator))>
    void remap_obj_indices (const hb_map_t& id_map,
                            Iterator subgraph,
                            bool only_wide = false)
    {
      if (!id_map) return;
      for (unsigned i : subgraph)
      {
        for (auto& link : vertices_[i].obj.all_links_writer ())
        {
          const unsigned *v;
          if (!id_map.has (link.objidx, &v)) continue;
          if (only_wide && !(link.width == 4 && !link.is_signed)) continue;
  
          reassign_link (link, i, *v);
        }
      }
    }
  
    /*
     * Updates all objidx's in all links using the provided mapping.
     */
    void remap_all_obj_indices (const hb_vector_t<unsigned>& id_map,
                                hb_vector_t<vertex_t>* sorted_graph) const
    {
      for (unsigned i = 0; i < sorted_graph->length; i++)
      {
        (*sorted_graph)[i].remap_parents (id_map);
        for (auto& link : (*sorted_graph)[i].obj.all_links_writer ())
        {
          link.objidx = id_map[link.objidx];
        }
      }
    }
  
    /*
     * Finds all nodes in targets that are reachable from start_idx, nodes in visited will be skipped.
     * For this search the graph is treated as being undirected.
     *
     * Connected targets will be added to connected and removed from targets. All visited nodes
     * will be added to visited.
     */
    void find_connected_nodes (unsigned start_idx,
                               hb_set_t& targets,
                               hb_set_t& visited,
                               hb_set_t& connected)
    {
      if (unlikely (!check_success (!visited.in_error ()))) return;
      if (visited.has (start_idx)) return;
      visited.add (start_idx);
  
      if (targets.has (start_idx))
      {
        targets.del (start_idx);
        connected.add (start_idx);
      }
  
      const auto& v = vertices_[start_idx];
  
      // Graph is treated as undirected so search children and parents of start_idx
      for (const auto& l : v.obj.all_links ())
        find_connected_nodes (l.objidx, targets, visited, connected);
  
      for (unsigned p : v.parents)
        find_connected_nodes (p, targets, visited, connected);
    }
  
   public:
    // TODO(garretrieger): make private, will need to move most of offset overflow code into graph.
    hb_vector_t<vertex_t> vertices_;
    hb_vector_t<vertex_t> vertices_scratch_;
   private:
    bool parents_invalid;
    bool distance_invalid;
    bool positions_invalid;
    bool successful;
    hb_vector_t<unsigned> num_roots_for_space_;
    hb_vector_t<char*> buffers;
  };
  
  }
  
  #endif  // GRAPH_GRAPH_HH
  

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