--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mupdf-source/thirdparty/harfbuzz/src/graph/graph.hh	Mon Sep 15 11:43:07 2025 +0200
@@ -0,0 +1,1385 @@
+/*
+ * 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;
+
+
+    bool link_positions_valid (unsigned num_objects, bool removed_nil)
+    {
+      hb_set_t assigned_bytes;
+      for (const auto& l : obj.real_links)
+      {
+        if (l.objidx >= num_objects
+            || (removed_nil && !l.objidx))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Invalid object index.");
+          return false;
+        }
+
+        unsigned start = l.position;
+        unsigned end = start + l.width - 1;
+
+        if (unlikely (l.width < 2 || l.width > 4))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Invalid link width.");
+          return false;
+        }
+
+        if (unlikely (end >= table_size ()))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Link position is out of bounds.");
+          return false;
+        }
+
+        if (unlikely (assigned_bytes.intersects (start, end)))
+        {
+          DEBUG_MSG (SUBSET_REPACK, nullptr,
+                     "Invalid graph. Found offsets whose positions overlap.");
+          return false;
+        }
+
+        assigned_bytes.add_range (start, end);
+      }
+
+      return !assigned_bytes.in_error ();
+    }
+
+    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",
+                   (unsigned long) table_size (),
+                   (unsigned long) 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_unordered (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_unordered (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++)
+    {
+      // 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];
+
+      check_success (v->link_positions_valid (objects.length, removed_nil));
+
+      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];
+
+      if (unlikely (!check_success(new_id >= 0))) {
+        // We are out of ids. Which means we've visited a node more than once.
+        // This graph contains a cycle which is not allowed.
+        DEBUG_MSG (SUBSET_REPACK, nullptr, "Invalid graph. Contains cycle.");
+        return;
+      }
+
+      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_mutable_table (unsigned parent, const void* offset, Ts... ds)
+  {
+    return as_table_from_index<T> (mutable_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)
+    {
+      uint32_t 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([&] (uint32_t node_idx) {
+          const uint32_t *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.
+    uint32_t next = HB_SET_VALUE_INVALID;
+    while (roots.next (&next))
+    {
+      const uint32_t *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 uint32_t *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.
+   */
+  unsigned duplicate_if_shared (unsigned parent_idx, unsigned child_idx)
+  {
+    unsigned new_idx = duplicate (parent_idx, child_idx);
+    if (new_idx == (unsigned) -1) return child_idx;
+    return new_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.
+   */
+  unsigned 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 -1;
+    }
+
+    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 clone_idx;
+  }
+
+
+  /*
+   * 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;
+  }
+
+  bool is_fully_connected ()
+  {
+    update_parents();
+
+    if (root().parents)
+      // Root cannot have parents.
+      return false;
+
+    for (unsigned i = 0; i < root_idx (); i++)
+    {
+      if (!vertices_[i].parents)
+        return false;
+    }
+    return true;
+  }
+
+#if 0
+  /*
+   * Saves the current graph to a packed binary format which the repacker fuzzer takes
+   * as a seed.
+   */
+  void save_fuzzer_seed (hb_tag_t tag) const
+  {
+    FILE* f = fopen ("./repacker_fuzzer_seed", "w");
+    fwrite ((void*) &tag, sizeof (tag), 1, f);
+
+    uint16_t num_objects = vertices_.length;
+    fwrite ((void*) &num_objects, sizeof (num_objects), 1, f);
+
+    for (const auto& v : vertices_)
+    {
+      uint16_t blob_size = v.table_size ();
+      fwrite ((void*) &blob_size, sizeof (blob_size), 1, f);
+      fwrite ((const void*) v.obj.head, blob_size, 1, f);
+    }
+
+    uint16_t link_count = 0;
+    for (const auto& v : vertices_)
+      link_count += v.obj.real_links.length;
+
+    fwrite ((void*) &link_count, sizeof (link_count), 1, f);
+
+    typedef struct
+    {
+      uint16_t parent;
+      uint16_t child;
+      uint16_t position;
+      uint8_t width;
+    } link_t;
+
+    for (unsigned i = 0; i < vertices_.length; i++)
+    {
+      for (const auto& l : vertices_[i].obj.real_links)
+      {
+        link_t link {
+          (uint16_t) i, (uint16_t) l.objidx,
+          (uint16_t) l.position, (uint8_t) l.width
+        };
+        fwrite ((void*) &link, sizeof (link), 1, f);
+      }
+    }
+
+    fclose (f);
+  }
+#endif
+
+  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();
+
+    if (root().parents) {
+      DEBUG_MSG (SUBSET_REPACK, nullptr, "Root node has incoming edges.");
+    }
+
+    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);
+      }
+    }
+
+    for (unsigned i = 0; i < vertices_.length; i++)
+      // parents arrays must be accurate or downstream operations like cycle detection
+      // and sorting won't work correctly.
+      check_success (!vertices_[i].parents.in_error ());
+
+    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 uint32_t *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