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feature/noverlay 19f5431cf6: * src/itree.c: Eliminate all prototypes for


From: Stefan Monnier
Subject: feature/noverlay 19f5431cf6: * src/itree.c: Eliminate all prototypes for static functions
Date: Mon, 17 Oct 2022 14:10:15 -0400 (EDT)

branch: feature/noverlay
commit 19f5431cf644517776e2945912dd5d5e8933b3dc
Author: Stefan Monnier <monnier@iro.umontreal.ca>
Commit: Stefan Monnier <monnier@iro.umontreal.ca>

    * src/itree.c: Eliminate all prototypes for static functions
    
    Massive code reorganization to move definitions of static functions
    before their first use, so as to remove the need for
    redundant prototypes.
    While at it, fix a few places where the used more than 80 column.
---
 src/itree.c | 1040 +++++++++++++++++++++++++++++------------------------------
 1 file changed, 508 insertions(+), 532 deletions(-)

diff --git a/src/itree.c b/src/itree.c
index 0ba9e662bc..aabf33fcb3 100644
--- a/src/itree.c
+++ b/src/itree.c
@@ -128,34 +128,33 @@ along with GNU Emacs.  If not, see 
<http://www.gnu.org/licenses/>.  */
    incremented whenever some node's offset has changed.
 */
 
-/* FIXME: The code seems to use "generator" and "iterator"
-   inconsistently/interchangeably.  We should fix this naming.  */
-
-static struct interval_node *interval_tree_validate (struct interval_tree *, 
struct interval_node *);
-static bool interval_node_intersects (const struct interval_node *, ptrdiff_t, 
ptrdiff_t);
-static int interval_tree_max_height (const struct interval_tree *);
-static void interval_tree_update_limit (struct interval_node *);
-static void interval_tree_inherit_offset (uintmax_t otick, struct 
interval_node *);
-static void interval_tree_propagate_limit (struct interval_node *);
-static void interval_tree_rotate_left (struct interval_tree *, struct 
interval_node *);
-static void interval_tree_rotate_right (struct interval_tree *, struct 
interval_node *);
-static void interval_tree_insert_fix (struct interval_tree *, struct 
interval_node *);
-static void interval_tree_replace_child (struct interval_tree *,
-                                        struct interval_node *,
-                                        struct interval_node *);
-static void interval_tree_transplant (struct interval_tree *tree,
-                                      struct interval_node *source,
-                                      struct interval_node *dest);
-static struct itree_iterator *
-itree_iterator_create (struct interval_tree *);
-static void interval_tree_insert (struct interval_tree *, struct interval_node 
*);
-static bool null_safe_is_red (struct interval_node *node);
-static bool null_safe_is_black (struct interval_node *node);
-
-/* 
+------------------------------------------------------------------------------------+
 */
+/* +=======================================================================+
+ * | Stack
+ * +=======================================================================+ */
 
 typedef uintptr_t nodeptr_and_flag;
 
+static inline nodeptr_and_flag
+make_nav (struct interval_node *ptr, bool flag)
+{
+  uintptr_t v = (uintptr_t) ptr;
+  /* We assume alignment imposes the LSB is clear for us to use it.  */
+  eassert (!(v & 1));
+  return v | !!flag;
+}
+
+static inline struct interval_node *
+nav_nodeptr (nodeptr_and_flag nav)
+{
+  return (struct interval_node *) (nav & (~(uintptr_t)1));
+}
+
+static inline bool
+nav_flag (nodeptr_and_flag nav)
+{
+  return (bool) (nav & 1);
+}
+
 /* Simple dynamic array. */
 struct interval_stack
 {
@@ -164,6 +163,82 @@ struct interval_stack
   size_t length;
 };
 
+/* This is just a simple dynamic array with stack semantics. */
+
+static struct interval_stack*
+interval_stack_create (intmax_t initial_size)
+{
+  struct interval_stack *stack = xmalloc (sizeof (struct interval_stack));
+  stack->size = max (0, initial_size);
+  stack->nodes = xmalloc (stack->size * sizeof (struct interval_node*));
+  stack->length = 0;
+  return stack;
+}
+
+static void
+interval_stack_destroy (struct interval_stack *stack)
+{
+  if (! stack)
+    return;
+  if (stack->nodes)
+    xfree (stack->nodes);
+  xfree (stack);
+}
+
+static void
+interval_stack_clear (struct interval_stack *stack)
+{
+  stack->length = 0;
+}
+
+static inline void
+interval_stack_ensure_space (struct interval_stack *stack, intmax_t nelements)
+{
+  if (nelements > stack->size)
+    {
+      stack->size = (nelements + 1) * 2;
+      stack->nodes = xrealloc (stack->nodes,
+                               stack->size * sizeof (*stack->nodes));
+    }
+}
+
+/* Push NODE on the STACK, while settings its visited flag to FLAG. */
+
+static inline void
+interval_stack_push_flagged (struct interval_stack *stack,
+                             struct interval_node *node, bool flag)
+{
+  eassert (node && node != ITREE_NULL);
+
+  /* FIXME: While the stack used in the iterator is bounded by the tree
+     depth and could be easily pre-allocated to a large enough size to avoid
+     this "ensure" check, `interval_stack_push` is also used elsewhere to
+     simply collect some subset of the overlays, where it's only bounded by
+     the total number of overlays in the buffer (which can be large and thus
+     preferably not pre-allocated needlessly).  */
+  interval_stack_ensure_space (stack, stack->length + 1);
+
+  stack->nodes[stack->length] = make_nav (node, flag);
+  stack->length++;
+}
+
+static inline void
+interval_stack_push (struct interval_stack *stack, struct interval_node *node)
+{
+  interval_stack_push_flagged (stack, node, false);
+}
+
+static inline nodeptr_and_flag
+interval_stack_pop (struct interval_stack *stack)
+{
+  if (stack->length == 0)
+    return make_nav (NULL, false);
+  return stack->nodes[--stack->length];
+}
+
+
+/* +-----------------------------------------------------------------------+ */
+
 /* State used when iterating interval. */
 struct itree_iterator
 {
@@ -184,6 +259,33 @@ struct itree_iterator
    So we just use a single global iterator instead for now.  */
 static struct itree_iterator *iter;
 
+static int
+interval_tree_max_height (const struct interval_tree *tree)
+{
+  return 2 * log (tree->size + 1) / log (2) + 0.5;
+}
+
+/* Allocate a new iterator for TREE. */
+
+static struct itree_iterator *
+itree_iterator_create (struct interval_tree *tree)
+{
+  struct itree_iterator *g = xmalloc (sizeof *g);
+  /* 19 here just avoids starting with a silly-small stack.
+     FIXME: Since this stack only needs to be about 2*max_depth
+     in the worst case, we could completely pre-allocate it to something
+     like word-bit-size * 2 and then never worry about growing it.  */
+  const int size = (tree ? interval_tree_max_height (tree) : 19) + 1;
+
+  g->stack = interval_stack_create (size);
+  g->running = false;
+  g->begin = 0;
+  g->end = 0;
+  g->file = NULL;
+  g->line = 0;
+  return g;
+}
+
 static void
 itree_init (void)
 {
@@ -289,108 +391,122 @@ check_tree (struct interval_tree *tree,
   return true;
 }
 
-/* 
+===================================================================================+
- * | Stack
- * 
+===================================================================================+
 */
+/* +=======================================================================+
+ * | Internal Functions
+ * +=======================================================================+ */
 
-static inline nodeptr_and_flag
-make_nav (struct interval_node *ptr, bool flag)
+static bool
+null_safe_is_red (struct interval_node *node)
 {
-  uintptr_t v = (uintptr_t) ptr;
-  /* We assume alignment imposes the LSB is clear for us to use it.  */
-  eassert (!(v & 1));
-  return v | !!flag;
+  return node != ITREE_NULL && node->red;
 }
 
-static inline struct interval_node *
-nav_nodeptr (nodeptr_and_flag nav)
+static bool
+null_safe_is_black (struct interval_node *node)
 {
-  return (struct interval_node *) (nav & (~(uintptr_t)1));
+  return node == ITREE_NULL || !node->red; /* NULL nodes are black */
 }
 
-static inline bool
-nav_flag (nodeptr_and_flag nav)
+static inline ptrdiff_t
+itree_newlimit (struct interval_node *node)
 {
-  return (bool) (nav & 1);
+  eassert (node != ITREE_NULL);
+  return max (node->end,
+              max (node->left == ITREE_NULL
+                     ? PTRDIFF_MIN
+                     : node->left->limit + node->left->offset,
+                   node->right == ITREE_NULL
+                     ? PTRDIFF_MIN
+                     : node->right->limit + node->right->offset));
 }
 
-/* This is just a simple dynamic array with stack semantics. */
-
-static struct interval_stack*
-interval_stack_create (intmax_t initial_size)
-{
-  struct interval_stack *stack = xmalloc (sizeof (struct interval_stack));
-  stack->size = max (0, initial_size);
-  stack->nodes = xmalloc (stack->size * sizeof (struct interval_node*));
-  stack->length = 0;
-  return stack;
-}
+/* Update NODE's limit attribute according to its children. */
 
 static void
-interval_stack_destroy (struct interval_stack *stack)
+interval_tree_update_limit (struct interval_node *node)
 {
-  if (! stack)
+  if (node == ITREE_NULL)
     return;
-  if (stack->nodes)
-    xfree (stack->nodes);
-  xfree (stack);
+
+  node->limit = itree_newlimit (node);
 }
 
+/* Apply NODE's offset to its begin, end and limit values and
+   propagate it to its children.
+
+   Does nothing, if NODE is clean, i.e. NODE.otick = tree.otick .
+*/
+
 static void
-interval_stack_clear (struct interval_stack *stack)
+interval_tree_inherit_offset (uintmax_t otick, struct interval_node *node)
 {
-  stack->length = 0;
-}
+  eassert (node->parent == ITREE_NULL || node->parent->otick >= node->otick);
+  if (node->otick == otick)
+    {
+      eassert (node->offset == 0);
+      return;
+    }
 
-static inline void
-interval_stack_ensure_space (struct interval_stack *stack, intmax_t nelements)
-{
-  if (nelements > stack->size)
+  /* Offsets can be inherited from dirty nodes (with out of date
+     otick) during removal, since we do not travel down from the root
+     in that case.  In this case rotations are performed on
+     potentially "dirty" nodes, where we only need to make sure the
+     *local* offsets are zero.  */
+
+  if (node->offset)
     {
-      stack->size = (nelements + 1) * 2;
-      stack->nodes = xrealloc (stack->nodes,
-                               stack->size * sizeof (*stack->nodes));
+      node->begin += node->offset;
+      node->end   += node->offset;
+      node->limit += node->offset;
+      if (node->left != ITREE_NULL)
+        node->left->offset += node->offset;
+      if (node->right != ITREE_NULL)
+        node->right->offset += node->offset;
+      node->offset = 0;
     }
+  /* The only thing that matters about `otick` is whether it's equal to
+     that of the tree.  We could also "blindly" inherit from parent->otick,
+     but we need to tree's `otick` anyway for when there's no parent.  */
+  if (node->parent == ITREE_NULL || node->parent->otick == otick)
+    node->otick = otick;
 }
 
-/* Push NODE on the STACK, while settings its visited flag to FLAG. */
+/* Update limit of NODE and its ancestors.  Stop when it becomes
+   stable, i.e. new_limit = old_limit.  */
 
-static inline void
-interval_stack_push_flagged (struct interval_stack *stack,
-                             struct interval_node *node, bool flag)
+static void
+interval_tree_propagate_limit (struct interval_node *node)
 {
-  eassert (node && node != ITREE_NULL);
-
-  /* FIXME: While the stack used in the iterator is bounded by the tree
-     depth and could be easily pre-allocated to a large enough size to avoid
-     this "ensure" check, `interval_stack_push` is also used elsewhere to
-     simply collect some subset of the overlays, where it's only bounded by
-     the total number of overlays in the buffer (which can be large and thus
-     preferably not pre-allocated needlessly).  */
-  interval_stack_ensure_space (stack, stack->length + 1);
+  if (node == ITREE_NULL)
+    return;
 
-  stack->nodes[stack->length] = make_nav (node, flag);
-  stack->length++;
+  while (1) {
+    ptrdiff_t newlimit = itree_newlimit (node);
+    if (newlimit == node->limit)
+      break;
+    node->limit = newlimit;
+    if (node->parent == ITREE_NULL)
+      break;
+    node = node->parent;
+  }
 }
 
-static inline void
-interval_stack_push (struct interval_stack *stack, struct interval_node *node)
+static struct interval_node*
+interval_tree_validate (struct interval_tree *tree, struct interval_node *node)
 {
-  interval_stack_push_flagged (stack, node, false);
-}
 
-static inline nodeptr_and_flag
-interval_stack_pop (struct interval_stack *stack)
-{
-  if (stack->length == 0)
-    return make_nav (NULL, false);
-  return stack->nodes[--stack->length];
+  if (tree->otick == node->otick || node == ITREE_NULL)
+    return node;
+  if (node != tree->root)
+    interval_tree_validate (tree, node->parent);
+
+  interval_tree_inherit_offset (tree->otick, node);
+  return node;
 }
 
-
-/* 
+===================================================================================+
+/* +=======================================================================+
  * | Tree operations
- * 
+===================================================================================+
 */
+ * +=======================================================================+ */
 
 /* Initialize an allocated node. */
 
@@ -399,6 +515,9 @@ interval_node_init (struct interval_node *node,
                     bool front_advance, bool rear_advance,
                     Lisp_Object data)
 {
+  node->parent = ITREE_NULL;
+  node->left = ITREE_NULL;
+  node->right = ITREE_NULL;
   node->begin = -1;
   node->end = -1;
   node->front_advance = front_advance;
@@ -426,29 +545,6 @@ interval_node_end (struct interval_tree *tree,
   return node->end;
 }
 
-/* Safely modify a node's interval. */
-
-void
-interval_node_set_region (struct interval_tree *tree,
-                          struct interval_node *node,
-                          ptrdiff_t begin, ptrdiff_t end)
-{
-  interval_tree_validate (tree, node);
-  if (begin != node->begin)
-    {
-      interval_tree_remove (tree, node);
-      node->begin = min (begin, PTRDIFF_MAX - 1);
-      node->end = max (node->begin, end);
-      interval_tree_insert (tree, node);
-    }
-  else if (end != node->end)
-    {
-      node->end = max (node->begin, end);
-      eassert (node != ITREE_NULL);
-      interval_tree_propagate_limit (node);
-    }
-}
-
 /* Allocate an interval_tree. Free with interval_tree_destroy. */
 
 struct interval_tree*
@@ -503,15 +599,177 @@ interval_tree_size (struct interval_tree *tree)
   return tree->size;
 }
 
-/* Insert a NODE into the TREE.
+/* Perform the familiar left-rotation on node NODE.  */
 
-   Note, that inserting a node twice results in undefined behaviour.
-*/
+static void
+interval_tree_rotate_left (struct interval_tree *tree,
+                           struct interval_node *node)
+{
+  eassert (node->right != ITREE_NULL);
+
+  struct interval_node *right = node->right;
+
+  interval_tree_inherit_offset (tree->otick, node);
+  interval_tree_inherit_offset (tree->otick, right);
+
+  /* Turn right's left subtree into node's right subtree.  */
+  node->right = right->left;
+  if (right->left != ITREE_NULL)
+    right->left->parent = node;
+
+  /* right's parent was node's parent.  */
+  if (right != ITREE_NULL)
+    right->parent = node->parent;
+
+  /* Get the parent to point to right instead of node.  */
+  if (node != tree->root)
+    {
+      if (node == node->parent->left)
+       node->parent->left = right;
+      else
+       node->parent->right = right;
+    }
+  else
+    tree->root = right;
+
+  /* Put node on right's left.  */
+  right->left = node;
+  if (node != ITREE_NULL)
+    node->parent = right;
+
+  /* Order matters here.  */
+  interval_tree_update_limit (node);
+  interval_tree_update_limit (right);
+}
+
+/* Perform the familiar right-rotation on node NODE.  */
+
+static void
+interval_tree_rotate_right (struct interval_tree *tree,
+                            struct interval_node *node)
+{
+  eassert (tree && node && node->left != ITREE_NULL);
+
+  struct interval_node *left = node->left;
+
+  interval_tree_inherit_offset (tree->otick, node);
+  interval_tree_inherit_offset (tree->otick, left);
+
+  node->left = left->right;
+  if (left->right != ITREE_NULL)
+    left->right->parent = node;
+
+  if (left != ITREE_NULL)
+    left->parent = node->parent;
+  if (node != tree->root)
+    {
+      if (node == node->parent->right)
+       node->parent->right = left;
+      else
+       node->parent->left = left;
+    }
+  else
+    tree->root = left;
+
+  left->right = node;
+  if (node != ITREE_NULL)
+    node->parent = left;
+
+  interval_tree_update_limit (left);
+  interval_tree_update_limit (node);
+}
+
+/* Repair the tree after an insertion.
+   The new NODE was added as red, so we may have 2 reds in a row.
+   Rebalance the parents as needed to re-establish the RB invariants.  */
+
+static void
+interval_tree_insert_fix (struct interval_tree *tree,
+                          struct interval_node *node)
+{
+  eassert (tree->root->red == false);
+
+  while (null_safe_is_red (node->parent))
+    {
+      /* NODE is red and its parent is red.  This is a violation of
+        red-black tree property #3.  */
+      eassert (node->red);
+
+      if (node->parent == node->parent->parent->left)
+       {
+         /* We're on the left side of our grandparent, and OTHER is
+            our "uncle".  */
+         struct interval_node *uncle = node->parent->parent->right;
+
+          if (null_safe_is_red (uncle)) /* case 1.a */
+           {
+             /* Uncle and parent are red but should be black because
+                NODE is red.  Change the colors accordingly and
+                proceed with the grandparent.  */
+             node->parent->red = false;
+             uncle->red = false;
+             node->parent->parent->red = true;
+             node = node->parent->parent;
+            }
+         else
+           {
+             /* Parent and uncle have different colors; parent is
+                red, uncle is black.  */
+             if (node == node->parent->right) /* case 2.a */
+               {
+                 node = node->parent;
+                 interval_tree_rotate_left (tree, node);
+                }
+              /* case 3.a */
+             node->parent->red = false;
+             node->parent->parent->red = true;
+             interval_tree_rotate_right (tree, node->parent->parent);
+            }
+        }
+      else
+       {
+         /* This is the symmetrical case of above.  */
+         struct interval_node *uncle = node->parent->parent->left;
+
+          if (null_safe_is_red (uncle)) /* case 1.b */
+           {
+             node->parent->red = false;
+             uncle->red = false;
+             node->parent->parent->red = true;
+             node = node->parent->parent;
+            }
+         else
+           {
+             if (node == node->parent->left) /* case 2.b */
+               {
+                 node = node->parent;
+                 interval_tree_rotate_right (tree, node);
+               }
+              /* case 3.b */
+             node->parent->red = false;
+             node->parent->parent->red = true;
+             interval_tree_rotate_left (tree, node->parent->parent);
+            }
+        }
+    }
+
+  /* The root may have been changed to red due to the algorithm.
+     Set it to black so that property #5 is satisfied.  */
+  tree->root->red = false;
+  eassert (check_tree (tree, true)); /* FIXME: Too expensive.  */
+}
+
+/* Insert a NODE into the TREE.
+   Note, that inserting a node twice results in undefined behaviour.  */
 
 static void
 interval_tree_insert (struct interval_tree *tree, struct interval_node *node)
 {
-  eassert (node && node->begin <= node->end && node != ITREE_NULL);
+  eassert (node->begin <= node->end && node != ITREE_NULL);
+  /* FIXME: The assertion below fails because `delete_all_overlays`
+     doesn't set left/right/parent to ITREE_NULL.  */
+  /* eassert (node->left == ITREE_NULL && node->right == ITREE_NULL
+             && node->parent == ITREE_NULL) */;
   eassert (check_tree (tree, true)); /* FIXME: Too expensive.  */
 
   struct interval_node *parent = ITREE_NULL;
@@ -546,15 +804,20 @@ interval_tree_insert (struct interval_tree *tree, struct 
interval_node *node)
   node->parent = parent;
   node->left = ITREE_NULL;
   node->right = ITREE_NULL;
-  node->red = node != tree->root;
   node->offset = 0;
   node->limit = node->end;
   eassert (node->parent == ITREE_NULL || node->parent->otick >= node->otick);
 
   /* Fix/update the tree */
   ++tree->size;
-  eassert (check_tree (tree, false)); /* FIXME: Too expensive.  */
-  interval_tree_insert_fix (tree, node);
+  if (node == tree->root)
+    node->red = false;
+  else
+    {
+      node->red = true;
+      eassert (check_tree (tree, false)); /* FIXME: Too expensive.  */
+      interval_tree_insert_fix (tree, node);
+    }
 }
 
 void
@@ -567,6 +830,29 @@ itree_insert_node (struct interval_tree *tree, struct 
interval_node *node,
   interval_tree_insert (tree, node);
 }
 
+/* Safely modify a node's interval. */
+
+void
+interval_node_set_region (struct interval_tree *tree,
+                          struct interval_node *node,
+                          ptrdiff_t begin, ptrdiff_t end)
+{
+  interval_tree_validate (tree, node);
+  if (begin != node->begin)
+    {
+      interval_tree_remove (tree, node);
+      node->begin = min (begin, PTRDIFF_MAX - 1);
+      node->end = max (node->begin, end);
+      interval_tree_insert (tree, node);
+    }
+  else if (end != node->end)
+    {
+      node->end = max (node->begin, end);
+      eassert (node != ITREE_NULL);
+      interval_tree_propagate_limit (node);
+    }
+}
+
 /* Return true, if NODE is a member of TREE. */
 
 static bool
@@ -584,19 +870,6 @@ interval_tree_contains (struct interval_tree *tree, struct 
interval_node *node)
   return false;
 }
 
-static inline ptrdiff_t
-itree_newlimit (struct interval_node *node)
-{
-  eassert (node != ITREE_NULL);
-  return max (node->end,
-              max (node->left == ITREE_NULL
-                     ? PTRDIFF_MIN
-                     : node->left->limit + node->left->offset,
-                   node->right == ITREE_NULL
-                     ? PTRDIFF_MIN
-                     : node->right->limit + node->right->offset));
-}
-
 static bool
 itree_limit_is_stable (struct interval_node *node)
 {
@@ -716,24 +989,86 @@ interval_tree_remove_fix (struct interval_tree *tree,
   node->red = false;
 }
 
-/* Remove NODE from TREE and return it.  NODE must exist in TREE.  */
-
-struct interval_node*
-interval_tree_remove (struct interval_tree *tree, struct interval_node *node)
+/* Return accumulated offsets of NODE's parents.  */
+static ptrdiff_t
+itree_total_offset (struct interval_node *node)
 {
-  eassert (interval_tree_contains (tree, node));
-  eassert (check_tree (tree, true)); /* FIXME: Too expensive.  */
-
-  /* Find `splice`, the leaf node to splice out of the tree.  When
-     `node` has at most one child this is `node` itself.  Otherwise,
-     it is the in order successor of `node`.  */
-  interval_tree_inherit_offset (tree->otick, node);
-  struct interval_node *splice
-    = (node->left == ITREE_NULL || node->right == ITREE_NULL)
-        ? node
-        : interval_tree_subtree_min (tree->otick, node->right);
+  eassert (node != ITREE_NULL);
+  ptrdiff_t offset = 0;
+  while (node->parent != ITREE_NULL)
+    {
+      node = node->parent;
+      offset += node->offset;
+    }
+  return offset;
+}
 
-  /* Find `subtree`, the only child of `splice` (may be NULL).  Note:
+/* Replace DEST with SOURCE as a child of DEST's parent.  Adjusts
+   *only* the parent linkage of SOURCE and either the parent's child
+   link the tree root.
+
+   Warning: DEST is left unmodified.  SOURCE's child links are
+   unchanged.  Caller is responsible for recalculation of `limit`.
+   Requires both nodes to be using the same effective `offset`.  */
+static void
+interval_tree_replace_child (struct interval_tree *tree,
+                             struct interval_node *source,
+                             struct interval_node *dest)
+{
+  eassert (tree && dest != ITREE_NULL);
+  eassert (source == ITREE_NULL
+           || itree_total_offset (source) == itree_total_offset (dest));
+
+  if (dest == tree->root)
+    tree->root = source;
+  else if (dest == dest->parent->left)
+    dest->parent->left = source;
+  else
+    dest->parent->right = source;
+
+  if (source != ITREE_NULL)
+    source->parent = dest->parent;
+}
+/* Replace DEST with SOURCE in the tree.  Copies the following fields
+   from DEST to SOURCE: red, parent, left, right.  Also updates
+   parent, left and right in surrounding nodes to point to SOURCE.
+
+   Warning: DEST is left unmodified.  Caller is responsible for
+   recalculation of `limit`.  Requires both nodes to be using the same
+   effective `offset`. */
+static void
+interval_tree_transplant (struct interval_tree *tree,
+                          struct interval_node *source,
+                          struct interval_node *dest)
+{
+  interval_tree_replace_child (tree, source, dest);
+  source->left = dest->left;
+  if (source->left != ITREE_NULL)
+    source->left->parent = source;
+  source->right = dest->right;
+  if (source->right != ITREE_NULL)
+    source->right->parent = source;
+  source->red = dest->red;
+}
+
+/* Remove NODE from TREE and return it.  NODE must exist in TREE.  */
+
+struct interval_node*
+interval_tree_remove (struct interval_tree *tree, struct interval_node *node)
+{
+  eassert (interval_tree_contains (tree, node));
+  eassert (check_tree (tree, true)); /* FIXME: Too expensive.  */
+
+  /* Find `splice`, the leaf node to splice out of the tree.  When
+     `node` has at most one child this is `node` itself.  Otherwise,
+     it is the in order successor of `node`.  */
+  interval_tree_inherit_offset (tree->otick, node);
+  struct interval_node *splice
+    = (node->left == ITREE_NULL || node->right == ITREE_NULL)
+        ? node
+        : interval_tree_subtree_min (tree->otick, node->right);
+
+  /* Find `subtree`, the only child of `splice` (may be NULL).  Note:
      `subtree` will not be modified other than changing its parent to
      `splice`.  */
   eassert (splice->left == ITREE_NULL || splice->right == ITREE_NULL);
@@ -764,14 +1099,13 @@ interval_tree_remove (struct interval_tree *tree, struct 
interval_node *node)
       interval_tree_transplant (tree, splice, node);
       interval_tree_propagate_limit (subtree_parent);
       if (splice != subtree_parent)
-        interval_tree_propagate_limit (splice);
+        interval_tree_update_limit (splice);
     }
   interval_tree_propagate_limit (splice->parent);
 
   --tree->size;
 
-  /* Fix any black height violation caused by removing a black
-     node.  */
+  /* Fix any black height violation caused by removing a black node.  */
   if (removed_black)
     interval_tree_remove_fix (tree, subtree, subtree_parent);
 
@@ -791,29 +1125,14 @@ interval_tree_remove (struct interval_tree *tree, struct 
interval_node *node)
   return node;
 }
 
-static struct interval_node*
-interval_tree_validate (struct interval_tree *tree, struct interval_node *node)
-{
-
-  if (tree->otick == node->otick || node == ITREE_NULL)
-    return node;
-  if (node != tree->root)
-    interval_tree_validate (tree, node->parent);
-
-  interval_tree_inherit_offset (tree->otick, node);
-  return node;
-}
-
 bool
 itree_iterator_busy_p (void)
 {
   return (iter && iter->running);
 }
 
-/* Start a generator iterating all intervals in [BEGIN,END) in the
-   given ORDER. Only one iterator per tree can be running at any
-   time.
-*/
+/* Start a iterator enumerating all intervals in [BEGIN,END) in the
+   given ORDER.  Only one iterator per tree can be running at any time.  */
 
 struct itree_iterator *
 itree_iterator_start (struct interval_tree *tree, ptrdiff_t begin,
@@ -852,29 +1171,24 @@ itree_iterator_finish (struct itree_iterator *iter)
   iter->running = false;
 }
 
-static int
-interval_tree_max_height (const struct interval_tree *tree)
-{
-  return 2 * log (tree->size + 1) / log (2) + 0.5;
-}
-
 
-/* 
+===================================================================================+
+/* +=======================================================================+
  * | Insert/Delete Gaps
- * 
+===================================================================================+
 */
+ * +=======================================================================+ */
 
 /* Insert a gap at POS of length LENGTH expanding all intervals
    intersecting it, while respecting their rear_advance and
    front_advance setting. */
 
 void
-interval_tree_insert_gap (struct interval_tree *tree, ptrdiff_t pos, ptrdiff_t 
length)
+interval_tree_insert_gap (struct interval_tree *tree,
+                          ptrdiff_t pos, ptrdiff_t length)
 {
   if (length <= 0 || tree->root == ITREE_NULL)
     return;
   uintmax_t ootick = tree->otick;
 
-  /* FIXME: Don't allocate generator/stack anew every time. */
+  /* FIXME: Don't allocate iterator/stack anew every time. */
 
   /* Nodes with front_advance starting at pos may mess up the tree
      order, so we need to remove them first. */
@@ -889,7 +1203,7 @@ interval_tree_insert_gap (struct interval_tree *tree, 
ptrdiff_t pos, ptrdiff_t l
   for (int i = 0; i < saved->length; ++i)
     interval_tree_remove (tree, nav_nodeptr (saved->nodes[i]));
 
-  /* We can't use a generator here, because we can't effectively
+  /* We can't use an iterator here, because we can't effectively
      narrow AND shift some subtree at the same time. */
   if (tree->root != ITREE_NULL)
     {
@@ -951,16 +1265,16 @@ interval_tree_insert_gap (struct interval_tree *tree, 
ptrdiff_t pos, ptrdiff_t l
    intersecting it. */
 
 void
-interval_tree_delete_gap (struct interval_tree *tree, ptrdiff_t pos, ptrdiff_t 
length)
+interval_tree_delete_gap (struct interval_tree *tree,
+                          ptrdiff_t pos, ptrdiff_t length)
 {
   if (length <= 0 || tree->root == ITREE_NULL)
     return;
 
   /* FIXME: Don't allocate stack anew every time. */
 
-  /* Can't use the generator here, because by decrementing begin, we
-     might unintentionally bring shifted nodes back into our search
-     space. */
+  /* Can't use the iterator here, because by decrementing begin, we
+     might unintentionally bring shifted nodes back into our search space. */
   const int size = interval_tree_max_height (tree) + 1;
   struct interval_stack *stack = interval_stack_create (size);
   struct interval_node *node;
@@ -1000,30 +1314,9 @@ interval_tree_delete_gap (struct interval_tree *tree, 
ptrdiff_t pos, ptrdiff_t l
 
 
 
-/* 
+===================================================================================+
- * | Generator
- * 
+===================================================================================+
 */
-
-/* Allocate a new generator for TREE. */
-
-static struct itree_iterator *
-itree_iterator_create (struct interval_tree *tree)
-{
-  struct itree_iterator *g = xmalloc (sizeof *g);
-  /* 19 here just avoids starting with a silly-small stack.
-     FIXME: Since this stack only needs to be about 2*max_depth
-     in the worst case, we could completely pre-allocate it to something
-     like word-bit-size * 2 and then never worry about growing it.  */
-  const int size = (tree ? interval_tree_max_height (tree) : 19) + 1;
-
-  g->stack = interval_stack_create (size);
-  g->running = false;
-  g->begin = 0;
-  g->end = 0;
-  g->file = NULL;
-  g->line = 0;
-  return g;
-}
+/* +=======================================================================+
+ * | Iterator
+ * +=======================================================================+ */
 
 /* Return true, if NODE's interval intersects with [BEGIN, END).
    Note: We always include empty nodes at BEGIN (and not at END),
@@ -1055,12 +1348,12 @@ itree_iterator_next (struct itree_iterator *g)
   /* The `visited` flag stored in each node is used here (and only here):
      We keep a "workstack" of nodes we need to consider.  This stack
      consist of nodes of two types: nodes that we have decided
-     should be returned by the generator, and nodes which we may
+     should be returned by the iterator, and nodes which we may
      need to consider (including checking their children).
      We start an iteration with a stack containing just the root
      node marked as "not visited" which means that it (and its children)
      needs to be considered but we haven't yet decided whether it's included
-     in the generator's output.  */
+     in the iterator's output.  */
 
   do {
     nodeptr_and_flag nav;
@@ -1082,7 +1375,7 @@ itree_iterator_next (struct itree_iterator *g)
               interval_stack_push_flagged (g->stack, right, false);
             if (interval_node_intersects (node, g->begin, g->end))
               interval_stack_push_flagged (g->stack, node, true);
-            /* Node's children may still be off-set and we need to add it. */
+            /* Node's children may still be off-set and we need to add it.  */
             if (left != null && g->begin <= left->limit + left->offset)
               interval_stack_push_flagged (g->stack, left, false);
             break;
@@ -1124,320 +1417,3 @@ itree_iterator_narrow (struct itree_iterator *g,
   g->begin =  max (begin, g->begin);
   g->end =  min (end, g->end);
 }
-
-
-/* 
+===================================================================================+
- * | Internal Functions
- * 
+===================================================================================+
 */
-
-static bool
-null_safe_is_red (struct interval_node *node)
-{
-  return node != ITREE_NULL && node->red;
-}
-
-static bool
-null_safe_is_black (struct interval_node *node)
-{
-  return node == ITREE_NULL || !node->red; /* NULL nodes are black */
-}
-
-/* Update NODE's limit attribute according to its children. */
-
-static void
-interval_tree_update_limit (struct interval_node *node)
-{
-  if (node == ITREE_NULL)
-    return;
-
-  node->limit = itree_newlimit (node);
-}
-
-/* Apply NODE's offset to its begin, end and limit values and
-   propagate it to its children.
-
-   Does nothing, if NODE is clean, i.e. NODE.otick = tree.otick .
-*/
-
-static void
-interval_tree_inherit_offset (uintmax_t otick, struct interval_node *node)
-{
-  eassert (node->parent == ITREE_NULL || node->parent->otick >= node->otick);
-  if (node->otick == otick)
-    {
-      eassert (node->offset == 0);
-      return;
-    }
-
-  /* Offsets can be inherited from dirty nodes (with out of date
-     otick) during removal, since we do not travel down from the root
-     in that case.  In this case rotations are performed on
-     potentially "dirty" nodes, where we only need to make sure the
-     *local* offsets are zero.  */
-
-  if (node->offset)
-    {
-      node->begin += node->offset;
-      node->end   += node->offset;
-      node->limit += node->offset;
-      if (node->left != ITREE_NULL)
-        node->left->offset += node->offset;
-      if (node->right != ITREE_NULL)
-        node->right->offset += node->offset;
-      node->offset = 0;
-    }
-  /* The only thing that matters about `otick` is whether it's equal to
-     that of the tree.  We could also "blindly" inherit from parent->otick,
-     but we need to tree's `otick` anyway for when there's no parent.  */
-  if (node->parent == ITREE_NULL || node->parent->otick == otick)
-    node->otick = otick;
-}
-
-/* Update limit of NODE and its ancestors.  Stop when it becomes
-   stable, i.e. new_limit = old_limit.
-*/
-
-static void
-interval_tree_propagate_limit (struct interval_node *node)
-{
-  if (node == ITREE_NULL)
-    return;
-
-  while (1) {
-    ptrdiff_t newlimit = itree_newlimit (node);
-    if (newlimit == node->limit)
-      break;
-    node->limit = newlimit;
-    if (node->parent == ITREE_NULL)
-      break;
-    node = node->parent;
-  }
-}
-
-/* Perform the familiar left-rotation on node NODE. */
-
-static void
-interval_tree_rotate_left (struct interval_tree *tree, struct interval_node 
*node)
-{
-  eassert (node->right != ITREE_NULL);
-
-  struct interval_node *right = node->right;
-
-  interval_tree_inherit_offset (tree->otick, node);
-  interval_tree_inherit_offset (tree->otick, right);
-
-  /* Turn right's left subtree into node's right subtree.  */
-  node->right = right->left;
-  if (right->left != ITREE_NULL)
-    right->left->parent = node;
-
-  /* right's parent was node's parent.  */
-  if (right != ITREE_NULL)
-    right->parent = node->parent;
-
-  /* Get the parent to point to right instead of node.  */
-  if (node != tree->root)
-    {
-      if (node == node->parent->left)
-       node->parent->left = right;
-      else
-       node->parent->right = right;
-    }
-  else
-    tree->root = right;
-
-  /* Put node on right's left.  */
-  right->left = node;
-  if (node != ITREE_NULL)
-    node->parent = right;
-
-  /* Order matters here. */
-  interval_tree_update_limit (node);
-  interval_tree_update_limit (right);
-}
-
-/* Perform the familiar right-rotation on node NODE. */
-
-static void
-interval_tree_rotate_right (struct interval_tree *tree, struct interval_node 
*node)
-{
-  eassert (tree && node && node->left != ITREE_NULL);
-
-  struct interval_node *left = node->left;
-
-  interval_tree_inherit_offset (tree->otick, node);
-  interval_tree_inherit_offset (tree->otick, left);
-
-  node->left = left->right;
-  if (left->right != ITREE_NULL)
-    left->right->parent = node;
-
-  if (left != ITREE_NULL)
-    left->parent = node->parent;
-  if (node != tree->root)
-    {
-      if (node == node->parent->right)
-       node->parent->right = left;
-      else
-       node->parent->left = left;
-    }
-  else
-    tree->root = left;
-
-  left->right = node;
-  if (node != ITREE_NULL)
-    node->parent = left;
-
-  interval_tree_update_limit (left);
-  interval_tree_update_limit (node);
-}
-
-/* Repair the tree after an insertion.
-   The new NODE was added as red, so we may have 2 reds in a row.
-   Rebalance the parents as needed to re-establish the RB invariants. */
-
-static void
-interval_tree_insert_fix (struct interval_tree *tree, struct interval_node 
*node)
-{
-  eassert (tree->root->red == false);
-
-  while (null_safe_is_red (node->parent))
-    {
-      /* NODE is red and its parent is red.  This is a violation of
-        red-black tree property #3.  */
-      eassert (node->red);
-
-      if (node->parent == node->parent->parent->left)
-       {
-         /* We're on the left side of our grandparent, and OTHER is
-            our "uncle".  */
-         struct interval_node *uncle = node->parent->parent->right;
-
-          if (null_safe_is_red (uncle)) /* case 1.a */
-           {
-             /* Uncle and parent are red but should be black because
-                NODE is red.  Change the colors accordingly and
-                proceed with the grandparent.  */
-             node->parent->red = false;
-             uncle->red = false;
-             node->parent->parent->red = true;
-             node = node->parent->parent;
-            }
-         else
-           {
-             /* Parent and uncle have different colors; parent is
-                red, uncle is black.  */
-             if (node == node->parent->right) /* case 2.a */
-               {
-                 node = node->parent;
-                 interval_tree_rotate_left (tree, node);
-                }
-              /* case 3.a */
-             node->parent->red = false;
-             node->parent->parent->red = true;
-             interval_tree_rotate_right (tree, node->parent->parent);
-            }
-        }
-      else
-       {
-         /* This is the symmetrical case of above.  */
-         struct interval_node *uncle = node->parent->parent->left;
-
-          if (null_safe_is_red (uncle)) /* case 1.b */
-           {
-             node->parent->red = false;
-             uncle->red = false;
-             node->parent->parent->red = true;
-             node = node->parent->parent;
-            }
-         else
-           {
-             if (node == node->parent->left) /* case 2.b */
-               {
-                 node = node->parent;
-                 interval_tree_rotate_right (tree, node);
-               }
-              /* case 3.b */
-             node->parent->red = false;
-             node->parent->parent->red = true;
-             interval_tree_rotate_left (tree, node->parent->parent);
-            }
-        }
-    }
-
-  /* The root may have been changed to red due to the algorithm.
-     Set it to black so that property #5 is satisfied.  */
-  tree->root->red = false;
-  eassert (check_tree (tree, true)); /* FIXME: Too expensive.  */
-}
-
-/* Return accumulated offsets of NODE's parents.  */
-static ptrdiff_t
-itree_total_offset (struct interval_node *node)
-{
-  eassert (node != ITREE_NULL);
-  ptrdiff_t offset = 0;
-  while (node->parent != ITREE_NULL)
-    {
-      node = node->parent;
-      offset += node->offset;
-    }
-  return offset;
-}
-
-/* Replace DEST with SOURCE as a child of DEST's parent.  Adjusts
-   *only* the parent linkage of SOURCE and either the parent's child
-   link the tree root.
-
-   Warning: DEST is left unmodified.  SOURCE's child links are
-   unchanged.  Caller is responsible for recalculation of `limit`.
-   Requires both nodes to be using the same effective `offset`.  */
-
-static void
-interval_tree_replace_child (struct interval_tree *tree,
-                             struct interval_node *source,
-                             struct interval_node *dest)
-{
-  eassert (tree && dest != ITREE_NULL);
-  eassert (source == ITREE_NULL
-           || itree_total_offset (source) == itree_total_offset (dest));
-
-  if (dest == tree->root)
-    tree->root = source;
-  else if (dest == dest->parent->left)
-    dest->parent->left = source;
-  else
-    dest->parent->right = source;
-
-  if (source != ITREE_NULL)
-    source->parent = dest->parent;
-}
-
-/* Replace DEST with SOURCE in the tree.  Copies the following fields
-   from DEST to SOURCE: red, parent, left, right.  Also updates
-   parent, left and right in surrounding nodes to point to SOURCE.
-
-   Warning: DEST is left unmodified.  Caller is responsible for
-   recalculation of `limit`.  Requires both nodes to be using the same
-   effective `offset`. */
-static void
-interval_tree_transplant (struct interval_tree *tree,
-                          struct interval_node *source,
-                          struct interval_node *dest)
-{
-  interval_tree_replace_child (tree, source, dest);
-  source->left = dest->left;
-  if (source->left != ITREE_NULL)
-    source->left->parent = source;
-  source->right = dest->right;
-  if (source->right != ITREE_NULL)
-    source->right->parent = source;
-  source->red = dest->red;
-}
-
-
-/* 
+===================================================================================+
- * | Debugging
- * 
+===================================================================================+
 */
-
-/* See Foverlay_tree in buffer.c */



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