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avl.c

/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2008 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma ident     "%Z%%M%     %I%   %E% SMI"


/*
 * AVL - generic AVL tree implementation for kernel use
 *
 * A complete description of AVL trees can be found in many CS textbooks.
 *
 * Here is a very brief overview. An AVL tree is a binary search tree that is
 * almost perfectly balanced. By "almost" perfectly balanced, we mean that at
 * any given node, the left and right subtrees are allowed to differ in height
 * by at most 1 level.
 *
 * This relaxation from a perfectly balanced binary tree allows doing
 * insertion and deletion relatively efficiently. Searching the tree is
 * still a fast operation, roughly O(log(N)).
 *
 * The key to insertion and deletion is a set of tree maniuplations called
 * rotations, which bring unbalanced subtrees back into the semi-balanced state.
 *
 * This implementation of AVL trees has the following peculiarities:
 *
 *    - The AVL specific data structures are physically embedded as fields
 *      in the "using" data structures.  To maintain generality the code
 *      must constantly translate between "avl_node_t *" and containing
 *      data structure "void *"s by adding/subracting the avl_offset.
 *
 *    - Since the AVL data is always embedded in other structures, there is
 *      no locking or memory allocation in the AVL routines. This must be
 *      provided for by the enclosing data structure's semantics. Typically,
 *      avl_insert()/_add()/_remove()/avl_insert_here() require some kind of
 *      exclusive write lock. Other operations require a read lock.
 *
 *      - The implementation uses iteration instead of explicit recursion,
 *      since it is intended to run on limited size kernel stacks. Since
 *      there is no recursion stack present to move "up" in the tree,
 *      there is an explicit "parent" link in the avl_node_t.
 *
 *      - The left/right children pointers of a node are in an array.
 *      In the code, variables (instead of constants) are used to represent
 *      left and right indices.  The implementation is written as if it only
 *      dealt with left handed manipulations.  By changing the value assigned
 *      to "left", the code also works for right handed trees.  The
 *      following variables/terms are frequently used:
 *
 *          int left;   // 0 when dealing with left children,
 *                      // 1 for dealing with right children
 *
 *          int left_heavy;   // -1 when left subtree is taller at some node,
 *                      // +1 when right subtree is taller
 *
 *          int right;  // will be the opposite of left (0 or 1)
 *          int right_heavy;// will be the opposite of left_heavy (-1 or 1)
 *
 *          int direction;  // 0 for "<" (ie. left child); 1 for ">" (right)
 *
 *      Though it is a little more confusing to read the code, the approach
 *      allows using half as much code (and hence cache footprint) for tree
 *      manipulations and eliminates many conditional branches.
 *
 *    - The avl_index_t is an opaque "cookie" used to find nodes at or
 *      adjacent to where a new value would be inserted in the tree. The value
 *      is a modified "avl_node_t *".  The bottom bit (normally 0 for a
 *      pointer) is set to indicate if that the new node has a value greater
 *      than the value of the indicated "avl_node_t *".
 */

#include <sys/types.h>
#include <sys/param.h>
#include <sys/stdint.h>
#include <sys/debug.h>
#include <sys/avl.h>

/*
 * Small arrays to translate between balance (or diff) values and child indeces.
 *
 * Code that deals with binary tree data structures will randomly use
 * left and right children when examining a tree.  C "if()" statements
 * which evaluate randomly suffer from very poor hardware branch prediction.
 * In this code we avoid some of the branch mispredictions by using the
 * following translation arrays. They replace random branches with an
 * additional memory reference. Since the translation arrays are both very
 * small the data should remain efficiently in cache.
 */
static const int  avl_child2balance[2]    = {-1, 1};
static const int  avl_balance2child[]     = {0, 0, 1};


/*
 * Walk from one node to the previous valued node (ie. an infix walk
 * towards the left). At any given node we do one of 2 things:
 *
 * - If there is a left child, go to it, then to it's rightmost descendant.
 *
 * - otherwise we return thru parent nodes until we've come from a right child.
 *
 * Return Value:
 * NULL - if at the end of the nodes
 * otherwise next node
 */
void *
avl_walk(avl_tree_t *tree, void     *oldnode, int left)
{
      size_t off = tree->avl_offset;
      avl_node_t *node = AVL_DATA2NODE(oldnode, off);
      int right = 1 - left;
      int was_child;


      /*
       * nowhere to walk to if tree is empty
       */
      if (node == NULL)
            return (NULL);

      /*
       * Visit the previous valued node. There are two possibilities:
       *
       * If this node has a left child, go down one left, then all
       * the way right.
       */
      if (node->avl_child[left] != NULL) {
            for (node = node->avl_child[left];
                node->avl_child[right] != NULL;
                node = node->avl_child[right])
                  ;
      /*
       * Otherwise, return thru left children as far as we can.
       */
      } else {
            for (;;) {
                  was_child = AVL_XCHILD(node);
                  node = AVL_XPARENT(node);
                  if (node == NULL)
                        return (NULL);
                  if (was_child == right)
                        break;
            }
      }

      return (AVL_NODE2DATA(node, off));
}

/*
 * Return the lowest valued node in a tree or NULL.
 * (leftmost child from root of tree)
 */
void *
avl_first(avl_tree_t *tree)
{
      avl_node_t *node;
      avl_node_t *prev = NULL;
      size_t off = tree->avl_offset;

      for (node = tree->avl_root; node != NULL; node = node->avl_child[0])
            prev = node;

      if (prev != NULL)
            return (AVL_NODE2DATA(prev, off));
      return (NULL);
}

/*
 * Return the highest valued node in a tree or NULL.
 * (rightmost child from root of tree)
 */
void *
avl_last(avl_tree_t *tree)
{
      avl_node_t *node;
      avl_node_t *prev = NULL;
      size_t off = tree->avl_offset;

      for (node = tree->avl_root; node != NULL; node = node->avl_child[1])
            prev = node;

      if (prev != NULL)
            return (AVL_NODE2DATA(prev, off));
      return (NULL);
}

/*
 * Access the node immediately before or after an insertion point.
 *
 * "avl_index_t" is a (avl_node_t *) with the bottom bit indicating a child
 *
 * Return value:
 *    NULL: no node in the given direction
 *    "void *"  of the found tree node
 */
void *
avl_nearest(avl_tree_t *tree, avl_index_t where, int direction)
{
      int child = AVL_INDEX2CHILD(where);
      avl_node_t *node = AVL_INDEX2NODE(where);
      void *data;
      size_t off = tree->avl_offset;

      if (node == NULL) {
            ASSERT(tree->avl_root == NULL);
            return (NULL);
      }
      data = AVL_NODE2DATA(node, off);
      if (child != direction)
            return (data);

      return (avl_walk(tree, data, direction));
}


/*
 * Search for the node which contains "value".  The algorithm is a
 * simple binary tree search.
 *
 * return value:
 *    NULL: the value is not in the AVL tree
 *          *where (if not NULL)  is set to indicate the insertion point
 *    "void *"  of the found tree node
 */
void *
avl_find(avl_tree_t *tree, void *value, avl_index_t *where)
{
      avl_node_t *node;
      avl_node_t *prev = NULL;
      int child = 0;
      int diff;
      size_t off = tree->avl_offset;

      for (node = tree->avl_root; node != NULL;
          node = node->avl_child[child]) {

            prev = node;

            diff = tree->avl_compar(value, AVL_NODE2DATA(node, off));
            ASSERT(-1 <= diff && diff <= 1);
            if (diff == 0) {
#ifdef DEBUG
                  if (where != NULL)
                        *where = 0;
#endif
                  return (AVL_NODE2DATA(node, off));
            }
            child = avl_balance2child[1 + diff];

      }

      if (where != NULL)
            *where = AVL_MKINDEX(prev, child);

      return (NULL);
}


/*
 * Perform a rotation to restore balance at the subtree given by depth.
 *
 * This routine is used by both insertion and deletion. The return value
 * indicates:
 *     0 : subtree did not change height
 *    !0 : subtree was reduced in height
 *
 * The code is written as if handling left rotations, right rotations are
 * symmetric and handled by swapping values of variables right/left[_heavy]
 *
 * On input balance is the "new" balance at "node". This value is either
 * -2 or +2.
 */
static int
avl_rotation(avl_tree_t *tree, avl_node_t *node, int balance)
{
      int left = !(balance < 0);    /* when balance = -2, left will be 0 */
      int right = 1 - left;
      int left_heavy = balance >> 1;
      int right_heavy = -left_heavy;
      avl_node_t *parent = AVL_XPARENT(node);
      avl_node_t *child = node->avl_child[left];
      avl_node_t *cright;
      avl_node_t *gchild;
      avl_node_t *gright;
      avl_node_t *gleft;
      int which_child = AVL_XCHILD(node);
      int child_bal = AVL_XBALANCE(child);

      /* BEGIN CSTYLED */
      /*
       * case 1 : node is overly left heavy, the left child is balanced or
       * also left heavy. This requires the following rotation.
       *
       *                   (node bal:-2)
       *                    /           \
       *                   /             \
       *              (child bal:0 or -1)
       *              /    \
       *             /      \
       *                     cright
       *
       * becomes:
       *
       *              (child bal:1 or 0)
       *              /        \
       *             /          \
       *                        (node bal:-1 or 0)
       *                         /     \
       *                        /       \
       *                     cright
       *
       * we detect this situation by noting that child's balance is not
       * right_heavy.
       */
      /* END CSTYLED */
      if (child_bal != right_heavy) {

            /*
             * compute new balance of nodes
             *
             * If child used to be left heavy (now balanced) we reduced
             * the height of this sub-tree -- used in "return...;" below
             */
            child_bal += right_heavy; /* adjust towards right */

            /*
             * move "cright" to be node's left child
             */
            cright = child->avl_child[right];
            node->avl_child[left] = cright;
            if (cright != NULL) {
                  AVL_SETPARENT(cright, node);
                  AVL_SETCHILD(cright, left);
            }

            /*
             * move node to be child's right child
             */
            child->avl_child[right] = node;
            AVL_SETBALANCE(node, -child_bal);
            AVL_SETCHILD(node, right);
            AVL_SETPARENT(node, child);

            /*
             * update the pointer into this subtree
             */
            AVL_SETBALANCE(child, child_bal);
            AVL_SETCHILD(child, which_child);
            AVL_SETPARENT(child, parent);
            if (parent != NULL)
                  parent->avl_child[which_child] = child;
            else
                  tree->avl_root = child;

            return (child_bal == 0);
      }

      /* BEGIN CSTYLED */
      /*
       * case 2 : When node is left heavy, but child is right heavy we use
       * a different rotation.
       *
       *                   (node b:-2)
       *                    /   \
       *                   /     \
       *                  /       \
       *             (child b:+1)
       *              /     \
       *             /       \
       *                   (gchild b: != 0)
       *                     /  \
       *                    /    \
       *                 gleft   gright
       *
       * becomes:
       *
       *              (gchild b:0)
       *              /       \
       *             /         \
       *            /           \
       *        (child b:?)   (node b:?)
       *         /  \          /   \
       *        /    \        /     \
       *            gleft   gright
       *
       * computing the new balances is more complicated. As an example:
       *     if gchild was right_heavy, then child is now left heavy
       *          else it is balanced
       */
      /* END CSTYLED */
      gchild = child->avl_child[right];
      gleft = gchild->avl_child[left];
      gright = gchild->avl_child[right];

      /*
       * move gright to left child of node and
       *
       * move gleft to right child of node
       */
      node->avl_child[left] = gright;
      if (gright != NULL) {
            AVL_SETPARENT(gright, node);
            AVL_SETCHILD(gright, left);
      }

      child->avl_child[right] = gleft;
      if (gleft != NULL) {
            AVL_SETPARENT(gleft, child);
            AVL_SETCHILD(gleft, right);
      }

      /*
       * move child to left child of gchild and
       *
       * move node to right child of gchild and
       *
       * fixup parent of all this to point to gchild
       */
      balance = AVL_XBALANCE(gchild);
      gchild->avl_child[left] = child;
      AVL_SETBALANCE(child, (balance == right_heavy ? left_heavy : 0));
      AVL_SETPARENT(child, gchild);
      AVL_SETCHILD(child, left);

      gchild->avl_child[right] = node;
      AVL_SETBALANCE(node, (balance == left_heavy ? right_heavy : 0));
      AVL_SETPARENT(node, gchild);
      AVL_SETCHILD(node, right);

      AVL_SETBALANCE(gchild, 0);
      AVL_SETPARENT(gchild, parent);
      AVL_SETCHILD(gchild, which_child);
      if (parent != NULL)
            parent->avl_child[which_child] = gchild;
      else
            tree->avl_root = gchild;

      return (1); /* the new tree is always shorter */
}


/*
 * Insert a new node into an AVL tree at the specified (from avl_find()) place.
 *
 * Newly inserted nodes are always leaf nodes in the tree, since avl_find()
 * searches out to the leaf positions.  The avl_index_t indicates the node
 * which will be the parent of the new node.
 *
 * After the node is inserted, a single rotation further up the tree may
 * be necessary to maintain an acceptable AVL balance.
 */
void
avl_insert(avl_tree_t *tree, void *new_data, avl_index_t where)
{
      avl_node_t *node;
      avl_node_t *parent = AVL_INDEX2NODE(where);
      int old_balance;
      int new_balance;
      int which_child = AVL_INDEX2CHILD(where);
      size_t off = tree->avl_offset;

      ASSERT(tree);
#ifdef _LP64
      ASSERT(((uintptr_t)new_data & 0x7) == 0);
#endif

      node = AVL_DATA2NODE(new_data, off);

      /*
       * First, add the node to the tree at the indicated position.
       */
      ++tree->avl_numnodes;

      node->avl_child[0] = NULL;
      node->avl_child[1] = NULL;

      AVL_SETCHILD(node, which_child);
      AVL_SETBALANCE(node, 0);
      AVL_SETPARENT(node, parent);
      if (parent != NULL) {
            ASSERT(parent->avl_child[which_child] == NULL);
            parent->avl_child[which_child] = node;
      } else {
            ASSERT(tree->avl_root == NULL);
            tree->avl_root = node;
      }
      /*
       * Now, back up the tree modifying the balance of all nodes above the
       * insertion point. If we get to a highly unbalanced ancestor, we
       * need to do a rotation.  If we back out of the tree we are done.
       * If we brought any subtree into perfect balance (0), we are also done.
       */
      for (;;) {
            node = parent;
            if (node == NULL)
                  return;

            /*
             * Compute the new balance
             */
            old_balance = AVL_XBALANCE(node);
            new_balance = old_balance + avl_child2balance[which_child];

            /*
             * If we introduced equal balance, then we are done immediately
             */
            if (new_balance == 0) {
                  AVL_SETBALANCE(node, 0);
                  return;
            }

            /*
             * If both old and new are not zero we went
             * from -1 to -2 balance, do a rotation.
             */
            if (old_balance != 0)
                  break;

            AVL_SETBALANCE(node, new_balance);
            parent = AVL_XPARENT(node);
            which_child = AVL_XCHILD(node);
      }

      /*
       * perform a rotation to fix the tree and return
       */
      (void) avl_rotation(tree, node, new_balance);
}

/*
 * Insert "new_data" in "tree" in the given "direction" either after or
 * before (AVL_AFTER, AVL_BEFORE) the data "here".
 *
 * Insertions can only be done at empty leaf points in the tree, therefore
 * if the given child of the node is already present we move to either
 * the AVL_PREV or AVL_NEXT and reverse the insertion direction. Since
 * every other node in the tree is a leaf, this always works.
 *
 * To help developers using this interface, we assert that the new node
 * is correctly ordered at every step of the way in DEBUG kernels.
 */
void
avl_insert_here(
      avl_tree_t *tree,
      void *new_data,
      void *here,
      int direction)
{
      avl_node_t *node;
      int child = direction;  /* rely on AVL_BEFORE == 0, AVL_AFTER == 1 */
#ifdef DEBUG
      int diff;
#endif

      ASSERT(tree != NULL);
      ASSERT(new_data != NULL);
      ASSERT(here != NULL);
      ASSERT(direction == AVL_BEFORE || direction == AVL_AFTER);

      /*
       * If corresponding child of node is not NULL, go to the neighboring
       * node and reverse the insertion direction.
       */
      node = AVL_DATA2NODE(here, tree->avl_offset);

#ifdef DEBUG
      diff = tree->avl_compar(new_data, here);
      ASSERT(-1 <= diff && diff <= 1);
      ASSERT(diff != 0);
      ASSERT(diff > 0 ? child == 1 : child == 0);
#endif

      if (node->avl_child[child] != NULL) {
            node = node->avl_child[child];
            child = 1 - child;
            while (node->avl_child[child] != NULL) {
#ifdef DEBUG
                  diff = tree->avl_compar(new_data,
                      AVL_NODE2DATA(node, tree->avl_offset));
                  ASSERT(-1 <= diff && diff <= 1);
                  ASSERT(diff != 0);
                  ASSERT(diff > 0 ? child == 1 : child == 0);
#endif
                  node = node->avl_child[child];
            }
#ifdef DEBUG
            diff = tree->avl_compar(new_data,
                AVL_NODE2DATA(node, tree->avl_offset));
            ASSERT(-1 <= diff && diff <= 1);
            ASSERT(diff != 0);
            ASSERT(diff > 0 ? child == 1 : child == 0);
#endif
      }
      ASSERT(node->avl_child[child] == NULL);

      avl_insert(tree, new_data, AVL_MKINDEX(node, child));
}

/*
 * Add a new node to an AVL tree.
 */
void
avl_add(avl_tree_t *tree, void *new_node)
{
      avl_index_t where;

      /*
       * This is unfortunate.  We want to call panic() here, even for
       * non-DEBUG kernels.  In userland, however, we can't depend on anything
       * in libc or else the rtld build process gets confused.  So, all we can
       * do in userland is resort to a normal ASSERT().
       */
      if (avl_find(tree, new_node, &where) != NULL)
#ifdef _KERNEL
            panic("avl_find() succeeded inside avl_add()");
#else
            ASSERT(0);
#endif
      avl_insert(tree, new_node, where);
}

/*
 * Delete a node from the AVL tree.  Deletion is similar to insertion, but
 * with 2 complications.
 *
 * First, we may be deleting an interior node. Consider the following subtree:
 *
 *     d           c            c
 *    / \         / \          / \
 *   b   e       b   e        b   e
 *  / \             / \          /
 * a   c       a            a
 *
 * When we are deleting node (d), we find and bring up an adjacent valued leaf
 * node, say (c), to take the interior node's place. In the code this is
 * handled by temporarily swapping (d) and (c) in the tree and then using
 * common code to delete (d) from the leaf position.
 *
 * Secondly, an interior deletion from a deep tree may require more than one
 * rotation to fix the balance. This is handled by moving up the tree through
 * parents and applying rotations as needed. The return value from
 * avl_rotation() is used to detect when a subtree did not change overall
 * height due to a rotation.
 */
void
avl_remove(avl_tree_t *tree, void *data)
{
      avl_node_t *delete;
      avl_node_t *parent;
      avl_node_t *node;
      avl_node_t tmp;
      int old_balance;
      int new_balance;
      int left;
      int right;
      int which_child;
      size_t off = tree->avl_offset;

      ASSERT(tree);

      delete = AVL_DATA2NODE(data, off);

      /*
       * Deletion is easiest with a node that has at most 1 child.
       * We swap a node with 2 children with a sequentially valued
       * neighbor node. That node will have at most 1 child. Note this
       * has no effect on the ordering of the remaining nodes.
       *
       * As an optimization, we choose the greater neighbor if the tree
       * is right heavy, otherwise the left neighbor. This reduces the
       * number of rotations needed.
       */
      if (delete->avl_child[0] != NULL && delete->avl_child[1] != NULL) {

            /*
             * choose node to swap from whichever side is taller
             */
            old_balance = AVL_XBALANCE(delete);
            left = avl_balance2child[old_balance + 1];
            right = 1 - left;

            /*
             * get to the previous value'd node
             * (down 1 left, as far as possible right)
             */
            for (node = delete->avl_child[left];
                node->avl_child[right] != NULL;
                node = node->avl_child[right])
                  ;

            /*
             * create a temp placeholder for 'node'
             * move 'node' to delete's spot in the tree
             */
            tmp = *node;

            *node = *delete;
            if (node->avl_child[left] == node)
                  node->avl_child[left] = &tmp;

            parent = AVL_XPARENT(node);
            if (parent != NULL)
                  parent->avl_child[AVL_XCHILD(node)] = node;
            else
                  tree->avl_root = node;
            AVL_SETPARENT(node->avl_child[left], node);
            AVL_SETPARENT(node->avl_child[right], node);

            /*
             * Put tmp where node used to be (just temporary).
             * It always has a parent and at most 1 child.
             */
            delete = &tmp;
            parent = AVL_XPARENT(delete);
            parent->avl_child[AVL_XCHILD(delete)] = delete;
            which_child = (delete->avl_child[1] != 0);
            if (delete->avl_child[which_child] != NULL)
                  AVL_SETPARENT(delete->avl_child[which_child], delete);
      }


      /*
       * Here we know "delete" is at least partially a leaf node. It can
       * be easily removed from the tree.
       */
      ASSERT(tree->avl_numnodes > 0);
      --tree->avl_numnodes;
      parent = AVL_XPARENT(delete);
      which_child = AVL_XCHILD(delete);
      if (delete->avl_child[0] != NULL)
            node = delete->avl_child[0];
      else
            node = delete->avl_child[1];

      /*
       * Connect parent directly to node (leaving out delete).
       */
      if (node != NULL) {
            AVL_SETPARENT(node, parent);
            AVL_SETCHILD(node, which_child);
      }
      if (parent == NULL) {
            tree->avl_root = node;
            return;
      }
      parent->avl_child[which_child] = node;


      /*
       * Since the subtree is now shorter, begin adjusting parent balances
       * and performing any needed rotations.
       */
      do {

            /*
             * Move up the tree and adjust the balance
             *
             * Capture the parent and which_child values for the next
             * iteration before any rotations occur.
             */
            node = parent;
            old_balance = AVL_XBALANCE(node);
            new_balance = old_balance - avl_child2balance[which_child];
            parent = AVL_XPARENT(node);
            which_child = AVL_XCHILD(node);

            /*
             * If a node was in perfect balance but isn't anymore then
             * we can stop, since the height didn't change above this point
             * due to a deletion.
             */
            if (old_balance == 0) {
                  AVL_SETBALANCE(node, new_balance);
                  break;
            }

            /*
             * If the new balance is zero, we don't need to rotate
             * else
             * need a rotation to fix the balance.
             * If the rotation doesn't change the height
             * of the sub-tree we have finished adjusting.
             */
            if (new_balance == 0)
                  AVL_SETBALANCE(node, new_balance);
            else if (!avl_rotation(tree, node, new_balance))
                  break;
      } while (parent != NULL);
}

#define     AVL_REINSERT(tree, obj)       \
      avl_remove((tree), (obj));    \
      avl_add((tree), (obj))

boolean_t
avl_update_lt(avl_tree_t *t, void *obj)
{
      void *neighbor;

      ASSERT(((neighbor = AVL_NEXT(t, obj)) == NULL) ||
          (t->avl_compar(obj, neighbor) <= 0));

      neighbor = AVL_PREV(t, obj);
      if ((neighbor != NULL) && (t->avl_compar(obj, neighbor) < 0)) {
            AVL_REINSERT(t, obj);
            return (B_TRUE);
      }

      return (B_FALSE);
}

boolean_t
avl_update_gt(avl_tree_t *t, void *obj)
{
      void *neighbor;

      ASSERT(((neighbor = AVL_PREV(t, obj)) == NULL) ||
          (t->avl_compar(obj, neighbor) >= 0));

      neighbor = AVL_NEXT(t, obj);
      if ((neighbor != NULL) && (t->avl_compar(obj, neighbor) > 0)) {
            AVL_REINSERT(t, obj);
            return (B_TRUE);
      }

      return (B_FALSE);
}

boolean_t
avl_update(avl_tree_t *t, void *obj)
{
      void *neighbor;

      neighbor = AVL_PREV(t, obj);
      if ((neighbor != NULL) && (t->avl_compar(obj, neighbor) < 0)) {
            AVL_REINSERT(t, obj);
            return (B_TRUE);
      }

      neighbor = AVL_NEXT(t, obj);
      if ((neighbor != NULL) && (t->avl_compar(obj, neighbor) > 0)) {
            AVL_REINSERT(t, obj);
            return (B_TRUE);
      }

      return (B_FALSE);
}

/*
 * initialize a new AVL tree
 */
void
avl_create(avl_tree_t *tree, int (*compar) (const void *, const void *),
    size_t size, size_t offset)
{
      ASSERT(tree);
      ASSERT(compar);
      ASSERT(size > 0);
      ASSERT(size >= offset + sizeof (avl_node_t));
#ifdef _LP64
      ASSERT((offset & 0x7) == 0);
#endif

      tree->avl_compar = compar;
      tree->avl_root = NULL;
      tree->avl_numnodes = 0;
      tree->avl_size = size;
      tree->avl_offset = offset;
}

/*
 * Delete a tree.
 */
/* ARGSUSED */
void
avl_destroy(avl_tree_t *tree)
{
      ASSERT(tree);
      ASSERT(tree->avl_numnodes == 0);
      ASSERT(tree->avl_root == NULL);
}


/*
 * Return the number of nodes in an AVL tree.
 */
ulong_t
avl_numnodes(avl_tree_t *tree)
{
      ASSERT(tree);
      return (tree->avl_numnodes);
}

boolean_t
avl_is_empty(avl_tree_t *tree)
{
      ASSERT(tree);
      return (tree->avl_numnodes == 0);
}

#define     CHILDBIT    (1L)

/*
 * Post-order tree walk used to visit all tree nodes and destroy the tree
 * in post order. This is used for destroying a tree w/o paying any cost
 * for rebalancing it.
 *
 * example:
 *
 *    void *cookie = NULL;
 *    my_data_t *node;
 *
 *    while ((node = avl_destroy_nodes(tree, &cookie)) != NULL)
 *          free(node);
 *    avl_destroy(tree);
 *
 * The cookie is really an avl_node_t to the current node's parent and
 * an indication of which child you looked at last.
 *
 * On input, a cookie value of CHILDBIT indicates the tree is done.
 */
void *
avl_destroy_nodes(avl_tree_t *tree, void **cookie)
{
      avl_node_t  *node;
      avl_node_t  *parent;
      int         child;
      void        *first;
      size_t            off = tree->avl_offset;

      /*
       * Initial calls go to the first node or it's right descendant.
       */
      if (*cookie == NULL) {
            first = avl_first(tree);

            /*
             * deal with an empty tree
             */
            if (first == NULL) {
                  *cookie = (void *)CHILDBIT;
                  return (NULL);
            }

            node = AVL_DATA2NODE(first, off);
            parent = AVL_XPARENT(node);
            goto check_right_side;
      }

      /*
       * If there is no parent to return to we are done.
       */
      parent = (avl_node_t *)((uintptr_t)(*cookie) & ~CHILDBIT);
      if (parent == NULL) {
            if (tree->avl_root != NULL) {
                  ASSERT(tree->avl_numnodes == 1);
                  tree->avl_root = NULL;
                  tree->avl_numnodes = 0;
            }
            return (NULL);
      }

      /*
       * Remove the child pointer we just visited from the parent and tree.
       */
      child = (uintptr_t)(*cookie) & CHILDBIT;
      parent->avl_child[child] = NULL;
      ASSERT(tree->avl_numnodes > 1);
      --tree->avl_numnodes;

      /*
       * If we just did a right child or there isn't one, go up to parent.
       */
      if (child == 1 || parent->avl_child[1] == NULL) {
            node = parent;
            parent = AVL_XPARENT(parent);
            goto done;
      }

      /*
       * Do parent's right child, then leftmost descendent.
       */
      node = parent->avl_child[1];
      while (node->avl_child[0] != NULL) {
            parent = node;
            node = node->avl_child[0];
      }

      /*
       * If here, we moved to a left child. It may have one
       * child on the right (when balance == +1).
       */
check_right_side:
      if (node->avl_child[1] != NULL) {
            ASSERT(AVL_XBALANCE(node) == 1);
            parent = node;
            node = node->avl_child[1];
            ASSERT(node->avl_child[0] == NULL &&
                node->avl_child[1] == NULL);
      } else {
            ASSERT(AVL_XBALANCE(node) <= 0);
      }

done:
      if (parent == NULL) {
            *cookie = (void *)CHILDBIT;
            ASSERT(node == tree->avl_root);
      } else {
            *cookie = (void *)((uintptr_t)parent | AVL_XCHILD(node));
      }

      return (AVL_NODE2DATA(node, off));
}

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