aboutsummaryrefslogblamecommitdiff
path: root/cddl/contrib/opensolaris/common/avl/avl.c
blob: dd39c12d215e9749d01f2a53ab4c77ff67856899 (plain) (tree)
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807




















                                                                      
                                                              


                                   
























































































































































































































                                                                                
                                                                 



















































































































































































































































































































































































































































































































































































                                                                                

























































                                                                       












































                                                                        





                                         

















































































































                                                                             
/*
 * 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 2009 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

/*
 * 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/debug.h>
#include <sys/avl.h>
#include <sys/cmn_err.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, const 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));
}