17c478bd9Sstevel@tonic-gate /* 27c478bd9Sstevel@tonic-gate * CDDL HEADER START 37c478bd9Sstevel@tonic-gate * 47c478bd9Sstevel@tonic-gate * The contents of this file are subject to the terms of the 57c478bd9Sstevel@tonic-gate * Common Development and Distribution License, Version 1.0 only 67c478bd9Sstevel@tonic-gate * (the "License"). You may not use this file except in compliance 77c478bd9Sstevel@tonic-gate * with the License. 87c478bd9Sstevel@tonic-gate * 97c478bd9Sstevel@tonic-gate * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 107c478bd9Sstevel@tonic-gate * or http://www.opensolaris.org/os/licensing. 117c478bd9Sstevel@tonic-gate * See the License for the specific language governing permissions 127c478bd9Sstevel@tonic-gate * and limitations under the License. 137c478bd9Sstevel@tonic-gate * 147c478bd9Sstevel@tonic-gate * When distributing Covered Code, include this CDDL HEADER in each 157c478bd9Sstevel@tonic-gate * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 167c478bd9Sstevel@tonic-gate * If applicable, add the following below this CDDL HEADER, with the 177c478bd9Sstevel@tonic-gate * fields enclosed by brackets "[]" replaced with your own identifying 187c478bd9Sstevel@tonic-gate * information: Portions Copyright [yyyy] [name of copyright owner] 197c478bd9Sstevel@tonic-gate * 207c478bd9Sstevel@tonic-gate * CDDL HEADER END 217c478bd9Sstevel@tonic-gate */ 227c478bd9Sstevel@tonic-gate /* 23*fa9e4066Sahrens * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 247c478bd9Sstevel@tonic-gate * Use is subject to license terms. 257c478bd9Sstevel@tonic-gate */ 267c478bd9Sstevel@tonic-gate 277c478bd9Sstevel@tonic-gate #pragma ident "%Z%%M% %I% %E% SMI" 287c478bd9Sstevel@tonic-gate 297c478bd9Sstevel@tonic-gate 307c478bd9Sstevel@tonic-gate /* 317c478bd9Sstevel@tonic-gate * AVL - generic AVL tree implementation for kernel use 327c478bd9Sstevel@tonic-gate * 337c478bd9Sstevel@tonic-gate * A complete description of AVL trees can be found in many CS textbooks. 347c478bd9Sstevel@tonic-gate * 357c478bd9Sstevel@tonic-gate * Here is a very brief overview. An AVL tree is a binary search tree that is 367c478bd9Sstevel@tonic-gate * almost perfectly balanced. By "almost" perfectly balanced, we mean that at 377c478bd9Sstevel@tonic-gate * any given node, the left and right subtrees are allowed to differ in height 387c478bd9Sstevel@tonic-gate * by at most 1 level. 397c478bd9Sstevel@tonic-gate * 407c478bd9Sstevel@tonic-gate * This relaxation from a perfectly balanced binary tree allows doing 417c478bd9Sstevel@tonic-gate * insertion and deletion relatively efficiently. Searching the tree is 427c478bd9Sstevel@tonic-gate * still a fast operation, roughly O(log(N)). 437c478bd9Sstevel@tonic-gate * 447c478bd9Sstevel@tonic-gate * The key to insertion and deletion is a set of tree maniuplations called 457c478bd9Sstevel@tonic-gate * rotations, which bring unbalanced subtrees back into the semi-balanced state. 467c478bd9Sstevel@tonic-gate * 477c478bd9Sstevel@tonic-gate * This implementation of AVL trees has the following peculiarities: 487c478bd9Sstevel@tonic-gate * 497c478bd9Sstevel@tonic-gate * - The AVL specific data structures are physically embedded as fields 507c478bd9Sstevel@tonic-gate * in the "using" data structures. To maintain generality the code 517c478bd9Sstevel@tonic-gate * must constantly translate between "avl_node_t *" and containing 527c478bd9Sstevel@tonic-gate * data structure "void *"s by adding/subracting the avl_offset. 537c478bd9Sstevel@tonic-gate * 547c478bd9Sstevel@tonic-gate * - Since the AVL data is always embedded in other structures, there is 557c478bd9Sstevel@tonic-gate * no locking or memory allocation in the AVL routines. This must be 567c478bd9Sstevel@tonic-gate * provided for by the enclosing data structure's semantics. Typically, 57*fa9e4066Sahrens * avl_insert()/_add()/_remove()/avl_insert_here() require some kind of 587c478bd9Sstevel@tonic-gate * exclusive write lock. Other operations require a read lock. 597c478bd9Sstevel@tonic-gate * 607c478bd9Sstevel@tonic-gate * - The implementation uses iteration instead of explicit recursion, 617c478bd9Sstevel@tonic-gate * since it is intended to run on limited size kernel stacks. Since 627c478bd9Sstevel@tonic-gate * there is no recursion stack present to move "up" in the tree, 637c478bd9Sstevel@tonic-gate * there is an explicit "parent" link in the avl_node_t. 647c478bd9Sstevel@tonic-gate * 657c478bd9Sstevel@tonic-gate * - The left/right children pointers of a node are in an array. 667c478bd9Sstevel@tonic-gate * In the code, variables (instead of constants) are used to represent 677c478bd9Sstevel@tonic-gate * left and right indices. The implementation is written as if it only 687c478bd9Sstevel@tonic-gate * dealt with left handed manipulations. By changing the value assigned 697c478bd9Sstevel@tonic-gate * to "left", the code also works for right handed trees. The 707c478bd9Sstevel@tonic-gate * following variables/terms are frequently used: 717c478bd9Sstevel@tonic-gate * 727c478bd9Sstevel@tonic-gate * int left; // 0 when dealing with left children, 737c478bd9Sstevel@tonic-gate * // 1 for dealing with right children 747c478bd9Sstevel@tonic-gate * 757c478bd9Sstevel@tonic-gate * int left_heavy; // -1 when left subtree is taller at some node, 767c478bd9Sstevel@tonic-gate * // +1 when right subtree is taller 777c478bd9Sstevel@tonic-gate * 787c478bd9Sstevel@tonic-gate * int right; // will be the opposite of left (0 or 1) 797c478bd9Sstevel@tonic-gate * int right_heavy;// will be the opposite of left_heavy (-1 or 1) 807c478bd9Sstevel@tonic-gate * 817c478bd9Sstevel@tonic-gate * int direction; // 0 for "<" (ie. left child); 1 for ">" (right) 827c478bd9Sstevel@tonic-gate * 837c478bd9Sstevel@tonic-gate * Though it is a little more confusing to read the code, the approach 847c478bd9Sstevel@tonic-gate * allows using half as much code (and hence cache footprint) for tree 857c478bd9Sstevel@tonic-gate * manipulations and eliminates many conditional branches. 867c478bd9Sstevel@tonic-gate * 877c478bd9Sstevel@tonic-gate * - The avl_index_t is an opaque "cookie" used to find nodes at or 887c478bd9Sstevel@tonic-gate * adjacent to where a new value would be inserted in the tree. The value 897c478bd9Sstevel@tonic-gate * is a modified "avl_node_t *". The bottom bit (normally 0 for a 907c478bd9Sstevel@tonic-gate * pointer) is set to indicate if that the new node has a value greater 917c478bd9Sstevel@tonic-gate * than the value of the indicated "avl_node_t *". 927c478bd9Sstevel@tonic-gate */ 937c478bd9Sstevel@tonic-gate 947c478bd9Sstevel@tonic-gate #include <sys/types.h> 957c478bd9Sstevel@tonic-gate #include <sys/param.h> 967c478bd9Sstevel@tonic-gate #include <sys/debug.h> 977c478bd9Sstevel@tonic-gate #include <sys/avl.h> 98*fa9e4066Sahrens #include <sys/cmn_err.h> 997c478bd9Sstevel@tonic-gate 1007c478bd9Sstevel@tonic-gate /* 1017c478bd9Sstevel@tonic-gate * Small arrays to translate between balance (or diff) values and child indeces. 1027c478bd9Sstevel@tonic-gate * 1037c478bd9Sstevel@tonic-gate * Code that deals with binary tree data structures will randomly use 1047c478bd9Sstevel@tonic-gate * left and right children when examining a tree. C "if()" statements 1057c478bd9Sstevel@tonic-gate * which evaluate randomly suffer from very poor hardware branch prediction. 1067c478bd9Sstevel@tonic-gate * In this code we avoid some of the branch mispredictions by using the 1077c478bd9Sstevel@tonic-gate * following translation arrays. They replace random branches with an 1087c478bd9Sstevel@tonic-gate * additional memory reference. Since the translation arrays are both very 1097c478bd9Sstevel@tonic-gate * small the data should remain efficiently in cache. 1107c478bd9Sstevel@tonic-gate */ 1117c478bd9Sstevel@tonic-gate static const int avl_child2balance[2] = {-1, 1}; 1127c478bd9Sstevel@tonic-gate static const int avl_balance2child[] = {0, 0, 1}; 1137c478bd9Sstevel@tonic-gate 1147c478bd9Sstevel@tonic-gate 1157c478bd9Sstevel@tonic-gate /* 1167c478bd9Sstevel@tonic-gate * Walk from one node to the previous valued node (ie. an infix walk 1177c478bd9Sstevel@tonic-gate * towards the left). At any given node we do one of 2 things: 1187c478bd9Sstevel@tonic-gate * 1197c478bd9Sstevel@tonic-gate * - If there is a left child, go to it, then to it's rightmost descendant. 1207c478bd9Sstevel@tonic-gate * 1217c478bd9Sstevel@tonic-gate * - otherwise we return thru parent nodes until we've come from a right child. 1227c478bd9Sstevel@tonic-gate * 1237c478bd9Sstevel@tonic-gate * Return Value: 1247c478bd9Sstevel@tonic-gate * NULL - if at the end of the nodes 1257c478bd9Sstevel@tonic-gate * otherwise next node 1267c478bd9Sstevel@tonic-gate */ 1277c478bd9Sstevel@tonic-gate void * 1287c478bd9Sstevel@tonic-gate avl_walk(avl_tree_t *tree, void *oldnode, int left) 1297c478bd9Sstevel@tonic-gate { 1307c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 1317c478bd9Sstevel@tonic-gate avl_node_t *node = AVL_DATA2NODE(oldnode, off); 1327c478bd9Sstevel@tonic-gate int right = 1 - left; 1337c478bd9Sstevel@tonic-gate int was_child; 1347c478bd9Sstevel@tonic-gate 1357c478bd9Sstevel@tonic-gate 1367c478bd9Sstevel@tonic-gate /* 1377c478bd9Sstevel@tonic-gate * nowhere to walk to if tree is empty 1387c478bd9Sstevel@tonic-gate */ 1397c478bd9Sstevel@tonic-gate if (node == NULL) 1407c478bd9Sstevel@tonic-gate return (NULL); 1417c478bd9Sstevel@tonic-gate 1427c478bd9Sstevel@tonic-gate /* 1437c478bd9Sstevel@tonic-gate * Visit the previous valued node. There are two possibilities: 1447c478bd9Sstevel@tonic-gate * 1457c478bd9Sstevel@tonic-gate * If this node has a left child, go down one left, then all 1467c478bd9Sstevel@tonic-gate * the way right. 1477c478bd9Sstevel@tonic-gate */ 1487c478bd9Sstevel@tonic-gate if (node->avl_child[left] != NULL) { 1497c478bd9Sstevel@tonic-gate for (node = node->avl_child[left]; 1507c478bd9Sstevel@tonic-gate node->avl_child[right] != NULL; 1517c478bd9Sstevel@tonic-gate node = node->avl_child[right]) 1527c478bd9Sstevel@tonic-gate ; 1537c478bd9Sstevel@tonic-gate /* 1547c478bd9Sstevel@tonic-gate * Otherwise, return thru left children as far as we can. 1557c478bd9Sstevel@tonic-gate */ 1567c478bd9Sstevel@tonic-gate } else { 1577c478bd9Sstevel@tonic-gate for (;;) { 1587c478bd9Sstevel@tonic-gate was_child = AVL_XCHILD(node); 1597c478bd9Sstevel@tonic-gate node = AVL_XPARENT(node); 1607c478bd9Sstevel@tonic-gate if (node == NULL) 1617c478bd9Sstevel@tonic-gate return (NULL); 1627c478bd9Sstevel@tonic-gate if (was_child == right) 1637c478bd9Sstevel@tonic-gate break; 1647c478bd9Sstevel@tonic-gate } 1657c478bd9Sstevel@tonic-gate } 1667c478bd9Sstevel@tonic-gate 1677c478bd9Sstevel@tonic-gate return (AVL_NODE2DATA(node, off)); 1687c478bd9Sstevel@tonic-gate } 1697c478bd9Sstevel@tonic-gate 1707c478bd9Sstevel@tonic-gate /* 1717c478bd9Sstevel@tonic-gate * Return the lowest valued node in a tree or NULL. 1727c478bd9Sstevel@tonic-gate * (leftmost child from root of tree) 1737c478bd9Sstevel@tonic-gate */ 1747c478bd9Sstevel@tonic-gate void * 1757c478bd9Sstevel@tonic-gate avl_first(avl_tree_t *tree) 1767c478bd9Sstevel@tonic-gate { 1777c478bd9Sstevel@tonic-gate avl_node_t *node; 1787c478bd9Sstevel@tonic-gate avl_node_t *prev = NULL; 1797c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 1807c478bd9Sstevel@tonic-gate 1817c478bd9Sstevel@tonic-gate for (node = tree->avl_root; node != NULL; node = node->avl_child[0]) 1827c478bd9Sstevel@tonic-gate prev = node; 1837c478bd9Sstevel@tonic-gate 1847c478bd9Sstevel@tonic-gate if (prev != NULL) 1857c478bd9Sstevel@tonic-gate return (AVL_NODE2DATA(prev, off)); 1867c478bd9Sstevel@tonic-gate return (NULL); 1877c478bd9Sstevel@tonic-gate } 1887c478bd9Sstevel@tonic-gate 1897c478bd9Sstevel@tonic-gate /* 1907c478bd9Sstevel@tonic-gate * Return the highest valued node in a tree or NULL. 1917c478bd9Sstevel@tonic-gate * (rightmost child from root of tree) 1927c478bd9Sstevel@tonic-gate */ 1937c478bd9Sstevel@tonic-gate void * 1947c478bd9Sstevel@tonic-gate avl_last(avl_tree_t *tree) 1957c478bd9Sstevel@tonic-gate { 1967c478bd9Sstevel@tonic-gate avl_node_t *node; 1977c478bd9Sstevel@tonic-gate avl_node_t *prev = NULL; 1987c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 1997c478bd9Sstevel@tonic-gate 2007c478bd9Sstevel@tonic-gate for (node = tree->avl_root; node != NULL; node = node->avl_child[1]) 2017c478bd9Sstevel@tonic-gate prev = node; 2027c478bd9Sstevel@tonic-gate 2037c478bd9Sstevel@tonic-gate if (prev != NULL) 2047c478bd9Sstevel@tonic-gate return (AVL_NODE2DATA(prev, off)); 2057c478bd9Sstevel@tonic-gate return (NULL); 2067c478bd9Sstevel@tonic-gate } 2077c478bd9Sstevel@tonic-gate 2087c478bd9Sstevel@tonic-gate /* 2097c478bd9Sstevel@tonic-gate * Access the node immediately before or after an insertion point. 2107c478bd9Sstevel@tonic-gate * 2117c478bd9Sstevel@tonic-gate * "avl_index_t" is a (avl_node_t *) with the bottom bit indicating a child 2127c478bd9Sstevel@tonic-gate * 2137c478bd9Sstevel@tonic-gate * Return value: 2147c478bd9Sstevel@tonic-gate * NULL: no node in the given direction 2157c478bd9Sstevel@tonic-gate * "void *" of the found tree node 2167c478bd9Sstevel@tonic-gate */ 2177c478bd9Sstevel@tonic-gate void * 2187c478bd9Sstevel@tonic-gate avl_nearest(avl_tree_t *tree, avl_index_t where, int direction) 2197c478bd9Sstevel@tonic-gate { 2207c478bd9Sstevel@tonic-gate int child = AVL_INDEX2CHILD(where); 2217c478bd9Sstevel@tonic-gate avl_node_t *node = AVL_INDEX2NODE(where); 2227c478bd9Sstevel@tonic-gate void *data; 2237c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 2247c478bd9Sstevel@tonic-gate 2257c478bd9Sstevel@tonic-gate if (node == NULL) { 2267c478bd9Sstevel@tonic-gate ASSERT(tree->avl_root == NULL); 2277c478bd9Sstevel@tonic-gate return (NULL); 2287c478bd9Sstevel@tonic-gate } 2297c478bd9Sstevel@tonic-gate data = AVL_NODE2DATA(node, off); 2307c478bd9Sstevel@tonic-gate if (child != direction) 2317c478bd9Sstevel@tonic-gate return (data); 2327c478bd9Sstevel@tonic-gate 2337c478bd9Sstevel@tonic-gate return (avl_walk(tree, data, direction)); 2347c478bd9Sstevel@tonic-gate } 2357c478bd9Sstevel@tonic-gate 2367c478bd9Sstevel@tonic-gate 2377c478bd9Sstevel@tonic-gate /* 2387c478bd9Sstevel@tonic-gate * Search for the node which contains "value". The algorithm is a 2397c478bd9Sstevel@tonic-gate * simple binary tree search. 2407c478bd9Sstevel@tonic-gate * 2417c478bd9Sstevel@tonic-gate * return value: 2427c478bd9Sstevel@tonic-gate * NULL: the value is not in the AVL tree 2437c478bd9Sstevel@tonic-gate * *where (if not NULL) is set to indicate the insertion point 2447c478bd9Sstevel@tonic-gate * "void *" of the found tree node 2457c478bd9Sstevel@tonic-gate */ 2467c478bd9Sstevel@tonic-gate void * 2477c478bd9Sstevel@tonic-gate avl_find(avl_tree_t *tree, void *value, avl_index_t *where) 2487c478bd9Sstevel@tonic-gate { 2497c478bd9Sstevel@tonic-gate avl_node_t *node; 2507c478bd9Sstevel@tonic-gate avl_node_t *prev = NULL; 2517c478bd9Sstevel@tonic-gate int child = 0; 2527c478bd9Sstevel@tonic-gate int diff; 2537c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 2547c478bd9Sstevel@tonic-gate 2557c478bd9Sstevel@tonic-gate for (node = tree->avl_root; node != NULL; 2567c478bd9Sstevel@tonic-gate node = node->avl_child[child]) { 2577c478bd9Sstevel@tonic-gate 2587c478bd9Sstevel@tonic-gate prev = node; 2597c478bd9Sstevel@tonic-gate 2607c478bd9Sstevel@tonic-gate diff = tree->avl_compar(value, AVL_NODE2DATA(node, off)); 2617c478bd9Sstevel@tonic-gate ASSERT(-1 <= diff && diff <= 1); 2627c478bd9Sstevel@tonic-gate if (diff == 0) { 2637c478bd9Sstevel@tonic-gate #ifdef DEBUG 2647c478bd9Sstevel@tonic-gate if (where != NULL) 2657c478bd9Sstevel@tonic-gate *where = NULL; 2667c478bd9Sstevel@tonic-gate #endif 2677c478bd9Sstevel@tonic-gate return (AVL_NODE2DATA(node, off)); 2687c478bd9Sstevel@tonic-gate } 2697c478bd9Sstevel@tonic-gate child = avl_balance2child[1 + diff]; 2707c478bd9Sstevel@tonic-gate 2717c478bd9Sstevel@tonic-gate } 2727c478bd9Sstevel@tonic-gate 2737c478bd9Sstevel@tonic-gate if (where != NULL) 2747c478bd9Sstevel@tonic-gate *where = AVL_MKINDEX(prev, child); 2757c478bd9Sstevel@tonic-gate 2767c478bd9Sstevel@tonic-gate return (NULL); 2777c478bd9Sstevel@tonic-gate } 2787c478bd9Sstevel@tonic-gate 2797c478bd9Sstevel@tonic-gate 2807c478bd9Sstevel@tonic-gate /* 2817c478bd9Sstevel@tonic-gate * Perform a rotation to restore balance at the subtree given by depth. 2827c478bd9Sstevel@tonic-gate * 2837c478bd9Sstevel@tonic-gate * This routine is used by both insertion and deletion. The return value 2847c478bd9Sstevel@tonic-gate * indicates: 2857c478bd9Sstevel@tonic-gate * 0 : subtree did not change height 2867c478bd9Sstevel@tonic-gate * !0 : subtree was reduced in height 2877c478bd9Sstevel@tonic-gate * 2887c478bd9Sstevel@tonic-gate * The code is written as if handling left rotations, right rotations are 2897c478bd9Sstevel@tonic-gate * symmetric and handled by swapping values of variables right/left[_heavy] 2907c478bd9Sstevel@tonic-gate * 2917c478bd9Sstevel@tonic-gate * On input balance is the "new" balance at "node". This value is either 2927c478bd9Sstevel@tonic-gate * -2 or +2. 2937c478bd9Sstevel@tonic-gate */ 2947c478bd9Sstevel@tonic-gate static int 2957c478bd9Sstevel@tonic-gate avl_rotation(avl_tree_t *tree, avl_node_t *node, int balance) 2967c478bd9Sstevel@tonic-gate { 2977c478bd9Sstevel@tonic-gate int left = !(balance < 0); /* when balance = -2, left will be 0 */ 2987c478bd9Sstevel@tonic-gate int right = 1 - left; 2997c478bd9Sstevel@tonic-gate int left_heavy = balance >> 1; 3007c478bd9Sstevel@tonic-gate int right_heavy = -left_heavy; 3017c478bd9Sstevel@tonic-gate avl_node_t *parent = AVL_XPARENT(node); 3027c478bd9Sstevel@tonic-gate avl_node_t *child = node->avl_child[left]; 3037c478bd9Sstevel@tonic-gate avl_node_t *cright; 3047c478bd9Sstevel@tonic-gate avl_node_t *gchild; 3057c478bd9Sstevel@tonic-gate avl_node_t *gright; 3067c478bd9Sstevel@tonic-gate avl_node_t *gleft; 3077c478bd9Sstevel@tonic-gate int which_child = AVL_XCHILD(node); 3087c478bd9Sstevel@tonic-gate int child_bal = AVL_XBALANCE(child); 3097c478bd9Sstevel@tonic-gate 3107c478bd9Sstevel@tonic-gate /* BEGIN CSTYLED */ 3117c478bd9Sstevel@tonic-gate /* 3127c478bd9Sstevel@tonic-gate * case 1 : node is overly left heavy, the left child is balanced or 3137c478bd9Sstevel@tonic-gate * also left heavy. This requires the following rotation. 3147c478bd9Sstevel@tonic-gate * 3157c478bd9Sstevel@tonic-gate * (node bal:-2) 3167c478bd9Sstevel@tonic-gate * / \ 3177c478bd9Sstevel@tonic-gate * / \ 3187c478bd9Sstevel@tonic-gate * (child bal:0 or -1) 3197c478bd9Sstevel@tonic-gate * / \ 3207c478bd9Sstevel@tonic-gate * / \ 3217c478bd9Sstevel@tonic-gate * cright 3227c478bd9Sstevel@tonic-gate * 3237c478bd9Sstevel@tonic-gate * becomes: 3247c478bd9Sstevel@tonic-gate * 3257c478bd9Sstevel@tonic-gate * (child bal:1 or 0) 3267c478bd9Sstevel@tonic-gate * / \ 3277c478bd9Sstevel@tonic-gate * / \ 3287c478bd9Sstevel@tonic-gate * (node bal:-1 or 0) 3297c478bd9Sstevel@tonic-gate * / \ 3307c478bd9Sstevel@tonic-gate * / \ 3317c478bd9Sstevel@tonic-gate * cright 3327c478bd9Sstevel@tonic-gate * 3337c478bd9Sstevel@tonic-gate * we detect this situation by noting that child's balance is not 3347c478bd9Sstevel@tonic-gate * right_heavy. 3357c478bd9Sstevel@tonic-gate */ 3367c478bd9Sstevel@tonic-gate /* END CSTYLED */ 3377c478bd9Sstevel@tonic-gate if (child_bal != right_heavy) { 3387c478bd9Sstevel@tonic-gate 3397c478bd9Sstevel@tonic-gate /* 3407c478bd9Sstevel@tonic-gate * compute new balance of nodes 3417c478bd9Sstevel@tonic-gate * 3427c478bd9Sstevel@tonic-gate * If child used to be left heavy (now balanced) we reduced 3437c478bd9Sstevel@tonic-gate * the height of this sub-tree -- used in "return...;" below 3447c478bd9Sstevel@tonic-gate */ 3457c478bd9Sstevel@tonic-gate child_bal += right_heavy; /* adjust towards right */ 3467c478bd9Sstevel@tonic-gate 3477c478bd9Sstevel@tonic-gate /* 3487c478bd9Sstevel@tonic-gate * move "cright" to be node's left child 3497c478bd9Sstevel@tonic-gate */ 3507c478bd9Sstevel@tonic-gate cright = child->avl_child[right]; 3517c478bd9Sstevel@tonic-gate node->avl_child[left] = cright; 3527c478bd9Sstevel@tonic-gate if (cright != NULL) { 3537c478bd9Sstevel@tonic-gate AVL_SETPARENT(cright, node); 3547c478bd9Sstevel@tonic-gate AVL_SETCHILD(cright, left); 3557c478bd9Sstevel@tonic-gate } 3567c478bd9Sstevel@tonic-gate 3577c478bd9Sstevel@tonic-gate /* 3587c478bd9Sstevel@tonic-gate * move node to be child's right child 3597c478bd9Sstevel@tonic-gate */ 3607c478bd9Sstevel@tonic-gate child->avl_child[right] = node; 3617c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, -child_bal); 3627c478bd9Sstevel@tonic-gate AVL_SETCHILD(node, right); 3637c478bd9Sstevel@tonic-gate AVL_SETPARENT(node, child); 3647c478bd9Sstevel@tonic-gate 3657c478bd9Sstevel@tonic-gate /* 3667c478bd9Sstevel@tonic-gate * update the pointer into this subtree 3677c478bd9Sstevel@tonic-gate */ 3687c478bd9Sstevel@tonic-gate AVL_SETBALANCE(child, child_bal); 3697c478bd9Sstevel@tonic-gate AVL_SETCHILD(child, which_child); 3707c478bd9Sstevel@tonic-gate AVL_SETPARENT(child, parent); 3717c478bd9Sstevel@tonic-gate if (parent != NULL) 3727c478bd9Sstevel@tonic-gate parent->avl_child[which_child] = child; 3737c478bd9Sstevel@tonic-gate else 3747c478bd9Sstevel@tonic-gate tree->avl_root = child; 3757c478bd9Sstevel@tonic-gate 3767c478bd9Sstevel@tonic-gate return (child_bal == 0); 3777c478bd9Sstevel@tonic-gate } 3787c478bd9Sstevel@tonic-gate 3797c478bd9Sstevel@tonic-gate /* BEGIN CSTYLED */ 3807c478bd9Sstevel@tonic-gate /* 3817c478bd9Sstevel@tonic-gate * case 2 : When node is left heavy, but child is right heavy we use 3827c478bd9Sstevel@tonic-gate * a different rotation. 3837c478bd9Sstevel@tonic-gate * 3847c478bd9Sstevel@tonic-gate * (node b:-2) 3857c478bd9Sstevel@tonic-gate * / \ 3867c478bd9Sstevel@tonic-gate * / \ 3877c478bd9Sstevel@tonic-gate * / \ 3887c478bd9Sstevel@tonic-gate * (child b:+1) 3897c478bd9Sstevel@tonic-gate * / \ 3907c478bd9Sstevel@tonic-gate * / \ 3917c478bd9Sstevel@tonic-gate * (gchild b: != 0) 3927c478bd9Sstevel@tonic-gate * / \ 3937c478bd9Sstevel@tonic-gate * / \ 3947c478bd9Sstevel@tonic-gate * gleft gright 3957c478bd9Sstevel@tonic-gate * 3967c478bd9Sstevel@tonic-gate * becomes: 3977c478bd9Sstevel@tonic-gate * 3987c478bd9Sstevel@tonic-gate * (gchild b:0) 3997c478bd9Sstevel@tonic-gate * / \ 4007c478bd9Sstevel@tonic-gate * / \ 4017c478bd9Sstevel@tonic-gate * / \ 4027c478bd9Sstevel@tonic-gate * (child b:?) (node b:?) 4037c478bd9Sstevel@tonic-gate * / \ / \ 4047c478bd9Sstevel@tonic-gate * / \ / \ 4057c478bd9Sstevel@tonic-gate * gleft gright 4067c478bd9Sstevel@tonic-gate * 4077c478bd9Sstevel@tonic-gate * computing the new balances is more complicated. As an example: 4087c478bd9Sstevel@tonic-gate * if gchild was right_heavy, then child is now left heavy 4097c478bd9Sstevel@tonic-gate * else it is balanced 4107c478bd9Sstevel@tonic-gate */ 4117c478bd9Sstevel@tonic-gate /* END CSTYLED */ 4127c478bd9Sstevel@tonic-gate gchild = child->avl_child[right]; 4137c478bd9Sstevel@tonic-gate gleft = gchild->avl_child[left]; 4147c478bd9Sstevel@tonic-gate gright = gchild->avl_child[right]; 4157c478bd9Sstevel@tonic-gate 4167c478bd9Sstevel@tonic-gate /* 4177c478bd9Sstevel@tonic-gate * move gright to left child of node and 4187c478bd9Sstevel@tonic-gate * 4197c478bd9Sstevel@tonic-gate * move gleft to right child of node 4207c478bd9Sstevel@tonic-gate */ 4217c478bd9Sstevel@tonic-gate node->avl_child[left] = gright; 4227c478bd9Sstevel@tonic-gate if (gright != NULL) { 4237c478bd9Sstevel@tonic-gate AVL_SETPARENT(gright, node); 4247c478bd9Sstevel@tonic-gate AVL_SETCHILD(gright, left); 4257c478bd9Sstevel@tonic-gate } 4267c478bd9Sstevel@tonic-gate 4277c478bd9Sstevel@tonic-gate child->avl_child[right] = gleft; 4287c478bd9Sstevel@tonic-gate if (gleft != NULL) { 4297c478bd9Sstevel@tonic-gate AVL_SETPARENT(gleft, child); 4307c478bd9Sstevel@tonic-gate AVL_SETCHILD(gleft, right); 4317c478bd9Sstevel@tonic-gate } 4327c478bd9Sstevel@tonic-gate 4337c478bd9Sstevel@tonic-gate /* 4347c478bd9Sstevel@tonic-gate * move child to left child of gchild and 4357c478bd9Sstevel@tonic-gate * 4367c478bd9Sstevel@tonic-gate * move node to right child of gchild and 4377c478bd9Sstevel@tonic-gate * 4387c478bd9Sstevel@tonic-gate * fixup parent of all this to point to gchild 4397c478bd9Sstevel@tonic-gate */ 4407c478bd9Sstevel@tonic-gate balance = AVL_XBALANCE(gchild); 4417c478bd9Sstevel@tonic-gate gchild->avl_child[left] = child; 4427c478bd9Sstevel@tonic-gate AVL_SETBALANCE(child, (balance == right_heavy ? left_heavy : 0)); 4437c478bd9Sstevel@tonic-gate AVL_SETPARENT(child, gchild); 4447c478bd9Sstevel@tonic-gate AVL_SETCHILD(child, left); 4457c478bd9Sstevel@tonic-gate 4467c478bd9Sstevel@tonic-gate gchild->avl_child[right] = node; 4477c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, (balance == left_heavy ? right_heavy : 0)); 4487c478bd9Sstevel@tonic-gate AVL_SETPARENT(node, gchild); 4497c478bd9Sstevel@tonic-gate AVL_SETCHILD(node, right); 4507c478bd9Sstevel@tonic-gate 4517c478bd9Sstevel@tonic-gate AVL_SETBALANCE(gchild, 0); 4527c478bd9Sstevel@tonic-gate AVL_SETPARENT(gchild, parent); 4537c478bd9Sstevel@tonic-gate AVL_SETCHILD(gchild, which_child); 4547c478bd9Sstevel@tonic-gate if (parent != NULL) 4557c478bd9Sstevel@tonic-gate parent->avl_child[which_child] = gchild; 4567c478bd9Sstevel@tonic-gate else 4577c478bd9Sstevel@tonic-gate tree->avl_root = gchild; 4587c478bd9Sstevel@tonic-gate 4597c478bd9Sstevel@tonic-gate return (1); /* the new tree is always shorter */ 4607c478bd9Sstevel@tonic-gate } 4617c478bd9Sstevel@tonic-gate 4627c478bd9Sstevel@tonic-gate 4637c478bd9Sstevel@tonic-gate /* 4647c478bd9Sstevel@tonic-gate * Insert a new node into an AVL tree at the specified (from avl_find()) place. 4657c478bd9Sstevel@tonic-gate * 4667c478bd9Sstevel@tonic-gate * Newly inserted nodes are always leaf nodes in the tree, since avl_find() 4677c478bd9Sstevel@tonic-gate * searches out to the leaf positions. The avl_index_t indicates the node 4687c478bd9Sstevel@tonic-gate * which will be the parent of the new node. 4697c478bd9Sstevel@tonic-gate * 4707c478bd9Sstevel@tonic-gate * After the node is inserted, a single rotation further up the tree may 4717c478bd9Sstevel@tonic-gate * be necessary to maintain an acceptable AVL balance. 4727c478bd9Sstevel@tonic-gate */ 4737c478bd9Sstevel@tonic-gate void 4747c478bd9Sstevel@tonic-gate avl_insert(avl_tree_t *tree, void *new_data, avl_index_t where) 4757c478bd9Sstevel@tonic-gate { 4767c478bd9Sstevel@tonic-gate avl_node_t *node; 4777c478bd9Sstevel@tonic-gate avl_node_t *parent = AVL_INDEX2NODE(where); 4787c478bd9Sstevel@tonic-gate int old_balance; 4797c478bd9Sstevel@tonic-gate int new_balance; 4807c478bd9Sstevel@tonic-gate int which_child = AVL_INDEX2CHILD(where); 4817c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 4827c478bd9Sstevel@tonic-gate 4837c478bd9Sstevel@tonic-gate ASSERT(tree); 4847c478bd9Sstevel@tonic-gate #ifdef _LP64 4857c478bd9Sstevel@tonic-gate ASSERT(((uintptr_t)new_data & 0x7) == 0); 4867c478bd9Sstevel@tonic-gate #endif 4877c478bd9Sstevel@tonic-gate 4887c478bd9Sstevel@tonic-gate node = AVL_DATA2NODE(new_data, off); 4897c478bd9Sstevel@tonic-gate 4907c478bd9Sstevel@tonic-gate /* 4917c478bd9Sstevel@tonic-gate * First, add the node to the tree at the indicated position. 4927c478bd9Sstevel@tonic-gate */ 4937c478bd9Sstevel@tonic-gate ++tree->avl_numnodes; 4947c478bd9Sstevel@tonic-gate 4957c478bd9Sstevel@tonic-gate node->avl_child[0] = NULL; 4967c478bd9Sstevel@tonic-gate node->avl_child[1] = NULL; 4977c478bd9Sstevel@tonic-gate 4987c478bd9Sstevel@tonic-gate AVL_SETCHILD(node, which_child); 4997c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, 0); 5007c478bd9Sstevel@tonic-gate AVL_SETPARENT(node, parent); 5017c478bd9Sstevel@tonic-gate if (parent != NULL) { 5027c478bd9Sstevel@tonic-gate ASSERT(parent->avl_child[which_child] == NULL); 5037c478bd9Sstevel@tonic-gate parent->avl_child[which_child] = node; 5047c478bd9Sstevel@tonic-gate } else { 5057c478bd9Sstevel@tonic-gate ASSERT(tree->avl_root == NULL); 5067c478bd9Sstevel@tonic-gate tree->avl_root = node; 5077c478bd9Sstevel@tonic-gate } 5087c478bd9Sstevel@tonic-gate /* 5097c478bd9Sstevel@tonic-gate * Now, back up the tree modifying the balance of all nodes above the 5107c478bd9Sstevel@tonic-gate * insertion point. If we get to a highly unbalanced ancestor, we 5117c478bd9Sstevel@tonic-gate * need to do a rotation. If we back out of the tree we are done. 5127c478bd9Sstevel@tonic-gate * If we brought any subtree into perfect balance (0), we are also done. 5137c478bd9Sstevel@tonic-gate */ 5147c478bd9Sstevel@tonic-gate for (;;) { 5157c478bd9Sstevel@tonic-gate node = parent; 5167c478bd9Sstevel@tonic-gate if (node == NULL) 5177c478bd9Sstevel@tonic-gate return; 5187c478bd9Sstevel@tonic-gate 5197c478bd9Sstevel@tonic-gate /* 5207c478bd9Sstevel@tonic-gate * Compute the new balance 5217c478bd9Sstevel@tonic-gate */ 5227c478bd9Sstevel@tonic-gate old_balance = AVL_XBALANCE(node); 5237c478bd9Sstevel@tonic-gate new_balance = old_balance + avl_child2balance[which_child]; 5247c478bd9Sstevel@tonic-gate 5257c478bd9Sstevel@tonic-gate /* 5267c478bd9Sstevel@tonic-gate * If we introduced equal balance, then we are done immediately 5277c478bd9Sstevel@tonic-gate */ 5287c478bd9Sstevel@tonic-gate if (new_balance == 0) { 5297c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, 0); 5307c478bd9Sstevel@tonic-gate return; 5317c478bd9Sstevel@tonic-gate } 5327c478bd9Sstevel@tonic-gate 5337c478bd9Sstevel@tonic-gate /* 5347c478bd9Sstevel@tonic-gate * If both old and new are not zero we went 5357c478bd9Sstevel@tonic-gate * from -1 to -2 balance, do a rotation. 5367c478bd9Sstevel@tonic-gate */ 5377c478bd9Sstevel@tonic-gate if (old_balance != 0) 5387c478bd9Sstevel@tonic-gate break; 5397c478bd9Sstevel@tonic-gate 5407c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, new_balance); 5417c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(node); 5427c478bd9Sstevel@tonic-gate which_child = AVL_XCHILD(node); 5437c478bd9Sstevel@tonic-gate } 5447c478bd9Sstevel@tonic-gate 5457c478bd9Sstevel@tonic-gate /* 5467c478bd9Sstevel@tonic-gate * perform a rotation to fix the tree and return 5477c478bd9Sstevel@tonic-gate */ 5487c478bd9Sstevel@tonic-gate (void) avl_rotation(tree, node, new_balance); 5497c478bd9Sstevel@tonic-gate } 5507c478bd9Sstevel@tonic-gate 5517c478bd9Sstevel@tonic-gate /* 5527c478bd9Sstevel@tonic-gate * Insert "new_data" in "tree" in the given "direction" either after or 5537c478bd9Sstevel@tonic-gate * before (AVL_AFTER, AVL_BEFORE) the data "here". 5547c478bd9Sstevel@tonic-gate * 5557c478bd9Sstevel@tonic-gate * Insertions can only be done at empty leaf points in the tree, therefore 5567c478bd9Sstevel@tonic-gate * if the given child of the node is already present we move to either 5577c478bd9Sstevel@tonic-gate * the AVL_PREV or AVL_NEXT and reverse the insertion direction. Since 5587c478bd9Sstevel@tonic-gate * every other node in the tree is a leaf, this always works. 5597c478bd9Sstevel@tonic-gate * 5607c478bd9Sstevel@tonic-gate * To help developers using this interface, we assert that the new node 5617c478bd9Sstevel@tonic-gate * is correctly ordered at every step of the way in DEBUG kernels. 5627c478bd9Sstevel@tonic-gate */ 5637c478bd9Sstevel@tonic-gate void 5647c478bd9Sstevel@tonic-gate avl_insert_here( 5657c478bd9Sstevel@tonic-gate avl_tree_t *tree, 5667c478bd9Sstevel@tonic-gate void *new_data, 5677c478bd9Sstevel@tonic-gate void *here, 5687c478bd9Sstevel@tonic-gate int direction) 5697c478bd9Sstevel@tonic-gate { 5707c478bd9Sstevel@tonic-gate avl_node_t *node; 5717c478bd9Sstevel@tonic-gate int child = direction; /* rely on AVL_BEFORE == 0, AVL_AFTER == 1 */ 5727c478bd9Sstevel@tonic-gate 5737c478bd9Sstevel@tonic-gate ASSERT(tree != NULL); 5747c478bd9Sstevel@tonic-gate ASSERT(new_data != NULL); 5757c478bd9Sstevel@tonic-gate ASSERT(here != NULL); 5767c478bd9Sstevel@tonic-gate ASSERT(direction == AVL_BEFORE || direction == AVL_AFTER); 5777c478bd9Sstevel@tonic-gate 5787c478bd9Sstevel@tonic-gate /* 5797c478bd9Sstevel@tonic-gate * If corresponding child of node is not NULL, go to the neighboring 5807c478bd9Sstevel@tonic-gate * node and reverse the insertion direction. 5817c478bd9Sstevel@tonic-gate */ 5827c478bd9Sstevel@tonic-gate node = AVL_DATA2NODE(here, tree->avl_offset); 5837c478bd9Sstevel@tonic-gate ASSERT(tree->avl_compar(new_data, here) > 0 ? child == 1 : child == 0); 5847c478bd9Sstevel@tonic-gate 5857c478bd9Sstevel@tonic-gate if (node->avl_child[child] != NULL) { 5867c478bd9Sstevel@tonic-gate node = node->avl_child[child]; 5877c478bd9Sstevel@tonic-gate child = 1 - child; 5887c478bd9Sstevel@tonic-gate while (node->avl_child[child] != NULL) { 5897c478bd9Sstevel@tonic-gate ASSERT(tree->avl_compar(new_data, 5907c478bd9Sstevel@tonic-gate AVL_NODE2DATA(node, tree->avl_offset)) > 0 ? 5917c478bd9Sstevel@tonic-gate child == 1 : child == 0); 5927c478bd9Sstevel@tonic-gate node = node->avl_child[child]; 5937c478bd9Sstevel@tonic-gate } 5947c478bd9Sstevel@tonic-gate ASSERT(tree->avl_compar(new_data, 5957c478bd9Sstevel@tonic-gate AVL_NODE2DATA(node, tree->avl_offset)) > 0 ? 5967c478bd9Sstevel@tonic-gate child == 1 : child == 0); 5977c478bd9Sstevel@tonic-gate } 5987c478bd9Sstevel@tonic-gate ASSERT(node->avl_child[child] == NULL); 5997c478bd9Sstevel@tonic-gate 6007c478bd9Sstevel@tonic-gate avl_insert(tree, new_data, AVL_MKINDEX(node, child)); 6017c478bd9Sstevel@tonic-gate } 6027c478bd9Sstevel@tonic-gate 603*fa9e4066Sahrens /* 604*fa9e4066Sahrens * Add a new node to an AVL tree. 605*fa9e4066Sahrens */ 606*fa9e4066Sahrens void 607*fa9e4066Sahrens avl_add(avl_tree_t *tree, void *new_node) 608*fa9e4066Sahrens { 609*fa9e4066Sahrens avl_index_t where; 610*fa9e4066Sahrens 611*fa9e4066Sahrens /* 612*fa9e4066Sahrens * This is unfortunate. We want to call panic() here, even for 613*fa9e4066Sahrens * non-DEBUG kernels. In userland, however, we can't depend on anything 614*fa9e4066Sahrens * in libc or else the rtld build process gets confused. So, all we can 615*fa9e4066Sahrens * do in userland is resort to a normal ASSERT(). 616*fa9e4066Sahrens */ 617*fa9e4066Sahrens if (avl_find(tree, new_node, &where) != NULL) 618*fa9e4066Sahrens #ifdef _KERNEL 619*fa9e4066Sahrens panic("avl_find() succeeded inside avl_add()"); 620*fa9e4066Sahrens #else 621*fa9e4066Sahrens ASSERT(0); 622*fa9e4066Sahrens #endif 623*fa9e4066Sahrens avl_insert(tree, new_node, where); 624*fa9e4066Sahrens } 625*fa9e4066Sahrens 6267c478bd9Sstevel@tonic-gate /* 6277c478bd9Sstevel@tonic-gate * Delete a node from the AVL tree. Deletion is similar to insertion, but 6287c478bd9Sstevel@tonic-gate * with 2 complications. 6297c478bd9Sstevel@tonic-gate * 6307c478bd9Sstevel@tonic-gate * First, we may be deleting an interior node. Consider the following subtree: 6317c478bd9Sstevel@tonic-gate * 6327c478bd9Sstevel@tonic-gate * d c c 6337c478bd9Sstevel@tonic-gate * / \ / \ / \ 6347c478bd9Sstevel@tonic-gate * b e b e b e 6357c478bd9Sstevel@tonic-gate * / \ / \ / 6367c478bd9Sstevel@tonic-gate * a c a a 6377c478bd9Sstevel@tonic-gate * 6387c478bd9Sstevel@tonic-gate * When we are deleting node (d), we find and bring up an adjacent valued leaf 6397c478bd9Sstevel@tonic-gate * node, say (c), to take the interior node's place. In the code this is 6407c478bd9Sstevel@tonic-gate * handled by temporarily swapping (d) and (c) in the tree and then using 6417c478bd9Sstevel@tonic-gate * common code to delete (d) from the leaf position. 6427c478bd9Sstevel@tonic-gate * 6437c478bd9Sstevel@tonic-gate * Secondly, an interior deletion from a deep tree may require more than one 6447c478bd9Sstevel@tonic-gate * rotation to fix the balance. This is handled by moving up the tree through 6457c478bd9Sstevel@tonic-gate * parents and applying rotations as needed. The return value from 6467c478bd9Sstevel@tonic-gate * avl_rotation() is used to detect when a subtree did not change overall 6477c478bd9Sstevel@tonic-gate * height due to a rotation. 6487c478bd9Sstevel@tonic-gate */ 6497c478bd9Sstevel@tonic-gate void 6507c478bd9Sstevel@tonic-gate avl_remove(avl_tree_t *tree, void *data) 6517c478bd9Sstevel@tonic-gate { 6527c478bd9Sstevel@tonic-gate avl_node_t *delete; 6537c478bd9Sstevel@tonic-gate avl_node_t *parent; 6547c478bd9Sstevel@tonic-gate avl_node_t *node; 6557c478bd9Sstevel@tonic-gate avl_node_t tmp; 6567c478bd9Sstevel@tonic-gate int old_balance; 6577c478bd9Sstevel@tonic-gate int new_balance; 6587c478bd9Sstevel@tonic-gate int left; 6597c478bd9Sstevel@tonic-gate int right; 6607c478bd9Sstevel@tonic-gate int which_child; 6617c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 6627c478bd9Sstevel@tonic-gate 6637c478bd9Sstevel@tonic-gate ASSERT(tree); 6647c478bd9Sstevel@tonic-gate 6657c478bd9Sstevel@tonic-gate delete = AVL_DATA2NODE(data, off); 6667c478bd9Sstevel@tonic-gate 6677c478bd9Sstevel@tonic-gate /* 6687c478bd9Sstevel@tonic-gate * Deletion is easiest with a node that has at most 1 child. 6697c478bd9Sstevel@tonic-gate * We swap a node with 2 children with a sequentially valued 6707c478bd9Sstevel@tonic-gate * neighbor node. That node will have at most 1 child. Note this 6717c478bd9Sstevel@tonic-gate * has no effect on the ordering of the remaining nodes. 6727c478bd9Sstevel@tonic-gate * 6737c478bd9Sstevel@tonic-gate * As an optimization, we choose the greater neighbor if the tree 6747c478bd9Sstevel@tonic-gate * is right heavy, otherwise the left neighbor. This reduces the 6757c478bd9Sstevel@tonic-gate * number of rotations needed. 6767c478bd9Sstevel@tonic-gate */ 6777c478bd9Sstevel@tonic-gate if (delete->avl_child[0] != NULL && delete->avl_child[1] != NULL) { 6787c478bd9Sstevel@tonic-gate 6797c478bd9Sstevel@tonic-gate /* 6807c478bd9Sstevel@tonic-gate * choose node to swap from whichever side is taller 6817c478bd9Sstevel@tonic-gate */ 6827c478bd9Sstevel@tonic-gate old_balance = AVL_XBALANCE(delete); 6837c478bd9Sstevel@tonic-gate left = avl_balance2child[old_balance + 1]; 6847c478bd9Sstevel@tonic-gate right = 1 - left; 6857c478bd9Sstevel@tonic-gate 6867c478bd9Sstevel@tonic-gate /* 6877c478bd9Sstevel@tonic-gate * get to the previous value'd node 6887c478bd9Sstevel@tonic-gate * (down 1 left, as far as possible right) 6897c478bd9Sstevel@tonic-gate */ 6907c478bd9Sstevel@tonic-gate for (node = delete->avl_child[left]; 6917c478bd9Sstevel@tonic-gate node->avl_child[right] != NULL; 6927c478bd9Sstevel@tonic-gate node = node->avl_child[right]) 6937c478bd9Sstevel@tonic-gate ; 6947c478bd9Sstevel@tonic-gate 6957c478bd9Sstevel@tonic-gate /* 6967c478bd9Sstevel@tonic-gate * create a temp placeholder for 'node' 6977c478bd9Sstevel@tonic-gate * move 'node' to delete's spot in the tree 6987c478bd9Sstevel@tonic-gate */ 6997c478bd9Sstevel@tonic-gate tmp = *node; 7007c478bd9Sstevel@tonic-gate 7017c478bd9Sstevel@tonic-gate *node = *delete; 7027c478bd9Sstevel@tonic-gate if (node->avl_child[left] == node) 7037c478bd9Sstevel@tonic-gate node->avl_child[left] = &tmp; 7047c478bd9Sstevel@tonic-gate 7057c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(node); 7067c478bd9Sstevel@tonic-gate if (parent != NULL) 7077c478bd9Sstevel@tonic-gate parent->avl_child[AVL_XCHILD(node)] = node; 7087c478bd9Sstevel@tonic-gate else 7097c478bd9Sstevel@tonic-gate tree->avl_root = node; 7107c478bd9Sstevel@tonic-gate AVL_SETPARENT(node->avl_child[left], node); 7117c478bd9Sstevel@tonic-gate AVL_SETPARENT(node->avl_child[right], node); 7127c478bd9Sstevel@tonic-gate 7137c478bd9Sstevel@tonic-gate /* 7147c478bd9Sstevel@tonic-gate * Put tmp where node used to be (just temporary). 7157c478bd9Sstevel@tonic-gate * It always has a parent and at most 1 child. 7167c478bd9Sstevel@tonic-gate */ 7177c478bd9Sstevel@tonic-gate delete = &tmp; 7187c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(delete); 7197c478bd9Sstevel@tonic-gate parent->avl_child[AVL_XCHILD(delete)] = delete; 7207c478bd9Sstevel@tonic-gate which_child = (delete->avl_child[1] != 0); 7217c478bd9Sstevel@tonic-gate if (delete->avl_child[which_child] != NULL) 7227c478bd9Sstevel@tonic-gate AVL_SETPARENT(delete->avl_child[which_child], delete); 7237c478bd9Sstevel@tonic-gate } 7247c478bd9Sstevel@tonic-gate 7257c478bd9Sstevel@tonic-gate 7267c478bd9Sstevel@tonic-gate /* 7277c478bd9Sstevel@tonic-gate * Here we know "delete" is at least partially a leaf node. It can 7287c478bd9Sstevel@tonic-gate * be easily removed from the tree. 7297c478bd9Sstevel@tonic-gate */ 7307c478bd9Sstevel@tonic-gate --tree->avl_numnodes; 7317c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(delete); 7327c478bd9Sstevel@tonic-gate which_child = AVL_XCHILD(delete); 7337c478bd9Sstevel@tonic-gate if (delete->avl_child[0] != NULL) 7347c478bd9Sstevel@tonic-gate node = delete->avl_child[0]; 7357c478bd9Sstevel@tonic-gate else 7367c478bd9Sstevel@tonic-gate node = delete->avl_child[1]; 7377c478bd9Sstevel@tonic-gate 7387c478bd9Sstevel@tonic-gate /* 7397c478bd9Sstevel@tonic-gate * Connect parent directly to node (leaving out delete). 7407c478bd9Sstevel@tonic-gate */ 7417c478bd9Sstevel@tonic-gate if (node != NULL) { 7427c478bd9Sstevel@tonic-gate AVL_SETPARENT(node, parent); 7437c478bd9Sstevel@tonic-gate AVL_SETCHILD(node, which_child); 7447c478bd9Sstevel@tonic-gate } 7457c478bd9Sstevel@tonic-gate if (parent == NULL) { 7467c478bd9Sstevel@tonic-gate tree->avl_root = node; 7477c478bd9Sstevel@tonic-gate return; 7487c478bd9Sstevel@tonic-gate } 7497c478bd9Sstevel@tonic-gate parent->avl_child[which_child] = node; 7507c478bd9Sstevel@tonic-gate 7517c478bd9Sstevel@tonic-gate 7527c478bd9Sstevel@tonic-gate /* 7537c478bd9Sstevel@tonic-gate * Since the subtree is now shorter, begin adjusting parent balances 7547c478bd9Sstevel@tonic-gate * and performing any needed rotations. 7557c478bd9Sstevel@tonic-gate */ 7567c478bd9Sstevel@tonic-gate do { 7577c478bd9Sstevel@tonic-gate 7587c478bd9Sstevel@tonic-gate /* 7597c478bd9Sstevel@tonic-gate * Move up the tree and adjust the balance 7607c478bd9Sstevel@tonic-gate * 7617c478bd9Sstevel@tonic-gate * Capture the parent and which_child values for the next 7627c478bd9Sstevel@tonic-gate * iteration before any rotations occur. 7637c478bd9Sstevel@tonic-gate */ 7647c478bd9Sstevel@tonic-gate node = parent; 7657c478bd9Sstevel@tonic-gate old_balance = AVL_XBALANCE(node); 7667c478bd9Sstevel@tonic-gate new_balance = old_balance - avl_child2balance[which_child]; 7677c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(node); 7687c478bd9Sstevel@tonic-gate which_child = AVL_XCHILD(node); 7697c478bd9Sstevel@tonic-gate 7707c478bd9Sstevel@tonic-gate /* 7717c478bd9Sstevel@tonic-gate * If a node was in perfect balance but isn't anymore then 7727c478bd9Sstevel@tonic-gate * we can stop, since the height didn't change above this point 7737c478bd9Sstevel@tonic-gate * due to a deletion. 7747c478bd9Sstevel@tonic-gate */ 7757c478bd9Sstevel@tonic-gate if (old_balance == 0) { 7767c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, new_balance); 7777c478bd9Sstevel@tonic-gate break; 7787c478bd9Sstevel@tonic-gate } 7797c478bd9Sstevel@tonic-gate 7807c478bd9Sstevel@tonic-gate /* 7817c478bd9Sstevel@tonic-gate * If the new balance is zero, we don't need to rotate 7827c478bd9Sstevel@tonic-gate * else 7837c478bd9Sstevel@tonic-gate * need a rotation to fix the balance. 7847c478bd9Sstevel@tonic-gate * If the rotation doesn't change the height 7857c478bd9Sstevel@tonic-gate * of the sub-tree we have finished adjusting. 7867c478bd9Sstevel@tonic-gate */ 7877c478bd9Sstevel@tonic-gate if (new_balance == 0) 7887c478bd9Sstevel@tonic-gate AVL_SETBALANCE(node, new_balance); 7897c478bd9Sstevel@tonic-gate else if (!avl_rotation(tree, node, new_balance)) 7907c478bd9Sstevel@tonic-gate break; 7917c478bd9Sstevel@tonic-gate } while (parent != NULL); 7927c478bd9Sstevel@tonic-gate } 7937c478bd9Sstevel@tonic-gate 7947c478bd9Sstevel@tonic-gate /* 7957c478bd9Sstevel@tonic-gate * initialize a new AVL tree 7967c478bd9Sstevel@tonic-gate */ 7977c478bd9Sstevel@tonic-gate void 7987c478bd9Sstevel@tonic-gate avl_create(avl_tree_t *tree, int (*compar) (const void *, const void *), 7997c478bd9Sstevel@tonic-gate size_t size, size_t offset) 8007c478bd9Sstevel@tonic-gate { 8017c478bd9Sstevel@tonic-gate ASSERT(tree); 8027c478bd9Sstevel@tonic-gate ASSERT(compar); 8037c478bd9Sstevel@tonic-gate ASSERT(size > 0); 8047c478bd9Sstevel@tonic-gate ASSERT(size >= offset + sizeof (avl_node_t)); 8057c478bd9Sstevel@tonic-gate #ifdef _LP64 8067c478bd9Sstevel@tonic-gate ASSERT((offset & 0x7) == 0); 8077c478bd9Sstevel@tonic-gate #endif 8087c478bd9Sstevel@tonic-gate 8097c478bd9Sstevel@tonic-gate tree->avl_compar = compar; 8107c478bd9Sstevel@tonic-gate tree->avl_root = NULL; 8117c478bd9Sstevel@tonic-gate tree->avl_numnodes = 0; 8127c478bd9Sstevel@tonic-gate tree->avl_size = size; 8137c478bd9Sstevel@tonic-gate tree->avl_offset = offset; 8147c478bd9Sstevel@tonic-gate } 8157c478bd9Sstevel@tonic-gate 8167c478bd9Sstevel@tonic-gate /* 8177c478bd9Sstevel@tonic-gate * Delete a tree. 8187c478bd9Sstevel@tonic-gate */ 8197c478bd9Sstevel@tonic-gate /* ARGSUSED */ 8207c478bd9Sstevel@tonic-gate void 8217c478bd9Sstevel@tonic-gate avl_destroy(avl_tree_t *tree) 8227c478bd9Sstevel@tonic-gate { 8237c478bd9Sstevel@tonic-gate ASSERT(tree); 8247c478bd9Sstevel@tonic-gate ASSERT(tree->avl_numnodes == 0); 8257c478bd9Sstevel@tonic-gate ASSERT(tree->avl_root == NULL); 8267c478bd9Sstevel@tonic-gate } 8277c478bd9Sstevel@tonic-gate 8287c478bd9Sstevel@tonic-gate 8297c478bd9Sstevel@tonic-gate /* 8307c478bd9Sstevel@tonic-gate * Return the number of nodes in an AVL tree. 8317c478bd9Sstevel@tonic-gate */ 8327c478bd9Sstevel@tonic-gate ulong_t 8337c478bd9Sstevel@tonic-gate avl_numnodes(avl_tree_t *tree) 8347c478bd9Sstevel@tonic-gate { 8357c478bd9Sstevel@tonic-gate ASSERT(tree); 8367c478bd9Sstevel@tonic-gate return (tree->avl_numnodes); 8377c478bd9Sstevel@tonic-gate } 8387c478bd9Sstevel@tonic-gate 8397c478bd9Sstevel@tonic-gate 8407c478bd9Sstevel@tonic-gate #define CHILDBIT (1L) 8417c478bd9Sstevel@tonic-gate 8427c478bd9Sstevel@tonic-gate /* 8437c478bd9Sstevel@tonic-gate * Post-order tree walk used to visit all tree nodes and destroy the tree 8447c478bd9Sstevel@tonic-gate * in post order. This is used for destroying a tree w/o paying any cost 8457c478bd9Sstevel@tonic-gate * for rebalancing it. 8467c478bd9Sstevel@tonic-gate * 8477c478bd9Sstevel@tonic-gate * example: 8487c478bd9Sstevel@tonic-gate * 8497c478bd9Sstevel@tonic-gate * void *cookie = NULL; 8507c478bd9Sstevel@tonic-gate * my_data_t *node; 8517c478bd9Sstevel@tonic-gate * 8527c478bd9Sstevel@tonic-gate * while ((node = avl_destroy_nodes(tree, &cookie)) != NULL) 8537c478bd9Sstevel@tonic-gate * free(node); 8547c478bd9Sstevel@tonic-gate * avl_destroy(tree); 8557c478bd9Sstevel@tonic-gate * 8567c478bd9Sstevel@tonic-gate * The cookie is really an avl_node_t to the current node's parent and 8577c478bd9Sstevel@tonic-gate * an indication of which child you looked at last. 8587c478bd9Sstevel@tonic-gate * 8597c478bd9Sstevel@tonic-gate * On input, a cookie value of CHILDBIT indicates the tree is done. 8607c478bd9Sstevel@tonic-gate */ 8617c478bd9Sstevel@tonic-gate void * 8627c478bd9Sstevel@tonic-gate avl_destroy_nodes(avl_tree_t *tree, void **cookie) 8637c478bd9Sstevel@tonic-gate { 8647c478bd9Sstevel@tonic-gate avl_node_t *node; 8657c478bd9Sstevel@tonic-gate avl_node_t *parent; 8667c478bd9Sstevel@tonic-gate int child; 8677c478bd9Sstevel@tonic-gate void *first; 8687c478bd9Sstevel@tonic-gate size_t off = tree->avl_offset; 8697c478bd9Sstevel@tonic-gate 8707c478bd9Sstevel@tonic-gate /* 8717c478bd9Sstevel@tonic-gate * Initial calls go to the first node or it's right descendant. 8727c478bd9Sstevel@tonic-gate */ 8737c478bd9Sstevel@tonic-gate if (*cookie == NULL) { 8747c478bd9Sstevel@tonic-gate first = avl_first(tree); 8757c478bd9Sstevel@tonic-gate 8767c478bd9Sstevel@tonic-gate /* 8777c478bd9Sstevel@tonic-gate * deal with an empty tree 8787c478bd9Sstevel@tonic-gate */ 8797c478bd9Sstevel@tonic-gate if (first == NULL) { 8807c478bd9Sstevel@tonic-gate *cookie = (void *)CHILDBIT; 8817c478bd9Sstevel@tonic-gate return (NULL); 8827c478bd9Sstevel@tonic-gate } 8837c478bd9Sstevel@tonic-gate 8847c478bd9Sstevel@tonic-gate node = AVL_DATA2NODE(first, off); 8857c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(node); 8867c478bd9Sstevel@tonic-gate goto check_right_side; 8877c478bd9Sstevel@tonic-gate } 8887c478bd9Sstevel@tonic-gate 8897c478bd9Sstevel@tonic-gate /* 8907c478bd9Sstevel@tonic-gate * If there is no parent to return to we are done. 8917c478bd9Sstevel@tonic-gate */ 8927c478bd9Sstevel@tonic-gate parent = (avl_node_t *)((uintptr_t)(*cookie) & ~CHILDBIT); 8937c478bd9Sstevel@tonic-gate if (parent == NULL) { 8947c478bd9Sstevel@tonic-gate if (tree->avl_root != NULL) { 8957c478bd9Sstevel@tonic-gate ASSERT(tree->avl_numnodes == 1); 8967c478bd9Sstevel@tonic-gate tree->avl_root = NULL; 8977c478bd9Sstevel@tonic-gate tree->avl_numnodes = 0; 8987c478bd9Sstevel@tonic-gate } 8997c478bd9Sstevel@tonic-gate return (NULL); 9007c478bd9Sstevel@tonic-gate } 9017c478bd9Sstevel@tonic-gate 9027c478bd9Sstevel@tonic-gate /* 9037c478bd9Sstevel@tonic-gate * Remove the child pointer we just visited from the parent and tree. 9047c478bd9Sstevel@tonic-gate */ 9057c478bd9Sstevel@tonic-gate child = (uintptr_t)(*cookie) & CHILDBIT; 9067c478bd9Sstevel@tonic-gate parent->avl_child[child] = NULL; 9077c478bd9Sstevel@tonic-gate ASSERT(tree->avl_numnodes > 1); 9087c478bd9Sstevel@tonic-gate --tree->avl_numnodes; 9097c478bd9Sstevel@tonic-gate 9107c478bd9Sstevel@tonic-gate /* 9117c478bd9Sstevel@tonic-gate * If we just did a right child or there isn't one, go up to parent. 9127c478bd9Sstevel@tonic-gate */ 9137c478bd9Sstevel@tonic-gate if (child == 1 || parent->avl_child[1] == NULL) { 9147c478bd9Sstevel@tonic-gate node = parent; 9157c478bd9Sstevel@tonic-gate parent = AVL_XPARENT(parent); 9167c478bd9Sstevel@tonic-gate goto done; 9177c478bd9Sstevel@tonic-gate } 9187c478bd9Sstevel@tonic-gate 9197c478bd9Sstevel@tonic-gate /* 9207c478bd9Sstevel@tonic-gate * Do parent's right child, then leftmost descendent. 9217c478bd9Sstevel@tonic-gate */ 9227c478bd9Sstevel@tonic-gate node = parent->avl_child[1]; 9237c478bd9Sstevel@tonic-gate while (node->avl_child[0] != NULL) { 9247c478bd9Sstevel@tonic-gate parent = node; 9257c478bd9Sstevel@tonic-gate node = node->avl_child[0]; 9267c478bd9Sstevel@tonic-gate } 9277c478bd9Sstevel@tonic-gate 9287c478bd9Sstevel@tonic-gate /* 9297c478bd9Sstevel@tonic-gate * If here, we moved to a left child. It may have one 9307c478bd9Sstevel@tonic-gate * child on the right (when balance == +1). 9317c478bd9Sstevel@tonic-gate */ 9327c478bd9Sstevel@tonic-gate check_right_side: 9337c478bd9Sstevel@tonic-gate if (node->avl_child[1] != NULL) { 9347c478bd9Sstevel@tonic-gate ASSERT(AVL_XBALANCE(node) == 1); 9357c478bd9Sstevel@tonic-gate parent = node; 9367c478bd9Sstevel@tonic-gate node = node->avl_child[1]; 9377c478bd9Sstevel@tonic-gate ASSERT(node->avl_child[0] == NULL && 9387c478bd9Sstevel@tonic-gate node->avl_child[1] == NULL); 9397c478bd9Sstevel@tonic-gate } else { 9407c478bd9Sstevel@tonic-gate ASSERT(AVL_XBALANCE(node) <= 0); 9417c478bd9Sstevel@tonic-gate } 9427c478bd9Sstevel@tonic-gate 9437c478bd9Sstevel@tonic-gate done: 9447c478bd9Sstevel@tonic-gate if (parent == NULL) { 9457c478bd9Sstevel@tonic-gate *cookie = (void *)CHILDBIT; 9467c478bd9Sstevel@tonic-gate ASSERT(node == tree->avl_root); 9477c478bd9Sstevel@tonic-gate } else { 9487c478bd9Sstevel@tonic-gate *cookie = (void *)((uintptr_t)parent | AVL_XCHILD(node)); 9497c478bd9Sstevel@tonic-gate } 9507c478bd9Sstevel@tonic-gate 9517c478bd9Sstevel@tonic-gate return (AVL_NODE2DATA(node, off)); 9527c478bd9Sstevel@tonic-gate } 953