[018d957e] | 1 | /*
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| 2 | * Copyright (C) 2006 Jakub Jermar
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| 3 | * All rights reserved.
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| 4 | *
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| 5 | * Redistribution and use in source and binary forms, with or without
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| 6 | * modification, are permitted provided that the following conditions
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| 7 | * are met:
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| 8 | *
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| 9 | * - Redistributions of source code must retain the above copyright
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| 10 | * notice, this list of conditions and the following disclaimer.
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| 11 | * - Redistributions in binary form must reproduce the above copyright
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| 12 | * notice, this list of conditions and the following disclaimer in the
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| 13 | * documentation and/or other materials provided with the distribution.
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| 14 | * - The name of the author may not be used to endorse or promote products
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| 15 | * derived from this software without specific prior written permission.
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| 16 | *
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| 17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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| 18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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| 19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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| 20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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| 21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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| 22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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| 23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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| 24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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| 25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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| 26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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| 27 | */
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| 28 |
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[9179d0a] | 29 | /**
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| 30 | * @file btree.c
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| 31 | * @brief B+tree implementation.
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| 32 | *
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| 33 | * This file implements B+tree type and operations.
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| 34 | *
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| 35 | * The B+tree has the following properties:
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| 36 | * @li it is a ballanced 3-4-5 tree (i.e. BTREE_M = 5)
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| 37 | * @li values (i.e. pointers to values) are stored only in leaves
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| 38 | * @li leaves are linked in a list
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[018d957e] | 39 | *
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[c715e9b] | 40 | * Be carefull when using these trees. They need to allocate
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| 41 | * and deallocate memory for their index nodes and as such
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| 42 | * can sleep.
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[018d957e] | 43 | */
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| 44 |
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| 45 | #include <adt/btree.h>
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| 46 | #include <adt/list.h>
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| 47 | #include <mm/slab.h>
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| 48 | #include <debug.h>
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| 49 | #include <panic.h>
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| 50 | #include <typedefs.h>
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| 51 | #include <print.h>
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| 52 |
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[152b2b0] | 53 | static void btree_destroy_subtree(btree_node_t *root);
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[b7f364e] | 54 | static void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node);
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| 55 | static void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node);
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[018d957e] | 56 | static void node_initialize(btree_node_t *node);
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[b7f364e] | 57 | static void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree);
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| 58 | static void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);
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| 59 | static void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key);
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| 60 | static void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key);
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| 61 | static btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median);
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[5b04fc7] | 62 | static btree_node_t *node_combine(btree_node_t *node);
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[cc27ae48] | 63 | static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right);
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[0cb56f5d] | 64 | static void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx);
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| 65 | static void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx);
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[b7f364e] | 66 | static bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);
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| 67 | static bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);
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[0cb56f5d] | 68 | static bool try_rotation_from_left(btree_node_t *rnode);
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| 69 | static bool try_rotation_from_right(btree_node_t *lnode);
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[018d957e] | 70 |
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| 71 | #define ROOT_NODE(n) (!(n)->parent)
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| 72 | #define INDEX_NODE(n) ((n)->subtree[0] != NULL)
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| 73 | #define LEAF_NODE(n) ((n)->subtree[0] == NULL)
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| 74 |
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[296cc1b] | 75 | #define FILL_FACTOR ((BTREE_M-1)/2)
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| 76 |
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[018d957e] | 77 | #define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2)
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| 78 | #define MEDIAN_HIGH_INDEX(n) ((n)->keys/2)
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| 79 | #define MEDIAN_LOW(n) ((n)->key[MEDIAN_LOW_INDEX((n))]);
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| 80 | #define MEDIAN_HIGH(n) ((n)->key[MEDIAN_HIGH_INDEX((n))]);
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| 81 |
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[2810636] | 82 | static slab_cache_t *btree_node_slab;
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| 83 |
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| 84 | /** Initialize B-trees. */
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| 85 | void btree_init(void)
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| 86 | {
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| 87 | btree_node_slab = slab_cache_create("btree_node_slab", sizeof(btree_node_t), 0, NULL, NULL, SLAB_CACHE_MAGDEFERRED);
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| 88 | }
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| 89 |
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[018d957e] | 90 | /** Create empty B-tree.
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| 91 | *
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| 92 | * @param t B-tree.
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| 93 | */
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| 94 | void btree_create(btree_t *t)
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| 95 | {
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| 96 | list_initialize(&t->leaf_head);
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[2810636] | 97 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0);
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[018d957e] | 98 | node_initialize(t->root);
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| 99 | list_append(&t->root->leaf_link, &t->leaf_head);
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| 100 | }
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| 101 |
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| 102 | /** Destroy empty B-tree. */
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| 103 | void btree_destroy(btree_t *t)
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| 104 | {
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[152b2b0] | 105 | btree_destroy_subtree(t->root);
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[018d957e] | 106 | }
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| 107 |
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| 108 | /** Insert key-value pair into B-tree.
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| 109 | *
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| 110 | * @param t B-tree.
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| 111 | * @param key Key to be inserted.
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| 112 | * @param value Value to be inserted.
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| 113 | * @param leaf_node Leaf node where the insertion should begin.
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| 114 | */
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[b7f364e] | 115 | void btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *leaf_node)
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[018d957e] | 116 | {
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| 117 | btree_node_t *lnode;
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| 118 |
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| 119 | ASSERT(value);
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| 120 |
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| 121 | lnode = leaf_node;
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| 122 | if (!lnode) {
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| 123 | if (btree_search(t, key, &lnode)) {
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[cf85e24c] | 124 | panic("B-tree %p already contains key %d\n", t, key);
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[018d957e] | 125 | }
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| 126 | }
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| 127 |
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| 128 | _btree_insert(t, key, value, NULL, lnode);
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| 129 | }
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| 130 |
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[152b2b0] | 131 | /** Destroy subtree rooted in a node.
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| 132 | *
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| 133 | * @param root Root of the subtree.
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| 134 | */
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| 135 | void btree_destroy_subtree(btree_node_t *root)
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| 136 | {
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| 137 | int i;
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| 138 |
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| 139 | if (root->keys) {
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| 140 | for (i = 0; i < root->keys + 1; i++) {
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| 141 | if (root->subtree[i])
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| 142 | btree_destroy_subtree(root->subtree[i]);
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| 143 | }
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| 144 | }
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| 145 | slab_free(btree_node_slab, root);
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| 146 | }
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| 147 |
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[018d957e] | 148 | /** Recursively insert into B-tree.
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| 149 | *
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| 150 | * @param t B-tree.
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| 151 | * @param key Key to be inserted.
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| 152 | * @param value Value to be inserted.
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| 153 | * @param rsubtree Right subtree of the inserted key.
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| 154 | * @param node Start inserting into this node.
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| 155 | */
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[b7f364e] | 156 | void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node)
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[018d957e] | 157 | {
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| 158 | if (node->keys < BTREE_MAX_KEYS) {
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| 159 | /*
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| 160 | * Node conatins enough space, the key can be stored immediately.
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| 161 | */
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[0cb56f5d] | 162 | node_insert_key_and_rsubtree(node, key, value, rsubtree);
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| 163 | } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) {
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[cc27ae48] | 164 | /*
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| 165 | * The key-value-rsubtree triplet has been inserted because
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| 166 | * some keys could have been moved to the left sibling.
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| 167 | */
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[0cb56f5d] | 168 | } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) {
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[cc27ae48] | 169 | /*
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| 170 | * The key-value-rsubtree triplet has been inserted because
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| 171 | * some keys could have been moved to the right sibling.
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| 172 | */
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[018d957e] | 173 | } else {
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| 174 | btree_node_t *rnode;
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[b7f364e] | 175 | btree_key_t median;
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[018d957e] | 176 |
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| 177 | /*
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[cc27ae48] | 178 | * Node is full and both siblings (if both exist) are full too.
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| 179 | * Split the node and insert the smallest key from the node containing
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| 180 | * bigger keys (i.e. the new node) into its parent.
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[018d957e] | 181 | */
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| 182 |
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| 183 | rnode = node_split(node, key, value, rsubtree, &median);
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| 184 |
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| 185 | if (LEAF_NODE(node)) {
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[5b04fc7] | 186 | list_prepend(&rnode->leaf_link, &node->leaf_link);
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[018d957e] | 187 | }
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| 188 |
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| 189 | if (ROOT_NODE(node)) {
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| 190 | /*
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| 191 | * We split the root node. Create new root.
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| 192 | */
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[2810636] | 193 | t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0);
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[018d957e] | 194 | node->parent = t->root;
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| 195 | rnode->parent = t->root;
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| 196 | node_initialize(t->root);
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| 197 |
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| 198 | /*
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| 199 | * Left-hand side subtree will be the old root (i.e. node).
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| 200 | * Right-hand side subtree will be rnode.
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| 201 | */
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| 202 | t->root->subtree[0] = node;
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| 203 |
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| 204 | t->root->depth = node->depth + 1;
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| 205 | }
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| 206 | _btree_insert(t, median, NULL, rnode, node->parent);
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| 207 | }
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| 208 |
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| 209 | }
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| 210 |
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[296cc1b] | 211 | /** Remove B-tree node.
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| 212 | *
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| 213 | * @param B-tree.
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| 214 | * @param key Key to be removed from the B-tree along with its associated value.
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| 215 | * @param leaf_node If not NULL, pointer to the leaf node where the key is found.
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| 216 | */
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[b7f364e] | 217 | void btree_remove(btree_t *t, btree_key_t key, btree_node_t *leaf_node)
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[018d957e] | 218 | {
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[296cc1b] | 219 | btree_node_t *lnode;
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| 220 |
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| 221 | lnode = leaf_node;
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| 222 | if (!lnode) {
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| 223 | if (!btree_search(t, key, &lnode)) {
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[cf85e24c] | 224 | panic("B-tree %p does not contain key %d\n", t, key);
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[296cc1b] | 225 | }
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| 226 | }
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| 227 |
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[0cb56f5d] | 228 | _btree_remove(t, key, lnode);
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| 229 | }
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| 230 |
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| 231 | /** Recursively remove B-tree node.
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| 232 | *
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| 233 | * @param B-tree.
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| 234 | * @param key Key to be removed from the B-tree along with its associated value.
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| 235 | * @param node Node where the key being removed resides.
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| 236 | */
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[b7f364e] | 237 | void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node)
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[0cb56f5d] | 238 | {
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| 239 | if (ROOT_NODE(node)) {
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| 240 | if (node->keys == 1 && node->subtree[0]) {
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| 241 | /*
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| 242 | * Free the current root and set new root.
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| 243 | */
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| 244 | t->root = node->subtree[0];
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| 245 | t->root->parent = NULL;
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[2810636] | 246 | slab_free(btree_node_slab, node);
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[0cb56f5d] | 247 | } else {
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| 248 | /*
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| 249 | * Remove the key from the root node.
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| 250 | * Note that the right subtree is removed because when
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| 251 | * combining two nodes, the left-side sibling is preserved
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| 252 | * and the right-side sibling is freed.
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| 253 | */
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| 254 | node_remove_key_and_rsubtree(node, key);
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| 255 | }
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| 256 | return;
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| 257 | }
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| 258 |
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| 259 | if (node->keys <= FILL_FACTOR) {
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| 260 | /*
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| 261 | * If the node is below the fill factor,
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| 262 | * try to borrow keys from left or right sibling.
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| 263 | */
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| 264 | if (!try_rotation_from_left(node))
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| 265 | try_rotation_from_right(node);
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| 266 | }
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| 267 |
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| 268 | if (node->keys > FILL_FACTOR) {
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| 269 | int i;
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| 270 |
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| 271 | /*
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| 272 | * The key can be immediatelly removed.
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| 273 | *
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| 274 | * Note that the right subtree is removed because when
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| 275 | * combining two nodes, the left-side sibling is preserved
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| 276 | * and the right-side sibling is freed.
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| 277 | */
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| 278 | node_remove_key_and_rsubtree(node, key);
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| 279 | for (i = 0; i < node->parent->keys; i++) {
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| 280 | if (node->parent->key[i] == key)
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| 281 | node->parent->key[i] = node->key[0];
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| 282 | }
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| 283 |
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| 284 | } else {
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| 285 | index_t idx;
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| 286 | btree_node_t *rnode, *parent;
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[296cc1b] | 287 |
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[0cb56f5d] | 288 | /*
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| 289 | * The node is below the fill factor as well as its left and right sibling.
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| 290 | * Resort to combining the node with one of its siblings.
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| 291 | * The node which is on the left is preserved and the node on the right is
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| 292 | * freed.
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| 293 | */
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| 294 | parent = node->parent;
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| 295 | node_remove_key_and_rsubtree(node, key);
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| 296 | rnode = node_combine(node);
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| 297 | if (LEAF_NODE(rnode))
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| 298 | list_remove(&rnode->leaf_link);
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| 299 | idx = find_key_by_subtree(parent, rnode, true);
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| 300 | ASSERT((int) idx != -1);
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[2810636] | 301 | slab_free(btree_node_slab, rnode);
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[0cb56f5d] | 302 | _btree_remove(t, parent->key[idx], parent);
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| 303 | }
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[018d957e] | 304 | }
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| 305 |
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| 306 | /** Search key in a B-tree.
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| 307 | *
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| 308 | * @param t B-tree.
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| 309 | * @param key Key to be searched.
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| 310 | * @param leaf_node Address where to put pointer to visited leaf node.
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| 311 | *
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| 312 | * @return Pointer to value or NULL if there is no such key.
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| 313 | */
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[b7f364e] | 314 | void *btree_search(btree_t *t, btree_key_t key, btree_node_t **leaf_node)
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[018d957e] | 315 | {
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| 316 | btree_node_t *cur, *next;
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| 317 |
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| 318 | /*
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[c715e9b] | 319 | * Iteratively descend to the leaf that can contain the searched key.
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[018d957e] | 320 | */
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| 321 | for (cur = t->root; cur; cur = next) {
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[c715e9b] | 322 |
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[018d957e] | 323 | /* Last iteration will set this with proper leaf node address. */
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| 324 | *leaf_node = cur;
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[c715e9b] | 325 |
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| 326 | /*
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| 327 | * The key can be in the leftmost subtree.
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| 328 | * Test it separately.
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| 329 | */
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| 330 | if (key < cur->key[0]) {
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| 331 | next = cur->subtree[0];
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| 332 | continue;
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| 333 | } else {
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| 334 | void *val;
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| 335 | int i;
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| 336 |
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| 337 | /*
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| 338 | * Now if the key is smaller than cur->key[i]
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| 339 | * it can only mean that the value is in cur->subtree[i]
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| 340 | * or it is not in the tree at all.
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| 341 | */
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| 342 | for (i = 1; i < cur->keys; i++) {
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| 343 | if (key < cur->key[i]) {
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| 344 | next = cur->subtree[i];
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| 345 | val = cur->value[i - 1];
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| 346 |
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| 347 | if (LEAF_NODE(cur))
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| 348 | return key == cur->key[i - 1] ? val : NULL;
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| 349 |
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| 350 | goto descend;
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| 351 | }
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[018d957e] | 352 | }
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[c715e9b] | 353 |
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| 354 | /*
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| 355 | * Last possibility is that the key is in the rightmost subtree.
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| 356 | */
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| 357 | next = cur->subtree[i];
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| 358 | val = cur->value[i - 1];
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| 359 | if (LEAF_NODE(cur))
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| 360 | return key == cur->key[i - 1] ? val : NULL;
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[018d957e] | 361 | }
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[c715e9b] | 362 | descend:
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| 363 | ;
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[018d957e] | 364 | }
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| 365 |
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| 366 | /*
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[c715e9b] | 367 | * The key was not found in the *leaf_node and is smaller than any of its keys.
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[018d957e] | 368 | */
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| 369 | return NULL;
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| 370 | }
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| 371 |
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[c47912f] | 372 | /** Return pointer to B-tree leaf node's left neighbour.
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[252127e] | 373 | *
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| 374 | * @param t B-tree.
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[c47912f] | 375 | * @param node Node whose left neighbour will be returned.
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[252127e] | 376 | *
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[c47912f] | 377 | * @return Left neighbour of the node or NULL if the node does not have the left neighbour.
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[252127e] | 378 | */
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[c47912f] | 379 | btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node)
|
---|
[252127e] | 380 | {
|
---|
| 381 | ASSERT(LEAF_NODE(node));
|
---|
| 382 | if (node->leaf_link.prev != &t->leaf_head)
|
---|
| 383 | return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link);
|
---|
| 384 | else
|
---|
| 385 | return NULL;
|
---|
| 386 | }
|
---|
| 387 |
|
---|
[c47912f] | 388 | /** Return pointer to B-tree leaf node's right neighbour.
|
---|
[252127e] | 389 | *
|
---|
| 390 | * @param t B-tree.
|
---|
[c47912f] | 391 | * @param node Node whose right neighbour will be returned.
|
---|
[252127e] | 392 | *
|
---|
[c47912f] | 393 | * @return Right neighbour of the node or NULL if the node does not have the right neighbour.
|
---|
[252127e] | 394 | */
|
---|
[c47912f] | 395 | btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node)
|
---|
[252127e] | 396 | {
|
---|
| 397 | ASSERT(LEAF_NODE(node));
|
---|
| 398 | if (node->leaf_link.next != &t->leaf_head)
|
---|
| 399 | return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link);
|
---|
| 400 | else
|
---|
| 401 | return NULL;
|
---|
| 402 | }
|
---|
| 403 |
|
---|
[018d957e] | 404 | /** Initialize B-tree node.
|
---|
| 405 | *
|
---|
| 406 | * @param node B-tree node.
|
---|
| 407 | */
|
---|
| 408 | void node_initialize(btree_node_t *node)
|
---|
| 409 | {
|
---|
| 410 | int i;
|
---|
| 411 |
|
---|
| 412 | node->keys = 0;
|
---|
| 413 |
|
---|
| 414 | /* Clean also space for the extra key. */
|
---|
| 415 | for (i = 0; i < BTREE_MAX_KEYS + 1; i++) {
|
---|
| 416 | node->key[i] = 0;
|
---|
| 417 | node->value[i] = NULL;
|
---|
| 418 | node->subtree[i] = NULL;
|
---|
| 419 | }
|
---|
| 420 | node->subtree[i] = NULL;
|
---|
| 421 |
|
---|
| 422 | node->parent = NULL;
|
---|
| 423 |
|
---|
| 424 | link_initialize(&node->leaf_link);
|
---|
| 425 |
|
---|
| 426 | link_initialize(&node->bfs_link);
|
---|
| 427 | node->depth = 0;
|
---|
| 428 | }
|
---|
| 429 |
|
---|
[cc27ae48] | 430 | /** Insert key-value-lsubtree triplet into B-tree node.
|
---|
| 431 | *
|
---|
| 432 | * It is actually possible to have more keys than BTREE_MAX_KEYS.
|
---|
| 433 | * This feature is used during insert by right rotation.
|
---|
| 434 | *
|
---|
| 435 | * @param node B-tree node into wich the new key is to be inserted.
|
---|
| 436 | * @param key The key to be inserted.
|
---|
| 437 | * @param value Pointer to value to be inserted.
|
---|
| 438 | * @param lsubtree Pointer to the left subtree.
|
---|
| 439 | */
|
---|
[b7f364e] | 440 | void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree)
|
---|
[cc27ae48] | 441 | {
|
---|
| 442 | int i;
|
---|
| 443 |
|
---|
| 444 | for (i = 0; i < node->keys; i++) {
|
---|
| 445 | if (key < node->key[i]) {
|
---|
| 446 | int j;
|
---|
| 447 |
|
---|
| 448 | for (j = node->keys; j > i; j--) {
|
---|
| 449 | node->key[j] = node->key[j - 1];
|
---|
| 450 | node->value[j] = node->value[j - 1];
|
---|
| 451 | node->subtree[j + 1] = node->subtree[j];
|
---|
| 452 | }
|
---|
| 453 | node->subtree[j + 1] = node->subtree[j];
|
---|
| 454 | break;
|
---|
| 455 | }
|
---|
| 456 | }
|
---|
| 457 | node->key[i] = key;
|
---|
| 458 | node->value[i] = value;
|
---|
| 459 | node->subtree[i] = lsubtree;
|
---|
| 460 |
|
---|
| 461 | node->keys++;
|
---|
| 462 | }
|
---|
| 463 |
|
---|
| 464 | /** Insert key-value-rsubtree triplet into B-tree node.
|
---|
[018d957e] | 465 | *
|
---|
| 466 | * It is actually possible to have more keys than BTREE_MAX_KEYS.
|
---|
| 467 | * This feature is used during splitting the node when the
|
---|
[cc27ae48] | 468 | * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation
|
---|
| 469 | * also makes use of this feature.
|
---|
[018d957e] | 470 | *
|
---|
| 471 | * @param node B-tree node into wich the new key is to be inserted.
|
---|
| 472 | * @param key The key to be inserted.
|
---|
| 473 | * @param value Pointer to value to be inserted.
|
---|
| 474 | * @param rsubtree Pointer to the right subtree.
|
---|
| 475 | */
|
---|
[b7f364e] | 476 | void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree)
|
---|
[018d957e] | 477 | {
|
---|
| 478 | int i;
|
---|
| 479 |
|
---|
| 480 | for (i = 0; i < node->keys; i++) {
|
---|
| 481 | if (key < node->key[i]) {
|
---|
| 482 | int j;
|
---|
| 483 |
|
---|
| 484 | for (j = node->keys; j > i; j--) {
|
---|
| 485 | node->key[j] = node->key[j - 1];
|
---|
| 486 | node->value[j] = node->value[j - 1];
|
---|
| 487 | node->subtree[j + 1] = node->subtree[j];
|
---|
| 488 | }
|
---|
| 489 | break;
|
---|
| 490 | }
|
---|
| 491 | }
|
---|
| 492 | node->key[i] = key;
|
---|
| 493 | node->value[i] = value;
|
---|
| 494 | node->subtree[i + 1] = rsubtree;
|
---|
| 495 |
|
---|
| 496 | node->keys++;
|
---|
| 497 | }
|
---|
| 498 |
|
---|
[5b04fc7] | 499 | /** Remove key and its left subtree pointer from B-tree node.
|
---|
| 500 | *
|
---|
| 501 | * Remove the key and eliminate gaps in node->key array.
|
---|
| 502 | * Note that the value pointer and the left subtree pointer
|
---|
| 503 | * is removed from the node as well.
|
---|
| 504 | *
|
---|
| 505 | * @param node B-tree node.
|
---|
| 506 | * @param key Key to be removed.
|
---|
| 507 | */
|
---|
[b7f364e] | 508 | void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key)
|
---|
[5b04fc7] | 509 | {
|
---|
| 510 | int i, j;
|
---|
| 511 |
|
---|
| 512 | for (i = 0; i < node->keys; i++) {
|
---|
| 513 | if (key == node->key[i]) {
|
---|
| 514 | for (j = i + 1; j < node->keys; j++) {
|
---|
| 515 | node->key[j - 1] = node->key[j];
|
---|
| 516 | node->value[j - 1] = node->value[j];
|
---|
| 517 | node->subtree[j - 1] = node->subtree[j];
|
---|
| 518 | }
|
---|
| 519 | node->subtree[j - 1] = node->subtree[j];
|
---|
| 520 | node->keys--;
|
---|
| 521 | return;
|
---|
| 522 | }
|
---|
| 523 | }
|
---|
[cf85e24c] | 524 | panic("node %p does not contain key %d\n", node, key);
|
---|
[5b04fc7] | 525 | }
|
---|
| 526 |
|
---|
| 527 | /** Remove key and its right subtree pointer from B-tree node.
|
---|
| 528 | *
|
---|
| 529 | * Remove the key and eliminate gaps in node->key array.
|
---|
| 530 | * Note that the value pointer and the right subtree pointer
|
---|
| 531 | * is removed from the node as well.
|
---|
| 532 | *
|
---|
| 533 | * @param node B-tree node.
|
---|
| 534 | * @param key Key to be removed.
|
---|
| 535 | */
|
---|
[b7f364e] | 536 | void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key)
|
---|
[5b04fc7] | 537 | {
|
---|
| 538 | int i, j;
|
---|
| 539 |
|
---|
| 540 | for (i = 0; i < node->keys; i++) {
|
---|
| 541 | if (key == node->key[i]) {
|
---|
| 542 | for (j = i + 1; j < node->keys; j++) {
|
---|
| 543 | node->key[j - 1] = node->key[j];
|
---|
| 544 | node->value[j - 1] = node->value[j];
|
---|
| 545 | node->subtree[j] = node->subtree[j + 1];
|
---|
| 546 | }
|
---|
| 547 | node->keys--;
|
---|
| 548 | return;
|
---|
| 549 | }
|
---|
| 550 | }
|
---|
[cf85e24c] | 551 | panic("node %p does not contain key %d\n", node, key);
|
---|
[5b04fc7] | 552 | }
|
---|
| 553 |
|
---|
[c715e9b] | 554 | /** Split full B-tree node and insert new key-value-right-subtree triplet.
|
---|
[018d957e] | 555 | *
|
---|
| 556 | * This function will split a node and return pointer to a newly created
|
---|
[c715e9b] | 557 | * node containing keys greater than or equal to the greater of medians
|
---|
| 558 | * (or median) of the old keys and the newly added key. It will also write
|
---|
| 559 | * the median key to a memory address supplied by the caller.
|
---|
[018d957e] | 560 | *
|
---|
[c715e9b] | 561 | * If the node being split is an index node, the median will not be
|
---|
| 562 | * included in the new node. If the node is a leaf node,
|
---|
| 563 | * the median will be copied there.
|
---|
[018d957e] | 564 | *
|
---|
| 565 | * @param node B-tree node wich is going to be split.
|
---|
| 566 | * @param key The key to be inserted.
|
---|
| 567 | * @param value Pointer to the value to be inserted.
|
---|
| 568 | * @param rsubtree Pointer to the right subtree of the key being added.
|
---|
| 569 | * @param median Address in memory, where the median key will be stored.
|
---|
| 570 | *
|
---|
| 571 | * @return Newly created right sibling of node.
|
---|
| 572 | */
|
---|
[b7f364e] | 573 | btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median)
|
---|
[018d957e] | 574 | {
|
---|
| 575 | btree_node_t *rnode;
|
---|
| 576 | int i, j;
|
---|
| 577 |
|
---|
| 578 | ASSERT(median);
|
---|
| 579 | ASSERT(node->keys == BTREE_MAX_KEYS);
|
---|
[cc27ae48] | 580 |
|
---|
[018d957e] | 581 | /*
|
---|
| 582 | * Use the extra space to store the extra node.
|
---|
| 583 | */
|
---|
[0cb56f5d] | 584 | node_insert_key_and_rsubtree(node, key, value, rsubtree);
|
---|
[018d957e] | 585 |
|
---|
| 586 | /*
|
---|
| 587 | * Compute median of keys.
|
---|
| 588 | */
|
---|
[c715e9b] | 589 | *median = MEDIAN_HIGH(node);
|
---|
[018d957e] | 590 |
|
---|
[c715e9b] | 591 | /*
|
---|
| 592 | * Allocate and initialize new right sibling.
|
---|
| 593 | */
|
---|
[2810636] | 594 | rnode = (btree_node_t *) slab_alloc(btree_node_slab, 0);
|
---|
[018d957e] | 595 | node_initialize(rnode);
|
---|
| 596 | rnode->parent = node->parent;
|
---|
| 597 | rnode->depth = node->depth;
|
---|
| 598 |
|
---|
| 599 | /*
|
---|
| 600 | * Copy big keys, values and subtree pointers to the new right sibling.
|
---|
[c715e9b] | 601 | * If this is an index node, do not copy the median.
|
---|
[018d957e] | 602 | */
|
---|
[c715e9b] | 603 | i = (int) INDEX_NODE(node);
|
---|
| 604 | for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) {
|
---|
[018d957e] | 605 | rnode->key[j] = node->key[i];
|
---|
| 606 | rnode->value[j] = node->value[i];
|
---|
| 607 | rnode->subtree[j] = node->subtree[i];
|
---|
| 608 |
|
---|
| 609 | /*
|
---|
| 610 | * Fix parent links in subtrees.
|
---|
| 611 | */
|
---|
| 612 | if (rnode->subtree[j])
|
---|
| 613 | rnode->subtree[j]->parent = rnode;
|
---|
| 614 |
|
---|
| 615 | }
|
---|
| 616 | rnode->subtree[j] = node->subtree[i];
|
---|
| 617 | if (rnode->subtree[j])
|
---|
| 618 | rnode->subtree[j]->parent = rnode;
|
---|
[c715e9b] | 619 |
|
---|
| 620 | rnode->keys = j; /* Set number of keys of the new node. */
|
---|
| 621 | node->keys /= 2; /* Shrink the old node. */
|
---|
[018d957e] | 622 |
|
---|
| 623 | return rnode;
|
---|
| 624 | }
|
---|
| 625 |
|
---|
[0cb56f5d] | 626 | /** Combine node with any of its siblings.
|
---|
| 627 | *
|
---|
| 628 | * The siblings are required to be below the fill factor.
|
---|
| 629 | *
|
---|
| 630 | * @param node Node to combine with one of its siblings.
|
---|
| 631 | *
|
---|
| 632 | * @return Pointer to the rightmost of the two nodes.
|
---|
| 633 | */
|
---|
| 634 | btree_node_t *node_combine(btree_node_t *node)
|
---|
| 635 | {
|
---|
| 636 | index_t idx;
|
---|
| 637 | btree_node_t *rnode;
|
---|
| 638 | int i;
|
---|
| 639 |
|
---|
| 640 | ASSERT(!ROOT_NODE(node));
|
---|
| 641 |
|
---|
| 642 | idx = find_key_by_subtree(node->parent, node, false);
|
---|
| 643 | if (idx == node->parent->keys) {
|
---|
| 644 | /*
|
---|
| 645 | * Rightmost subtree of its parent, combine with the left sibling.
|
---|
| 646 | */
|
---|
| 647 | idx--;
|
---|
| 648 | rnode = node;
|
---|
| 649 | node = node->parent->subtree[idx];
|
---|
| 650 | } else {
|
---|
| 651 | rnode = node->parent->subtree[idx + 1];
|
---|
| 652 | }
|
---|
| 653 |
|
---|
| 654 | /* Index nodes need to insert parent node key in between left and right node. */
|
---|
| 655 | if (INDEX_NODE(node))
|
---|
| 656 | node->key[node->keys++] = node->parent->key[idx];
|
---|
| 657 |
|
---|
| 658 | /* Copy the key-value-subtree triplets from the right node. */
|
---|
| 659 | for (i = 0; i < rnode->keys; i++) {
|
---|
| 660 | node->key[node->keys + i] = rnode->key[i];
|
---|
| 661 | node->value[node->keys + i] = rnode->value[i];
|
---|
| 662 | if (INDEX_NODE(node)) {
|
---|
| 663 | node->subtree[node->keys + i] = rnode->subtree[i];
|
---|
| 664 | rnode->subtree[i]->parent = node;
|
---|
| 665 | }
|
---|
| 666 | }
|
---|
| 667 | if (INDEX_NODE(node)) {
|
---|
| 668 | node->subtree[node->keys + i] = rnode->subtree[i];
|
---|
| 669 | rnode->subtree[i]->parent = node;
|
---|
| 670 | }
|
---|
| 671 |
|
---|
| 672 | node->keys += rnode->keys;
|
---|
| 673 |
|
---|
| 674 | return rnode;
|
---|
| 675 | }
|
---|
| 676 |
|
---|
[cc27ae48] | 677 | /** Find key by its left or right subtree.
|
---|
| 678 | *
|
---|
| 679 | * @param node B-tree node.
|
---|
| 680 | * @param subtree Left or right subtree of a key found in node.
|
---|
| 681 | * @param right If true, subtree is a right subtree. If false, subtree is a left subtree.
|
---|
| 682 | *
|
---|
| 683 | * @return Index of the key associated with the subtree.
|
---|
| 684 | */
|
---|
| 685 | index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right)
|
---|
[c715e9b] | 686 | {
|
---|
[cc27ae48] | 687 | int i;
|
---|
| 688 |
|
---|
| 689 | for (i = 0; i < node->keys + 1; i++) {
|
---|
| 690 | if (subtree == node->subtree[i])
|
---|
| 691 | return i - (int) (right != false);
|
---|
| 692 | }
|
---|
[cf85e24c] | 693 | panic("node %p does not contain subtree %p\n", node, subtree);
|
---|
[cc27ae48] | 694 | }
|
---|
| 695 |
|
---|
[0cb56f5d] | 696 | /** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling.
|
---|
| 697 | *
|
---|
| 698 | * The biggest key and its value and right subtree is rotated from the left node
|
---|
| 699 | * to the right. If the node is an index node, than the parent node key belonging to
|
---|
| 700 | * the left node takes part in the rotation.
|
---|
| 701 | *
|
---|
| 702 | * @param lnode Left sibling.
|
---|
| 703 | * @param rnode Right sibling.
|
---|
| 704 | * @param idx Index of the parent node key that is taking part in the rotation.
|
---|
| 705 | */
|
---|
| 706 | void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx)
|
---|
| 707 | {
|
---|
[b7f364e] | 708 | btree_key_t key;
|
---|
[0cb56f5d] | 709 |
|
---|
| 710 | key = lnode->key[lnode->keys - 1];
|
---|
| 711 |
|
---|
| 712 | if (LEAF_NODE(lnode)) {
|
---|
| 713 | void *value;
|
---|
| 714 |
|
---|
| 715 | value = lnode->value[lnode->keys - 1];
|
---|
| 716 | node_remove_key_and_rsubtree(lnode, key);
|
---|
| 717 | node_insert_key_and_lsubtree(rnode, key, value, NULL);
|
---|
| 718 | lnode->parent->key[idx] = key;
|
---|
| 719 | } else {
|
---|
| 720 | btree_node_t *rsubtree;
|
---|
| 721 |
|
---|
| 722 | rsubtree = lnode->subtree[lnode->keys];
|
---|
| 723 | node_remove_key_and_rsubtree(lnode, key);
|
---|
| 724 | node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree);
|
---|
| 725 | lnode->parent->key[idx] = key;
|
---|
| 726 |
|
---|
| 727 | /* Fix parent link of the reconnected right subtree. */
|
---|
| 728 | rsubtree->parent = rnode;
|
---|
| 729 | }
|
---|
| 730 |
|
---|
| 731 | }
|
---|
| 732 |
|
---|
| 733 | /** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling.
|
---|
| 734 | *
|
---|
| 735 | * The smallest key and its value and left subtree is rotated from the right node
|
---|
| 736 | * to the left. If the node is an index node, than the parent node key belonging to
|
---|
| 737 | * the right node takes part in the rotation.
|
---|
| 738 | *
|
---|
| 739 | * @param lnode Left sibling.
|
---|
| 740 | * @param rnode Right sibling.
|
---|
| 741 | * @param idx Index of the parent node key that is taking part in the rotation.
|
---|
| 742 | */
|
---|
| 743 | void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx)
|
---|
| 744 | {
|
---|
[b7f364e] | 745 | btree_key_t key;
|
---|
[0cb56f5d] | 746 |
|
---|
| 747 | key = rnode->key[0];
|
---|
| 748 |
|
---|
| 749 | if (LEAF_NODE(rnode)) {
|
---|
| 750 | void *value;
|
---|
| 751 |
|
---|
| 752 | value = rnode->value[0];
|
---|
| 753 | node_remove_key_and_lsubtree(rnode, key);
|
---|
| 754 | node_insert_key_and_rsubtree(lnode, key, value, NULL);
|
---|
| 755 | rnode->parent->key[idx] = rnode->key[0];
|
---|
| 756 | } else {
|
---|
| 757 | btree_node_t *lsubtree;
|
---|
| 758 |
|
---|
| 759 | lsubtree = rnode->subtree[0];
|
---|
| 760 | node_remove_key_and_lsubtree(rnode, key);
|
---|
| 761 | node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree);
|
---|
| 762 | rnode->parent->key[idx] = key;
|
---|
| 763 |
|
---|
| 764 | /* Fix parent link of the reconnected left subtree. */
|
---|
| 765 | lsubtree->parent = lnode;
|
---|
| 766 | }
|
---|
| 767 |
|
---|
| 768 | }
|
---|
| 769 |
|
---|
[cc27ae48] | 770 | /** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done.
|
---|
| 771 | *
|
---|
| 772 | * Left sibling of the node (if it exists) is checked for free space.
|
---|
| 773 | * If there is free space, the key is inserted and the smallest key of
|
---|
| 774 | * the node is moved there. The index node which is the parent of both
|
---|
| 775 | * nodes is fixed.
|
---|
| 776 | *
|
---|
| 777 | * @param node B-tree node.
|
---|
| 778 | * @param inskey Key to be inserted.
|
---|
| 779 | * @param insvalue Value to be inserted.
|
---|
| 780 | * @param rsubtree Right subtree of inskey.
|
---|
| 781 | *
|
---|
| 782 | * @return True if the rotation was performed, false otherwise.
|
---|
| 783 | */
|
---|
[b7f364e] | 784 | bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree)
|
---|
[cc27ae48] | 785 | {
|
---|
| 786 | index_t idx;
|
---|
| 787 | btree_node_t *lnode;
|
---|
| 788 |
|
---|
| 789 | /*
|
---|
| 790 | * If this is root node, the rotation can not be done.
|
---|
| 791 | */
|
---|
| 792 | if (ROOT_NODE(node))
|
---|
| 793 | return false;
|
---|
| 794 |
|
---|
| 795 | idx = find_key_by_subtree(node->parent, node, true);
|
---|
| 796 | if ((int) idx == -1) {
|
---|
| 797 | /*
|
---|
| 798 | * If this node is the leftmost subtree of its parent,
|
---|
| 799 | * the rotation can not be done.
|
---|
| 800 | */
|
---|
| 801 | return false;
|
---|
| 802 | }
|
---|
| 803 |
|
---|
| 804 | lnode = node->parent->subtree[idx];
|
---|
| 805 | if (lnode->keys < BTREE_MAX_KEYS) {
|
---|
| 806 | /*
|
---|
| 807 | * The rotaion can be done. The left sibling has free space.
|
---|
| 808 | */
|
---|
[0cb56f5d] | 809 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree);
|
---|
| 810 | rotate_from_right(lnode, node, idx);
|
---|
[cc27ae48] | 811 | return true;
|
---|
| 812 | }
|
---|
| 813 |
|
---|
| 814 | return false;
|
---|
| 815 | }
|
---|
| 816 |
|
---|
| 817 | /** Insert key-value-rsubtree triplet and rotate the node to the right, if this operation can be done.
|
---|
| 818 | *
|
---|
| 819 | * Right sibling of the node (if it exists) is checked for free space.
|
---|
| 820 | * If there is free space, the key is inserted and the biggest key of
|
---|
| 821 | * the node is moved there. The index node which is the parent of both
|
---|
| 822 | * nodes is fixed.
|
---|
| 823 | *
|
---|
| 824 | * @param node B-tree node.
|
---|
| 825 | * @param inskey Key to be inserted.
|
---|
| 826 | * @param insvalue Value to be inserted.
|
---|
| 827 | * @param rsubtree Right subtree of inskey.
|
---|
| 828 | *
|
---|
| 829 | * @return True if the rotation was performed, false otherwise.
|
---|
| 830 | */
|
---|
[b7f364e] | 831 | bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree)
|
---|
[cc27ae48] | 832 | {
|
---|
| 833 | index_t idx;
|
---|
| 834 | btree_node_t *rnode;
|
---|
| 835 |
|
---|
| 836 | /*
|
---|
| 837 | * If this is root node, the rotation can not be done.
|
---|
| 838 | */
|
---|
| 839 | if (ROOT_NODE(node))
|
---|
| 840 | return false;
|
---|
| 841 |
|
---|
| 842 | idx = find_key_by_subtree(node->parent, node, false);
|
---|
| 843 | if (idx == node->parent->keys) {
|
---|
| 844 | /*
|
---|
| 845 | * If this node is the rightmost subtree of its parent,
|
---|
| 846 | * the rotation can not be done.
|
---|
| 847 | */
|
---|
| 848 | return false;
|
---|
| 849 | }
|
---|
| 850 |
|
---|
| 851 | rnode = node->parent->subtree[idx + 1];
|
---|
| 852 | if (rnode->keys < BTREE_MAX_KEYS) {
|
---|
| 853 | /*
|
---|
| 854 | * The rotaion can be done. The right sibling has free space.
|
---|
| 855 | */
|
---|
[0cb56f5d] | 856 | node_insert_key_and_rsubtree(node, inskey, insvalue, rsubtree);
|
---|
| 857 | rotate_from_left(node, rnode, idx);
|
---|
| 858 | return true;
|
---|
| 859 | }
|
---|
[cc27ae48] | 860 |
|
---|
[0cb56f5d] | 861 | return false;
|
---|
| 862 | }
|
---|
[cc27ae48] | 863 |
|
---|
[0cb56f5d] | 864 | /** Rotate in a key from the left sibling or from the index node, if this operation can be done.
|
---|
| 865 | *
|
---|
| 866 | * @param rnode Node into which to add key from its left sibling or from the index node.
|
---|
| 867 | *
|
---|
| 868 | * @return True if the rotation was performed, false otherwise.
|
---|
| 869 | */
|
---|
| 870 | bool try_rotation_from_left(btree_node_t *rnode)
|
---|
| 871 | {
|
---|
| 872 | index_t idx;
|
---|
| 873 | btree_node_t *lnode;
|
---|
[cc27ae48] | 874 |
|
---|
[0cb56f5d] | 875 | /*
|
---|
| 876 | * If this is root node, the rotation can not be done.
|
---|
| 877 | */
|
---|
| 878 | if (ROOT_NODE(rnode))
|
---|
| 879 | return false;
|
---|
| 880 |
|
---|
| 881 | idx = find_key_by_subtree(rnode->parent, rnode, true);
|
---|
| 882 | if ((int) idx == -1) {
|
---|
| 883 | /*
|
---|
| 884 | * If this node is the leftmost subtree of its parent,
|
---|
| 885 | * the rotation can not be done.
|
---|
| 886 | */
|
---|
| 887 | return false;
|
---|
| 888 | }
|
---|
| 889 |
|
---|
| 890 | lnode = rnode->parent->subtree[idx];
|
---|
| 891 | if (lnode->keys > FILL_FACTOR) {
|
---|
| 892 | rotate_from_left(lnode, rnode, idx);
|
---|
[cc27ae48] | 893 | return true;
|
---|
| 894 | }
|
---|
[0cb56f5d] | 895 |
|
---|
| 896 | return false;
|
---|
| 897 | }
|
---|
| 898 |
|
---|
| 899 | /** Rotate in a key from the right sibling or from the index node, if this operation can be done.
|
---|
| 900 | *
|
---|
| 901 | * @param rnode Node into which to add key from its right sibling or from the index node.
|
---|
| 902 | *
|
---|
| 903 | * @return True if the rotation was performed, false otherwise.
|
---|
| 904 | */
|
---|
| 905 | bool try_rotation_from_right(btree_node_t *lnode)
|
---|
| 906 | {
|
---|
| 907 | index_t idx;
|
---|
| 908 | btree_node_t *rnode;
|
---|
| 909 |
|
---|
| 910 | /*
|
---|
| 911 | * If this is root node, the rotation can not be done.
|
---|
| 912 | */
|
---|
| 913 | if (ROOT_NODE(lnode))
|
---|
| 914 | return false;
|
---|
| 915 |
|
---|
| 916 | idx = find_key_by_subtree(lnode->parent, lnode, false);
|
---|
| 917 | if (idx == lnode->parent->keys) {
|
---|
| 918 | /*
|
---|
| 919 | * If this node is the rightmost subtree of its parent,
|
---|
| 920 | * the rotation can not be done.
|
---|
| 921 | */
|
---|
| 922 | return false;
|
---|
| 923 | }
|
---|
| 924 |
|
---|
| 925 | rnode = lnode->parent->subtree[idx + 1];
|
---|
| 926 | if (rnode->keys > FILL_FACTOR) {
|
---|
| 927 | rotate_from_right(lnode, rnode, idx);
|
---|
| 928 | return true;
|
---|
| 929 | }
|
---|
[cc27ae48] | 930 |
|
---|
| 931 | return false;
|
---|
[c715e9b] | 932 | }
|
---|
| 933 |
|
---|
[018d957e] | 934 | /** Print B-tree.
|
---|
| 935 | *
|
---|
| 936 | * @param t Print out B-tree.
|
---|
| 937 | */
|
---|
| 938 | void btree_print(btree_t *t)
|
---|
| 939 | {
|
---|
| 940 | int i, depth = t->root->depth;
|
---|
[5b04fc7] | 941 | link_t head, *cur;
|
---|
| 942 |
|
---|
| 943 | printf("Printing B-tree:\n");
|
---|
[018d957e] | 944 | list_initialize(&head);
|
---|
| 945 | list_append(&t->root->bfs_link, &head);
|
---|
| 946 |
|
---|
| 947 | /*
|
---|
| 948 | * Use BFS search to print out the tree.
|
---|
| 949 | * Levels are distinguished from one another by node->depth.
|
---|
| 950 | */
|
---|
| 951 | while (!list_empty(&head)) {
|
---|
| 952 | link_t *hlp;
|
---|
| 953 | btree_node_t *node;
|
---|
| 954 |
|
---|
| 955 | hlp = head.next;
|
---|
| 956 | ASSERT(hlp != &head);
|
---|
| 957 | node = list_get_instance(hlp, btree_node_t, bfs_link);
|
---|
| 958 | list_remove(hlp);
|
---|
| 959 |
|
---|
| 960 | ASSERT(node);
|
---|
| 961 |
|
---|
| 962 | if (node->depth != depth) {
|
---|
| 963 | printf("\n");
|
---|
| 964 | depth = node->depth;
|
---|
| 965 | }
|
---|
| 966 |
|
---|
| 967 | printf("(");
|
---|
| 968 | for (i = 0; i < node->keys; i++) {
|
---|
[280a27e] | 969 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : "");
|
---|
[018d957e] | 970 | if (node->depth && node->subtree[i]) {
|
---|
| 971 | list_append(&node->subtree[i]->bfs_link, &head);
|
---|
| 972 | }
|
---|
| 973 | }
|
---|
| 974 | if (node->depth && node->subtree[i]) {
|
---|
| 975 | list_append(&node->subtree[i]->bfs_link, &head);
|
---|
| 976 | }
|
---|
| 977 | printf(")");
|
---|
| 978 | }
|
---|
| 979 | printf("\n");
|
---|
[5b04fc7] | 980 |
|
---|
| 981 | printf("Printing list of leaves:\n");
|
---|
| 982 | for (cur = t->leaf_head.next; cur != &t->leaf_head; cur = cur->next) {
|
---|
| 983 | btree_node_t *node;
|
---|
| 984 |
|
---|
| 985 | node = list_get_instance(cur, btree_node_t, leaf_link);
|
---|
| 986 |
|
---|
| 987 | ASSERT(node);
|
---|
| 988 |
|
---|
| 989 | printf("(");
|
---|
| 990 | for (i = 0; i < node->keys; i++)
|
---|
[280a27e] | 991 | printf("%lld%s", node->key[i], i < node->keys - 1 ? "," : "");
|
---|
[5b04fc7] | 992 | printf(")");
|
---|
| 993 | }
|
---|
| 994 | printf("\n");
|
---|
[018d957e] | 995 | }
|
---|