Subversion Repositories HelenOS-historic

/*

 * Copyright (C) 2006 Jakub Jermar

 * All rights reserved.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 *

 * - Redistributions of source code must retain the above copyright

 *   notice, this list of conditions and the following disclaimer.

 * - Redistributions in binary form must reproduce the above copyright

 *   notice, this list of conditions and the following disclaimer in the

 *   documentation and/or other materials provided with the distribution.

 * - The name of the author may not be used to endorse or promote products

 *   derived from this software without specific prior written permission.

 *

 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR

 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES

 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.

 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,

 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT

 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,

 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY

 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT

 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF

 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 */

/**

 * @file    btree.c

 * @brief   B+tree implementation.

 *

 * This file implements B+tree type and operations.

 *

 * The B+tree has the following properties:

 * @li it is a ballanced 3-4-5 tree (i.e. BTREE_M = 5)

 * @li values (i.e. pointers to values) are stored only in leaves

 * @li leaves are linked in a list

 *

 * Be carefull when using these trees. They need to allocate

 * and deallocate memory for their index nodes and as such

 * can sleep.

 */

#include <adt/btree.h>

#include <adt/list.h>

#include <mm/slab.h>

#include <debug.h>

#include <panic.h>

#include <typedefs.h>

#include <print.h>

static void btree_destroy_subtree(btree_node_t *root);

static void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node);

static void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node);

static void node_initialize(btree_node_t *node);

static void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree);

static void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);

static void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key);

static void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key);

static btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median);

static btree_node_t *node_combine(btree_node_t *node);

static index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right);

static void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx);

static void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx);

static bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);

static bool try_insert_by_rotation_to_right(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree);

static bool try_rotation_from_left(btree_node_t *rnode);

static bool try_rotation_from_right(btree_node_t *lnode);

#define ROOT_NODE(n)        (!(n)->parent)

#define INDEX_NODE(n)       ((n)->subtree[0] != NULL)

#define LEAF_NODE(n)        ((n)->subtree[0] == NULL)

#define FILL_FACTOR     ((BTREE_M-1)/2)

#define MEDIAN_LOW_INDEX(n) (((n)->keys-1)/2)

#define MEDIAN_HIGH_INDEX(n)    ((n)->keys/2)

#define MEDIAN_LOW(n)       ((n)->key[MEDIAN_LOW_INDEX((n))]);

#define MEDIAN_HIGH(n)      ((n)->key[MEDIAN_HIGH_INDEX((n))]);

static slab_cache_t *btree_node_slab;

/** Initialize B-trees. */

void btree_init(void)

{

    btree_node_slab = slab_cache_create("btree_node_slab", sizeof(btree_node_t), 0, NULL, NULL, SLAB_CACHE_MAGDEFERRED);

}

/** Create empty B-tree.

 *

 * @param t B-tree.

 */

void btree_create(btree_t *t)

{

    list_initialize(&t->leaf_head);

    t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0);

    node_initialize(t->root);

    list_append(&t->root->leaf_link, &t->leaf_head);

}

/** Destroy empty B-tree. */

void btree_destroy(btree_t *t)

{

    btree_destroy_subtree(t->root);

}

/** Insert key-value pair into B-tree.

 *

 * @param t B-tree.

 * @param key Key to be inserted.

 * @param value Value to be inserted.

 * @param leaf_node Leaf node where the insertion should begin.

 */

void btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *leaf_node)

{

    btree_node_t *lnode;

    ASSERT(value);

    lnode = leaf_node;

    if (!lnode) {

        if (btree_search(t, key, &lnode)) {

            panic("B-tree %p already contains key %d\n", t, key);

        }

    }

    _btree_insert(t, key, value, NULL, lnode);

}

/** Destroy subtree rooted in a node.

 *

 * @param root Root of the subtree.

 */

void btree_destroy_subtree(btree_node_t *root)

{

    int i;

    if (root->keys) {

        for (i = 0; i < root->keys + 1; i++) {

            if (root->subtree[i])

                btree_destroy_subtree(root->subtree[i]);

        }

    }

    slab_free(btree_node_slab, root);

}

/** Recursively insert into B-tree.

 *

 * @param t B-tree.

 * @param key Key to be inserted.

 * @param value Value to be inserted.

 * @param rsubtree Right subtree of the inserted key.

 * @param node Start inserting into this node.

 */

void _btree_insert(btree_t *t, btree_key_t key, void *value, btree_node_t *rsubtree, btree_node_t *node)

{

    if (node->keys < BTREE_MAX_KEYS) {

        /*

         * Node conatins enough space, the key can be stored immediately.

         */

        node_insert_key_and_rsubtree(node, key, value, rsubtree);

    } else if (try_insert_by_rotation_to_left(node, key, value, rsubtree)) {

        /*

         * The key-value-rsubtree triplet has been inserted because

         * some keys could have been moved to the left sibling.

         */

    } else if (try_insert_by_rotation_to_right(node, key, value, rsubtree)) {

        /*

         * The key-value-rsubtree triplet has been inserted because

         * some keys could have been moved to the right sibling.

         */

    } else {

        btree_node_t *rnode;

        btree_key_t median;

        /*

         * Node is full and both siblings (if both exist) are full too.

         * Split the node and insert the smallest key from the node containing

         * bigger keys (i.e. the new node) into its parent.

         */

        rnode = node_split(node, key, value, rsubtree, &median);

        if (LEAF_NODE(node)) {

            list_prepend(&rnode->leaf_link, &node->leaf_link);

        }

        if (ROOT_NODE(node)) {

            /*

             * We split the root node. Create new root.

             */

            t->root = (btree_node_t *) slab_alloc(btree_node_slab, 0);

            node->parent = t->root;

            rnode->parent = t->root;

            node_initialize(t->root);

            /*

             * Left-hand side subtree will be the old root (i.e. node).

             * Right-hand side subtree will be rnode.

             */        

            t->root->subtree[0] = node;

            t->root->depth = node->depth + 1;

        }

        _btree_insert(t, median, NULL, rnode, node->parent);

    }  

}

/** Remove B-tree node.

 *

 * @param B-tree.

 * @param key Key to be removed from the B-tree along with its associated value.

 * @param leaf_node If not NULL, pointer to the leaf node where the key is found.

 */

void btree_remove(btree_t *t, btree_key_t key, btree_node_t *leaf_node)

{

    btree_node_t *lnode;

    lnode = leaf_node;

    if (!lnode) {

        if (!btree_search(t, key, &lnode)) {

            panic("B-tree %p does not contain key %d\n", t, key);

        }

    }

    _btree_remove(t, key, lnode);

}

/** Recursively remove B-tree node.

 *

 * @param B-tree.

 * @param key Key to be removed from the B-tree along with its associated value.

 * @param node Node where the key being removed resides.

 */

void _btree_remove(btree_t *t, btree_key_t key, btree_node_t *node)

{

    if (ROOT_NODE(node)) {

        if (node->keys == 1 && node->subtree[0]) {

            /*

             * Free the current root and set new root.

             */

            t->root = node->subtree[0];

            t->root->parent = NULL;

            slab_free(btree_node_slab, node);

        } else {

            /*

             * Remove the key from the root node.

             * Note that the right subtree is removed because when

             * combining two nodes, the left-side sibling is preserved

             * and the right-side sibling is freed.

             */

            node_remove_key_and_rsubtree(node, key);

        }

        return;

    }

    if (node->keys <= FILL_FACTOR) {

        /*

         * If the node is below the fill factor,

         * try to borrow keys from left or right sibling.

         */

        if (!try_rotation_from_left(node))

            try_rotation_from_right(node);

    }

    if (node->keys > FILL_FACTOR) {

        int i;

        /*

         * The key can be immediatelly removed.

         *

         * Note that the right subtree is removed because when

         * combining two nodes, the left-side sibling is preserved

         * and the right-side sibling is freed.

         */

        node_remove_key_and_rsubtree(node, key);

        for (i = 0; i < node->parent->keys; i++) {

            if (node->parent->key[i] == key)

                node->parent->key[i] = node->key[0];

        }

    } else {

        index_t idx;

        btree_node_t *rnode, *parent;

        /*

         * The node is below the fill factor as well as its left and right sibling.

         * Resort to combining the node with one of its siblings.

         * The node which is on the left is preserved and the node on the right is

         * freed.

         */

        parent = node->parent;

        node_remove_key_and_rsubtree(node, key);

        rnode = node_combine(node);

        if (LEAF_NODE(rnode))

            list_remove(&rnode->leaf_link);

        idx = find_key_by_subtree(parent, rnode, true);

        ASSERT((int) idx != -1);

        slab_free(btree_node_slab, rnode);

        _btree_remove(t, parent->key[idx], parent);

    }

}

/** Search key in a B-tree.

 *

 * @param t B-tree.

 * @param key Key to be searched.

 * @param leaf_node Address where to put pointer to visited leaf node.

 *

 * @return Pointer to value or NULL if there is no such key.

 */

void *btree_search(btree_t *t, btree_key_t key, btree_node_t **leaf_node)

{

    btree_node_t *cur, *next;

    /*

     * Iteratively descend to the leaf that can contain the searched key.

     */

    for (cur = t->root; cur; cur = next) {

        /* Last iteration will set this with proper leaf node address. */

        *leaf_node = cur;

        /*

         * The key can be in the leftmost subtree.

         * Test it separately.

         */

        if (key < cur->key[0]) {

            next = cur->subtree[0];

            continue;

        } else {

            void *val;

            int i;

            /*

             * Now if the key is smaller than cur->key[i]

             * it can only mean that the value is in cur->subtree[i]

             * or it is not in the tree at all.

             */

            for (i = 1; i < cur->keys; i++) {

                if (key < cur->key[i]) {

                    next = cur->subtree[i];

                    val = cur->value[i - 1];

                    if (LEAF_NODE(cur))

                        return key == cur->key[i - 1] ? val : NULL;

                    goto descend;

                }

            }

            /*

             * Last possibility is that the key is in the rightmost subtree.

             */

            next = cur->subtree[i];

            val = cur->value[i - 1];

            if (LEAF_NODE(cur))

                return key == cur->key[i - 1] ? val : NULL;

        }

        descend:

            ;

    }

    /*

     * The key was not found in the *leaf_node and is smaller than any of its keys.

     */

    return NULL;

}

/** Return pointer to B-tree leaf node's left neighbour.

 *

 * @param t B-tree.

 * @param node Node whose left neighbour will be returned.

 *

 * @return Left neighbour of the node or NULL if the node does not have the left neighbour.

 */

btree_node_t *btree_leaf_node_left_neighbour(btree_t *t, btree_node_t *node)

{

    ASSERT(LEAF_NODE(node));

    if (node->leaf_link.prev != &t->leaf_head)

        return list_get_instance(node->leaf_link.prev, btree_node_t, leaf_link);

    else

        return NULL;

}

/** Return pointer to B-tree leaf node's right neighbour.

 *

 * @param t B-tree.

 * @param node Node whose right neighbour will be returned.

 *

 * @return Right neighbour of the node or NULL if the node does not have the right neighbour.

 */

btree_node_t *btree_leaf_node_right_neighbour(btree_t *t, btree_node_t *node)

{

    ASSERT(LEAF_NODE(node));

    if (node->leaf_link.next != &t->leaf_head)

        return list_get_instance(node->leaf_link.next, btree_node_t, leaf_link);

    else

        return NULL;

}

/** Initialize B-tree node.

 *

 * @param node B-tree node.

 */

void node_initialize(btree_node_t *node)

{

    int i;

    node->keys = 0;

    /* Clean also space for the extra key. */

    for (i = 0; i < BTREE_MAX_KEYS + 1; i++) {

        node->key[i] = 0;

        node->value[i] = NULL;

        node->subtree[i] = NULL;

    }

    node->subtree[i] = NULL;

    node->parent = NULL;

    link_initialize(&node->leaf_link);

    link_initialize(&node->bfs_link);

    node->depth = 0;

}

/** Insert key-value-lsubtree triplet into B-tree node.

 *

 * It is actually possible to have more keys than BTREE_MAX_KEYS.

 * This feature is used during insert by right rotation.

 *

 * @param node B-tree node into wich the new key is to be inserted.

 * @param key The key to be inserted.

 * @param value Pointer to value to be inserted.

 * @param lsubtree Pointer to the left subtree.

 */

void node_insert_key_and_lsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *lsubtree)

{

    int i;

    for (i = 0; i < node->keys; i++) {

        if (key < node->key[i]) {

            int j;

            for (j = node->keys; j > i; j--) {

                node->key[j] = node->key[j - 1];

                node->value[j] = node->value[j - 1];

                node->subtree[j + 1] = node->subtree[j];

            }

            node->subtree[j + 1] = node->subtree[j];

            break; 

        }

    }

    node->key[i] = key;

    node->value[i] = value;

    node->subtree[i] = lsubtree;

    node->keys++;

}

/** Insert key-value-rsubtree triplet into B-tree node.

 *

 * It is actually possible to have more keys than BTREE_MAX_KEYS.

 * This feature is used during splitting the node when the

 * number of keys is BTREE_MAX_KEYS + 1. Insert by left rotation

 * also makes use of this feature.

 *

 * @param node B-tree node into wich the new key is to be inserted.

 * @param key The key to be inserted.

 * @param value Pointer to value to be inserted.

 * @param rsubtree Pointer to the right subtree.

 */

void node_insert_key_and_rsubtree(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree)

{

    int i;

    for (i = 0; i < node->keys; i++) {

        if (key < node->key[i]) {

            int j;

            for (j = node->keys; j > i; j--) {

                node->key[j] = node->key[j - 1];

                node->value[j] = node->value[j - 1];

                node->subtree[j + 1] = node->subtree[j];

            }

            break; 

        }

    }

    node->key[i] = key;

    node->value[i] = value;

    node->subtree[i + 1] = rsubtree;

    node->keys++;

}

/** Remove key and its left subtree pointer from B-tree node.

 *

 * Remove the key and eliminate gaps in node->key array.

 * Note that the value pointer and the left subtree pointer

 * is removed from the node as well.

 *

 * @param node B-tree node.

 * @param key Key to be removed.

 */

void node_remove_key_and_lsubtree(btree_node_t *node, btree_key_t key)

{

    int i, j;

    for (i = 0; i < node->keys; i++) {

        if (key == node->key[i]) {

            for (j = i + 1; j < node->keys; j++) {

                node->key[j - 1] = node->key[j];

                node->value[j - 1] = node->value[j];

                node->subtree[j - 1] = node->subtree[j];

            }

            node->subtree[j - 1] = node->subtree[j];

            node->keys--;

            return;

        }

    }

    panic("node %p does not contain key %d\n", node, key);

}

/** Remove key and its right subtree pointer from B-tree node.

 *

 * Remove the key and eliminate gaps in node->key array.

 * Note that the value pointer and the right subtree pointer

 * is removed from the node as well.

 *

 * @param node B-tree node.

 * @param key Key to be removed.

 */

void node_remove_key_and_rsubtree(btree_node_t *node, btree_key_t key)

{

    int i, j;

    for (i = 0; i < node->keys; i++) {

        if (key == node->key[i]) {

            for (j = i + 1; j < node->keys; j++) {

                node->key[j - 1] = node->key[j];

                node->value[j - 1] = node->value[j];

                node->subtree[j] = node->subtree[j + 1];

            }

            node->keys--;

            return;

        }

    }

    panic("node %p does not contain key %d\n", node, key);

}

/** Split full B-tree node and insert new key-value-right-subtree triplet.

 *

 * This function will split a node and return pointer to a newly created

 * node containing keys greater than or equal to the greater of medians

 * (or median) of the old keys and the newly added key. It will also write

 * the median key to a memory address supplied by the caller.

 *

 * If the node being split is an index node, the median will not be

 * included in the new node. If the node is a leaf node,

 * the median will be copied there.

 *

 * @param node B-tree node wich is going to be split.

 * @param key The key to be inserted.

 * @param value Pointer to the value to be inserted.

 * @param rsubtree Pointer to the right subtree of the key being added.

 * @param median Address in memory, where the median key will be stored.

 *

 * @return Newly created right sibling of node.

 */

btree_node_t *node_split(btree_node_t *node, btree_key_t key, void *value, btree_node_t *rsubtree, btree_key_t *median)

{

    btree_node_t *rnode;

    int i, j;

    ASSERT(median);

    ASSERT(node->keys == BTREE_MAX_KEYS);

    /*

     * Use the extra space to store the extra node.

     */

    node_insert_key_and_rsubtree(node, key, value, rsubtree);

    /*

     * Compute median of keys.

     */

    *median = MEDIAN_HIGH(node);

    /*

     * Allocate and initialize new right sibling.

     */

    rnode = (btree_node_t *) slab_alloc(btree_node_slab, 0);

    node_initialize(rnode);

    rnode->parent = node->parent;

    rnode->depth = node->depth;

    /*

     * Copy big keys, values and subtree pointers to the new right sibling.

     * If this is an index node, do not copy the median.

     */

    i = (int) INDEX_NODE(node);

    for (i += MEDIAN_HIGH_INDEX(node), j = 0; i < node->keys; i++, j++) {

        rnode->key[j] = node->key[i];

        rnode->value[j] = node->value[i];

        rnode->subtree[j] = node->subtree[i];

        /*

         * Fix parent links in subtrees.

         */

        if (rnode->subtree[j])

            rnode->subtree[j]->parent = rnode;

    }

    rnode->subtree[j] = node->subtree[i];

    if (rnode->subtree[j])

        rnode->subtree[j]->parent = rnode;

    rnode->keys = j;    /* Set number of keys of the new node. */

    node->keys /= 2;    /* Shrink the old node. */

    return rnode;

}

/** Combine node with any of its siblings.

 *

 * The siblings are required to be below the fill factor.

 *

 * @param node Node to combine with one of its siblings.

 *

 * @return Pointer to the rightmost of the two nodes.

 */

btree_node_t *node_combine(btree_node_t *node)

{

    index_t idx;

    btree_node_t *rnode;

    int i;

    ASSERT(!ROOT_NODE(node));

    idx = find_key_by_subtree(node->parent, node, false);

    if (idx == node->parent->keys) {

        /*

         * Rightmost subtree of its parent, combine with the left sibling.

         */

        idx--;

        rnode = node;

        node = node->parent->subtree[idx];

    } else {

        rnode = node->parent->subtree[idx + 1];

    }

    /* Index nodes need to insert parent node key in between left and right node. */

    if (INDEX_NODE(node))

        node->key[node->keys++] = node->parent->key[idx];

    /* Copy the key-value-subtree triplets from the right node. */

    for (i = 0; i < rnode->keys; i++) {

        node->key[node->keys + i] = rnode->key[i];

        node->value[node->keys + i] = rnode->value[i];

        if (INDEX_NODE(node)) {

            node->subtree[node->keys + i] = rnode->subtree[i];

            rnode->subtree[i]->parent = node;

        }

    }

    if (INDEX_NODE(node)) {

        node->subtree[node->keys + i] = rnode->subtree[i];

        rnode->subtree[i]->parent = node;

    }

    node->keys += rnode->keys;

    return rnode;

}

/** Find key by its left or right subtree.

 *

 * @param node B-tree node.

 * @param subtree Left or right subtree of a key found in node.

 * @param right If true, subtree is a right subtree. If false, subtree is a left subtree.

 *

 * @return Index of the key associated with the subtree.

 */

index_t find_key_by_subtree(btree_node_t *node, btree_node_t *subtree, bool right)

{

    int i;

    for (i = 0; i < node->keys + 1; i++) {

        if (subtree == node->subtree[i])

            return i - (int) (right != false);

    }

    panic("node %p does not contain subtree %p\n", node, subtree);

}

/** Rotate one key-value-rsubtree triplet from the left sibling to the right sibling.

 *

 * The biggest key and its value and right subtree is rotated from the left node

 * to the right. If the node is an index node, than the parent node key belonging to

 * the left node takes part in the rotation.

 *

 * @param lnode Left sibling.

 * @param rnode Right sibling.

 * @param idx Index of the parent node key that is taking part in the rotation.

 */

void rotate_from_left(btree_node_t *lnode, btree_node_t *rnode, index_t idx)

{

    btree_key_t key;

    key = lnode->key[lnode->keys - 1];

    if (LEAF_NODE(lnode)) {

        void *value;

        value = lnode->value[lnode->keys - 1];

        node_remove_key_and_rsubtree(lnode, key);

        node_insert_key_and_lsubtree(rnode, key, value, NULL);

        lnode->parent->key[idx] = key;

    } else {

        btree_node_t *rsubtree;

        rsubtree = lnode->subtree[lnode->keys];

        node_remove_key_and_rsubtree(lnode, key);

        node_insert_key_and_lsubtree(rnode, lnode->parent->key[idx], NULL, rsubtree);

        lnode->parent->key[idx] = key;

        /* Fix parent link of the reconnected right subtree. */

        rsubtree->parent = rnode;

    }

}

/** Rotate one key-value-lsubtree triplet from the right sibling to the left sibling.

 *

 * The smallest key and its value and left subtree is rotated from the right node

 * to the left. If the node is an index node, than the parent node key belonging to

 * the right node takes part in the rotation.

 *

 * @param lnode Left sibling.

 * @param rnode Right sibling.

 * @param idx Index of the parent node key that is taking part in the rotation.

 */

void rotate_from_right(btree_node_t *lnode, btree_node_t *rnode, index_t idx)

{

    btree_key_t key;

    key = rnode->key[0];

    if (LEAF_NODE(rnode)) {

        void *value;

        value = rnode->value[0];

        node_remove_key_and_lsubtree(rnode, key);

        node_insert_key_and_rsubtree(lnode, key, value, NULL);

        rnode->parent->key[idx] = rnode->key[0];

    } else {

        btree_node_t *lsubtree;

        lsubtree = rnode->subtree[0];

        node_remove_key_and_lsubtree(rnode, key);

        node_insert_key_and_rsubtree(lnode, rnode->parent->key[idx], NULL, lsubtree);

        rnode->parent->key[idx] = key;

        /* Fix parent link of the reconnected left subtree. */

        lsubtree->parent = lnode;

    }

}

/** Insert key-value-rsubtree triplet and rotate the node to the left, if this operation can be done.

 *

 * Left sibling of the node (if it exists) is checked for free space.

 * If there is free space, the key is inserted and the smallest key of

 * the node is moved there. The index node which is the parent of both

 * nodes is fixed.

 *

 * @param node B-tree node.

 * @param inskey Key to be inserted.

 * @param insvalue Value to be inserted.

 * @param rsubtree Right subtree of inskey.

 *

 * @return True if the rotation was performed, false otherwise.

 */

bool try_insert_by_rotation_to_left(btree_node_t *node, btree_key_t inskey, void *insvalue, btree_node_t *rsubtree)

{

    index_t idx;

    btree_node_t *lnode;

    /*

     * If this is root node, the rotation can not be done.

     */

    if (ROOT_NODE(node))

        return false;

    idx = find_key_by_subtree(node->parent, node, true);

    if ((int) idx == -1) {