/* Produced by texiweb from libavl.w. */

/* libavl - library for manipulation of binary trees.
   Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software
   Foundation, Inc.

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 3 of the License, or (at your option) any later version.

   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA.
 */

/* Nov 2016, Markus Metz
 * from libavl-2.0.3
 * added safety checks and speed optimizations
 */

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include "tavl.h"

/* Creates and returns a new table
   with comparison function |compare| using parameter |param|
   and memory allocator |allocator|.
   Returns |NULL| if memory allocation failed. */
struct tavl_table *tavl_create(tavl_comparison_func *compare, void *param,
                               struct libavl_allocator *allocator)
{
    struct tavl_table *tree;

    assert(compare != NULL);

    if (allocator == NULL)
        allocator = &tavl_allocator_default;

    tree = allocator->libavl_malloc(allocator, sizeof *tree);
    if (tree == NULL)
        return NULL;

    tree->tavl_root = NULL;
    tree->tavl_compare = compare;
    tree->tavl_param = param;
    tree->tavl_alloc = allocator;
    tree->tavl_count = 0;

    return tree;
}

/* Search |tree| for an item matching |item|, and return it if found.
   Otherwise return |NULL|. */
void *tavl_find(const struct tavl_table *tree, const void *item)
{
    const struct tavl_node *p;

    assert(tree != NULL && item != NULL);

    p = tree->tavl_root;
    while (p != NULL) {
        int cmp, dir;

        cmp = tree->tavl_compare(item, p->tavl_data, tree->tavl_param);
        if (cmp == 0)
            return p->tavl_data;

        dir = cmp > 0;
        if (p->tavl_tag[dir] == TAVL_CHILD)
            p = p->tavl_link[dir];
        else
            p = NULL;
    }

    return NULL;
}

/* Inserts |item| into |tree| and returns a pointer to |item|'s address.
   If a duplicate item is found in the tree,
   returns a pointer to the duplicate without inserting |item|.
   Returns |NULL| in case of memory allocation failure. */
void **tavl_probe(struct tavl_table *tree, void *item)
{
    struct tavl_node *y,
        *z; /* Top node to update balance factor, and parent. */
    struct tavl_node *p, *q; /* Iterator, and parent. */
    struct tavl_node *n;     /* Newly inserted node. */
    struct tavl_node *w;     /* New root of rebalanced subtree. */
    int dir;                 /* Direction to descend. */

    unsigned char da[TAVL_MAX_HEIGHT]; /* Cached comparison results. */
    int k = 0;                         /* Number of cached results. */

    assert(tree != NULL && item != NULL);

    z = (struct tavl_node *)&tree->tavl_root;
    y = tree->tavl_root;
    dir = 0;
    q = z, p = y;
    while (p != NULL) {
        int cmp = tree->tavl_compare(item, p->tavl_data, tree->tavl_param);
        if (cmp == 0)
            return &p->tavl_data;

        if (p->tavl_balance != 0)
            z = q, y = p, k = 0;
        da[k++] = dir = cmp > 0;

        if (p->tavl_tag[dir] == TAVL_THREAD)
            break;
        q = p, p = p->tavl_link[dir];
    }

    n = tree->tavl_alloc->libavl_malloc(tree->tavl_alloc, sizeof *n);
    if (n == NULL)
        return NULL;

    tree->tavl_count++;
    n->tavl_data = item;
    n->tavl_tag[0] = n->tavl_tag[1] = TAVL_THREAD;
    n->tavl_balance = 0;
    if (y == NULL) {
        n->tavl_link[0] = n->tavl_link[1] = NULL;
        tree->tavl_root = n;

        return &n->tavl_data;
    }
    n->tavl_link[dir] = p->tavl_link[dir];
    n->tavl_link[!dir] = p;
    p->tavl_tag[dir] = TAVL_CHILD;
    p->tavl_link[dir] = n;

    p = y, k = 0;
    while (p != n) {
        if (da[k] == 0)
            p->tavl_balance--;
        else
            p->tavl_balance++;
        p = p->tavl_link[da[k]], k++;
    }

    if (y->tavl_balance == -2) {
        struct tavl_node *x = y->tavl_link[0];

        if (x->tavl_balance == -1) {
            w = x;
            if (x->tavl_tag[1] == TAVL_THREAD) {
                x->tavl_tag[1] = TAVL_CHILD;
                y->tavl_tag[0] = TAVL_THREAD;
                y->tavl_link[0] = x;
            }
            else
                y->tavl_link[0] = x->tavl_link[1];
            x->tavl_link[1] = y;
            x->tavl_balance = y->tavl_balance = 0;
        }
        else {
            assert(x->tavl_balance == +1);
            w = x->tavl_link[1];
            x->tavl_link[1] = w->tavl_link[0];
            w->tavl_link[0] = x;
            y->tavl_link[0] = w->tavl_link[1];
            w->tavl_link[1] = y;
            if (w->tavl_balance == -1)
                x->tavl_balance = 0, y->tavl_balance = +1;
            else if (w->tavl_balance == 0)
                x->tavl_balance = y->tavl_balance = 0;
            else /* |w->tavl_balance == +1| */
                x->tavl_balance = -1, y->tavl_balance = 0;
            w->tavl_balance = 0;
            if (w->tavl_tag[0] == TAVL_THREAD) {
                x->tavl_tag[1] = TAVL_THREAD;
                x->tavl_link[1] = w;
                w->tavl_tag[0] = TAVL_CHILD;
            }
            if (w->tavl_tag[1] == TAVL_THREAD) {
                y->tavl_tag[0] = TAVL_THREAD;
                y->tavl_link[0] = w;
                w->tavl_tag[1] = TAVL_CHILD;
            }
        }
    }
    else if (y->tavl_balance == +2) {
        struct tavl_node *x = y->tavl_link[1];

        if (x->tavl_balance == +1) {
            w = x;
            if (x->tavl_tag[0] == TAVL_THREAD) {
                x->tavl_tag[0] = TAVL_CHILD;
                y->tavl_tag[1] = TAVL_THREAD;
                y->tavl_link[1] = x;
            }
            else
                y->tavl_link[1] = x->tavl_link[0];
            x->tavl_link[0] = y;
            x->tavl_balance = y->tavl_balance = 0;
        }
        else {
            assert(x->tavl_balance == -1);
            w = x->tavl_link[0];
            x->tavl_link[0] = w->tavl_link[1];
            w->tavl_link[1] = x;
            y->tavl_link[1] = w->tavl_link[0];
            w->tavl_link[0] = y;
            if (w->tavl_balance == +1)
                x->tavl_balance = 0, y->tavl_balance = -1;
            else if (w->tavl_balance == 0)
                x->tavl_balance = y->tavl_balance = 0;
            else /* |w->tavl_balance == -1| */
                x->tavl_balance = +1, y->tavl_balance = 0;
            w->tavl_balance = 0;
            if (w->tavl_tag[0] == TAVL_THREAD) {
                y->tavl_tag[1] = TAVL_THREAD;
                y->tavl_link[1] = w;
                w->tavl_tag[0] = TAVL_CHILD;
            }
            if (w->tavl_tag[1] == TAVL_THREAD) {
                x->tavl_tag[0] = TAVL_THREAD;
                x->tavl_link[0] = w;
                w->tavl_tag[1] = TAVL_CHILD;
            }
        }
    }
    else
        return &n->tavl_data;
    z->tavl_link[y != z->tavl_link[0]] = w;

    return &n->tavl_data;
}

/* Inserts |item| into |table|.
   Returns |NULL| if |item| was successfully inserted
   or if a memory allocation error occurred.
   Otherwise, returns the duplicate item. */
void *tavl_insert(struct tavl_table *table, void *item)
{
    void **p = tavl_probe(table, item);

    return p == NULL || *p == item ? NULL : *p;
}

/* Inserts |item| into |table|, replacing any duplicate item.
   Returns |NULL| if |item| was inserted without replacing a duplicate,
   or if a memory allocation error occurred.
   Otherwise, returns the item that was replaced. */
void *tavl_replace(struct tavl_table *table, void *item)
{
    void **p = tavl_probe(table, item);

    if (p == NULL || *p == item)
        return NULL;
    else {
        void *r = *p;

        *p = item;

        return r;
    }
}

/* Returns the parent of |node| within |tree|,
   or a pointer to |tavl_root| if |s| is the root of the tree. */
static struct tavl_node *find_parent(struct tavl_table *tree,
                                     struct tavl_node *node)
{
    if (node != tree->tavl_root) {
        struct tavl_node *x, *y;

        for (x = y = node;; x = x->tavl_link[0], y = y->tavl_link[1])
            if (y->tavl_tag[1] == TAVL_THREAD) {
                struct tavl_node *p = y->tavl_link[1];

                if (p == NULL || p->tavl_link[0] != node) {
                    while (x->tavl_tag[0] == TAVL_CHILD)
                        x = x->tavl_link[0];
                    p = x->tavl_link[0];
                }
                return p;
            }
            else if (x->tavl_tag[0] == TAVL_THREAD) {
                struct tavl_node *p = x->tavl_link[0];

                if (p == NULL || p->tavl_link[1] != node) {
                    while (y->tavl_tag[1] == TAVL_CHILD)
                        y = y->tavl_link[1];
                    p = y->tavl_link[1];
                }
                return p;
            }
    }
    else
        return (struct tavl_node *)&tree->tavl_root;
}

/* Deletes from |tree| and returns an item matching |item|.
   Returns a null pointer if no matching item found. */
void *tavl_delete(struct tavl_table *tree, const void *item)
{
    struct tavl_node *p; /* Traverses tree to find node to delete. */
    struct tavl_node *q; /* Parent of |p|. */
    int dir;             /* Index into |q->tavl_link[]| to get |p|. */
    int cmp;             /* Result of comparison between |item| and |p|. */

    assert(tree != NULL && item != NULL);

    q = (struct tavl_node *)&tree->tavl_root;
    p = tree->tavl_root;
    dir = 0;
    while (p != NULL) {
        cmp = tree->tavl_compare(item, p->tavl_data, tree->tavl_param);

        if (cmp == 0)
            break;

        dir = cmp > 0;

        q = p;
        if (p->tavl_tag[dir] == TAVL_CHILD)
            p = p->tavl_link[dir];
        else
            p = NULL;
    }
    if (p == NULL)
        return NULL;

    item = p->tavl_data;

    if (p->tavl_tag[1] == TAVL_THREAD) {
        if (p->tavl_tag[0] == TAVL_CHILD) {
            struct tavl_node *t = p->tavl_link[0];

            while (t->tavl_tag[1] == TAVL_CHILD)
                t = t->tavl_link[1];
            t->tavl_link[1] = p->tavl_link[1];
            q->tavl_link[dir] = p->tavl_link[0];
        }
        else {
            q->tavl_link[dir] = p->tavl_link[dir];
            if (q != (struct tavl_node *)&tree->tavl_root)
                q->tavl_tag[dir] = TAVL_THREAD;
        }
    }
    else {
        struct tavl_node *r = p->tavl_link[1];

        if (r->tavl_tag[0] == TAVL_THREAD) {
            r->tavl_link[0] = p->tavl_link[0];
            r->tavl_tag[0] = p->tavl_tag[0];
            if (r->tavl_tag[0] == TAVL_CHILD) {
                struct tavl_node *t = r->tavl_link[0];

                while (t->tavl_tag[1] == TAVL_CHILD)
                    t = t->tavl_link[1];
                t->tavl_link[1] = r;
            }
            q->tavl_link[dir] = r;
            r->tavl_balance = p->tavl_balance;
            q = r;
            dir = 1;
        }
        else {
            struct tavl_node *s;

            while (r != NULL) {
                s = r->tavl_link[0];
                if (s->tavl_tag[0] == TAVL_THREAD)
                    break;

                r = s;
            }

            if (s->tavl_tag[1] == TAVL_CHILD)
                r->tavl_link[0] = s->tavl_link[1];
            else {
                r->tavl_link[0] = s;
                r->tavl_tag[0] = TAVL_THREAD;
            }

            s->tavl_link[0] = p->tavl_link[0];
            if (p->tavl_tag[0] == TAVL_CHILD) {
                struct tavl_node *t = p->tavl_link[0];

                while (t->tavl_tag[1] == TAVL_CHILD)
                    t = t->tavl_link[1];
                t->tavl_link[1] = s;

                s->tavl_tag[0] = TAVL_CHILD;
            }

            s->tavl_link[1] = p->tavl_link[1];
            s->tavl_tag[1] = TAVL_CHILD;

            q->tavl_link[dir] = s;
            s->tavl_balance = p->tavl_balance;
            q = r;
            dir = 0;
        }
    }

    tree->tavl_alloc->libavl_free(tree->tavl_alloc, p);

    while (q != (struct tavl_node *)&tree->tavl_root) {
        struct tavl_node *y = q;

        q = find_parent(tree, y);

        if (dir == 0) {
            dir = q->tavl_link[0] != y;
            y->tavl_balance++;
            if (y->tavl_balance == +1)
                break;
            else if (y->tavl_balance == +2) {
                struct tavl_node *x = y->tavl_link[1];

                assert(x != NULL);
                if (x->tavl_balance == -1) {
                    struct tavl_node *w;

                    assert(x->tavl_balance == -1);
                    w = x->tavl_link[0];
                    x->tavl_link[0] = w->tavl_link[1];
                    w->tavl_link[1] = x;
                    y->tavl_link[1] = w->tavl_link[0];
                    w->tavl_link[0] = y;
                    if (w->tavl_balance == +1)
                        x->tavl_balance = 0, y->tavl_balance = -1;
                    else if (w->tavl_balance == 0)
                        x->tavl_balance = y->tavl_balance = 0;
                    else /* |w->tavl_balance == -1| */
                        x->tavl_balance = +1, y->tavl_balance = 0;
                    w->tavl_balance = 0;
                    if (w->tavl_tag[0] == TAVL_THREAD) {
                        y->tavl_tag[1] = TAVL_THREAD;
                        y->tavl_link[1] = w;
                        w->tavl_tag[0] = TAVL_CHILD;
                    }
                    if (w->tavl_tag[1] == TAVL_THREAD) {
                        x->tavl_tag[0] = TAVL_THREAD;
                        x->tavl_link[0] = w;
                        w->tavl_tag[1] = TAVL_CHILD;
                    }
                    q->tavl_link[dir] = w;
                }
                else {
                    q->tavl_link[dir] = x;

                    if (x->tavl_balance == 0) {
                        y->tavl_link[1] = x->tavl_link[0];
                        x->tavl_link[0] = y;
                        x->tavl_balance = -1;
                        y->tavl_balance = +1;
                        break;
                    }
                    else { /* |x->tavl_balance == +1| */

                        if (x->tavl_tag[0] == TAVL_CHILD)
                            y->tavl_link[1] = x->tavl_link[0];
                        else {
                            y->tavl_tag[1] = TAVL_THREAD;
                            x->tavl_tag[0] = TAVL_CHILD;
                        }
                        x->tavl_link[0] = y;
                        y->tavl_balance = x->tavl_balance = 0;
                    }
                }
            }
        }
        else {
            dir = q->tavl_link[0] != y;
            y->tavl_balance--;
            if (y->tavl_balance == -1)
                break;
            else if (y->tavl_balance == -2) {
                struct tavl_node *x = y->tavl_link[0];

                assert(x != NULL);
                if (x->tavl_balance == +1) {
                    struct tavl_node *w;

                    assert(x->tavl_balance == +1);
                    w = x->tavl_link[1];
                    x->tavl_link[1] = w->tavl_link[0];
                    w->tavl_link[0] = x;
                    y->tavl_link[0] = w->tavl_link[1];
                    w->tavl_link[1] = y;
                    if (w->tavl_balance == -1)
                        x->tavl_balance = 0, y->tavl_balance = +1;
                    else if (w->tavl_balance == 0)
                        x->tavl_balance = y->tavl_balance = 0;
                    else /* |w->tavl_balance == +1| */
                        x->tavl_balance = -1, y->tavl_balance = 0;
                    w->tavl_balance = 0;
                    if (w->tavl_tag[0] == TAVL_THREAD) {
                        x->tavl_tag[1] = TAVL_THREAD;
                        x->tavl_link[1] = w;
                        w->tavl_tag[0] = TAVL_CHILD;
                    }
                    if (w->tavl_tag[1] == TAVL_THREAD) {
                        y->tavl_tag[0] = TAVL_THREAD;
                        y->tavl_link[0] = w;
                        w->tavl_tag[1] = TAVL_CHILD;
                    }
                    q->tavl_link[dir] = w;
                }
                else {
                    q->tavl_link[dir] = x;

                    if (x->tavl_balance == 0) {
                        y->tavl_link[0] = x->tavl_link[1];
                        x->tavl_link[1] = y;
                        x->tavl_balance = +1;
                        y->tavl_balance = -1;
                        break;
                    }
                    else { /* |x->tavl_balance == -1| */

                        if (x->tavl_tag[1] == TAVL_CHILD)
                            y->tavl_link[0] = x->tavl_link[1];
                        else {
                            y->tavl_tag[0] = TAVL_THREAD;
                            x->tavl_tag[1] = TAVL_CHILD;
                        }
                        x->tavl_link[1] = y;
                        y->tavl_balance = x->tavl_balance = 0;
                    }
                }
            }
        }
    }

    tree->tavl_count--;

    return (void *)item;
}

/* Initializes |trav| for use with |tree|
   and selects the null node. */
void tavl_t_init(struct tavl_traverser *trav, struct tavl_table *tree)
{
    trav->tavl_table = tree;
    trav->tavl_node = NULL;
}

/* Initializes |trav| for |tree|.
   Returns data item in |tree| with the least value,
   or |NULL| if |tree| is empty. */
void *tavl_t_first(struct tavl_traverser *trav, struct tavl_table *tree)
{
    assert(tree != NULL && trav != NULL);

    trav->tavl_table = tree;
    trav->tavl_node = tree->tavl_root;
    if (trav->tavl_node != NULL) {
        while (trav->tavl_node->tavl_tag[0] == TAVL_CHILD)
            trav->tavl_node = trav->tavl_node->tavl_link[0];
        return trav->tavl_node->tavl_data;
    }
    else
        return NULL;
}

/* Initializes |trav| for |tree|.
   Returns data item in |tree| with the greatest value,
   or |NULL| if |tree| is empty. */
void *tavl_t_last(struct tavl_traverser *trav, struct tavl_table *tree)
{
    assert(tree != NULL && trav != NULL);

    trav->tavl_table = tree;
    trav->tavl_node = tree->tavl_root;
    if (trav->tavl_node != NULL) {
        while (trav->tavl_node->tavl_tag[1] == TAVL_CHILD)
            trav->tavl_node = trav->tavl_node->tavl_link[1];
        return trav->tavl_node->tavl_data;
    }
    else
        return NULL;
}

/* Searches for |item| in |tree|.
   If found, initializes |trav| to the item found and returns the item
   as well.
   If there is no matching item, initializes |trav| to the null item
   and returns |NULL|. */
void *tavl_t_find(struct tavl_traverser *trav, struct tavl_table *tree,
                  void *item)
{
    struct tavl_node *p;

    assert(trav != NULL && tree != NULL && item != NULL);

    trav->tavl_table = tree;
    trav->tavl_node = NULL;

    p = tree->tavl_root;
    while (p != NULL) {
        int cmp, dir;

        cmp = tree->tavl_compare(item, p->tavl_data, tree->tavl_param);
        if (cmp == 0) {
            trav->tavl_node = p;

            return p->tavl_data;
        }

        dir = cmp > 0;
        if (p->tavl_tag[dir] == TAVL_CHILD)
            p = p->tavl_link[dir];
        else
            p = NULL;
    }

    trav->tavl_node = NULL;

    return NULL;
}

/* Attempts to insert |item| into |tree|.
   If |item| is inserted successfully, it is returned and |trav| is
   initialized to its location.
   If a duplicate is found, it is returned and |trav| is initialized to
   its location.  No replacement of the item occurs.
   If a memory allocation failure occurs, |NULL| is returned and |trav|
   is initialized to the null item. */
void *tavl_t_insert(struct tavl_traverser *trav, struct tavl_table *tree,
                    void *item)
{
    void **p;

    assert(trav != NULL && tree != NULL && item != NULL);

    p = tavl_probe(tree, item);
    if (p != NULL) {
        trav->tavl_table = tree;
        trav->tavl_node =
            ((struct tavl_node *)((char *)p -
                                  offsetof(struct tavl_node, tavl_data)));
        return *p;
    }
    else {
        tavl_t_init(trav, tree);

        return NULL;
    }
}

/* Initializes |trav| to have the same current node as |src|. */
void *tavl_t_copy(struct tavl_traverser *trav, const struct tavl_traverser *src)
{
    assert(trav != NULL && src != NULL);

    trav->tavl_table = src->tavl_table;
    trav->tavl_node = src->tavl_node;

    return trav->tavl_node != NULL ? trav->tavl_node->tavl_data : NULL;
}

/* Returns the next data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *tavl_t_next(struct tavl_traverser *trav)
{
    assert(trav != NULL);

    if (trav->tavl_node == NULL)
        return tavl_t_first(trav, trav->tavl_table);
    else if (trav->tavl_node->tavl_tag[1] == TAVL_THREAD) {
        trav->tavl_node = trav->tavl_node->tavl_link[1];
        return trav->tavl_node != NULL ? trav->tavl_node->tavl_data : NULL;
    }
    else {
        trav->tavl_node = trav->tavl_node->tavl_link[1];
        while (trav->tavl_node->tavl_tag[0] == TAVL_CHILD)
            trav->tavl_node = trav->tavl_node->tavl_link[0];
        return trav->tavl_node->tavl_data;
    }
}

/* Returns the previous data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *tavl_t_prev(struct tavl_traverser *trav)
{
    assert(trav != NULL);

    if (trav->tavl_node == NULL)
        return tavl_t_last(trav, trav->tavl_table);
    else if (trav->tavl_node->tavl_tag[0] == TAVL_THREAD) {
        trav->tavl_node = trav->tavl_node->tavl_link[0];
        return trav->tavl_node != NULL ? trav->tavl_node->tavl_data : NULL;
    }
    else {
        trav->tavl_node = trav->tavl_node->tavl_link[0];
        while (trav->tavl_node->tavl_tag[1] == TAVL_CHILD)
            trav->tavl_node = trav->tavl_node->tavl_link[1];
        return trav->tavl_node->tavl_data;
    }
}

/* Returns |trav|'s current item. */
void *tavl_t_cur(struct tavl_traverser *trav)
{
    assert(trav != NULL);

    return trav->tavl_node != NULL ? trav->tavl_node->tavl_data : NULL;
}

/* Replaces the current item in |trav| by |new| and returns the item replaced.
   |trav| must not have the null item selected.
   The new item must not upset the ordering of the tree. */
void *tavl_t_replace(struct tavl_traverser *trav, void *new)
{
    void *old;

    assert(trav != NULL && trav->tavl_node != NULL && new != NULL);
    old = trav->tavl_node->tavl_data;
    trav->tavl_node->tavl_data = new;

    return old;
}

/* Creates a new node as a child of |dst| on side |dir|.
   Copies data and |tavl_balance| from |src| into the new node,
   applying |copy()|, if non-null.
   Returns nonzero only if fully successful.
   Regardless of success, integrity of the tree structure is assured,
   though failure may leave a null pointer in a |tavl_data| member. */
static int copy_node(struct tavl_table *tree, struct tavl_node *dst, int dir,
                     const struct tavl_node *src, tavl_copy_func *copy)
{
    struct tavl_node *new =
        tree->tavl_alloc->libavl_malloc(tree->tavl_alloc, sizeof *new);
    if (new == NULL)
        return 0;

    new->tavl_link[dir] = dst->tavl_link[dir];
    new->tavl_tag[dir] = TAVL_THREAD;
    new->tavl_link[!dir] = dst;
    new->tavl_tag[!dir] = TAVL_THREAD;
    dst->tavl_link[dir] = new;
    dst->tavl_tag[dir] = TAVL_CHILD;

    new->tavl_balance = src->tavl_balance;
    if (copy == NULL)
        new->tavl_data = src->tavl_data;
    else {
        new->tavl_data = copy(src->tavl_data, tree->tavl_param);
        if (new->tavl_data == NULL)
            return 0;
    }

    return 1;
}

/* Destroys |new| with |tavl_destroy (new, destroy)|,
   first initializing the right link in |new| that has
   not yet been initialized. */
static void copy_error_recovery(struct tavl_node *p, struct tavl_table *new,
                                tavl_item_func *destroy)
{
    new->tavl_root = p;
    if (p != NULL) {
        while (p->tavl_tag[1] == TAVL_CHILD)
            p = p->tavl_link[1];
        p->tavl_link[1] = NULL;
    }
    tavl_destroy(new, destroy);
}

/* Copies |org| to a newly created tree, which is returned.
   If |copy != NULL|, each data item in |org| is first passed to |copy|,
   and the return values are inserted into the tree,
   with |NULL| return values taken as indications of failure.
   On failure, destroys the partially created new tree,
   applying |destroy|, if non-null, to each item in the new tree so far,
   and returns |NULL|.
   If |allocator != NULL|, it is used for allocation in the new tree.
   Otherwise, the same allocator used for |org| is used. */
struct tavl_table *tavl_copy(const struct tavl_table *org, tavl_copy_func *copy,
                             tavl_item_func *destroy,
                             struct libavl_allocator *allocator)
{
    struct tavl_table *new;

    const struct tavl_node *p;
    struct tavl_node *q;
    struct tavl_node rp, rq;

    assert(org != NULL);
    new = tavl_create(org->tavl_compare, org->tavl_param,
                      allocator != NULL ? allocator : org->tavl_alloc);
    if (new == NULL)
        return NULL;

    new->tavl_count = org->tavl_count;
    if (new->tavl_count == 0)
        return new;

    p = &rp;
    rp.tavl_link[0] = org->tavl_root;
    rp.tavl_tag[0] = TAVL_CHILD;

    q = &rq;
    rq.tavl_link[0] = NULL;
    rq.tavl_tag[0] = TAVL_THREAD;

    while (p != NULL) {
        if (p->tavl_tag[0] == TAVL_CHILD) {
            if (!copy_node(new, q, 0, p->tavl_link[0], copy)) {
                copy_error_recovery(rq.tavl_link[0], new, destroy);
                return NULL;
            }

            p = p->tavl_link[0];
            q = q->tavl_link[0];
        }
        else {
            while (p->tavl_tag[1] == TAVL_THREAD) {
                p = p->tavl_link[1];
                if (p == NULL) {
                    q->tavl_link[1] = NULL;
                    new->tavl_root = rq.tavl_link[0];
                    return new;
                }

                q = q->tavl_link[1];
            }

            p = p->tavl_link[1];
            q = q->tavl_link[1];
        }

        if (p->tavl_tag[1] == TAVL_CHILD)
            if (!copy_node(new, q, 1, p->tavl_link[1], copy)) {
                copy_error_recovery(rq.tavl_link[0], new, destroy);
                return NULL;
            }
    }

    return new;
}

/* Frees storage allocated for |tree|.
   If |destroy != NULL|, applies it to each data item in inorder. */
void tavl_destroy(struct tavl_table *tree, tavl_item_func *destroy)
{
    struct tavl_node *p; /* Current node. */
    struct tavl_node *n; /* Next node. */

    p = tree->tavl_root;
    if (p != NULL) {
        while (p->tavl_tag[0] == TAVL_CHILD)
            p = p->tavl_link[0];
    }

    while (p != NULL) {
        n = p->tavl_link[1];
        if (p->tavl_tag[1] == TAVL_CHILD)
            while (n->tavl_tag[0] == TAVL_CHILD)
                n = n->tavl_link[0];

        if (destroy != NULL && p->tavl_data != NULL)
            destroy(p->tavl_data, tree->tavl_param);
        tree->tavl_alloc->libavl_free(tree->tavl_alloc, p);

        p = n;
    }

    tree->tavl_alloc->libavl_free(tree->tavl_alloc, tree);
}

/* Allocates |size| bytes of space using |malloc()|.
   Returns a null pointer if allocation fails. */
void *tavl_malloc(struct libavl_allocator *allocator, size_t size)
{
    assert(allocator != NULL && size > 0);
    return malloc(size);
}

/* Frees |block|. */
void tavl_free(struct libavl_allocator *allocator, void *block)
{
    assert(allocator != NULL && block != NULL);
    free(block);
}

/* Default memory allocator that uses |malloc()| and |free()|. */
struct libavl_allocator tavl_allocator_default = {tavl_malloc, tavl_free};

#undef NDEBUG
#include <assert.h>

/* Asserts that |tavl_insert()| succeeds at inserting |item| into |table|. */
void(tavl_assert_insert)(struct tavl_table *table, void *item)
{
    void **p = tavl_probe(table, item);

    assert(p != NULL && *p == item);
}

/* Asserts that |tavl_delete()| really removes |item| from |table|,
   and returns the removed item. */
void *(tavl_assert_delete)(struct tavl_table *table, void *item)
{
    void *p = tavl_delete(table, item);

    assert(p != NULL);

    return p;
}
