/*      $NetBSD: prop_rb.c,v 1.9 2008/06/17 21:29:47 thorpej Exp $      */

/*-
 * Copyright (c) 2001 The NetBSD Foundation, Inc.
 * All rights reserved.
 *
 * This code is derived from software contributed to The NetBSD Foundation
 * by Matt Thomas <matt@3am-software.com>.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. 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.
 *
 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
 * ``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 FOUNDATION OR CONTRIBUTORS
 * 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.
 */

#include <libprop/proplib.h>

#include "prop_object_impl.h"
#include "prop_rb_impl.h"

#undef KASSERT
#ifdef RBDEBUG
#define KASSERT(x)      _PROP_ASSERT(x)
#else
#define KASSERT(x)      /* nothing */
#endif

#ifndef __predict_false
#define __predict_false(x)      (x)
#endif

static void rb_tree_insert_rebalance(struct rb_tree *, struct rb_node *);
static void rb_tree_removal_rebalance(struct rb_tree *, struct rb_node *,
        unsigned int);
#ifdef RBDEBUG
static const struct rb_node *rb_tree_iterate_const(const struct rb_tree *,
        const struct rb_node *, const unsigned int);
static bool rb_tree_check_node(const struct rb_tree *, const struct rb_node *,
        const struct rb_node *, bool);
#else
#define rb_tree_check_node(a, b, c, d)  true
#endif

#ifdef RBDEBUG
#define RBT_COUNT_INCR(rbt)     (rbt)->rbt_count++
#define RBT_COUNT_DECR(rbt)     (rbt)->rbt_count--
#else
#define RBT_COUNT_INCR(rbt)     /* nothing */
#define RBT_COUNT_DECR(rbt)     /* nothing */
#endif

#define RBUNCONST(a)    ((void *)(unsigned long)(const void *)(a))

#define RB_NODETOITEM(rbto, rbn)        \
    ((void *)((uintptr_t)(rbn) - (rbto)->rbto_node_offset))
#define RB_ITEMTONODE(rbto, rbn)        \
    ((rb_node_t *)((uintptr_t)(rbn) + (rbto)->rbto_node_offset))

#define RB_SENTINEL_NODE        NULL

void
_prop_rb_tree_init(struct rb_tree *rbt, const rb_tree_ops_t *ops)
{
        RB_TAILQ_INIT(&rbt->rbt_nodes);
#ifdef RBDEBUG
        rbt->rbt_count = 0;
#endif
        rbt->rbt_ops = ops;
        rbt->rbt_root = RB_SENTINEL_NODE;
}


void *
_prop_rb_tree_find(struct rb_tree *rbt, const void *key)
{
        const rb_tree_ops_t *rbto = rbt->rbt_ops;
        rbto_compare_key_fn compare_key = rbto->rbto_compare_key;
        struct rb_node *parent = rbt->rbt_root;

        while (!RB_SENTINEL_P(parent)) {
                void *pobj = RB_NODETOITEM(rbto, parent);
                const signed int diff = (*compare_key)(rbto->rbto_context,
                    pobj, key);
                if (diff == 0)
                        return pobj;
                parent = parent->rb_nodes[diff < 0];
        }

        return NULL;
}

void *
_prop_rb_tree_insert_node(struct rb_tree *rbt, void *object)
{
        const rb_tree_ops_t *rbto = rbt->rbt_ops;
        rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes;
        struct rb_node *parent, *tmp, *self = RB_ITEMTONODE(rbto, object);
        unsigned int position;
        bool rebalance;

        RBSTAT_INC(rbt->rbt_insertions);

        tmp = rbt->rbt_root;
        /*
         * This is a hack.  Because rbt->rbt_root is just a struct rb_node *,
         * just like rb_node->rb_nodes[RB_DIR_LEFT], we can use this fact to
         * avoid a lot of tests for root and know that even at root,
         * updating RB_FATHER(rb_node)->rb_nodes[RB_POSITION(rb_node)] will
         * update rbt->rbt_root.
         */
        parent = (struct rb_node *)(void *)&rbt->rbt_root;
        position = RB_DIR_LEFT;

        /*
         * Find out where to place this new leaf.
         */
        while (!RB_SENTINEL_P(tmp)) {
                void *tobj = RB_NODETOITEM(rbto, tmp);
                const signed int diff = (*compare_nodes)(rbto->rbto_context,
                    tobj, object);
                if (__predict_false(diff == 0)) {
                        /*
                         * Node already exists; return it.
                         */
                        return tobj;
                }
                parent = tmp;
                position = (diff < 0);
                tmp = parent->rb_nodes[position];
        }

#ifdef RBDEBUG
        {
                struct rb_node *prev = NULL, *next = NULL;

                if (position == RB_DIR_RIGHT)
                        prev = parent;
                else if (tmp != rbt->rbt_root)
                        next = parent;

                /*
                 * Verify our sequential position
                 */
                KASSERT(prev == NULL || !RB_SENTINEL_P(prev));
                KASSERT(next == NULL || !RB_SENTINEL_P(next));
                if (prev != NULL && next == NULL)
                        next = TAILQ_NEXT(prev, rb_link);
                if (prev == NULL && next != NULL)
                        prev = TAILQ_PREV(next, rb_node_qh, rb_link);
                KASSERT(prev == NULL || !RB_SENTINEL_P(prev));
                KASSERT(next == NULL || !RB_SENTINEL_P(next));
                KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context,
                    RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0);
                KASSERT(next == NULL || (*compare_nodes)(rbto->rbto_context,
                    RB_NODETOITEM(rbto, self), RB_NODETOITEM(rbto, next)) < 0);
        }
#endif

        /*
         * Initialize the node and insert as a leaf into the tree.
         */
        RB_SET_FATHER(self, parent);
        RB_SET_POSITION(self, position);
        if (__predict_false(parent == (struct rb_node *)(void *)&rbt->rbt_root)) {
                RB_MARK_BLACK(self);            /* root is always black */
#ifndef RBSMALL
                rbt->rbt_minmax[RB_DIR_LEFT] = self;
                rbt->rbt_minmax[RB_DIR_RIGHT] = self;
#endif
                rebalance = false;
        } else {
                KASSERT(position == RB_DIR_LEFT || position == RB_DIR_RIGHT);
#ifndef RBSMALL
                /*
                 * Keep track of the minimum and maximum nodes.  If our
                 * parent is a minmax node and we on their min/max side,
                 * we must be the new min/max node.
                 */
                if (parent == rbt->rbt_minmax[position])
                        rbt->rbt_minmax[position] = self;
#endif /* !RBSMALL */
                /*
                 * All new nodes are colored red.  We only need to rebalance
                 * if our parent is also red.
                 */
                RB_MARK_RED(self);
                rebalance = RB_RED_P(parent);
        }
        KASSERT(RB_SENTINEL_P(parent->rb_nodes[position]));
        self->rb_left = parent->rb_nodes[position];
        self->rb_right = parent->rb_nodes[position];
        parent->rb_nodes[position] = self;
        KASSERT(RB_CHILDLESS_P(self));

        /*
         * Insert the new node into a sorted list for easy sequential access
         */
        RBSTAT_INC(rbt->rbt_count);
#ifdef RBDEBUG
        if (RB_ROOT_P(rbt, self)) {
                RB_TAILQ_INSERT_HEAD(&rbt->rbt_nodes, self, rb_link);
        } else if (position == RB_DIR_LEFT) {
                KASSERT((*compare_nodes)(rbto->rbto_context,
                    RB_NODETOITEM(rbto, self),
                    RB_NODETOITEM(rbto, RB_FATHER(self))) < 0);
                RB_TAILQ_INSERT_BEFORE(RB_FATHER(self), self, rb_link);
        } else {
                KASSERT((*compare_nodes)(rbto->rbto_context,
                    RB_NODETOITEM(rbto, RB_FATHER(self)),
                    RB_NODETOITEM(rbto, self)) < 0);
                RB_TAILQ_INSERT_AFTER(&rbt->rbt_nodes, RB_FATHER(self),
                    self, rb_link);
        }
#endif
        KASSERT(rb_tree_check_node(rbt, self, NULL, !rebalance));

        /*
         * Rebalance tree after insertion
         */
        if (rebalance) {
                rb_tree_insert_rebalance(rbt, self);
                KASSERT(rb_tree_check_node(rbt, self, NULL, true));
        }

        /* Succesfully inserted, return our node pointer. */
        return object;
}

/*
 * Swap the location and colors of 'self' and its child @ which.  The child
 * can not be a sentinel node.  This is our rotation function.  However,
 * since it preserves coloring, it great simplifies both insertion and
 * removal since rotation almost always involves the exchanging of colors
 * as a separate step.
 */
/*ARGSUSED*/
static void
rb_tree_reparent_nodes(struct rb_tree *rbt, struct rb_node *old_father,
        const unsigned int which)
{
        const unsigned int other = which ^ RB_DIR_OTHER;
        struct rb_node * const grandpa = RB_FATHER(old_father);
        struct rb_node * const old_child = old_father->rb_nodes[which];
        struct rb_node * const new_father = old_child;
        struct rb_node * const new_child = old_father;

        KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);

        KASSERT(!RB_SENTINEL_P(old_child));
        KASSERT(RB_FATHER(old_child) == old_father);

        KASSERT(rb_tree_check_node(rbt, old_father, NULL, false));
        KASSERT(rb_tree_check_node(rbt, old_child, NULL, false));
        KASSERT(RB_ROOT_P(rbt, old_father) ||
            rb_tree_check_node(rbt, grandpa, NULL, false));

        /*
         * Exchange descendant linkages.
         */
        grandpa->rb_nodes[RB_POSITION(old_father)] = new_father;
        new_child->rb_nodes[which] = old_child->rb_nodes[other];
        new_father->rb_nodes[other] = new_child;

        /*
         * Update ancestor linkages
         */
        RB_SET_FATHER(new_father, grandpa);
        RB_SET_FATHER(new_child, new_father);

        /*
         * Exchange properties between new_father and new_child.  The only
         * change is that new_child's position is now on the other side.
         */
#if 0
        {
                struct rb_node tmp;
                tmp.rb_info = 0;
                RB_COPY_PROPERTIES(&tmp, old_child);
                RB_COPY_PROPERTIES(new_father, old_father);
                RB_COPY_PROPERTIES(new_child, &tmp);
        }
#else
        RB_SWAP_PROPERTIES(new_father, new_child);
#endif
        RB_SET_POSITION(new_child, other);

        /*
         * Make sure to reparent the new child to ourself.
         */
        if (!RB_SENTINEL_P(new_child->rb_nodes[which])) {
                RB_SET_FATHER(new_child->rb_nodes[which], new_child);
                RB_SET_POSITION(new_child->rb_nodes[which], which);
        }

        KASSERT(rb_tree_check_node(rbt, new_father, NULL, false));
        KASSERT(rb_tree_check_node(rbt, new_child, NULL, false));
        KASSERT(RB_ROOT_P(rbt, new_father) ||
            rb_tree_check_node(rbt, grandpa, NULL, false));
}

static void
rb_tree_insert_rebalance(struct rb_tree *rbt, struct rb_node *self)
{
        struct rb_node * father = RB_FATHER(self);
        struct rb_node * grandpa = RB_FATHER(father);
        struct rb_node * uncle;
        unsigned int which;
        unsigned int other;

        KASSERT(!RB_ROOT_P(rbt, self));
        KASSERT(RB_RED_P(self));
        KASSERT(RB_RED_P(father));
        RBSTAT_INC(rbt->rbt_insertion_rebalance_calls);

        for (;;) {
                KASSERT(!RB_SENTINEL_P(self));

                KASSERT(RB_RED_P(self));
                KASSERT(RB_RED_P(father));
                /*
                 * We are red and our parent is red, therefore we must have a
                 * grandfather and he must be black.
                 */
                grandpa = RB_FATHER(father);
                KASSERT(RB_BLACK_P(grandpa));
                KASSERT(RB_DIR_RIGHT == 1 && RB_DIR_LEFT == 0);
                which = (father == grandpa->rb_right);
                other = which ^ RB_DIR_OTHER;
                uncle = grandpa->rb_nodes[other];

                if (RB_BLACK_P(uncle))
                        break;

                RBSTAT_INC(rbt->rbt_insertion_rebalance_passes);
                /*
                 * Case 1: our uncle is red
                 *   Simply invert the colors of our parent and
                 *   uncle and make our grandparent red.  And
                 *   then solve the problem up at his level.
                 */
                RB_MARK_BLACK(uncle);
                RB_MARK_BLACK(father);
                if (__predict_false(RB_ROOT_P(rbt, grandpa))) {
                        /*
                         * If our grandpa is root, don't bother
                         * setting him to red, just return.
                         */
                        KASSERT(RB_BLACK_P(grandpa));
                        return;
                }
                RB_MARK_RED(grandpa);
                self = grandpa;
                father = RB_FATHER(self);
                KASSERT(RB_RED_P(self));
                if (RB_BLACK_P(father)) {
                        /*
                         * If our greatgrandpa is black, we're done.
                         */
                        KASSERT(RB_BLACK_P(rbt->rbt_root));
                        return;
                }
        }

        KASSERT(!RB_ROOT_P(rbt, self));
        KASSERT(RB_RED_P(self));
        KASSERT(RB_RED_P(father));
        KASSERT(RB_BLACK_P(uncle));
        KASSERT(RB_BLACK_P(grandpa));
        /*
         * Case 2&3: our uncle is black.
         */
        if (self == father->rb_nodes[other]) {
                /*
                 * Case 2: we are on the same side as our uncle
                 *   Swap ourselves with our parent so this case
                 *   becomes case 3.  Basically our parent becomes our
                 *   child.
                 */
                rb_tree_reparent_nodes(rbt, father, other);
                KASSERT(RB_FATHER(father) == self);
                KASSERT(self->rb_nodes[which] == father);
                KASSERT(RB_FATHER(self) == grandpa);
                self = father;
                father = RB_FATHER(self);
        }
        KASSERT(RB_RED_P(self) && RB_RED_P(father));
        KASSERT(grandpa->rb_nodes[which] == father);
        /*
         * Case 3: we are opposite a child of a black uncle.
         *   Swap our parent and grandparent.  Since our grandfather
         *   is black, our father will become black and our new sibling
         *   (former grandparent) will become red.
         */
        rb_tree_reparent_nodes(rbt, grandpa, which);
        KASSERT(RB_FATHER(self) == father);
        KASSERT(RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER] == grandpa);
        KASSERT(RB_RED_P(self));
        KASSERT(RB_BLACK_P(father));
        KASSERT(RB_RED_P(grandpa));

        /*
         * Final step: Set the root to black.
         */
        RB_MARK_BLACK(rbt->rbt_root);
}

static void
rb_tree_prune_node(struct rb_tree *rbt, struct rb_node *self, bool rebalance)
{
        const unsigned int which = RB_POSITION(self);
        struct rb_node *father = RB_FATHER(self);
#ifndef RBSMALL
        const bool was_root = RB_ROOT_P(rbt, self);
#endif

        KASSERT(rebalance || (RB_ROOT_P(rbt, self) || RB_RED_P(self)));
        KASSERT(!rebalance || RB_BLACK_P(self));
        KASSERT(RB_CHILDLESS_P(self));
        KASSERT(rb_tree_check_node(rbt, self, NULL, false));

        /*
         * Since we are childless, we know that self->rb_left is pointing
         * to the sentinel node.
         */
        father->rb_nodes[which] = self->rb_left;

        /*
         * Remove ourselves from the node list, decrement the count,
         * and update min/max.
         */
        RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
        RBSTAT_DEC(rbt->rbt_count);
#ifndef RBSMALL
        if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self)) {
                rbt->rbt_minmax[RB_POSITION(self)] = father;
                /*
                 * When removing the root, rbt->rbt_minmax[RB_DIR_LEFT] is
                 * updated automatically, but we also need to update 
                 * rbt->rbt_minmax[RB_DIR_RIGHT];
                 */
                if (__predict_false(was_root)) {
                        rbt->rbt_minmax[RB_DIR_RIGHT] = father;
                }
        }
        RB_SET_FATHER(self, NULL);
#endif

        /*
         * Rebalance if requested.
         */
        if (rebalance)
                rb_tree_removal_rebalance(rbt, father, which);
        KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true));
}

/*
 * When deleting an interior node
 */
static void
rb_tree_swap_prune_and_rebalance(struct rb_tree *rbt, struct rb_node *self,
        struct rb_node *standin)
{
        const unsigned int standin_which = RB_POSITION(standin);
        unsigned int standin_other = standin_which ^ RB_DIR_OTHER;
        struct rb_node *standin_son;
        struct rb_node *standin_father = RB_FATHER(standin);
        bool rebalance = RB_BLACK_P(standin);

        if (standin_father == self) {
                /*
                 * As a child of self, any childen would be opposite of
                 * our parent.
                 */
                KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other]));
                standin_son = standin->rb_nodes[standin_which];
        } else {
                /*
                 * Since we aren't a child of self, any childen would be
                 * on the same side as our parent.
                 */
                KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_which]));
                standin_son = standin->rb_nodes[standin_other];
        }

        /*
         * the node we are removing must have two children.
         */
        KASSERT(RB_TWOCHILDREN_P(self));
        /*
         * If standin has a child, it must be red.
         */
        KASSERT(RB_SENTINEL_P(standin_son) || RB_RED_P(standin_son));

        /*
         * Verify things are sane.
         */
        KASSERT(rb_tree_check_node(rbt, self, NULL, false));
        KASSERT(rb_tree_check_node(rbt, standin, NULL, false));

        if (__predict_false(RB_RED_P(standin_son))) {
                /*
                 * We know we have a red child so if we flip it to black
                 * we don't have to rebalance.
                 */
                KASSERT(rb_tree_check_node(rbt, standin_son, NULL, true));
                RB_MARK_BLACK(standin_son);
                rebalance = false;

                if (standin_father == self) {
                        KASSERT(RB_POSITION(standin_son) == standin_which);
                } else {
                        KASSERT(RB_POSITION(standin_son) == standin_other);
                        /*
                         * Change the son's parentage to point to his grandpa.
                         */
                        RB_SET_FATHER(standin_son, standin_father);
                        RB_SET_POSITION(standin_son, standin_which);
                }
        }

        if (standin_father == self) {
                /*
                 * If we are about to delete the standin's father, then when
                 * we call rebalance, we need to use ourselves as our father.
                 * Otherwise remember our original father.  Also, sincef we are
                 * our standin's father we only need to reparent the standin's
                 * brother.
                 *
                 * |    R      -->     S    |
                 * |  Q   S    -->   Q   T  |
                 * |        t  -->          |
                 */
                KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other]));
                KASSERT(!RB_SENTINEL_P(self->rb_nodes[standin_other]));
                KASSERT(self->rb_nodes[standin_which] == standin);
                /*
                 * Have our son/standin adopt his brother as his new son.
                 */
                standin_father = standin;
        } else {
                /*
                 * |    R          -->    S       .  |
                 * |   / \  |   T  -->   / \  |  /   |
                 * |  ..... | S    -->  ..... | T    |
                 *
                 * Sever standin's connection to his father.
                 */
                standin_father->rb_nodes[standin_which] = standin_son;
                /*
                 * Adopt the far son.
                 */
                standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
                RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
                KASSERT(RB_POSITION(self->rb_nodes[standin_other]) == standin_other);
                /*
                 * Use standin_other because we need to preserve standin_which
                 * for the removal_rebalance.
                 */
                standin_other = standin_which;
        }

        /*
         * Move the only remaining son to our standin.  If our standin is our
         * son, this will be the only son needed to be moved.
         */
        KASSERT(standin->rb_nodes[standin_other] != self->rb_nodes[standin_other]);
        standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
        RB_SET_FATHER(standin->rb_nodes[standin_other], standin);

        /*
         * Now copy the result of self to standin and then replace
         * self with standin in the tree.
         */
        RB_COPY_PROPERTIES(standin, self);
        RB_SET_FATHER(standin, RB_FATHER(self));
        RB_FATHER(standin)->rb_nodes[RB_POSITION(standin)] = standin;

        /*
         * Remove ourselves from the node list, decrement the count,
         * and update min/max.
         */
        RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
        RBSTAT_DEC(rbt->rbt_count);
#ifndef RBSMALL
        if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self))
                rbt->rbt_minmax[RB_POSITION(self)] = RB_FATHER(self);
        RB_SET_FATHER(self, NULL);
#endif

        KASSERT(rb_tree_check_node(rbt, standin, NULL, false));
        KASSERT(RB_FATHER_SENTINEL_P(standin)
                || rb_tree_check_node(rbt, standin_father, NULL, false));
        KASSERT(RB_LEFT_SENTINEL_P(standin)
                || rb_tree_check_node(rbt, standin->rb_left, NULL, false));
        KASSERT(RB_RIGHT_SENTINEL_P(standin)
                || rb_tree_check_node(rbt, standin->rb_right, NULL, false));

        if (!rebalance)
                return;

        rb_tree_removal_rebalance(rbt, standin_father, standin_which);
        KASSERT(rb_tree_check_node(rbt, standin, NULL, true));
}

/*
 * We could do this by doing
 *      rb_tree_node_swap(rbt, self, which);
 *      rb_tree_prune_node(rbt, self, false);
 *
 * But it's more efficient to just evalate and recolor the child.
 */
static void
rb_tree_prune_blackred_branch(struct rb_tree *rbt, struct rb_node *self,
        unsigned int which)
{
        struct rb_node *father = RB_FATHER(self);
        struct rb_node *son = self->rb_nodes[which];
#ifndef RBSMALL
        const bool was_root = RB_ROOT_P(rbt, self);
#endif

        KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);
        KASSERT(RB_BLACK_P(self) && RB_RED_P(son));
        KASSERT(!RB_TWOCHILDREN_P(son));
        KASSERT(RB_CHILDLESS_P(son));
        KASSERT(rb_tree_check_node(rbt, self, NULL, false));
        KASSERT(rb_tree_check_node(rbt, son, NULL, false));

        /*
         * Remove ourselves from the tree and give our former child our
         * properties (position, color, root).
         */
        RB_COPY_PROPERTIES(son, self);
        father->rb_nodes[RB_POSITION(son)] = son;
        RB_SET_FATHER(son, father);

        /*
         * Remove ourselves from the node list, decrement the count,
         * and update minmax.
         */
        RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
        RBSTAT_DEC(rbt->rbt_count);
#ifndef RBSMALL
        if (__predict_false(was_root)) {
                KASSERT(rbt->rbt_minmax[which] == son);
                rbt->rbt_minmax[which ^ RB_DIR_OTHER] = son;
        } else if (rbt->rbt_minmax[RB_POSITION(self)] == self) {
                rbt->rbt_minmax[RB_POSITION(self)] = son;
        }
        RB_SET_FATHER(self, NULL);
#endif

        KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true));
        KASSERT(rb_tree_check_node(rbt, son, NULL, true));
}

void
_prop_rb_tree_remove_node(struct rb_tree *rbt, void *object)
{
        const rb_tree_ops_t *rbto = rbt->rbt_ops;
        struct rb_node *standin, *self = RB_ITEMTONODE(rbto, object);
        unsigned int which;

        KASSERT(!RB_SENTINEL_P(self));
        RBSTAT_INC(rbt->rbt_removals);

        /*
         * In the following diagrams, we (the node to be removed) are S.  Red
         * nodes are lowercase.  T could be either red or black.
         *
         * Remember the major axiom of the red-black tree: the number of
         * black nodes from the root to each leaf is constant across all
         * leaves, only the number of red nodes varies.
         *
         * Thus removing a red leaf doesn't require any other changes to a
         * red-black tree.  So if we must remove a node, attempt to rearrange
         * the tree so we can remove a red node.
         *
         * The simpliest case is a childless red node or a childless root node:
         *
         * |    T  -->    T  |    or    |  R  -->  *  |
         * |  s    -->  *    |
         */
        if (RB_CHILDLESS_P(self)) {
                const bool rebalance = RB_BLACK_P(self) && !RB_ROOT_P(rbt, self);
                rb_tree_prune_node(rbt, self, rebalance);
                return;
        }
        KASSERT(!RB_CHILDLESS_P(self));
        if (!RB_TWOCHILDREN_P(self)) {
                /*
                 * The next simpliest case is the node we are deleting is
                 * black and has one red child.
                 *
                 * |      T  -->      T  -->      T  |
                 * |    S    -->  R      -->  R      |
                 * |  r      -->    s    -->    *    |
                 */
                which = RB_LEFT_SENTINEL_P(self) ? RB_DIR_RIGHT : RB_DIR_LEFT;
                KASSERT(RB_BLACK_P(self));
                KASSERT(RB_RED_P(self->rb_nodes[which]));
                KASSERT(RB_CHILDLESS_P(self->rb_nodes[which]));
                rb_tree_prune_blackred_branch(rbt, self, which);
                return;
        }
        KASSERT(RB_TWOCHILDREN_P(self));

        /*
         * We invert these because we prefer to remove from the inside of
         * the tree.
         */
        which = RB_POSITION(self) ^ RB_DIR_OTHER;

        /*
         * Let's find the node closes to us opposite of our parent
         * Now swap it with ourself, "prune" it, and rebalance, if needed.
         */
        standin = RB_ITEMTONODE(rbto, _prop_rb_tree_iterate(rbt, object, which));
        rb_tree_swap_prune_and_rebalance(rbt, self, standin);
}

static void
rb_tree_removal_rebalance(struct rb_tree *rbt, struct rb_node *parent,
        unsigned int which)
{
        KASSERT(!RB_SENTINEL_P(parent));
        KASSERT(RB_SENTINEL_P(parent->rb_nodes[which]));
        KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);
        RBSTAT_INC(rbt->rbt_removal_rebalance_calls);

        while (RB_BLACK_P(parent->rb_nodes[which])) {
                unsigned int other = which ^ RB_DIR_OTHER;
                struct rb_node *brother = parent->rb_nodes[other];

                RBSTAT_INC(rbt->rbt_removal_rebalance_passes);

                KASSERT(!RB_SENTINEL_P(brother));
                /*
                 * For cases 1, 2a, and 2b, our brother's children must
                 * be black and our father must be black
                 */
                if (RB_BLACK_P(parent)
                    && RB_BLACK_P(brother->rb_left)
                    && RB_BLACK_P(brother->rb_right)) {
                        if (RB_RED_P(brother)) {
                                /*
                                 * Case 1: Our brother is red, swap its
                                 * position (and colors) with our parent. 
                                 * This should now be case 2b (unless C or E
                                 * has a red child which is case 3; thus no
                                 * explicit branch to case 2b).
                                 *
                                 *    B         ->        D
                                 *  A     d     ->    b     E
                                 *      C   E   ->  A   C
                                 */
                                KASSERT(RB_BLACK_P(parent));
                                rb_tree_reparent_nodes(rbt, parent, other);
                                brother = parent->rb_nodes[other];
                                KASSERT(!RB_SENTINEL_P(brother));
                                KASSERT(RB_RED_P(parent));
                                KASSERT(RB_BLACK_P(brother));
                                KASSERT(rb_tree_check_node(rbt, brother, NULL, false));
                                KASSERT(rb_tree_check_node(rbt, parent, NULL, false));
                        } else {
                                /*
                                 * Both our parent and brother are black.
                                 * Change our brother to red, advance up rank
                                 * and go through the loop again.
                                 *
                                 *    B         ->   *B
                                 * *A     D     ->  A     d
                                 *      C   E   ->      C   E
                                 */
                                RB_MARK_RED(brother);
                                KASSERT(RB_BLACK_P(brother->rb_left));
                                KASSERT(RB_BLACK_P(brother->rb_right));
                                if (RB_ROOT_P(rbt, parent))
                                        return; /* root == parent == black */
                                KASSERT(rb_tree_check_node(rbt, brother, NULL, false));
                                KASSERT(rb_tree_check_node(rbt, parent, NULL, false));
                                which = RB_POSITION(parent);
                                parent = RB_FATHER(parent);
                                continue;
                        }
                }
                /*
                 * Avoid an else here so that case 2a above can hit either
                 * case 2b, 3, or 4.
                 */
                if (RB_RED_P(parent)
                    && RB_BLACK_P(brother)
                    && RB_BLACK_P(brother->rb_left)
                    && RB_BLACK_P(brother->rb_right)) {
                        KASSERT(RB_RED_P(parent));
                        KASSERT(RB_BLACK_P(brother));
                        KASSERT(RB_BLACK_P(brother->rb_left));
                        KASSERT(RB_BLACK_P(brother->rb_right));
                        /*
                         * We are black, our father is red, our brother and
                         * both nephews are black.  Simply invert/exchange the
                         * colors of our father and brother (to black and red
                         * respectively).
                         *
                         *      |    f        -->    F        |
                         *      |  *     B    -->  *     b    |
                         *      |      N   N  -->      N   N  |
                         */
                        RB_MARK_BLACK(parent);
                        RB_MARK_RED(brother);
                        KASSERT(rb_tree_check_node(rbt, brother, NULL, true));
                        break;          /* We're done! */
                } else {
                        /*
                         * Our brother must be black and have at least one
                         * red child (it may have two).
                         */
                        KASSERT(RB_BLACK_P(brother));
                        KASSERT(RB_RED_P(brother->rb_nodes[which]) ||
                                RB_RED_P(brother->rb_nodes[other]));
                        if (RB_BLACK_P(brother->rb_nodes[other])) {
                                /*
                                 * Case 3: our brother is black, our near
                                 * nephew is red, and our far nephew is black.
                                 * Swap our brother with our near nephew.  
                                 * This result in a tree that matches case 4.
                                 * (Our father could be red or black).
                                 *
                                 *      |    F      -->    F      |
                                 *      |  x     B  -->  x   B    |
                                 *      |      n    -->        n  |
                                 */
                                KASSERT(RB_RED_P(brother->rb_nodes[which]));
                                rb_tree_reparent_nodes(rbt, brother, which);
                                KASSERT(RB_FATHER(brother) == parent->rb_nodes[other]);
                                brother = parent->rb_nodes[other];
                                KASSERT(RB_RED_P(brother->rb_nodes[other]));
                        }
                        /*
                         * Case 4: our brother is black and our far nephew
                         * is red.  Swap our father and brother locations and
                         * change our far nephew to black.  (these can be
                         * done in either order so we change the color first).
                         * The result is a valid red-black tree and is a
                         * terminal case.  (again we don't care about the
                         * father's color)
                         *
                         * If the father is red, we will get a red-black-black
                         * tree:
                         *      |  f      ->  f      -->    b    |
                         *      |    B    ->    B    -->  F   N  |
                         *      |      n  ->      N  -->         |
                         *
                         * If the father is black, we will get an all black
                         * tree:
                         *      |  F      ->  F      -->    B    |
                         *      |    B    ->    B    -->  F   N  |
                         *      |      n  ->      N  -->         |
                         *
                         * If we had two red nephews, then after the swap,
                         * our former father would have a red grandson. 
                         */
                        KASSERT(RB_BLACK_P(brother));
                        KASSERT(RB_RED_P(brother->rb_nodes[other]));
                        RB_MARK_BLACK(brother->rb_nodes[other]);
                        rb_tree_reparent_nodes(rbt, parent, other);
                        break;          /* We're done! */
                }
        }
        KASSERT(rb_tree_check_node(rbt, parent, NULL, true));
}

void *
_prop_rb_tree_iterate(struct rb_tree *rbt, void *object, const unsigned int direction)
{
        const rb_tree_ops_t *rbto = rbt->rbt_ops;
        const unsigned int other = direction ^ RB_DIR_OTHER;
        struct rb_node *self;

        KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT);

        if (object == NULL) {
#ifndef RBSMALL
                if (RB_SENTINEL_P(rbt->rbt_root))
                        return NULL;
                return RB_NODETOITEM(rbto, rbt->rbt_minmax[direction]);
#else
                self = rbt->rbt_root;
                if (RB_SENTINEL_P(self))
                        return NULL;
                while (!RB_SENTINEL_P(self->rb_nodes[direction]))
                        self = self->rb_nodes[direction];
                return RB_NODETOITEM(rbto, self);
#endif /* !RBSMALL */
        }
        self = RB_ITEMTONODE(rbto, object);
        KASSERT(!RB_SENTINEL_P(self));
        /*
         * We can't go any further in this direction.  We proceed up in the
         * opposite direction until our parent is in direction we want to go.
         */
        if (RB_SENTINEL_P(self->rb_nodes[direction])) {
                while (!RB_ROOT_P(rbt, self)) {
                        if (other == RB_POSITION(self))
                                return RB_NODETOITEM(rbto, RB_FATHER(self));
                        self = RB_FATHER(self);
                }
                return NULL;
        }

        /*
         * Advance down one in current direction and go down as far as possible
         * in the opposite direction.
         */
        self = self->rb_nodes[direction];
        KASSERT(!RB_SENTINEL_P(self));
        while (!RB_SENTINEL_P(self->rb_nodes[other]))
                self = self->rb_nodes[other];
        return RB_NODETOITEM(rbto, self);
}

#ifdef RBDEBUG
static const struct rb_node *
rb_tree_iterate_const(const struct rb_tree *rbt, const struct rb_node *self,
        const unsigned int direction)
{
        const unsigned int other = direction ^ RB_DIR_OTHER;
        KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT);

        if (self == NULL) {
#ifndef RBSMALL
                if (RB_SENTINEL_P(rbt->rbt_root))
                        return NULL;
                return rbt->rbt_minmax[direction];
#else
                self = rbt->rbt_root;
                if (RB_SENTINEL_P(self))
                        return NULL;
                while (!RB_SENTINEL_P(self->rb_nodes[direction]))
                        self = self->rb_nodes[direction];
                return self;
#endif /* !RBSMALL */
        }
        KASSERT(!RB_SENTINEL_P(self));
        /*
         * We can't go any further in this direction.  We proceed up in the
         * opposite direction until our parent is in direction we want to go.
         */
        if (RB_SENTINEL_P(self->rb_nodes[direction])) {
                while (!RB_ROOT_P(rbt, self)) {
                        if (other == RB_POSITION(self))
                                return RB_FATHER(self);
                        self = RB_FATHER(self);
                }
                return NULL;
        }

        /*
         * Advance down one in current direction and go down as far as possible
         * in the opposite direction.
         */
        self = self->rb_nodes[direction];
        KASSERT(!RB_SENTINEL_P(self));
        while (!RB_SENTINEL_P(self->rb_nodes[other]))
                self = self->rb_nodes[other];
        return self;
}

static unsigned int
rb_tree_count_black(const struct rb_node *self)
{
        unsigned int left, right;

        if (RB_SENTINEL_P(self))
                return 0;

        left = rb_tree_count_black(self->rb_left);
        right = rb_tree_count_black(self->rb_right);

        KASSERT(left == right);

        return left + RB_BLACK_P(self);
}

static bool
rb_tree_check_node(const struct rb_tree *rbt, const struct rb_node *self,
        const struct rb_node *prev, bool red_check)
{
        const rb_tree_ops_t *rbto = rbt->rbt_ops;
        rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes;

        KASSERT(!RB_SENTINEL_P(self));
        KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context,
            RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0);

        /*
         * Verify our relationship to our parent.
         */
        if (RB_ROOT_P(rbt, self)) {
                KASSERT(self == rbt->rbt_root);
                KASSERT(RB_POSITION(self) == RB_DIR_LEFT);
                KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self);
                KASSERT(RB_FATHER(self) == (const struct rb_node *) &rbt->rbt_root);
        } else {
                int diff = (*compare_nodes)(rbto->rbto_context,
                    RB_NODETOITEM(rbto, self),
                    RB_NODETOITEM(rbto, RB_FATHER(self)));

                KASSERT(self != rbt->rbt_root);
                KASSERT(!RB_FATHER_SENTINEL_P(self));
                if (RB_POSITION(self) == RB_DIR_LEFT) {
                        KASSERT(diff < 0);
                        KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self);
                } else {
                        KASSERT(diff > 0);
                        KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_RIGHT] == self);
                }
        }

        /*
         * Verify our position in the linked list against the tree itself.
         */
        {
                const struct rb_node *prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT);
                const struct rb_node *next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT);
                KASSERT(prev0 == TAILQ_PREV(self, rb_node_qh, rb_link));
                KASSERT(next0 == TAILQ_NEXT(self, rb_link));
#ifndef RBSMALL
                KASSERT(prev0 != NULL || self == rbt->rbt_minmax[RB_DIR_LEFT]);
                KASSERT(next0 != NULL || self == rbt->rbt_minmax[RB_DIR_RIGHT]);
#endif
        }

        /*
         * The root must be black.
         * There can never be two adjacent red nodes. 
         */
        if (red_check) {
                KASSERT(!RB_ROOT_P(rbt, self) || RB_BLACK_P(self));
                (void) rb_tree_count_black(self);
                if (RB_RED_P(self)) {
                        const struct rb_node *brother;
                        KASSERT(!RB_ROOT_P(rbt, self));
                        brother = RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER];
                        KASSERT(RB_BLACK_P(RB_FATHER(self)));
                        /* 
                         * I'm red and have no children, then I must either
                         * have no brother or my brother also be red and
                         * also have no children.  (black count == 0)
                         */
                        KASSERT(!RB_CHILDLESS_P(self)
                                || RB_SENTINEL_P(brother)
                                || RB_RED_P(brother)
                                || RB_CHILDLESS_P(brother));
                        /*
                         * If I'm not childless, I must have two children
                         * and they must be both be black.
                         */
                        KASSERT(RB_CHILDLESS_P(self)
                                || (RB_TWOCHILDREN_P(self)
                                    && RB_BLACK_P(self->rb_left)
                                    && RB_BLACK_P(self->rb_right)));
                        /*
                         * If I'm not childless, thus I have black children,
                         * then my brother must either be black or have two
                         * black children.
                         */
                        KASSERT(RB_CHILDLESS_P(self)
                                || RB_BLACK_P(brother)
                                || (RB_TWOCHILDREN_P(brother)
                                    && RB_BLACK_P(brother->rb_left)
                                    && RB_BLACK_P(brother->rb_right)));
                } else {
                        /*
                         * If I'm black and have one child, that child must
                         * be red and childless.
                         */
                        KASSERT(RB_CHILDLESS_P(self)
                                || RB_TWOCHILDREN_P(self)
                                || (!RB_LEFT_SENTINEL_P(self)
                                    && RB_RIGHT_SENTINEL_P(self)
                                    && RB_RED_P(self->rb_left)
                                    && RB_CHILDLESS_P(self->rb_left))
                                || (!RB_RIGHT_SENTINEL_P(self)
                                    && RB_LEFT_SENTINEL_P(self)
                                    && RB_RED_P(self->rb_right)
                                    && RB_CHILDLESS_P(self->rb_right)));

                        /*
                         * If I'm a childless black node and my parent is
                         * black, my 2nd closet relative away from my parent
                         * is either red or has a red parent or red children.
                         */
                        if (!RB_ROOT_P(rbt, self)
                            && RB_CHILDLESS_P(self)
                            && RB_BLACK_P(RB_FATHER(self))) {
                                const unsigned int which = RB_POSITION(self);
                                const unsigned int other = which ^ RB_DIR_OTHER;
                                const struct rb_node *relative0, *relative;

                                relative0 = rb_tree_iterate_const(rbt,
                                    self, other);
                                KASSERT(relative0 != NULL);
                                relative = rb_tree_iterate_const(rbt,
                                    relative0, other);
                                KASSERT(relative != NULL);
                                KASSERT(RB_SENTINEL_P(relative->rb_nodes[which]));
#if 0
                                KASSERT(RB_RED_P(relative)
                                        || RB_RED_P(relative->rb_left)
                                        || RB_RED_P(relative->rb_right)
                                        || RB_RED_P(RB_FATHER(relative)));
#endif
                        }
                }
                /*
                 * A grandparent's children must be real nodes and not
                 * sentinels.  First check out grandparent.
                 */
                KASSERT(RB_ROOT_P(rbt, self)
                        || RB_ROOT_P(rbt, RB_FATHER(self))
                        || RB_TWOCHILDREN_P(RB_FATHER(RB_FATHER(self))));
                /*
                 * If we are have grandchildren on our left, then
                 * we must have a child on our right.
                 */
                KASSERT(RB_LEFT_SENTINEL_P(self)
                        || RB_CHILDLESS_P(self->rb_left)
                        || !RB_RIGHT_SENTINEL_P(self));
                /*
                 * If we are have grandchildren on our right, then
                 * we must have a child on our left.
                 */
                KASSERT(RB_RIGHT_SENTINEL_P(self)
                        || RB_CHILDLESS_P(self->rb_right)
                        || !RB_LEFT_SENTINEL_P(self));

                /*
                 * If we have a child on the left and it doesn't have two
                 * children make sure we don't have great-great-grandchildren on
                 * the right.
                 */
                KASSERT(RB_TWOCHILDREN_P(self->rb_left)
                        || RB_CHILDLESS_P(self->rb_right)
                        || RB_CHILDLESS_P(self->rb_right->rb_left)
                        || RB_CHILDLESS_P(self->rb_right->rb_left->rb_left)
                        || RB_CHILDLESS_P(self->rb_right->rb_left->rb_right)
                        || RB_CHILDLESS_P(self->rb_right->rb_right)
                        || RB_CHILDLESS_P(self->rb_right->rb_right->rb_left)
                        || RB_CHILDLESS_P(self->rb_right->rb_right->rb_right));

                /*
                 * If we have a child on the right and it doesn't have two
                 * children make sure we don't have great-great-grandchildren on
                 * the left.
                 */
                KASSERT(RB_TWOCHILDREN_P(self->rb_right)
                        || RB_CHILDLESS_P(self->rb_left)
                        || RB_CHILDLESS_P(self->rb_left->rb_left)
                        || RB_CHILDLESS_P(self->rb_left->rb_left->rb_left)
                        || RB_CHILDLESS_P(self->rb_left->rb_left->rb_right)
                        || RB_CHILDLESS_P(self->rb_left->rb_right)
                        || RB_CHILDLESS_P(self->rb_left->rb_right->rb_left)
                        || RB_CHILDLESS_P(self->rb_left->rb_right->rb_right));

                /*
                 * If we are fully interior node, then our predecessors and
                 * successors must have no children in our direction.
                 */
                if (RB_TWOCHILDREN_P(self)) {
                        const struct rb_node *prev0;
                        const struct rb_node *next0;

                        prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT);
                        KASSERT(prev0 != NULL);
                        KASSERT(RB_RIGHT_SENTINEL_P(prev0));

                        next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT);
                        KASSERT(next0 != NULL);
                        KASSERT(RB_LEFT_SENTINEL_P(next0));
                }
        }

        return true;
}

void
rb_tree_check(const struct rb_tree *rbt, bool red_check)
{
        const struct rb_node *self;
        const struct rb_node *prev;
#ifdef RBSTATS
        unsigned int count = 0;
#endif

        KASSERT(rbt->rbt_root != NULL);
        KASSERT(RB_LEFT_P(rbt->rbt_root));

#if defined(RBSTATS) && !defined(RBSMALL)
        KASSERT(rbt->rbt_count > 1
            || rbt->rbt_minmax[RB_DIR_LEFT] == rbt->rbt_minmax[RB_DIR_RIGHT]);
#endif

        prev = NULL;
        TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) {
                rb_tree_check_node(rbt, self, prev, false);
#ifdef RBSTATS
                count++;
#endif
        }
#ifdef RBSTATS
        KASSERT(rbt->rbt_count == count);
#endif
        if (red_check) {
                KASSERT(RB_BLACK_P(rbt->rbt_root));
                KASSERT(RB_SENTINEL_P(rbt->rbt_root)
                        || rb_tree_count_black(rbt->rbt_root));

                /*
                 * The root must be black.
                 * There can never be two adjacent red nodes. 
                 */
                TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) {
                        rb_tree_check_node(rbt, self, NULL, true);
                }
        }
}
#endif /* RBDEBUG */

#ifdef RBSTATS
static void
rb_tree_mark_depth(const struct rb_tree *rbt, const struct rb_node *self,
        size_t *depths, size_t depth)
{
        if (RB_SENTINEL_P(self))
                return;

        if (RB_TWOCHILDREN_P(self)) {
                rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1);
                rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1);
                return;
        }
        depths[depth]++;
        if (!RB_LEFT_SENTINEL_P(self)) {
                rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1);
        }
        if (!RB_RIGHT_SENTINEL_P(self)) {
                rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1);
        }
}

void
rb_tree_depths(const struct rb_tree *rbt, size_t *depths)
{
        rb_tree_mark_depth(rbt, rbt->rbt_root, depths, 1);
}
#endif /* RBSTATS */