/*
  Red Black Trees
  (C) 1999  Andrea Arcangeli <andrea@suse.de>
  (C) 2002  David Woodhouse <dwmw2@infradead.org>
  (C) 2012  Michel Lespinasse <walken@google.com>

  This program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation; either version 2 of the License, or
  (at your option) any later version.

  This program 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 General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

  linux/lib/rbtree.c
*/

#include <linux/rbtree_augmented.h>

/*
 * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
 *
 *  1) A node is either red or black
 *  2) The root is black
 *  3) All leaves (NULL) are black
 *  4) Both children of every red node are black
 *  5) Every simple path from root to leaves contains the same number
 *     of black nodes.
 *
 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 *  consecutive red nodes in a path and every red node is therefore followed by
 *  a black. So if B is the number of black nodes on every simple path (as per
 *  5), then the longest possible path due to 4 is 2B.
 *
 *  We shall indicate color with case, where black nodes are uppercase and red
 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 *  parentheses and have some accompanying text comment.
 */

static inline void rb_set_black(struct rb_node *rb)
{
        rb->__rb_parent_color |= RB_BLACK;
}

static inline struct rb_node *rb_red_parent(struct rb_node *red)
{
        return (struct rb_node *)red->__rb_parent_color;
}

/*
 * Helper function for rotations:
 * - old's parent and color get assigned to new
 * - old gets assigned new as a parent and 'color' as a color.
 */
static inline void
__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
                        struct rb_root *root, int color)
{
        struct rb_node *parent = rb_parent(old);
        new->__rb_parent_color = old->__rb_parent_color;
        rb_set_parent_color(old, new, color);
        __rb_change_child(old, new, parent, root);
}

static __always_inline void
__rb_insert(struct rb_node *node, struct rb_root *root,
            void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
        struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;

        while (true) {
                /*
                 * Loop invariant: node is red
                 *
                 * If there is a black parent, we are done.
                 * Otherwise, take some corrective action as we don't
                 * want a red root or two consecutive red nodes.
                 */
                if (!parent) {
                        rb_set_parent_color(node, NULL, RB_BLACK);
                        break;
                } else if (rb_is_black(parent))
                        break;

                gparent = rb_red_parent(parent);

                tmp = gparent->rb_right;
                if (parent != tmp) {    /* parent == gparent->rb_left */
                        if (tmp && rb_is_red(tmp)) {
                                /*
                                 * Case 1 - color flips
                                 *
                                 *       G            g
                                 *      / \          / \
                                 *     p   u  -->   P   U
                                 *    /            /
                                 *   n            n
                                 *
                                 * However, since g's parent might be red, and
                                 * 4) does not allow this, we need to recurse
                                 * at g.
                                 */
                                rb_set_parent_color(tmp, gparent, RB_BLACK);
                                rb_set_parent_color(parent, gparent, RB_BLACK);
                                node = gparent;
                                parent = rb_parent(node);
                                rb_set_parent_color(node, parent, RB_RED);
                                continue;
                        }

                        tmp = parent->rb_right;
                        if (node == tmp) {
                                /*
                                 * Case 2 - left rotate at parent
                                 *
                                 *      G             G
                                 *     / \           / \
                                 *    p   U  -->    n   U
                                 *     \           /
                                 *      n         p
                                 *
                                 * This still leaves us in violation of 4), the
                                 * continuation into Case 3 will fix that.
                                 */
                                parent->rb_right = tmp = node->rb_left;
                                node->rb_left = parent;
                                if (tmp)
                                        rb_set_parent_color(tmp, parent,
                                                            RB_BLACK);
                                rb_set_parent_color(parent, node, RB_RED);
                                augment_rotate(parent, node);
                                parent = node;
                                tmp = node->rb_right;
                        }

                        /*
                         * Case 3 - right rotate at gparent
                         *
                         *        G           P
                         *       / \         / \
                         *      p   U  -->  n   g
                         *     /                 \
                         *    n                   U
                         */
                        gparent->rb_left = tmp;  /* == parent->rb_right */
                        parent->rb_right = gparent;
                        if (tmp)
                                rb_set_parent_color(tmp, gparent, RB_BLACK);
                        __rb_rotate_set_parents(gparent, parent, root, RB_RED);
                        augment_rotate(gparent, parent);
                        break;
                } else {
                        tmp = gparent->rb_left;
                        if (tmp && rb_is_red(tmp)) {
                                /* Case 1 - color flips */
                                rb_set_parent_color(tmp, gparent, RB_BLACK);
                                rb_set_parent_color(parent, gparent, RB_BLACK);
                                node = gparent;
                                parent = rb_parent(node);
                                rb_set_parent_color(node, parent, RB_RED);
                                continue;
                        }

                        tmp = parent->rb_left;
                        if (node == tmp) {
                                /* Case 2 - right rotate at parent */
                                parent->rb_left = tmp = node->rb_right;
                                node->rb_right = parent;
                                if (tmp)
                                        rb_set_parent_color(tmp, parent,
                                                            RB_BLACK);
                                rb_set_parent_color(parent, node, RB_RED);
                                augment_rotate(parent, node);
                                parent = node;
                                tmp = node->rb_left;
                        }

                        /* Case 3 - left rotate at gparent */
                        gparent->rb_right = tmp;  /* == parent->rb_left */
                        parent->rb_left = gparent;
                        if (tmp)
                                rb_set_parent_color(tmp, gparent, RB_BLACK);
                        __rb_rotate_set_parents(gparent, parent, root, RB_RED);
                        augment_rotate(gparent, parent);
                        break;
                }
        }
}

/*
 * Inline version for rb_erase() use - we want to be able to inline
 * and eliminate the dummy_rotate callback there
 */
static __always_inline void
____rb_erase_color(struct rb_node *parent, struct rb_root *root,
        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
        struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;

        while (true) {
                /*
                 * Loop invariants:
                 * - node is black (or NULL on first iteration)
                 * - node is not the root (parent is not NULL)
                 * - All leaf paths going through parent and node have a
                 *   black node count that is 1 lower than other leaf paths.
                 */
                sibling = parent->rb_right;
                if (node != sibling) {  /* node == parent->rb_left */
                        if (rb_is_red(sibling)) {
                                /*
                                 * Case 1 - left rotate at parent
                                 *
                                 *     P               S
                                 *    / \             / \
                                 *   N   s    -->    p   Sr
                                 *      / \         / \
                                 *     Sl  Sr      N   Sl
                                 */
                                parent->rb_right = tmp1 = sibling->rb_left;
                                sibling->rb_left = parent;
                                rb_set_parent_color(tmp1, parent, RB_BLACK);
                                __rb_rotate_set_parents(parent, sibling, root,
                                                        RB_RED);
                                augment_rotate(parent, sibling);
                                sibling = tmp1;
                        }
                        tmp1 = sibling->rb_right;
                        if (!tmp1 || rb_is_black(tmp1)) {
                                tmp2 = sibling->rb_left;
                                if (!tmp2 || rb_is_black(tmp2)) {
                                        /*
                                         * Case 2 - sibling color flip
                                         * (p could be either color here)
                                         *
                                         *    (p)           (p)
                                         *    / \           / \
                                         *   N   S    -->  N   s
                                         *      / \           / \
                                         *     Sl  Sr        Sl  Sr
                                         *
                                         * This leaves us violating 5) which
                                         * can be fixed by flipping p to black
                                         * if it was red, or by recursing at p.
                                         * p is red when coming from Case 1.
                                         */
                                        rb_set_parent_color(sibling, parent,
                                                            RB_RED);
                                        if (rb_is_red(parent))
                                                rb_set_black(parent);
                                        else {
                                                node = parent;
                                                parent = rb_parent(node);
                                                if (parent)
                                                        continue;
                                        }
                                        break;
                                }
                                /*
                                 * Case 3 - right rotate at sibling
                                 * (p could be either color here)
                                 *
                                 *   (p)           (p)
                                 *   / \           / \
                                 *  N   S    -->  N   Sl
                                 *     / \             \
                                 *    sl  Sr            s
                                 *                       \
                                 *                        Sr
                                 */
                                sibling->rb_left = tmp1 = tmp2->rb_right;
                                tmp2->rb_right = sibling;
                                parent->rb_right = tmp2;
                                if (tmp1)
                                        rb_set_parent_color(tmp1, sibling,
                                                            RB_BLACK);
                                augment_rotate(sibling, tmp2);
                                tmp1 = sibling;
                                sibling = tmp2;
                        }
                        /*
                         * Case 4 - left rotate at parent + color flips
                         * (p and sl could be either color here.
                         *  After rotation, p becomes black, s acquires
                         *  p's color, and sl keeps its color)
                         *
                         *      (p)             (s)
                         *      / \             / \
                         *     N   S     -->   P   Sr
                         *        / \         / \
                         *      (sl) sr      N  (sl)
                         */
                        parent->rb_right = tmp2 = sibling->rb_left;
                        sibling->rb_left = parent;
                        rb_set_parent_color(tmp1, sibling, RB_BLACK);
                        if (tmp2)
                                rb_set_parent(tmp2, parent);
                        __rb_rotate_set_parents(parent, sibling, root,
                                                RB_BLACK);
                        augment_rotate(parent, sibling);
                        break;
                } else {
                        sibling = parent->rb_left;
                        if (rb_is_red(sibling)) {
                                /* Case 1 - right rotate at parent */
                                parent->rb_left = tmp1 = sibling->rb_right;
                                sibling->rb_right = parent;
                                rb_set_parent_color(tmp1, parent, RB_BLACK);
                                __rb_rotate_set_parents(parent, sibling, root,
                                                        RB_RED);
                                augment_rotate(parent, sibling);
                                sibling = tmp1;
                        }
                        tmp1 = sibling->rb_left;
                        if (!tmp1 || rb_is_black(tmp1)) {
                                tmp2 = sibling->rb_right;
                                if (!tmp2 || rb_is_black(tmp2)) {
                                        /* Case 2 - sibling color flip */
                                        rb_set_parent_color(sibling, parent,
                                                            RB_RED);
                                        if (rb_is_red(parent))
                                                rb_set_black(parent);
                                        else {
                                                node = parent;
                                                parent = rb_parent(node);
                                                if (parent)
                                                        continue;
                                        }
                                        break;
                                }
                                /* Case 3 - right rotate at sibling */
                                sibling->rb_right = tmp1 = tmp2->rb_left;
                                tmp2->rb_left = sibling;
                                parent->rb_left = tmp2;
                                if (tmp1)
                                        rb_set_parent_color(tmp1, sibling,
                                                            RB_BLACK);
                                augment_rotate(sibling, tmp2);
                                tmp1 = sibling;
                                sibling = tmp2;
                        }
                        /* Case 4 - left rotate at parent + color flips */
                        parent->rb_left = tmp2 = sibling->rb_right;
                        sibling->rb_right = parent;
                        rb_set_parent_color(tmp1, sibling, RB_BLACK);
                        if (tmp2)
                                rb_set_parent(tmp2, parent);
                        __rb_rotate_set_parents(parent, sibling, root,
                                                RB_BLACK);
                        augment_rotate(parent, sibling);
                        break;
                }
        }
}

/* Non-inline version for rb_erase_augmented() use */
void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
        ____rb_erase_color(parent, root, augment_rotate);
}

/*
 * Non-augmented rbtree manipulation functions.
 *
 * We use dummy augmented callbacks here, and have the compiler optimize them
 * out of the rb_insert_color() and rb_erase() function definitions.
 */

static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}

static const struct rb_augment_callbacks dummy_callbacks = {
        dummy_propagate, dummy_copy, dummy_rotate
};

void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
        __rb_insert(node, root, dummy_rotate);
}

void rb_erase(struct rb_node *node, struct rb_root *root)
{
        struct rb_node *rebalance;
        rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
        if (rebalance)
                ____rb_erase_color(rebalance, root, dummy_rotate);
}

/*
 * Augmented rbtree manipulation functions.
 *
 * This instantiates the same __always_inline functions as in the non-augmented
 * case, but this time with user-defined callbacks.
 */

void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
        __rb_insert(node, root, augment_rotate);
}

/*
 * This function returns the first node (in sort order) of the tree.
 */
struct rb_node *rb_first(const struct rb_root *root)
{
        struct rb_node  *n;

        n = root->rb_node;
        if (!n)
                return NULL;
        while (n->rb_left)
                n = n->rb_left;
        return n;
}

struct rb_node *rb_last(const struct rb_root *root)
{
        struct rb_node  *n;

        n = root->rb_node;
        if (!n)
                return NULL;
        while (n->rb_right)
                n = n->rb_right;
        return n;
}

struct rb_node *rb_next(const struct rb_node *node)
{
        struct rb_node *parent;

        if (RB_EMPTY_NODE(node))
                return NULL;

        /*
         * If we have a right-hand child, go down and then left as far
         * as we can.
         */
        if (node->rb_right) {
                node = node->rb_right;
                while (node->rb_left)
                        node=node->rb_left;
                return (struct rb_node *)node;
        }

        /*
         * No right-hand children. Everything down and left is smaller than us,
         * so any 'next' node must be in the general direction of our parent.
         * Go up the tree; any time the ancestor is a right-hand child of its
         * parent, keep going up. First time it's a left-hand child of its
         * parent, said parent is our 'next' node.
         */
        while ((parent = rb_parent(node)) && node == parent->rb_right)
                node = parent;

        return parent;
}

struct rb_node *rb_prev(const struct rb_node *node)
{
        struct rb_node *parent;

        if (RB_EMPTY_NODE(node))
                return NULL;

        /*
         * If we have a left-hand child, go down and then right as far
         * as we can.
         */
        if (node->rb_left) {
                node = node->rb_left;
                while (node->rb_right)
                        node=node->rb_right;
                return (struct rb_node *)node;
        }

        /*
         * No left-hand children. Go up till we find an ancestor which
         * is a right-hand child of its parent.
         */
        while ((parent = rb_parent(node)) && node == parent->rb_left)
                node = parent;

        return parent;
}

void rb_replace_node(struct rb_node *victim, struct rb_node *new,
                     struct rb_root *root)
{
        struct rb_node *parent = rb_parent(victim);

        /* Set the surrounding nodes to point to the replacement */
        __rb_change_child(victim, new, parent, root);
        if (victim->rb_left)
                rb_set_parent(victim->rb_left, new);
        if (victim->rb_right)
                rb_set_parent(victim->rb_right, new);

        /* Copy the pointers/colour from the victim to the replacement */
        *new = *victim;
}

static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
{
        for (;;) {
                if (node->rb_left)
                        node = node->rb_left;
                else if (node->rb_right)
                        node = node->rb_right;
                else
                        return (struct rb_node *)node;
        }
}

struct rb_node *rb_next_postorder(const struct rb_node *node)
{
        const struct rb_node *parent;
        if (!node)
                return NULL;
        parent = rb_parent(node);

        /* If we're sitting on node, we've already seen our children */
        if (parent && node == parent->rb_left && parent->rb_right) {
                /* If we are the parent's left node, go to the parent's right
                 * node then all the way down to the left */
                return rb_left_deepest_node(parent->rb_right);
        } else
                /* Otherwise we are the parent's right node, and the parent
                 * should be next */
                return (struct rb_node *)parent;
}

struct rb_node *rb_first_postorder(const struct rb_root *root)
{
        if (!root->rb_node)
                return NULL;

        return rb_left_deepest_node(root->rb_node);
}