/*
    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>

  #include <linux/export.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.

   */

  /*
   * Notes on lockless lookups:
   *
   * All stores to the tree structure (rb_left and rb_right) must be done using
   * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
   * tree structure as seen in program order.
   *
   * These two requirements will allow lockless iteration of the tree -- not
   * correct iteration mind you, tree rotations are not atomic so a lookup might
   * miss entire subtrees.
   *
   * But they do guarantee that any such traversal will only see valid elements
   * and that it will indeed complete -- does not get stuck in a loop.
   *
   * It also guarantees that if the lookup returns an element it is the 'correct'
   * one. But not returning an element does _NOT_ mean it's not present.
   *
   * NOTE:
   *
   * Stores to __rb_parent_color are not important for simple lookups so those
   * are left undone as of now. Nor did I check for loops involving parent
   * pointers.
   */

  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,

  	    bool newleft, struct rb_node **leftmost,

  	    void (*augment_rotate)(struct rb_node *old, struct rb_node *new))

  {

  	struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;

  	if (newleft)
  		*leftmost = node;

  	while (true) {
  		/*

  		 * Loop invariant: node is red.

  		 */

  		if (unlikely(!parent)) {
  			/*
  			 * The inserted node is root. Either this is the
  			 * first node, or we recursed at Case 1 below and
  			 * are no longer violating 4).
  			 */

  			rb_set_parent_color(node, NULL, RB_BLACK);

  			break;

  		}
  
  		/*
  		 * If there is a black parent, we are done.
  		 * Otherwise, take some corrective action as,
  		 * per 4), we don't want a red root or two
  		 * consecutive red nodes.
  		 */
  		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 - node's uncle is red (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 - node's uncle is black and node is
  				 * the parent's right child (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.
  				 */

  				tmp = node->rb_left;
  				WRITE_ONCE(parent->rb_right, tmp);
  				WRITE_ONCE(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 - node's uncle is black and node is
  			 * the parent's left child (right rotate at gparent).

  			 *
  			 *        G           P
  			 *       / \         / \
  			 *      p   U  -->  n   g
  			 *     /                 \
  			 *    n                   U
  			 */

  			WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
  			WRITE_ONCE(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 */

  				tmp = node->rb_right;
  				WRITE_ONCE(parent->rb_left, tmp);
  				WRITE_ONCE(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 */

  			WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
  			WRITE_ONCE(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
  				 */

  				tmp1 = sibling->rb_left;
  				WRITE_ONCE(parent->rb_right, tmp1);
  				WRITE_ONCE(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

  				 *
  				 * Note: p might be red, and then both
  				 * p and sl are red after rotation(which
  				 * breaks property 4). This is fixed in
  				 * Case 4 (in __rb_rotate_set_parents()
  				 *         which set sl the color of p
  				 *         and set p RB_BLACK)
  				 *
  				 *   (p)            (sl)
  				 *   / \            /  \
  				 *  N   sl   -->   P    S
  				 *       \        /      \
  				 *        S      N        Sr
  				 *         \
  				 *          Sr

  				 */

  				tmp1 = tmp2->rb_right;
  				WRITE_ONCE(sibling->rb_left, tmp1);
  				WRITE_ONCE(tmp2->rb_right, sibling);
  				WRITE_ONCE(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)
  			 */

  			tmp2 = sibling->rb_left;
  			WRITE_ONCE(parent->rb_right, tmp2);
  			WRITE_ONCE(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 */

  				tmp1 = sibling->rb_right;
  				WRITE_ONCE(parent->rb_left, tmp1);
  				WRITE_ONCE(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 - left rotate at sibling */

  				tmp1 = tmp2->rb_left;
  				WRITE_ONCE(sibling->rb_right, tmp1);
  				WRITE_ONCE(tmp2->rb_left, sibling);
  				WRITE_ONCE(parent->rb_left, tmp2);

  				if (tmp1)
  					rb_set_parent_color(tmp1, sibling,
  							    RB_BLACK);

  				augment_rotate(sibling, tmp2);

  				tmp1 = sibling;
  				sibling = tmp2;

  			}

  			/* Case 4 - right rotate at parent + color flips */

  			tmp2 = sibling->rb_right;
  			WRITE_ONCE(parent->rb_left, tmp2);
  			WRITE_ONCE(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);
  }

  EXPORT_SYMBOL(__rb_erase_color);

  
  /*
   * 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 = {

  	.propagate = dummy_propagate,
  	.copy = dummy_copy,
  	.rotate = dummy_rotate

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

  	__rb_insert(node, root, false, NULL, dummy_rotate);

  }
  EXPORT_SYMBOL(rb_insert_color);
  
  void rb_erase(struct rb_node *node, struct rb_root *root)
  {

  	struct rb_node *rebalance;

  	rebalance = __rb_erase_augmented(node, root,
  					 NULL, &dummy_callbacks);

  	if (rebalance)
  		____rb_erase_color(rebalance, root, dummy_rotate);

  }
  EXPORT_SYMBOL(rb_erase);

  void rb_insert_color_cached(struct rb_node *node,
  			    struct rb_root_cached *root, bool leftmost)
  {
  	__rb_insert(node, &root->rb_root, leftmost,
  		    &root->rb_leftmost, dummy_rotate);
  }
  EXPORT_SYMBOL(rb_insert_color_cached);
  
  void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
  {
  	struct rb_node *rebalance;
  	rebalance = __rb_erase_augmented(node, &root->rb_root,
  					 &root->rb_leftmost, &dummy_callbacks);
  	if (rebalance)
  		____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
  }
  EXPORT_SYMBOL(rb_erase_cached);

  /*
   * 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,

  			   bool newleft, struct rb_node **leftmost,

  	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
  {

  	__rb_insert(node, root, newleft, leftmost, augment_rotate);

  }
  EXPORT_SYMBOL(__rb_insert_augmented);

  /*
   * 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;
  }
  EXPORT_SYMBOL(rb_first);

  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;
  }
  EXPORT_SYMBOL(rb_last);

  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;

  }
  EXPORT_SYMBOL(rb_next);

  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;

  }
  EXPORT_SYMBOL(rb_prev);
  
  void rb_replace_node(struct rb_node *victim, struct rb_node *new,
  		     struct rb_root *root)
  {

  	struct rb_node *parent = rb_parent(victim);

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

  	/* Set the surrounding nodes to point to the replacement */

  	if (victim->rb_left)

  		rb_set_parent(victim->rb_left, new);

  	if (victim->rb_right)

  		rb_set_parent(victim->rb_right, new);

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

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

  
  	/* Set the surrounding nodes to point to the replacement */
  	if (victim->rb_left)
  		rb_set_parent(victim->rb_left, new);
  	if (victim->rb_right)
  		rb_set_parent(victim->rb_right, new);
  
  	/* Set the parent's pointer to the new node last after an RCU barrier
  	 * so that the pointers onwards are seen to be set correctly when doing
  	 * an RCU walk over the tree.
  	 */
  	__rb_change_child_rcu(victim, new, parent, root);

  }

  EXPORT_SYMBOL(rb_replace_node_rcu);

  
  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;
  }
  EXPORT_SYMBOL(rb_next_postorder);
  
  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);
  }
  EXPORT_SYMBOL(rb_first_postorder);