[people/ms/u-boot.git] / lib / rbtree.c

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

 * SPDX-License-Identifier:	GPL-2.0+

  linux/lib/rbtree.c
*/

#include <linux/rbtree_augmented.h>
#ifndef __UBOOT__
#include <linux/export.h>
#else
#include <ubi_uboot.h>
#endif
/*
 * 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);
}
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 = {
	dummy_propagate, dummy_copy, dummy_rotate
};

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

/*
 * 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);
}
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);

	/* 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;
}
EXPORT_SYMBOL(rb_replace_node);

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);
Commit	Line	Data
7ba890bf KP	1	/*
	2	Red Black Trees
	3	(C) 1999 Andrea Arcangeli <andrea@suse.de>
	4	(C) 2002 David Woodhouse <dwmw2@infradead.org>
9dd228b5	5	(C) 2012 Michel Lespinasse <walken@google.com>
7ba890bf	6
1a459660	7	* SPDX-License-Identifier: GPL-2.0+
7ba890bf KP	8
	9	linux/lib/rbtree.c
	10	*/
	11
9dd228b5 HS	12	#include <linux/rbtree_augmented.h>
	13	#ifndef __UBOOT__
	14	#include <linux/export.h>
	15	#else
7ba890bf	16	#include <ubi_uboot.h>
9dd228b5 HS	17	#endif
	18	/*
	19	* red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
	20	*
	21	* 1) A node is either red or black
	22	* 2) The root is black
	23	* 3) All leaves (NULL) are black
	24	* 4) Both children of every red node are black
	25	* 5) Every simple path from root to leaves contains the same number
	26	* of black nodes.
	27	*
	28	* 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
	29	* consecutive red nodes in a path and every red node is therefore followed by
	30	* a black. So if B is the number of black nodes on every simple path (as per
	31	* 5), then the longest possible path due to 4 is 2B.
	32	*
	33	* We shall indicate color with case, where black nodes are uppercase and red
	34	* nodes will be lowercase. Unknown color nodes shall be drawn as red within
	35	* parentheses and have some accompanying text comment.
	36	*/
7ba890bf	37
9dd228b5	38	static inline void rb_set_black(struct rb_node *rb)
7ba890bf	39	{
9dd228b5	40	rb->__rb_parent_color \|= RB_BLACK;
7ba890bf KP	41	}
7ba890bf KP	42
9dd228b5	43	static inline struct rb_node rb_red_parent(struct rb_node red)
7ba890bf	44	{
9dd228b5 HS	45	return (struct rb_node *)red->__rb_parent_color;
9dd228b5 HS	46	}
7ba890bf	47
9dd228b5 HS	48	/*
	49	* Helper function for rotations:
	50	* - old's parent and color get assigned to new
	51	* - old gets assigned new as a parent and 'color' as a color.
	52	*/
	53	static inline void
	54	__rb_rotate_set_parents(struct rb_node old, struct rb_node new,
	55	struct rb_root *root, int color)
	56	{
	57	struct rb_node *parent = rb_parent(old);
	58	new->__rb_parent_color = old->__rb_parent_color;
	59	rb_set_parent_color(old, new, color);
	60	__rb_change_child(old, new, parent, root);
7ba890bf KP	61	}
7ba890bf KP	62
9dd228b5 HS	63	static __always_inline void
	64	__rb_insert(struct rb_node node, struct rb_root root,
	65	void (augment_rotate)(struct rb_node old, struct rb_node *new))
7ba890bf	66	{
9dd228b5 HS	67	struct rb_node parent = rb_red_parent(node), gparent, *tmp;
	68
	69	while (true) {
	70	/*
	71	* Loop invariant: node is red
	72	*
	73	* If there is a black parent, we are done.
	74	* Otherwise, take some corrective action as we don't
	75	* want a red root or two consecutive red nodes.
	76	*/
	77	if (!parent) {
	78	rb_set_parent_color(node, NULL, RB_BLACK);
	79	break;
	80	} else if (rb_is_black(parent))
	81	break;
	82
	83	gparent = rb_red_parent(parent);
	84
	85	tmp = gparent->rb_right;
	86	if (parent != tmp) { /* parent == gparent->rb_left */
	87	if (tmp && rb_is_red(tmp)) {
	88	/*
	89	* Case 1 - color flips
	90	*
	91	* G g
	92	* / \ / \
	93	* p u --> P U
	94	* / /
	95	* n N
	96	*
	97	* However, since g's parent might be red, and
	98	* 4) does not allow this, we need to recurse
	99	* at g.
	100	*/
	101	rb_set_parent_color(tmp, gparent, RB_BLACK);
	102	rb_set_parent_color(parent, gparent, RB_BLACK);
	103	node = gparent;
	104	parent = rb_parent(node);
	105	rb_set_parent_color(node, parent, RB_RED);
	106	continue;
7ba890bf KP	107	}
7ba890bf KP	108
9dd228b5 HS	109	tmp = parent->rb_right;
	110	if (node == tmp) {
	111	/*
	112	* Case 2 - left rotate at parent
	113	*
	114	* G G
	115	* / \ / \
	116	* p U --> n U
	117	* \ /
	118	* n p
	119	*
	120	* This still leaves us in violation of 4), the
	121	* continuation into Case 3 will fix that.
	122	*/
	123	parent->rb_right = tmp = node->rb_left;
	124	node->rb_left = parent;
	125	if (tmp)
	126	rb_set_parent_color(tmp, parent,
	127	RB_BLACK);
	128	rb_set_parent_color(parent, node, RB_RED);
	129	augment_rotate(parent, node);
7ba890bf	130	parent = node;
9dd228b5	131	tmp = node->rb_right;
7ba890bf KP	132	}
7ba890bf KP	133
9dd228b5 HS	134	/*
	135	* Case 3 - right rotate at gparent
	136	*
	137	* G P
	138	* / \ / \
	139	* p U --> n g
	140	* / \
	141	* n U
	142	*/
	143	gparent->rb_left = tmp; /* == parent->rb_right */
	144	parent->rb_right = gparent;
	145	if (tmp)
	146	rb_set_parent_color(tmp, gparent, RB_BLACK);
	147	__rb_rotate_set_parents(gparent, parent, root, RB_RED);
	148	augment_rotate(gparent, parent);
	149	break;
7ba890bf	150	} else {
9dd228b5 HS	151	tmp = gparent->rb_left;
	152	if (tmp && rb_is_red(tmp)) {
	153	/* Case 1 - color flips */
	154	rb_set_parent_color(tmp, gparent, RB_BLACK);
	155	rb_set_parent_color(parent, gparent, RB_BLACK);
	156	node = gparent;
	157	parent = rb_parent(node);
	158	rb_set_parent_color(node, parent, RB_RED);
	159	continue;
7ba890bf KP	160	}
7ba890bf KP	161
9dd228b5 HS	162	tmp = parent->rb_left;
	163	if (node == tmp) {
	164	/* Case 2 - right rotate at parent */
	165	parent->rb_left = tmp = node->rb_right;
	166	node->rb_right = parent;
	167	if (tmp)
	168	rb_set_parent_color(tmp, parent,
	169	RB_BLACK);
	170	rb_set_parent_color(parent, node, RB_RED);
	171	augment_rotate(parent, node);
7ba890bf	172	parent = node;
9dd228b5	173	tmp = node->rb_left;
7ba890bf KP	174	}
7ba890bf KP	175
9dd228b5 HS	176	/* Case 3 - left rotate at gparent */
	177	gparent->rb_right = tmp; /* == parent->rb_left */
	178	parent->rb_left = gparent;
	179	if (tmp)
	180	rb_set_parent_color(tmp, gparent, RB_BLACK);
	181	__rb_rotate_set_parents(gparent, parent, root, RB_RED);
	182	augment_rotate(gparent, parent);
	183	break;
7ba890bf KP	184	}
7ba890bf KP	185	}
7ba890bf KP	186	}
7ba890bf KP	187
9dd228b5 HS	188	/*
	189	* Inline version for rb_erase() use - we want to be able to inline
	190	* and eliminate the dummy_rotate callback there
	191	*/
	192	static __always_inline void
	193	____rb_erase_color(struct rb_node parent, struct rb_root root,
	194	void (augment_rotate)(struct rb_node old, struct rb_node *new))
7ba890bf	195	{
9dd228b5 HS	196	struct rb_node node = NULL, sibling, tmp1, tmp2;
	197
	198	while (true) {
	199	/*
	200	* Loop invariants:
	201	* - node is black (or NULL on first iteration)
	202	* - node is not the root (parent is not NULL)
	203	* - All leaf paths going through parent and node have a
	204	* black node count that is 1 lower than other leaf paths.
	205	*/
	206	sibling = parent->rb_right;
	207	if (node != sibling) { /* node == parent->rb_left */
	208	if (rb_is_red(sibling)) {
	209	/*
	210	* Case 1 - left rotate at parent
	211	*
	212	* P S
	213	* / \ / \
	214	* N s --> p Sr
	215	* / \ / \
	216	* Sl Sr N Sl
	217	*/
	218	parent->rb_right = tmp1 = sibling->rb_left;
	219	sibling->rb_left = parent;
	220	rb_set_parent_color(tmp1, parent, RB_BLACK);
	221	__rb_rotate_set_parents(parent, sibling, root,
	222	RB_RED);
	223	augment_rotate(parent, sibling);
	224	sibling = tmp1;
7ba890bf	225	}
9dd228b5 HS	226	tmp1 = sibling->rb_right;
	227	if (!tmp1 \|\| rb_is_black(tmp1)) {
	228	tmp2 = sibling->rb_left;
	229	if (!tmp2 \|\| rb_is_black(tmp2)) {
	230	/*
	231	* Case 2 - sibling color flip
	232	* (p could be either color here)
	233	*
	234	* (p) (p)
	235	* / \ / \
	236	* N S --> N s
	237	* / \ / \
	238	* Sl Sr Sl Sr
	239	*
	240	* This leaves us violating 5) which
	241	* can be fixed by flipping p to black
	242	* if it was red, or by recursing at p.
	243	* p is red when coming from Case 1.
	244	*/
	245	rb_set_parent_color(sibling, parent,
	246	RB_RED);
	247	if (rb_is_red(parent))
	248	rb_set_black(parent);
	249	else {
	250	node = parent;
	251	parent = rb_parent(node);
	252	if (parent)
	253	continue;
	254	}
	255	break;
7ba890bf	256	}
9dd228b5 HS	257	/*
	258	* Case 3 - right rotate at sibling
	259	* (p could be either color here)
	260	*
	261	* (p) (p)
	262	* / \ / \
	263	* N S --> N Sl
	264	* / \ \
	265	* sl Sr s
	266	* \
	267	* Sr
	268	*/
	269	sibling->rb_left = tmp1 = tmp2->rb_right;
	270	tmp2->rb_right = sibling;
	271	parent->rb_right = tmp2;
	272	if (tmp1)
	273	rb_set_parent_color(tmp1, sibling,
	274	RB_BLACK);
	275	augment_rotate(sibling, tmp2);
	276	tmp1 = sibling;
	277	sibling = tmp2;
7ba890bf	278	}
9dd228b5 HS	279	/*
	280	* Case 4 - left rotate at parent + color flips
	281	* (p and sl could be either color here.
	282	* After rotation, p becomes black, s acquires
	283	* p's color, and sl keeps its color)
	284	*
	285	* (p) (s)
	286	* / \ / \
	287	* N S --> P Sr
	288	* / \ / \
	289	* (sl) sr N (sl)
	290	*/
	291	parent->rb_right = tmp2 = sibling->rb_left;
	292	sibling->rb_left = parent;
	293	rb_set_parent_color(tmp1, sibling, RB_BLACK);
	294	if (tmp2)
	295	rb_set_parent(tmp2, parent);
	296	__rb_rotate_set_parents(parent, sibling, root,
	297	RB_BLACK);
	298	augment_rotate(parent, sibling);
	299	break;
	300	} else {
	301	sibling = parent->rb_left;
	302	if (rb_is_red(sibling)) {
	303	/* Case 1 - right rotate at parent */
	304	parent->rb_left = tmp1 = sibling->rb_right;
	305	sibling->rb_right = parent;
	306	rb_set_parent_color(tmp1, parent, RB_BLACK);
	307	__rb_rotate_set_parents(parent, sibling, root,
	308	RB_RED);
	309	augment_rotate(parent, sibling);
	310	sibling = tmp1;
7ba890bf	311	}
9dd228b5 HS	312	tmp1 = sibling->rb_left;
	313	if (!tmp1 \|\| rb_is_black(tmp1)) {
	314	tmp2 = sibling->rb_right;
	315	if (!tmp2 \|\| rb_is_black(tmp2)) {
	316	/* Case 2 - sibling color flip */
	317	rb_set_parent_color(sibling, parent,
	318	RB_RED);
	319	if (rb_is_red(parent))
	320	rb_set_black(parent);
	321	else {
	322	node = parent;
	323	parent = rb_parent(node);
	324	if (parent)
	325	continue;
	326	}
	327	break;
7ba890bf	328	}
9dd228b5 HS	329	/* Case 3 - right rotate at sibling */
	330	sibling->rb_right = tmp1 = tmp2->rb_left;
	331	tmp2->rb_left = sibling;
	332	parent->rb_left = tmp2;
	333	if (tmp1)
	334	rb_set_parent_color(tmp1, sibling,
	335	RB_BLACK);
	336	augment_rotate(sibling, tmp2);
	337	tmp1 = sibling;
	338	sibling = tmp2;
7ba890bf	339	}
9dd228b5 HS	340	/* Case 4 - left rotate at parent + color flips */
	341	parent->rb_left = tmp2 = sibling->rb_right;
	342	sibling->rb_right = parent;
	343	rb_set_parent_color(tmp1, sibling, RB_BLACK);
	344	if (tmp2)
	345	rb_set_parent(tmp2, parent);
	346	__rb_rotate_set_parents(parent, sibling, root,
	347	RB_BLACK);
	348	augment_rotate(parent, sibling);
	349	break;
7ba890bf KP	350	}
7ba890bf KP	351	}
7ba890bf KP	352	}
7ba890bf KP	353
9dd228b5 HS	354	/* Non-inline version for rb_erase_augmented() use */
	355	void __rb_erase_color(struct rb_node parent, struct rb_root root,
	356	void (augment_rotate)(struct rb_node old, struct rb_node *new))
	357	{
	358	____rb_erase_color(parent, root, augment_rotate);
	359	}
	360	EXPORT_SYMBOL(__rb_erase_color);
	361
	362	/*
	363	* Non-augmented rbtree manipulation functions.
	364	*
	365	* We use dummy augmented callbacks here, and have the compiler optimize them
	366	* out of the rb_insert_color() and rb_erase() function definitions.
	367	*/
	368
	369	static inline void dummy_propagate(struct rb_node node, struct rb_node stop) {}
	370	static inline void dummy_copy(struct rb_node old, struct rb_node new) {}
	371	static inline void dummy_rotate(struct rb_node old, struct rb_node new) {}
	372
	373	static const struct rb_augment_callbacks dummy_callbacks = {
	374	dummy_propagate, dummy_copy, dummy_rotate
	375	};
	376
	377	void rb_insert_color(struct rb_node node, struct rb_root root)
	378	{
	379	__rb_insert(node, root, dummy_rotate);
	380	}
	381	EXPORT_SYMBOL(rb_insert_color);
	382
7ba890bf KP	383	void rb_erase(struct rb_node node, struct rb_root root)
7ba890bf KP	384	{
9dd228b5 HS	385	struct rb_node *rebalance;
	386	rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
	387	if (rebalance)
	388	____rb_erase_color(rebalance, root, dummy_rotate);
	389	}
	390	EXPORT_SYMBOL(rb_erase);
7ba890bf	391
9dd228b5 HS	392	/*
	393	* Augmented rbtree manipulation functions.
	394	*
	395	* This instantiates the same __always_inline functions as in the non-augmented
	396	* case, but this time with user-defined callbacks.
	397	*/
7ba890bf	398
9dd228b5 HS	399	void __rb_insert_augmented(struct rb_node node, struct rb_root root,
	400	void (augment_rotate)(struct rb_node old, struct rb_node *new))
	401	{
	402	__rb_insert(node, root, augment_rotate);
7ba890bf	403	}
9dd228b5	404	EXPORT_SYMBOL(__rb_insert_augmented);
7ba890bf KP	405
	406	/*
	407	* This function returns the first node (in sort order) of the tree.
	408	*/
9dd228b5	409	struct rb_node rb_first(const struct rb_root root)
7ba890bf KP	410	{
	411	struct rb_node *n;
	412
	413	n = root->rb_node;
	414	if (!n)
	415	return NULL;
	416	while (n->rb_left)
	417	n = n->rb_left;
	418	return n;
	419	}
9dd228b5	420	EXPORT_SYMBOL(rb_first);
7ba890bf	421
9dd228b5	422	struct rb_node rb_last(const struct rb_root root)
7ba890bf KP	423	{
	424	struct rb_node *n;
	425
	426	n = root->rb_node;
	427	if (!n)
	428	return NULL;
	429	while (n->rb_right)
	430	n = n->rb_right;
	431	return n;
	432	}
9dd228b5	433	EXPORT_SYMBOL(rb_last);
7ba890bf	434
9dd228b5	435	struct rb_node rb_next(const struct rb_node node)
7ba890bf KP	436	{
	437	struct rb_node *parent;
	438
9dd228b5	439	if (RB_EMPTY_NODE(node))
7ba890bf KP	440	return NULL;
7ba890bf KP	441
9dd228b5 HS	442	/*
	443	* If we have a right-hand child, go down and then left as far
	444	* as we can.
	445	*/
7ba890bf	446	if (node->rb_right) {
9dd228b5	447	node = node->rb_right;
7ba890bf KP	448	while (node->rb_left)
7ba890bf KP	449	node=node->rb_left;
9dd228b5	450	return (struct rb_node *)node;
7ba890bf KP	451	}
7ba890bf KP	452
9dd228b5 HS	453	/*
	454	* No right-hand children. Everything down and left is smaller than us,
	455	* so any 'next' node must be in the general direction of our parent.
	456	* Go up the tree; any time the ancestor is a right-hand child of its
	457	* parent, keep going up. First time it's a left-hand child of its
	458	* parent, said parent is our 'next' node.
	459	*/
7ba890bf KP	460	while ((parent = rb_parent(node)) && node == parent->rb_right)
	461	node = parent;
	462
	463	return parent;
	464	}
9dd228b5	465	EXPORT_SYMBOL(rb_next);
7ba890bf	466
9dd228b5	467	struct rb_node rb_prev(const struct rb_node node)
7ba890bf KP	468	{
	469	struct rb_node *parent;
	470
9dd228b5	471	if (RB_EMPTY_NODE(node))
7ba890bf KP	472	return NULL;
7ba890bf KP	473
9dd228b5 HS	474	/*
	475	* If we have a left-hand child, go down and then right as far
	476	* as we can.
	477	*/
7ba890bf	478	if (node->rb_left) {
9dd228b5	479	node = node->rb_left;
7ba890bf KP	480	while (node->rb_right)
7ba890bf KP	481	node=node->rb_right;
9dd228b5	482	return (struct rb_node *)node;
7ba890bf KP	483	}
7ba890bf KP	484
9dd228b5 HS	485	/*
	486	* No left-hand children. Go up till we find an ancestor which
	487	* is a right-hand child of its parent.
	488	*/
7ba890bf KP	489	while ((parent = rb_parent(node)) && node == parent->rb_left)
	490	node = parent;
	491
	492	return parent;
	493	}
9dd228b5	494	EXPORT_SYMBOL(rb_prev);
7ba890bf KP	495
	496	void rb_replace_node(struct rb_node victim, struct rb_node new,
	497	struct rb_root *root)
	498	{
	499	struct rb_node *parent = rb_parent(victim);
	500
	501	/* Set the surrounding nodes to point to the replacement */
9dd228b5	502	__rb_change_child(victim, new, parent, root);
7ba890bf KP	503	if (victim->rb_left)
	504	rb_set_parent(victim->rb_left, new);
	505	if (victim->rb_right)
	506	rb_set_parent(victim->rb_right, new);
	507
	508	/* Copy the pointers/colour from the victim to the replacement */
	509	new = victim;
	510	}
9dd228b5 HS	511	EXPORT_SYMBOL(rb_replace_node);
	512
	513	static struct rb_node rb_left_deepest_node(const struct rb_node node)
	514	{
	515	for (;;) {
	516	if (node->rb_left)
	517	node = node->rb_left;
	518	else if (node->rb_right)
	519	node = node->rb_right;
	520	else
	521	return (struct rb_node *)node;
	522	}
	523	}
	524
	525	struct rb_node rb_next_postorder(const struct rb_node node)
	526	{
	527	const struct rb_node *parent;
	528	if (!node)
	529	return NULL;
	530	parent = rb_parent(node);
	531
	532	/* If we're sitting on node, we've already seen our children */
	533	if (parent && node == parent->rb_left && parent->rb_right) {
	534	/* If we are the parent's left node, go to the parent's right
	535	* node then all the way down to the left */
	536	return rb_left_deepest_node(parent->rb_right);
	537	} else
	538	/* Otherwise we are the parent's right node, and the parent
	539	* should be next */
	540	return (struct rb_node *)parent;
	541	}
	542	EXPORT_SYMBOL(rb_next_postorder);
	543
	544	struct rb_node rb_first_postorder(const struct rb_root root)
	545	{
	546	if (!root->rb_node)
	547	return NULL;
	548
	549	return rb_left_deepest_node(root->rb_node);
	550	}
	551	EXPORT_SYMBOL(rb_first_postorder);