[deliverable/linux.git] / lib / prio_tree.c

/*
 * lib/prio_tree.c - priority search tree
 *
 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
 *
 * This file is released under the GPL v2.
 *
 * Based on the radix priority search tree proposed by Edward M. McCreight
 * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
 *
 * 02Feb2004	Initial version
 */

#include <linux/init.h>
#include <linux/mm.h>
#include <linux/prio_tree.h>
#include <linux/export.h>

/*
 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
 * which is useful for storing intervals, e.g, we can consider a vma as a closed
 * interval of file pages [offset_begin, offset_end], and store all vmas that
 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
 * time where 'log n' is the height of the PST, and 'm' is the number of stored
 * intervals (vmas) that overlap (map) with the input interval X (the set of
 * consecutive file pages).
 *
 * In our implementation, we store closed intervals of the form [radix_index,
 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
 * is designed for storing intervals with unique radix indices, i.e., each
 * interval have different radix_index. However, this limitation can be easily
 * overcome by using the size, i.e., heap_index - radix_index, as part of the
 * index, so we index the tree using [(radix_index,size), heap_index].
 *
 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
 * machine, the maximum height of a PST can be 64. We can use a balanced version
 * of the priority search tree to optimize the tree height, but the balanced
 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
 */

/*
 * The following macros are used for implementing prio_tree for i_mmap
 */

#define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
#define VMA_SIZE(vma)	  (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
/* avoid overflow */
#define HEAP_INDEX(vma)	  ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))


static void get_index(const struct prio_tree_root *root,
    const struct prio_tree_node *node,
    unsigned long *radix, unsigned long *heap)
{
	if (root->raw) {
		struct vm_area_struct *vma = prio_tree_entry(
		    node, struct vm_area_struct, shared.prio_tree_node);

		*radix = RADIX_INDEX(vma);
		*heap = HEAP_INDEX(vma);
	}
	else {
		*radix = node->start;
		*heap = node->last;
	}
}

static unsigned long index_bits_to_maxindex[BITS_PER_LONG];

void __init prio_tree_init(void)
{
	unsigned int i;

	for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
		index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
	index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
}

/*
 * Maximum heap_index that can be stored in a PST with index_bits bits
 */
static inline unsigned long prio_tree_maxindex(unsigned int bits)
{
	return index_bits_to_maxindex[bits - 1];
}

static void prio_set_parent(struct prio_tree_node *parent,
			    struct prio_tree_node *child, bool left)
{
	if (left)
		parent->left = child;
	else
		parent->right = child;

	child->parent = parent;
}

/*
 * Extend a priority search tree so that it can store a node with heap_index
 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 * However, this function is used rarely and the common case performance is
 * not bad.
 */
static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
		struct prio_tree_node *node, unsigned long max_heap_index)
{
	struct prio_tree_node *prev;

	if (max_heap_index > prio_tree_maxindex(root->index_bits))
		root->index_bits++;

	prev = node;
	INIT_PRIO_TREE_NODE(node);

	while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
		struct prio_tree_node *tmp = root->prio_tree_node;

		root->index_bits++;

		if (prio_tree_empty(root))
			continue;

		prio_tree_remove(root, root->prio_tree_node);
		INIT_PRIO_TREE_NODE(tmp);

		prio_set_parent(prev, tmp, true);
		prev = tmp;
	}

	if (!prio_tree_empty(root))
		prio_set_parent(prev, root->prio_tree_node, true);

	root->prio_tree_node = node;
	return node;
}

/*
 * Replace a prio_tree_node with a new node and return the old node
 */
struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
		struct prio_tree_node *old, struct prio_tree_node *node)
{
	INIT_PRIO_TREE_NODE(node);

	if (prio_tree_root(old)) {
		BUG_ON(root->prio_tree_node != old);
		/*
		 * We can reduce root->index_bits here. However, it is complex
		 * and does not help much to improve performance (IMO).
		 */
		root->prio_tree_node = node;
	} else
		prio_set_parent(old->parent, node, old->parent->left == old);

	if (!prio_tree_left_empty(old))
		prio_set_parent(node, old->left, true);

	if (!prio_tree_right_empty(old))
		prio_set_parent(node, old->right, false);

	return old;
}

/*
 * Insert a prio_tree_node @node into a radix priority search tree @root. The
 * algorithm typically takes O(log n) time where 'log n' is the number of bits
 * required to represent the maximum heap_index. In the worst case, the algo
 * can take O((log n)^2) - check prio_tree_expand.
 *
 * If a prior node with same radix_index and heap_index is already found in
 * the tree, then returns the address of the prior node. Otherwise, inserts
 * @node into the tree and returns @node.
 */
struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
		struct prio_tree_node *node)
{
	struct prio_tree_node *cur, *res = node;
	unsigned long radix_index, heap_index;
	unsigned long r_index, h_index, index, mask;
	int size_flag = 0;

	get_index(root, node, &radix_index, &heap_index);

	if (prio_tree_empty(root) ||
			heap_index > prio_tree_maxindex(root->index_bits))
		return prio_tree_expand(root, node, heap_index);

	cur = root->prio_tree_node;
	mask = 1UL << (root->index_bits - 1);

	while (mask) {
		get_index(root, cur, &r_index, &h_index);

		if (r_index == radix_index && h_index == heap_index)
			return cur;

                if (h_index < heap_index ||
		    (h_index == heap_index && r_index > radix_index)) {
			struct prio_tree_node *tmp = node;
			node = prio_tree_replace(root, cur, node);
			cur = tmp;
			/* swap indices */
			index = r_index;
			r_index = radix_index;
			radix_index = index;
			index = h_index;
			h_index = heap_index;
			heap_index = index;
		}

		if (size_flag)
			index = heap_index - radix_index;
		else
			index = radix_index;

		if (index & mask) {
			if (prio_tree_right_empty(cur)) {
				INIT_PRIO_TREE_NODE(node);
				prio_set_parent(cur, node, false);
				return res;
			} else
				cur = cur->right;
		} else {
			if (prio_tree_left_empty(cur)) {
				INIT_PRIO_TREE_NODE(node);
				prio_set_parent(cur, node, true);
				return res;
			} else
				cur = cur->left;
		}

		mask >>= 1;

		if (!mask) {
			mask = 1UL << (BITS_PER_LONG - 1);
			size_flag = 1;
		}
	}
	/* Should not reach here */
	BUG();
	return NULL;
}
EXPORT_SYMBOL(prio_tree_insert);

/*
 * Remove a prio_tree_node @node from a radix priority search tree @root. The
 * algorithm takes O(log n) time where 'log n' is the number of bits required
 * to represent the maximum heap_index.
 */
void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
{
	struct prio_tree_node *cur;
	unsigned long r_index, h_index_right, h_index_left;

	cur = node;

	while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
		if (!prio_tree_left_empty(cur))
			get_index(root, cur->left, &r_index, &h_index_left);
		else {
			cur = cur->right;
			continue;
		}

		if (!prio_tree_right_empty(cur))
			get_index(root, cur->right, &r_index, &h_index_right);
		else {
			cur = cur->left;
			continue;
		}

		/* both h_index_left and h_index_right cannot be 0 */
		if (h_index_left >= h_index_right)
			cur = cur->left;
		else
			cur = cur->right;
	}

	if (prio_tree_root(cur)) {
		BUG_ON(root->prio_tree_node != cur);
		__INIT_PRIO_TREE_ROOT(root, root->raw);
		return;
	}

	if (cur->parent->right == cur)
		cur->parent->right = cur->parent;
	else
		cur->parent->left = cur->parent;

	while (cur != node)
		cur = prio_tree_replace(root, cur->parent, cur);
}
EXPORT_SYMBOL(prio_tree_remove);

static void iter_walk_down(struct prio_tree_iter *iter)
{
	iter->mask >>= 1;
	if (iter->mask) {
		if (iter->size_level)
			iter->size_level++;
		return;
	}

	if (iter->size_level) {
		BUG_ON(!prio_tree_left_empty(iter->cur));
		BUG_ON(!prio_tree_right_empty(iter->cur));
		iter->size_level++;
		iter->mask = ULONG_MAX;
	} else {
		iter->size_level = 1;
		iter->mask = 1UL << (BITS_PER_LONG - 1);
	}
}

static void iter_walk_up(struct prio_tree_iter *iter)
{
	if (iter->mask == ULONG_MAX)
		iter->mask = 1UL;
	else if (iter->size_level == 1)
		iter->mask = 1UL;
	else
		iter->mask <<= 1;
	if (iter->size_level)
		iter->size_level--;
	if (!iter->size_level && (iter->value & iter->mask))
		iter->value ^= iter->mask;
}

/*
 * Following functions help to enumerate all prio_tree_nodes in the tree that
 * overlap with the input interval X [radix_index, heap_index]. The enumeration
 * takes O(log n + m) time where 'log n' is the height of the tree (which is
 * proportional to # of bits required to represent the maximum heap_index) and
 * 'm' is the number of prio_tree_nodes that overlap the interval X.
 */

static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
		unsigned long *r_index, unsigned long *h_index)
{
	if (prio_tree_left_empty(iter->cur))
		return NULL;

	get_index(iter->root, iter->cur->left, r_index, h_index);

	if (iter->r_index <= *h_index) {
		iter->cur = iter->cur->left;
		iter_walk_down(iter);
		return iter->cur;
	}

	return NULL;
}

static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
		unsigned long *r_index, unsigned long *h_index)
{
	unsigned long value;

	if (prio_tree_right_empty(iter->cur))
		return NULL;

	if (iter->size_level)
		value = iter->value;
	else
		value = iter->value | iter->mask;

	if (iter->h_index < value)
		return NULL;

	get_index(iter->root, iter->cur->right, r_index, h_index);

	if (iter->r_index <= *h_index) {
		iter->cur = iter->cur->right;
		iter_walk_down(iter);
		return iter->cur;
	}

	return NULL;
}

static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
{
	iter->cur = iter->cur->parent;
	iter_walk_up(iter);
	return iter->cur;
}

static inline int overlap(struct prio_tree_iter *iter,
		unsigned long r_index, unsigned long h_index)
{
	return iter->h_index >= r_index && iter->r_index <= h_index;
}

/*
 * prio_tree_first:
 *
 * Get the first prio_tree_node that overlaps with the interval [radix_index,
 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 * traversal of the tree.
 */
static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
{
	struct prio_tree_root *root;
	unsigned long r_index, h_index;

	INIT_PRIO_TREE_ITER(iter);

	root = iter->root;
	if (prio_tree_empty(root))
		return NULL;

	get_index(root, root->prio_tree_node, &r_index, &h_index);

	if (iter->r_index > h_index)
		return NULL;

	iter->mask = 1UL << (root->index_bits - 1);
	iter->cur = root->prio_tree_node;

	while (1) {
		if (overlap(iter, r_index, h_index))
			return iter->cur;

		if (prio_tree_left(iter, &r_index, &h_index))
			continue;

		if (prio_tree_right(iter, &r_index, &h_index))
			continue;

		break;
	}
	return NULL;
}

/*
 * prio_tree_next:
 *
 * Get the next prio_tree_node that overlaps with the input interval in iter
 */
struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
{
	unsigned long r_index, h_index;

	if (iter->cur == NULL)
		return prio_tree_first(iter);

repeat:
	while (prio_tree_left(iter, &r_index, &h_index))
		if (overlap(iter, r_index, h_index))
			return iter->cur;

	while (!prio_tree_right(iter, &r_index, &h_index)) {
	    	while (!prio_tree_root(iter->cur) &&
				iter->cur->parent->right == iter->cur)
			prio_tree_parent(iter);

		if (prio_tree_root(iter->cur))
			return NULL;

		prio_tree_parent(iter);
	}

	if (overlap(iter, r_index, h_index))
		return iter->cur;

	goto repeat;
}
EXPORT_SYMBOL(prio_tree_next);
Commit	Line	Data
1da177e4 LT	1	/*
	2	* lib/prio_tree.c - priority search tree
	3	*
	4	* Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
	5	*
	6	* This file is released under the GPL v2.
	7	*
	8	* Based on the radix priority search tree proposed by Edward M. McCreight
	9	* SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
	10	*
	11	* 02Feb2004 Initial version
	12	*/
	13
	14	#include <linux/init.h>
	15	#include <linux/mm.h>
	16	#include <linux/prio_tree.h>
fff3fd8a	17	#include <linux/export.h>
1da177e4 LT	18
	19	/*
	20	* A clever mix of heap and radix trees forms a radix priority search tree (PST)
	21	* which is useful for storing intervals, e.g, we can consider a vma as a closed
	22	* interval of file pages [offset_begin, offset_end], and store all vmas that
	23	* map a file in a PST. Then, using the PST, we can answer a stabbing query,
	24	* i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
	25	* given input interval X (a set of consecutive file pages), in "O(log n + m)"
	26	* time where 'log n' is the height of the PST, and 'm' is the number of stored
	27	* intervals (vmas) that overlap (map) with the input interval X (the set of
	28	* consecutive file pages).
	29	*
	30	* In our implementation, we store closed intervals of the form [radix_index,
	31	* heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
	32	* is designed for storing intervals with unique radix indices, i.e., each
	33	* interval have different radix_index. However, this limitation can be easily
	34	* overcome by using the size, i.e., heap_index - radix_index, as part of the
	35	* index, so we index the tree using [(radix_index,size), heap_index].
	36	*
	37	* When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
	38	* machine, the maximum height of a PST can be 64. We can use a balanced version
	39	* of the priority search tree to optimize the tree height, but the balanced
	40	* tree proposed by McCreight is too complex and memory-hungry for our purpose.
	41	*/
	42
	43	/*
	44	* The following macros are used for implementing prio_tree for i_mmap
	45	*/
	46
	47	#define RADIX_INDEX(vma) ((vma)->vm_pgoff)
	48	#define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
	49	/* avoid overflow */
	50	#define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
	51
	52
	53	static void get_index(const struct prio_tree_root *root,
	54	const struct prio_tree_node *node,
	55	unsigned long radix, unsigned long heap)
	56	{
	57	if (root->raw) {
	58	struct vm_area_struct *vma = prio_tree_entry(
	59	node, struct vm_area_struct, shared.prio_tree_node);
	60
	61	*radix = RADIX_INDEX(vma);
	62	*heap = HEAP_INDEX(vma);
	63	}
	64	else {
	65	*radix = node->start;
	66	*heap = node->last;
	67	}
	68	}
	69
	70	static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
	71
	72	void __init prio_tree_init(void)
	73	{
	74	unsigned int i;
	75
	76	for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
	77	index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
	78	index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
	79	}
	80
	81	/*
82	* Maximum heap_index that can be stored in a PST with index_bits bits
83	*/
84	static inline unsigned long prio_tree_maxindex(unsigned int bits)
85	{
86	return index_bits_to_maxindex[bits - 1];
87	}
88
97e834c5 XG	89	static void prio_set_parent(struct prio_tree_node *parent,
	90	struct prio_tree_node *child, bool left)
	91	{
	92	if (left)
	93	parent->left = child;
	94	else
	95	parent->right = child;
	96
	97	child->parent = parent;
	98	}
	99
1da177e4 LT	100	/*
	101	* Extend a priority search tree so that it can store a node with heap_index
	102	* max_heap_index. In the worst case, this algorithm takes O((log n)^2).
	103	* However, this function is used rarely and the common case performance is
	104	* not bad.
	105	*/
	106	static struct prio_tree_node prio_tree_expand(struct prio_tree_root root,
	107	struct prio_tree_node *node, unsigned long max_heap_index)
	108	{
742245d5	109	struct prio_tree_node *prev;
1da177e4 LT	110
	111	if (max_heap_index > prio_tree_maxindex(root->index_bits))
	112	root->index_bits++;
	113
742245d5 XG	114	prev = node;
	115	INIT_PRIO_TREE_NODE(node);
	116
1da177e4	117	while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
742245d5 XG	118	struct prio_tree_node *tmp = root->prio_tree_node;
742245d5 XG	119
1da177e4 LT	120	root->index_bits++;
	121
	122	if (prio_tree_empty(root))
	123	continue;
	124
742245d5 XG	125	prio_tree_remove(root, root->prio_tree_node);
742245d5 XG	126	INIT_PRIO_TREE_NODE(tmp);
1da177e4	127
97e834c5	128	prio_set_parent(prev, tmp, true);
742245d5 XG	129	prev = tmp;
742245d5 XG	130	}
1da177e4	131
97e834c5 XG	132	if (!prio_tree_empty(root))
97e834c5 XG	133	prio_set_parent(prev, root->prio_tree_node, true);
1da177e4 LT	134
	135	root->prio_tree_node = node;
	136	return node;
	137	}
	138
	139	/*
	140	* Replace a prio_tree_node with a new node and return the old node
	141	*/
	142	struct prio_tree_node prio_tree_replace(struct prio_tree_root root,
	143	struct prio_tree_node old, struct prio_tree_node node)
	144	{
	145	INIT_PRIO_TREE_NODE(node);
	146
	147	if (prio_tree_root(old)) {
	148	BUG_ON(root->prio_tree_node != old);
	149	/*
	150	* We can reduce root->index_bits here. However, it is complex
	151	* and does not help much to improve performance (IMO).
	152	*/
1da177e4	153	root->prio_tree_node = node;
97e834c5 XG	154	} else
97e834c5 XG	155	prio_set_parent(old->parent, node, old->parent->left == old);
1da177e4	156
97e834c5 XG	157	if (!prio_tree_left_empty(old))
97e834c5 XG	158	prio_set_parent(node, old->left, true);
1da177e4	159
97e834c5 XG	160	if (!prio_tree_right_empty(old))
97e834c5 XG	161	prio_set_parent(node, old->right, false);
1da177e4 LT	162
	163	return old;
	164	}
	165
	166	/*
	167	* Insert a prio_tree_node @node into a radix priority search tree @root. The
	168	* algorithm typically takes O(log n) time where 'log n' is the number of bits
	169	* required to represent the maximum heap_index. In the worst case, the algo
	170	* can take O((log n)^2) - check prio_tree_expand.
	171	*
	172	* If a prior node with same radix_index and heap_index is already found in
	173	* the tree, then returns the address of the prior node. Otherwise, inserts
	174	* @node into the tree and returns @node.
	175	*/
	176	struct prio_tree_node prio_tree_insert(struct prio_tree_root root,
	177	struct prio_tree_node *node)
	178	{
	179	struct prio_tree_node cur, res = node;
	180	unsigned long radix_index, heap_index;
	181	unsigned long r_index, h_index, index, mask;
	182	int size_flag = 0;
	183
	184	get_index(root, node, &radix_index, &heap_index);
	185
	186	if (prio_tree_empty(root) \|\|
	187	heap_index > prio_tree_maxindex(root->index_bits))
	188	return prio_tree_expand(root, node, heap_index);
	189
	190	cur = root->prio_tree_node;
	191	mask = 1UL << (root->index_bits - 1);
	192
	193	while (mask) {
	194	get_index(root, cur, &r_index, &h_index);
	195
	196	if (r_index == radix_index && h_index == heap_index)
	197	return cur;
	198
	199	if (h_index < heap_index \|\|
	200	(h_index == heap_index && r_index > radix_index)) {
	201	struct prio_tree_node *tmp = node;
	202	node = prio_tree_replace(root, cur, node);
	203	cur = tmp;
	204	/* swap indices */
	205	index = r_index;
	206	r_index = radix_index;
	207	radix_index = index;
	208	index = h_index;
	209	h_index = heap_index;
	210	heap_index = index;
	211	}
	212
	213	if (size_flag)
	214	index = heap_index - radix_index;
	215	else
	216	index = radix_index;
	217
	218	if (index & mask) {
	219	if (prio_tree_right_empty(cur)) {
	220	INIT_PRIO_TREE_NODE(node);
97e834c5	221	prio_set_parent(cur, node, false);
1da177e4 LT	222	return res;
	223	} else
	224	cur = cur->right;
	225	} else {
	226	if (prio_tree_left_empty(cur)) {
	227	INIT_PRIO_TREE_NODE(node);
97e834c5	228	prio_set_parent(cur, node, true);
1da177e4 LT	229	return res;
	230	} else
	231	cur = cur->left;
	232	}
	233
	234	mask >>= 1;
	235
	236	if (!mask) {
	237	mask = 1UL << (BITS_PER_LONG - 1);
	238	size_flag = 1;
	239	}
	240	}
	241	/* Should not reach here */
	242	BUG();
	243	return NULL;
	244	}
fff3fd8a	245	EXPORT_SYMBOL(prio_tree_insert);
1da177e4 LT	246
	247	/*
	248	* Remove a prio_tree_node @node from a radix priority search tree @root. The
	249	* algorithm takes O(log n) time where 'log n' is the number of bits required
	250	* to represent the maximum heap_index.
	251	*/
	252	void prio_tree_remove(struct prio_tree_root root, struct prio_tree_node node)
	253	{
	254	struct prio_tree_node *cur;
	255	unsigned long r_index, h_index_right, h_index_left;
	256
	257	cur = node;
	258
	259	while (!prio_tree_left_empty(cur) \|\| !prio_tree_right_empty(cur)) {
	260	if (!prio_tree_left_empty(cur))
	261	get_index(root, cur->left, &r_index, &h_index_left);
	262	else {
	263	cur = cur->right;
	264	continue;
	265	}
	266
	267	if (!prio_tree_right_empty(cur))
	268	get_index(root, cur->right, &r_index, &h_index_right);
	269	else {
	270	cur = cur->left;
	271	continue;
	272	}
	273
	274	/* both h_index_left and h_index_right cannot be 0 */
	275	if (h_index_left >= h_index_right)
	276	cur = cur->left;
	277	else
	278	cur = cur->right;
	279	}
	280
	281	if (prio_tree_root(cur)) {
	282	BUG_ON(root->prio_tree_node != cur);
	283	__INIT_PRIO_TREE_ROOT(root, root->raw);
	284	return;
	285	}
	286
	287	if (cur->parent->right == cur)
	288	cur->parent->right = cur->parent;
	289	else
	290	cur->parent->left = cur->parent;
	291
	292	while (cur != node)
	293	cur = prio_tree_replace(root, cur->parent, cur);
	294	}
fff3fd8a	295	EXPORT_SYMBOL(prio_tree_remove);
1da177e4	296
f35368dd XG	297	static void iter_walk_down(struct prio_tree_iter *iter)
	298	{
	299	iter->mask >>= 1;
	300	if (iter->mask) {
	301	if (iter->size_level)
	302	iter->size_level++;
	303	return;
	304	}
	305
	306	if (iter->size_level) {
	307	BUG_ON(!prio_tree_left_empty(iter->cur));
	308	BUG_ON(!prio_tree_right_empty(iter->cur));
	309	iter->size_level++;
	310	iter->mask = ULONG_MAX;
	311	} else {
	312	iter->size_level = 1;
	313	iter->mask = 1UL << (BITS_PER_LONG - 1);
	314	}
	315	}
	316
	317	static void iter_walk_up(struct prio_tree_iter *iter)
	318	{
	319	if (iter->mask == ULONG_MAX)
	320	iter->mask = 1UL;
	321	else if (iter->size_level == 1)
	322	iter->mask = 1UL;
	323	else
	324	iter->mask <<= 1;
	325	if (iter->size_level)
	326	iter->size_level--;
	327	if (!iter->size_level && (iter->value & iter->mask))
	328	iter->value ^= iter->mask;
	329	}
	330
1da177e4 LT	331	/*
	332	* Following functions help to enumerate all prio_tree_nodes in the tree that
	333	* overlap with the input interval X [radix_index, heap_index]. The enumeration
	334	* takes O(log n + m) time where 'log n' is the height of the tree (which is
	335	* proportional to # of bits required to represent the maximum heap_index) and
	336	* 'm' is the number of prio_tree_nodes that overlap the interval X.
	337	*/
	338
	339	static struct prio_tree_node prio_tree_left(struct prio_tree_iter iter,
	340	unsigned long r_index, unsigned long h_index)
	341	{
	342	if (prio_tree_left_empty(iter->cur))
	343	return NULL;
	344
	345	get_index(iter->root, iter->cur->left, r_index, h_index);
	346
	347	if (iter->r_index <= *h_index) {
	348	iter->cur = iter->cur->left;
f35368dd	349	iter_walk_down(iter);
1da177e4 LT	350	return iter->cur;
	351	}
	352
	353	return NULL;
	354	}
	355
	356	static struct prio_tree_node prio_tree_right(struct prio_tree_iter iter,
	357	unsigned long r_index, unsigned long h_index)
	358	{
	359	unsigned long value;
	360
	361	if (prio_tree_right_empty(iter->cur))
	362	return NULL;
	363
	364	if (iter->size_level)
	365	value = iter->value;
	366	else
	367	value = iter->value \| iter->mask;
	368
	369	if (iter->h_index < value)
	370	return NULL;
	371
	372	get_index(iter->root, iter->cur->right, r_index, h_index);
	373
	374	if (iter->r_index <= *h_index) {
	375	iter->cur = iter->cur->right;
f35368dd	376	iter_walk_down(iter);
1da177e4 LT	377	return iter->cur;
	378	}
	379
	380	return NULL;
	381	}
	382
	383	static struct prio_tree_node prio_tree_parent(struct prio_tree_iter iter)
	384	{
	385	iter->cur = iter->cur->parent;
f35368dd	386	iter_walk_up(iter);
1da177e4 LT	387	return iter->cur;
	388	}
	389
	390	static inline int overlap(struct prio_tree_iter *iter,
	391	unsigned long r_index, unsigned long h_index)
	392	{
	393	return iter->h_index >= r_index && iter->r_index <= h_index;
	394	}
	395
	396	/*
	397	* prio_tree_first:
	398	*
	399	* Get the first prio_tree_node that overlaps with the interval [radix_index,
	400	* heap_index]. Note that always radix_index <= heap_index. We do a pre-order
	401	* traversal of the tree.
	402	*/
	403	static struct prio_tree_node prio_tree_first(struct prio_tree_iter iter)
	404	{
	405	struct prio_tree_root *root;
	406	unsigned long r_index, h_index;
	407
	408	INIT_PRIO_TREE_ITER(iter);
	409
	410	root = iter->root;
	411	if (prio_tree_empty(root))
	412	return NULL;
	413
	414	get_index(root, root->prio_tree_node, &r_index, &h_index);
	415
	416	if (iter->r_index > h_index)
	417	return NULL;
	418
	419	iter->mask = 1UL << (root->index_bits - 1);
	420	iter->cur = root->prio_tree_node;
	421
	422	while (1) {
	423	if (overlap(iter, r_index, h_index))
	424	return iter->cur;
	425
	426	if (prio_tree_left(iter, &r_index, &h_index))
	427	continue;
	428
	429	if (prio_tree_right(iter, &r_index, &h_index))
	430	continue;
	431
	432	break;
	433	}
	434	return NULL;
	435	}
	436
	437	/*
	438	* prio_tree_next:
	439	*
	440	* Get the next prio_tree_node that overlaps with the input interval in iter
	441	*/
	442	struct prio_tree_node prio_tree_next(struct prio_tree_iter iter)
	443	{
	444	unsigned long r_index, h_index;
	445
	446	if (iter->cur == NULL)
	447	return prio_tree_first(iter);
	448
	449	repeat:
	450	while (prio_tree_left(iter, &r_index, &h_index))
451	if (overlap(iter, r_index, h_index))
452	return iter->cur;
453
454	while (!prio_tree_right(iter, &r_index, &h_index)) {
455	while (!prio_tree_root(iter->cur) &&
456	iter->cur->parent->right == iter->cur)
457	prio_tree_parent(iter);
458
459	if (prio_tree_root(iter->cur))
460	return NULL;
461
462	prio_tree_parent(iter);
463	}
464
465	if (overlap(iter, r_index, h_index))
466	return iter->cur;
467
468	goto repeat;
469	}
fff3fd8a	470	EXPORT_SYMBOL(prio_tree_next);