[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>

/*
 * 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;
}

/*
 * 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);
}

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