[mirror_ubuntu-artful-kernel.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];
}

/*
 * 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);

		prev->left = tmp;
		tmp->parent = prev;
		prev = tmp;
	}

	if (!prio_tree_empty(root)) {
		prev->left = root->prio_tree_node;
		prev->left->parent = prev;
	}

	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 {
		node->parent = old->parent;
		if (old->parent->left == old)
			old->parent->left = node;
		else
			old->parent->right = node;
	}

	if (!prio_tree_left_empty(old)) {
		node->left = old->left;
		old->left->parent = node;
	}

	if (!prio_tree_right_empty(old)) {
		node->right = old->right;
		old->right->parent = node;
	}

	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);
				cur->right = node;
				node->parent = cur;
				return res;
			} else
				cur = cur->right;
		} else {
			if (prio_tree_left_empty(cur)) {
				INIT_PRIO_TREE_NODE(node);
				cur->left = node;
				node->parent = cur;
				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
88	/*
89	* Extend a priority search tree so that it can store a node with heap_index
90	* max_heap_index. In the worst case, this algorithm takes O((log n)^2).
91	* However, this function is used rarely and the common case performance is
92	* not bad.
93	*/
94	static struct prio_tree_node prio_tree_expand(struct prio_tree_root root,
95	struct prio_tree_node *node, unsigned long max_heap_index)
96	{
742245d5	97	struct prio_tree_node *prev;
1da177e4 LT	98
	99	if (max_heap_index > prio_tree_maxindex(root->index_bits))
	100	root->index_bits++;
	101
742245d5 XG	102	prev = node;
	103	INIT_PRIO_TREE_NODE(node);
	104
1da177e4	105	while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
742245d5 XG	106	struct prio_tree_node *tmp = root->prio_tree_node;
742245d5 XG	107
1da177e4 LT	108	root->index_bits++;
	109
	110	if (prio_tree_empty(root))
	111	continue;
	112
742245d5 XG	113	prio_tree_remove(root, root->prio_tree_node);
742245d5 XG	114	INIT_PRIO_TREE_NODE(tmp);
1da177e4	115
742245d5 XG	116	prev->left = tmp;
	117	tmp->parent = prev;
	118	prev = tmp;
	119	}
1da177e4 LT	120
1da177e4 LT	121	if (!prio_tree_empty(root)) {
742245d5 XG	122	prev->left = root->prio_tree_node;
742245d5 XG	123	prev->left->parent = prev;
1da177e4 LT	124	}
	125
	126	root->prio_tree_node = node;
	127	return node;
	128	}
	129
	130	/*
	131	* Replace a prio_tree_node with a new node and return the old node
	132	*/
	133	struct prio_tree_node prio_tree_replace(struct prio_tree_root root,
	134	struct prio_tree_node old, struct prio_tree_node node)
	135	{
	136	INIT_PRIO_TREE_NODE(node);
	137
	138	if (prio_tree_root(old)) {
	139	BUG_ON(root->prio_tree_node != old);
	140	/*
	141	* We can reduce root->index_bits here. However, it is complex
	142	* and does not help much to improve performance (IMO).
	143	*/
1da177e4 LT	144	root->prio_tree_node = node;
	145	} else {
	146	node->parent = old->parent;
	147	if (old->parent->left == old)
	148	old->parent->left = node;
	149	else
	150	old->parent->right = node;
	151	}
	152
	153	if (!prio_tree_left_empty(old)) {
	154	node->left = old->left;
	155	old->left->parent = node;
	156	}
	157
	158	if (!prio_tree_right_empty(old)) {
	159	node->right = old->right;
	160	old->right->parent = node;
	161	}
	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);
221	cur->right = node;
222	node->parent = cur;
223	return res;
224	} else
225	cur = cur->right;
226	} else {
227	if (prio_tree_left_empty(cur)) {
228	INIT_PRIO_TREE_NODE(node);
229	cur->left = node;
230	node->parent = cur;
231	return res;
232	} else
233	cur = cur->left;
234	}
235
236	mask >>= 1;
237
238	if (!mask) {
239	mask = 1UL << (BITS_PER_LONG - 1);
240	size_flag = 1;
241	}
242	}
243	/* Should not reach here */
244	BUG();
245	return NULL;
246	}
247
248	/*
249	* Remove a prio_tree_node @node from a radix priority search tree @root. The
250	* algorithm takes O(log n) time where 'log n' is the number of bits required
251	* to represent the maximum heap_index.
252	*/
253	void prio_tree_remove(struct prio_tree_root root, struct prio_tree_node node)
254	{
255	struct prio_tree_node *cur;
256	unsigned long r_index, h_index_right, h_index_left;
257
258	cur = node;
259
260	while (!prio_tree_left_empty(cur) \|\| !prio_tree_right_empty(cur)) {
261	if (!prio_tree_left_empty(cur))
262	get_index(root, cur->left, &r_index, &h_index_left);
263	else {
264	cur = cur->right;
265	continue;
266	}
267
268	if (!prio_tree_right_empty(cur))
269	get_index(root, cur->right, &r_index, &h_index_right);
270	else {
271	cur = cur->left;
272	continue;
273	}
274
275	/* both h_index_left and h_index_right cannot be 0 */
276	if (h_index_left >= h_index_right)
277	cur = cur->left;
278	else
279	cur = cur->right;
280	}
281
282	if (prio_tree_root(cur)) {
283	BUG_ON(root->prio_tree_node != cur);
284	__INIT_PRIO_TREE_ROOT(root, root->raw);
285	return;
286	}
287
288	if (cur->parent->right == cur)
289	cur->parent->right = cur->parent;
290	else
291	cur->parent->left = cur->parent;
292
293	while (cur != node)
294	cur = prio_tree_replace(root, cur->parent, cur);
295	}
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	}