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DEFINITIONS
This source file includes following definitions.
- get_index
- prio_tree_init
- prio_tree_maxindex
- prio_tree_expand
- prio_tree_replace
- prio_tree_insert
- prio_tree_remove
- prio_tree_left
- prio_tree_right
- prio_tree_parent
- overlap
- prio_tree_first
- prio_tree_next
/*
* 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 *first = NULL, *prev, *last = NULL;
if (max_heap_index > prio_tree_maxindex(root->index_bits))
root->index_bits++;
while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
root->index_bits++;
if (prio_tree_empty(root))
continue;
if (first == NULL) {
first = root->prio_tree_node;
prio_tree_remove(root, root->prio_tree_node);
INIT_PRIO_TREE_NODE(first);
last = first;
} else {
prev = last;
last = root->prio_tree_node;
prio_tree_remove(root, root->prio_tree_node);
INIT_PRIO_TREE_NODE(last);
prev->left = last;
last->parent = prev;
}
}
INIT_PRIO_TREE_NODE(node);
if (first) {
node->left = first;
first->parent = node;
} else
last = node;
if (!prio_tree_empty(root)) {
last->left = root->prio_tree_node;
last->left->parent = last;
}
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).
*/
node->parent = node;
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);
}
/*
* 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->mask >>= 1;
if (iter->mask) {
if (iter->size_level)
iter->size_level++;
} else {
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);
}
}
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->mask >>= 1;
iter->value = value;
if (iter->mask) {
if (iter->size_level)
iter->size_level++;
} else {
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);
}
}
return iter->cur;
}
return NULL;
}
static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
{
iter->cur = iter->cur->parent;
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;
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;
}