--- /dev/null
+/*
+ * mm/prio_tree.c - priority search tree for mapping->i_mmap{,_shared}
+ *
+ * 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/module.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{_shared}
+ */
+
+#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))
+
+#define GET_INDEX_VMA(vma, radix, heap) \
+do { \
+ radix = RADIX_INDEX(vma); \
+ heap = HEAP_INDEX(vma); \
+} while (0)
+
+#define GET_INDEX(node, radix, heap) \
+do { \
+ struct vm_area_struct *__tmp = \
+ prio_tree_entry(node, struct vm_area_struct, shared.prio_tree_node);\
+ GET_INDEX_VMA(__tmp, radix, heap); \
+} while (0)
+
+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)
+{
+ static void prio_tree_remove(struct prio_tree_root *,
+ struct prio_tree_node *);
+ 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
+ */
+static 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.
+ */
+static 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(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(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 << (root->index_bits - 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.
+ */
+static 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(cur->left, r_index, h_index_left);
+ else {
+ cur = cur->right;
+ continue;
+ }
+
+ if (!prio_tree_right_empty(cur))
+ GET_INDEX(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);
+ 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_root *root, struct prio_tree_iter *iter,
+ unsigned long radix_index, unsigned long heap_index,
+ unsigned long *r_index, unsigned long *h_index)
+{
+ if (prio_tree_left_empty(iter->cur))
+ return NULL;
+
+ GET_INDEX(iter->cur->left, *r_index, *h_index);
+
+ if (radix_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 << (root->index_bits - 1);
+ }
+ }
+ return iter->cur;
+ }
+
+ return NULL;
+}
+
+static struct prio_tree_node *prio_tree_right(
+ struct prio_tree_root *root, struct prio_tree_iter *iter,
+ unsigned long radix_index, unsigned long heap_index,
+ 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 (heap_index < value)
+ return NULL;
+
+ GET_INDEX(iter->cur->right, *r_index, *h_index);
+
+ if (radix_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 << (root->index_bits - 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(unsigned long radix_index, unsigned long heap_index,
+ unsigned long r_index, unsigned long h_index)
+{
+ return heap_index >= r_index && radix_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_root *root,
+ struct prio_tree_iter *iter, unsigned long radix_index,
+ unsigned long heap_index)
+{
+ unsigned long r_index, h_index;
+
+ INIT_PRIO_TREE_ITER(iter);
+
+ if (prio_tree_empty(root))
+ return NULL;
+
+ GET_INDEX(root->prio_tree_node, r_index, h_index);
+
+ if (radix_index > h_index)
+ return NULL;
+
+ iter->mask = 1UL << (root->index_bits - 1);
+ iter->cur = root->prio_tree_node;
+
+ while (1) {
+ if (overlap(radix_index, heap_index, r_index, h_index))
+ return iter->cur;
+
+ if (prio_tree_left(root, iter, radix_index, heap_index,
+ &r_index, &h_index))
+ continue;
+
+ if (prio_tree_right(root, iter, radix_index, heap_index,
+ &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
+ */
+static struct prio_tree_node *prio_tree_next(struct prio_tree_root *root,
+ struct prio_tree_iter *iter, unsigned long radix_index,
+ unsigned long heap_index)
+{
+ unsigned long r_index, h_index;
+
+repeat:
+ while (prio_tree_left(root, iter, radix_index,
+ heap_index, &r_index, &h_index)) {
+ if (overlap(radix_index, heap_index, r_index, h_index))
+ return iter->cur;
+ }
+
+ while (!prio_tree_right(root, iter, radix_index,
+ heap_index, &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(radix_index, heap_index, r_index, h_index))
+ return iter->cur;
+
+ goto repeat;
+}
+
+/*
+ * Radix priority search tree for address_space->i_mmap_{_shared}
+ *
+ * For each vma that map a unique set of file pages i.e., unique [radix_index,
+ * heap_index] value, we have a corresponing priority search tree node. If
+ * multiple vmas have identical [radix_index, heap_index] value, then one of
+ * them is used as a tree node and others are stored in a vm_set list. The tree
+ * node points to the first vma (head) of the list using vm_set.head.
+ *
+ * prio_tree_root
+ * |
+ * A vm_set.head
+ * / \ /
+ * L R -> H-I-J-K-M-N-O-P-Q-S
+ * ^ ^ <-- vm_set.list -->
+ * tree nodes
+ *
+ * We need some way to identify whether a vma is a tree node, head of a vm_set
+ * list, or just a member of a vm_set list. We cannot use vm_flags to store
+ * such information. The reason is, in the above figure, it is possible that
+ * vm_flags' of R and H are covered by the different mmap_sems. When R is
+ * removed under R->mmap_sem, H replaces R as a tree node. Since we do not hold
+ * H->mmap_sem, we cannot use H->vm_flags for marking that H is a tree node now.
+ * That's why some trick involving shared.vm_set.parent is used for identifying
+ * tree nodes and list head nodes.
+ *
+ * vma radix priority search tree node rules:
+ *
+ * vma->shared.vm_set.parent != NULL ==> a tree node
+ * vma->shared.vm_set.head != NULL ==> list of others mapping same range
+ * vma->shared.vm_set.head == NULL ==> no others map the same range
+ *
+ * vma->shared.vm_set.parent == NULL
+ * vma->shared.vm_set.head != NULL ==> list head of vmas mapping same range
+ * vma->shared.vm_set.head == NULL ==> a list node
+ */
+
+/*
+ * Add a new vma known to map the same set of pages as the old vma:
+ * useful for fork's dup_mmap as well as vma_prio_tree_insert below.
+ */
+void vma_prio_tree_add(struct vm_area_struct *vma, struct vm_area_struct *old)
+{
+ /* Leave these BUG_ONs till prio_tree patch stabilizes */
+ BUG_ON(RADIX_INDEX(vma) != RADIX_INDEX(old));
+ BUG_ON(HEAP_INDEX(vma) != HEAP_INDEX(old));
+
+ if (!old->shared.vm_set.parent)
+ list_add(&vma->shared.vm_set.list,
+ &old->shared.vm_set.list);
+ else if (old->shared.vm_set.head)
+ list_add_tail(&vma->shared.vm_set.list,
+ &old->shared.vm_set.head->shared.vm_set.list);
+ else {
+ INIT_LIST_HEAD(&vma->shared.vm_set.list);
+ vma->shared.vm_set.head = old;
+ old->shared.vm_set.head = vma;
+ }
+}
+
+void vma_prio_tree_insert(struct vm_area_struct *vma,
+ struct prio_tree_root *root)
+{
+ struct prio_tree_node *ptr;
+ struct vm_area_struct *old;
+
+ ptr = prio_tree_insert(root, &vma->shared.prio_tree_node);
+ if (ptr != &vma->shared.prio_tree_node) {
+ old = prio_tree_entry(ptr, struct vm_area_struct,
+ shared.prio_tree_node);
+ vma_prio_tree_add(vma, old);
+ }
+}
+
+void vma_prio_tree_remove(struct vm_area_struct *vma,
+ struct prio_tree_root *root)
+{
+ struct vm_area_struct *node, *head, *new_head;
+
+ if (!vma->shared.vm_set.head) {
+ if (!vma->shared.vm_set.parent)
+ list_del_init(&vma->shared.vm_set.list);
+ else
+ prio_tree_remove(root, &vma->shared.prio_tree_node);
+ } else {
+ /* Leave this BUG_ON till prio_tree patch stabilizes */
+ BUG_ON(vma->shared.vm_set.head->shared.vm_set.head != vma);
+ if (vma->shared.vm_set.parent) {
+ head = vma->shared.vm_set.head;
+ if (!list_empty(&head->shared.vm_set.list)) {
+ new_head = list_entry(
+ head->shared.vm_set.list.next,
+ struct vm_area_struct,
+ shared.vm_set.list);
+ list_del_init(&head->shared.vm_set.list);
+ } else
+ new_head = NULL;
+
+ prio_tree_replace(root, &vma->shared.prio_tree_node,
+ &head->shared.prio_tree_node);
+ head->shared.vm_set.head = new_head;
+ if (new_head)
+ new_head->shared.vm_set.head = head;
+
+ } else {
+ node = vma->shared.vm_set.head;
+ if (!list_empty(&vma->shared.vm_set.list)) {
+ new_head = list_entry(
+ vma->shared.vm_set.list.next,
+ struct vm_area_struct,
+ shared.vm_set.list);
+ list_del_init(&vma->shared.vm_set.list);
+ node->shared.vm_set.head = new_head;
+ new_head->shared.vm_set.head = node;
+ } else
+ node->shared.vm_set.head = NULL;
+ }
+ }
+}
+
+/*
+ * Helper function to enumerate vmas that map a given file page or a set of
+ * contiguous file pages. The function returns vmas that at least map a single
+ * page in the given range of contiguous file pages.
+ */
+struct vm_area_struct *vma_prio_tree_next(struct vm_area_struct *vma,
+ struct prio_tree_root *root, struct prio_tree_iter *iter,
+ pgoff_t begin, pgoff_t end)
+{
+ struct prio_tree_node *ptr;
+ struct vm_area_struct *next;
+
+ if (!vma) {
+ /*
+ * First call is with NULL vma
+ */
+ ptr = prio_tree_first(root, iter, begin, end);
+ if (ptr)
+ return prio_tree_entry(ptr, struct vm_area_struct,
+ shared.prio_tree_node);
+ else
+ return NULL;
+ }
+
+ if (vma->shared.vm_set.parent) {
+ if (vma->shared.vm_set.head)
+ return vma->shared.vm_set.head;
+ } else {
+ next = list_entry(vma->shared.vm_set.list.next,
+ struct vm_area_struct, shared.vm_set.list);
+ if (!next->shared.vm_set.head)
+ return next;
+ }
+
+ ptr = prio_tree_next(root, iter, begin, end);
+ if (ptr)
+ return prio_tree_entry(ptr, struct vm_area_struct,
+ shared.prio_tree_node);
+ else
+ return NULL;
+}
+EXPORT_SYMBOL(vma_prio_tree_next);
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