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authorMatthew Wilcox2016-12-14 15:08:49 -0800
committerLinus Torvalds2016-12-14 16:04:10 -0800
commit148deab223b23734069abcacb5c7118b0e7deadc (patch)
tree56aae9c91802e9262312f7fcbb3571eb9c8ec0e9
parentb35df27a39f40e39fabf1b1e9569c7b24e1add6a (diff)
radix-tree: improve multiorder iterators
This fixes several interlinked problems with the iterators in the presence of multiorder entries. 1. radix_tree_iter_next() would only advance by one slot, which would result in the iterators returning the same entry more than once if there were sibling entries. 2. radix_tree_next_slot() could return an internal pointer instead of a user pointer if a tagged multiorder entry was immediately followed by an entry of lower order. 3. radix_tree_next_slot() expanded to a lot more code than it used to when multiorder support was compiled in. And I wasn't comfortable with entry_to_node() being in a header file. Fixing radix_tree_iter_next() for the presence of sibling entries necessarily involves examining the contents of the radix tree, so we now need to pass 'slot' to radix_tree_iter_next(), and we need to change the calling convention so it is called *before* dropping the lock which protects the tree. Also rename it to radix_tree_iter_resume(), as some people thought it was necessary to call radix_tree_iter_next() each time around the loop. radix_tree_next_slot() becomes closer to how it looked before multiorder support was introduced. It only checks to see if the next entry in the chunk is a sibling entry or a pointer to a node; this should be rare enough that handling this case out of line is not a performance impact (and such impact is amortised by the fact that the entry we just processed was a multiorder entry). Also, radix_tree_next_slot() used to force a new chunk lookup for untagged entries, which is more expensive than the out of line sibling entry skipping. Link: http://lkml.kernel.org/r/1480369871-5271-55-git-send-email-mawilcox@linuxonhyperv.com Signed-off-by: Matthew Wilcox <mawilcox@microsoft.com> Tested-by: Kirill A. Shutemov <kirill.shutemov@linux.intel.com> Cc: Konstantin Khlebnikov <koct9i@gmail.com> Cc: Ross Zwisler <ross.zwisler@linux.intel.com> Cc: Matthew Wilcox <mawilcox@microsoft.com> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
-rw-r--r--fs/btrfs/tests/btrfs-tests.c2
-rw-r--r--include/linux/radix-tree.h71
-rw-r--r--lib/radix-tree.c138
-rw-r--r--mm/khugepaged.c7
-rw-r--r--mm/shmem.c6
-rw-r--r--tools/testing/radix-tree/iteration_check.c12
-rw-r--r--tools/testing/radix-tree/multiorder.c28
-rw-r--r--tools/testing/radix-tree/regression3.c8
-rw-r--r--tools/testing/radix-tree/test.h1
9 files changed, 188 insertions, 85 deletions
diff --git a/fs/btrfs/tests/btrfs-tests.c b/fs/btrfs/tests/btrfs-tests.c
index 73076a0ea6a9..00ee006a8aa2 100644
--- a/fs/btrfs/tests/btrfs-tests.c
+++ b/fs/btrfs/tests/btrfs-tests.c
@@ -162,7 +162,7 @@ void btrfs_free_dummy_fs_info(struct btrfs_fs_info *fs_info)
slot = radix_tree_iter_retry(&iter);
continue;
}
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
spin_unlock(&fs_info->buffer_lock);
free_extent_buffer_stale(eb);
spin_lock(&fs_info->buffer_lock);
diff --git a/include/linux/radix-tree.h b/include/linux/radix-tree.h
index d04073ac3a9f..289d007d487b 100644
--- a/include/linux/radix-tree.h
+++ b/include/linux/radix-tree.h
@@ -403,20 +403,17 @@ __radix_tree_iter_add(struct radix_tree_iter *iter, unsigned long slots)
}
/**
- * radix_tree_iter_next - resume iterating when the chunk may be invalid
- * @iter: iterator state
+ * radix_tree_iter_resume - resume iterating when the chunk may be invalid
+ * @slot: pointer to current slot
+ * @iter: iterator state
+ * Returns: New slot pointer
*
* If the iterator needs to release then reacquire a lock, the chunk may
* have been invalidated by an insertion or deletion. Call this function
- * to continue the iteration from the next index.
+ * before releasing the lock to continue the iteration from the next index.
*/
-static inline __must_check
-void **radix_tree_iter_next(struct radix_tree_iter *iter)
-{
- iter->next_index = __radix_tree_iter_add(iter, 1);
- iter->tags = 0;
- return NULL;
-}
+void **__must_check radix_tree_iter_resume(void **slot,
+ struct radix_tree_iter *iter);
/**
* radix_tree_chunk_size - get current chunk size
@@ -430,10 +427,17 @@ radix_tree_chunk_size(struct radix_tree_iter *iter)
return (iter->next_index - iter->index) >> iter_shift(iter);
}
-static inline struct radix_tree_node *entry_to_node(void *ptr)
+#ifdef CONFIG_RADIX_TREE_MULTIORDER
+void ** __radix_tree_next_slot(void **slot, struct radix_tree_iter *iter,
+ unsigned flags);
+#else
+/* Can't happen without sibling entries, but the compiler can't tell that */
+static inline void ** __radix_tree_next_slot(void **slot,
+ struct radix_tree_iter *iter, unsigned flags)
{
- return (void *)((unsigned long)ptr & ~RADIX_TREE_INTERNAL_NODE);
+ return slot;
}
+#endif
/**
* radix_tree_next_slot - find next slot in chunk
@@ -447,7 +451,7 @@ static inline struct radix_tree_node *entry_to_node(void *ptr)
* For tagged lookup it also eats @iter->tags.
*
* There are several cases where 'slot' can be passed in as NULL to this
- * function. These cases result from the use of radix_tree_iter_next() or
+ * function. These cases result from the use of radix_tree_iter_resume() or
* radix_tree_iter_retry(). In these cases we don't end up dereferencing
* 'slot' because either:
* a) we are doing tagged iteration and iter->tags has been set to 0, or
@@ -458,51 +462,31 @@ static __always_inline void **
radix_tree_next_slot(void **slot, struct radix_tree_iter *iter, unsigned flags)
{
if (flags & RADIX_TREE_ITER_TAGGED) {
- void *canon = slot;
-
iter->tags >>= 1;
if (unlikely(!iter->tags))
return NULL;
- while (IS_ENABLED(CONFIG_RADIX_TREE_MULTIORDER) &&
- radix_tree_is_internal_node(slot[1])) {
- if (entry_to_node(slot[1]) == canon) {
- iter->tags >>= 1;
- iter->index = __radix_tree_iter_add(iter, 1);
- slot++;
- continue;
- }
- iter->next_index = __radix_tree_iter_add(iter, 1);
- return NULL;
- }
if (likely(iter->tags & 1ul)) {
iter->index = __radix_tree_iter_add(iter, 1);
- return slot + 1;
+ slot++;
+ goto found;
}
if (!(flags & RADIX_TREE_ITER_CONTIG)) {
unsigned offset = __ffs(iter->tags);
- iter->tags >>= offset;
- iter->index = __radix_tree_iter_add(iter, offset + 1);
- return slot + offset + 1;
+ iter->tags >>= offset++;
+ iter->index = __radix_tree_iter_add(iter, offset);
+ slot += offset;
+ goto found;
}
} else {
long count = radix_tree_chunk_size(iter);
- void *canon = slot;
while (--count > 0) {
slot++;
iter->index = __radix_tree_iter_add(iter, 1);
- if (IS_ENABLED(CONFIG_RADIX_TREE_MULTIORDER) &&
- radix_tree_is_internal_node(*slot)) {
- if (entry_to_node(*slot) == canon)
- continue;
- iter->next_index = iter->index;
- break;
- }
-
if (likely(*slot))
- return slot;
+ goto found;
if (flags & RADIX_TREE_ITER_CONTIG) {
/* forbid switching to the next chunk */
iter->next_index = 0;
@@ -511,6 +495,11 @@ radix_tree_next_slot(void **slot, struct radix_tree_iter *iter, unsigned flags)
}
}
return NULL;
+
+ found:
+ if (unlikely(radix_tree_is_internal_node(*slot)))
+ return __radix_tree_next_slot(slot, iter, flags);
+ return slot;
}
/**
@@ -561,6 +550,6 @@ radix_tree_next_slot(void **slot, struct radix_tree_iter *iter, unsigned flags)
slot || (slot = radix_tree_next_chunk(root, iter, \
RADIX_TREE_ITER_TAGGED | tag)) ; \
slot = radix_tree_next_slot(slot, iter, \
- RADIX_TREE_ITER_TAGGED))
+ RADIX_TREE_ITER_TAGGED | tag))
#endif /* _LINUX_RADIX_TREE_H */
diff --git a/lib/radix-tree.c b/lib/radix-tree.c
index dbf4e8c8e100..0a7ac0fb4a65 100644
--- a/lib/radix-tree.c
+++ b/lib/radix-tree.c
@@ -69,6 +69,11 @@ struct radix_tree_preload {
};
static DEFINE_PER_CPU(struct radix_tree_preload, radix_tree_preloads) = { 0, };
+static inline struct radix_tree_node *entry_to_node(void *ptr)
+{
+ return (void *)((unsigned long)ptr & ~RADIX_TREE_INTERNAL_NODE);
+}
+
static inline void *node_to_entry(void *ptr)
{
return (void *)((unsigned long)ptr | RADIX_TREE_INTERNAL_NODE);
@@ -1104,6 +1109,120 @@ static inline void __set_iter_shift(struct radix_tree_iter *iter,
#endif
}
+/* Construct iter->tags bit-mask from node->tags[tag] array */
+static void set_iter_tags(struct radix_tree_iter *iter,
+ struct radix_tree_node *node, unsigned offset,
+ unsigned tag)
+{
+ unsigned tag_long = offset / BITS_PER_LONG;
+ unsigned tag_bit = offset % BITS_PER_LONG;
+
+ iter->tags = node->tags[tag][tag_long] >> tag_bit;
+
+ /* This never happens if RADIX_TREE_TAG_LONGS == 1 */
+ if (tag_long < RADIX_TREE_TAG_LONGS - 1) {
+ /* Pick tags from next element */
+ if (tag_bit)
+ iter->tags |= node->tags[tag][tag_long + 1] <<
+ (BITS_PER_LONG - tag_bit);
+ /* Clip chunk size, here only BITS_PER_LONG tags */
+ iter->next_index = __radix_tree_iter_add(iter, BITS_PER_LONG);
+ }
+}
+
+#ifdef CONFIG_RADIX_TREE_MULTIORDER
+static void **skip_siblings(struct radix_tree_node **nodep,
+ void **slot, struct radix_tree_iter *iter)
+{
+ void *sib = node_to_entry(slot - 1);
+
+ while (iter->index < iter->next_index) {
+ *nodep = rcu_dereference_raw(*slot);
+ if (*nodep && *nodep != sib)
+ return slot;
+ slot++;
+ iter->index = __radix_tree_iter_add(iter, 1);
+ iter->tags >>= 1;
+ }
+
+ *nodep = NULL;
+ return NULL;
+}
+
+void ** __radix_tree_next_slot(void **slot, struct radix_tree_iter *iter,
+ unsigned flags)
+{
+ unsigned tag = flags & RADIX_TREE_ITER_TAG_MASK;
+ struct radix_tree_node *node = rcu_dereference_raw(*slot);
+
+ slot = skip_siblings(&node, slot, iter);
+
+ while (radix_tree_is_internal_node(node)) {
+ unsigned offset;
+ unsigned long next_index;
+
+ if (node == RADIX_TREE_RETRY)
+ return slot;
+ node = entry_to_node(node);
+ iter->shift = node->shift;
+
+ if (flags & RADIX_TREE_ITER_TAGGED) {
+ offset = radix_tree_find_next_bit(node, tag, 0);
+ if (offset == RADIX_TREE_MAP_SIZE)
+ return NULL;
+ slot = &node->slots[offset];
+ iter->index = __radix_tree_iter_add(iter, offset);
+ set_iter_tags(iter, node, offset, tag);
+ node = rcu_dereference_raw(*slot);
+ } else {
+ offset = 0;
+ slot = &node->slots[0];
+ for (;;) {
+ node = rcu_dereference_raw(*slot);
+ if (node)
+ break;
+ slot++;
+ offset++;
+ if (offset == RADIX_TREE_MAP_SIZE)
+ return NULL;
+ }
+ iter->index = __radix_tree_iter_add(iter, offset);
+ }
+ if ((flags & RADIX_TREE_ITER_CONTIG) && (offset > 0))
+ goto none;
+ next_index = (iter->index | shift_maxindex(iter->shift)) + 1;
+ if (next_index < iter->next_index)
+ iter->next_index = next_index;
+ }
+
+ return slot;
+ none:
+ iter->next_index = 0;
+ return NULL;
+}
+EXPORT_SYMBOL(__radix_tree_next_slot);
+#else
+static void **skip_siblings(struct radix_tree_node **nodep,
+ void **slot, struct radix_tree_iter *iter)
+{
+ return slot;
+}
+#endif
+
+void **radix_tree_iter_resume(void **slot, struct radix_tree_iter *iter)
+{
+ struct radix_tree_node *node;
+
+ slot++;
+ iter->index = __radix_tree_iter_add(iter, 1);
+ node = rcu_dereference_raw(*slot);
+ skip_siblings(&node, slot, iter);
+ iter->next_index = iter->index;
+ iter->tags = 0;
+ return NULL;
+}
+EXPORT_SYMBOL(radix_tree_iter_resume);
+
/**
* radix_tree_next_chunk - find next chunk of slots for iteration
*
@@ -1191,23 +1310,8 @@ void **radix_tree_next_chunk(struct radix_tree_root *root,
iter->next_index = (index | node_maxindex(node)) + 1;
__set_iter_shift(iter, node->shift);
- /* Construct iter->tags bit-mask from node->tags[tag] array */
- if (flags & RADIX_TREE_ITER_TAGGED) {
- unsigned tag_long, tag_bit;
-
- tag_long = offset / BITS_PER_LONG;
- tag_bit = offset % BITS_PER_LONG;
- iter->tags = node->tags[tag][tag_long] >> tag_bit;
- /* This never happens if RADIX_TREE_TAG_LONGS == 1 */
- if (tag_long < RADIX_TREE_TAG_LONGS - 1) {
- /* Pick tags from next element */
- if (tag_bit)
- iter->tags |= node->tags[tag][tag_long + 1] <<
- (BITS_PER_LONG - tag_bit);
- /* Clip chunk size, here only BITS_PER_LONG tags */
- iter->next_index = index + BITS_PER_LONG;
- }
- }
+ if (flags & RADIX_TREE_ITER_TAGGED)
+ set_iter_tags(iter, node, offset, tag);
return node->slots + offset;
}
diff --git a/mm/khugepaged.c b/mm/khugepaged.c
index 7434a63cac94..e32389a97030 100644
--- a/mm/khugepaged.c
+++ b/mm/khugepaged.c
@@ -1446,7 +1446,7 @@ static void collapse_shmem(struct mm_struct *mm,
radix_tree_replace_slot(&mapping->page_tree, slot,
new_page + (index % HPAGE_PMD_NR));
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
index++;
continue;
out_lru:
@@ -1546,7 +1546,6 @@ tree_unlocked:
/* Put holes back where they were */
radix_tree_delete(&mapping->page_tree,
iter.index);
- slot = radix_tree_iter_next(&iter);
continue;
}
@@ -1557,11 +1556,11 @@ tree_unlocked:
page_ref_unfreeze(page, 2);
radix_tree_replace_slot(&mapping->page_tree,
slot, page);
+ slot = radix_tree_iter_resume(slot, &iter);
spin_unlock_irq(&mapping->tree_lock);
putback_lru_page(page);
unlock_page(page);
spin_lock_irq(&mapping->tree_lock);
- slot = radix_tree_iter_next(&iter);
}
VM_BUG_ON(nr_none);
spin_unlock_irq(&mapping->tree_lock);
@@ -1641,8 +1640,8 @@ static void khugepaged_scan_shmem(struct mm_struct *mm,
present++;
if (need_resched()) {
+ slot = radix_tree_iter_resume(slot, &iter);
cond_resched_rcu();
- slot = radix_tree_iter_next(&iter);
}
}
rcu_read_unlock();
diff --git a/mm/shmem.c b/mm/shmem.c
index abd7403aba41..be11c6dd414a 100644
--- a/mm/shmem.c
+++ b/mm/shmem.c
@@ -661,8 +661,8 @@ unsigned long shmem_partial_swap_usage(struct address_space *mapping,
swapped++;
if (need_resched()) {
+ slot = radix_tree_iter_resume(slot, &iter);
cond_resched_rcu();
- slot = radix_tree_iter_next(&iter);
}
}
@@ -2447,8 +2447,8 @@ static void shmem_tag_pins(struct address_space *mapping)
}
if (need_resched()) {
+ slot = radix_tree_iter_resume(slot, &iter);
cond_resched_rcu();
- slot = radix_tree_iter_next(&iter);
}
}
rcu_read_unlock();
@@ -2517,8 +2517,8 @@ static int shmem_wait_for_pins(struct address_space *mapping)
spin_unlock_irq(&mapping->tree_lock);
continue_resched:
if (need_resched()) {
+ slot = radix_tree_iter_resume(slot, &iter);
cond_resched_rcu();
- slot = radix_tree_iter_next(&iter);
}
}
rcu_read_unlock();
diff --git a/tools/testing/radix-tree/iteration_check.c b/tools/testing/radix-tree/iteration_check.c
index df71cb841385..f328a66899b4 100644
--- a/tools/testing/radix-tree/iteration_check.c
+++ b/tools/testing/radix-tree/iteration_check.c
@@ -48,8 +48,8 @@ static void *add_entries_fn(void *arg)
/*
* Iterate over the tagged entries, doing a radix_tree_iter_retry() as we find
* things that have been removed and randomly resetting our iteration to the
- * next chunk with radix_tree_iter_next(). Both radix_tree_iter_retry() and
- * radix_tree_iter_next() cause radix_tree_next_slot() to be called with a
+ * next chunk with radix_tree_iter_resume(). Both radix_tree_iter_retry() and
+ * radix_tree_iter_resume() cause radix_tree_next_slot() to be called with a
* NULL 'slot' variable.
*/
static void *tagged_iteration_fn(void *arg)
@@ -79,7 +79,7 @@ static void *tagged_iteration_fn(void *arg)
}
if (rand_r(&seeds[0]) % 50 == 0) {
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
rcu_read_unlock();
rcu_barrier();
rcu_read_lock();
@@ -96,8 +96,8 @@ static void *tagged_iteration_fn(void *arg)
/*
* Iterate over the entries, doing a radix_tree_iter_retry() as we find things
* that have been removed and randomly resetting our iteration to the next
- * chunk with radix_tree_iter_next(). Both radix_tree_iter_retry() and
- * radix_tree_iter_next() cause radix_tree_next_slot() to be called with a
+ * chunk with radix_tree_iter_resume(). Both radix_tree_iter_retry() and
+ * radix_tree_iter_resume() cause radix_tree_next_slot() to be called with a
* NULL 'slot' variable.
*/
static void *untagged_iteration_fn(void *arg)
@@ -127,7 +127,7 @@ static void *untagged_iteration_fn(void *arg)
}
if (rand_r(&seeds[1]) % 50 == 0) {
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
rcu_read_unlock();
rcu_barrier();
rcu_read_lock();
diff --git a/tools/testing/radix-tree/multiorder.c b/tools/testing/radix-tree/multiorder.c
index 8d5865c95664..b9be8856d652 100644
--- a/tools/testing/radix-tree/multiorder.c
+++ b/tools/testing/radix-tree/multiorder.c
@@ -231,11 +231,14 @@ void multiorder_iteration(void)
radix_tree_for_each_slot(slot, &tree, &iter, j) {
int height = order[i] / RADIX_TREE_MAP_SHIFT;
int shift = height * RADIX_TREE_MAP_SHIFT;
- int mask = (1 << order[i]) - 1;
+ unsigned long mask = (1UL << order[i]) - 1;
+ struct item *item = *slot;
- assert(iter.index >= (index[i] &~ mask));
- assert(iter.index <= (index[i] | mask));
+ assert((iter.index | mask) == (index[i] | mask));
assert(iter.shift == shift);
+ assert(!radix_tree_is_internal_node(item));
+ assert((item->index | mask) == (index[i] | mask));
+ assert(item->order == order[i]);
i++;
}
}
@@ -269,7 +272,7 @@ void multiorder_tagged_iteration(void)
assert(radix_tree_tag_set(&tree, tag_index[i], 1));
for (j = 0; j < 256; j++) {
- int mask, k;
+ int k;
for (i = 0; i < TAG_ENTRIES; i++) {
for (k = i; index[k] < tag_index[i]; k++)
@@ -279,12 +282,16 @@ void multiorder_tagged_iteration(void)
}
radix_tree_for_each_tagged(slot, &tree, &iter, j, 1) {
+ unsigned long mask;
+ struct item *item = *slot;
for (k = i; index[k] < tag_index[i]; k++)
;
- mask = (1 << order[k]) - 1;
+ mask = (1UL << order[k]) - 1;
- assert(iter.index >= (tag_index[i] &~ mask));
- assert(iter.index <= (tag_index[i] | mask));
+ assert((iter.index | mask) == (tag_index[i] | mask));
+ assert(!radix_tree_is_internal_node(item));
+ assert((item->index | mask) == (tag_index[i] | mask));
+ assert(item->order == order[k]);
i++;
}
}
@@ -303,12 +310,15 @@ void multiorder_tagged_iteration(void)
}
radix_tree_for_each_tagged(slot, &tree, &iter, j, 2) {
+ struct item *item = *slot;
for (k = i; index[k] < tag_index[i]; k++)
;
mask = (1 << order[k]) - 1;
- assert(iter.index >= (tag_index[i] &~ mask));
- assert(iter.index <= (tag_index[i] | mask));
+ assert((iter.index | mask) == (tag_index[i] | mask));
+ assert(!radix_tree_is_internal_node(item));
+ assert((item->index | mask) == (tag_index[i] | mask));
+ assert(item->order == order[k]);
i++;
}
}
diff --git a/tools/testing/radix-tree/regression3.c b/tools/testing/radix-tree/regression3.c
index 1f06ed73d0a8..b594841fae85 100644
--- a/tools/testing/radix-tree/regression3.c
+++ b/tools/testing/radix-tree/regression3.c
@@ -5,7 +5,7 @@
* In following radix_tree_next_slot current chunk size becomes zero.
* This isn't checked and it tries to dereference null pointer in slot.
*
- * Helper radix_tree_iter_next reset slot to NULL and next_index to index + 1,
+ * Helper radix_tree_iter_resume reset slot to NULL and next_index to index + 1,
* for tagger iteraction it also must reset cached tags in iterator to abort
* next radix_tree_next_slot and go to slow-path into radix_tree_next_chunk.
*
@@ -88,7 +88,7 @@ void regression3_test(void)
printf("slot %ld %p\n", iter.index, *slot);
if (!iter.index) {
printf("next at %ld\n", iter.index);
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
}
}
@@ -96,7 +96,7 @@ void regression3_test(void)
printf("contig %ld %p\n", iter.index, *slot);
if (!iter.index) {
printf("next at %ld\n", iter.index);
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
}
}
@@ -106,7 +106,7 @@ void regression3_test(void)
printf("tagged %ld %p\n", iter.index, *slot);
if (!iter.index) {
printf("next at %ld\n", iter.index);
- slot = radix_tree_iter_next(&iter);
+ slot = radix_tree_iter_resume(slot, &iter);
}
}
diff --git a/tools/testing/radix-tree/test.h b/tools/testing/radix-tree/test.h
index 423c528aaee9..617416ec3c5e 100644
--- a/tools/testing/radix-tree/test.h
+++ b/tools/testing/radix-tree/test.h
@@ -41,6 +41,7 @@ void verify_tag_consistency(struct radix_tree_root *root, unsigned int tag);
extern int nr_allocated;
/* Normally private parts of lib/radix-tree.c */
+struct radix_tree_node *entry_to_node(void *ptr);
void radix_tree_dump(struct radix_tree_root *root);
int root_tag_get(struct radix_tree_root *root, unsigned int tag);
unsigned long node_maxindex(struct radix_tree_node *);