d72da4a4d9
Change the insert and erase code such that lockless searches are
non-fatal.
In and of itself an rbtree cannot be correctly searched while
in-modification, we can however provide weaker guarantees that will
allow the rbtree to be used in conjunction with other techniques, such
as latches; see 9b0fd802e8 ("seqcount: Add raw_write_seqcount_latch()").
For this to work we need the following guarantees from the rbtree
code:
1) a lockless reader must not see partial stores, this would allow it
to observe nodes that are invalid memory.
2) there must not be (temporary) loops in the tree structure in the
modifier's program order, this would cause a lookup which
interrupts the modifier to get stuck indefinitely.
For 1) we must use WRITE_ONCE() for all updates to the tree structure;
in particular this patch only does rb_{left,right} as those are the
only element required for simple searches.
It generates slightly worse code, probably because volatile. But in
pointer chasing heavy code a few instructions more should not matter.
For 2) I have carefully audited the code and drawn every intermediate
link state and not found a loop.
Cc: Mathieu Desnoyers <mathieu.desnoyers@efficios.com>
Cc: "Paul E. McKenney" <paulmck@linux.vnet.ibm.com>
Cc: Oleg Nesterov <oleg@redhat.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: David Woodhouse <David.Woodhouse@intel.com>
Cc: Rik van Riel <riel@redhat.com>
Reviewed-by: Michel Lespinasse <walken@google.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Signed-off-by: Rusty Russell <rusty@rustcorp.com.au>
593 lines
16 KiB
C
593 lines
16 KiB
C
/*
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Red Black Trees
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(C) 1999 Andrea Arcangeli <andrea@suse.de>
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(C) 2002 David Woodhouse <dwmw2@infradead.org>
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(C) 2012 Michel Lespinasse <walken@google.com>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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linux/lib/rbtree.c
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*/
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#include <linux/rbtree_augmented.h>
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#include <linux/export.h>
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/*
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* red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
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*
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* 1) A node is either red or black
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* 2) The root is black
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* 3) All leaves (NULL) are black
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* 4) Both children of every red node are black
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* 5) Every simple path from root to leaves contains the same number
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* of black nodes.
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*
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* 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
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* consecutive red nodes in a path and every red node is therefore followed by
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* a black. So if B is the number of black nodes on every simple path (as per
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* 5), then the longest possible path due to 4 is 2B.
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*
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* We shall indicate color with case, where black nodes are uppercase and red
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* nodes will be lowercase. Unknown color nodes shall be drawn as red within
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* parentheses and have some accompanying text comment.
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*/
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/*
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* Notes on lockless lookups:
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*
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* All stores to the tree structure (rb_left and rb_right) must be done using
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* WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
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* tree structure as seen in program order.
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*
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* These two requirements will allow lockless iteration of the tree -- not
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* correct iteration mind you, tree rotations are not atomic so a lookup might
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* miss entire subtrees.
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*
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* But they do guarantee that any such traversal will only see valid elements
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* and that it will indeed complete -- does not get stuck in a loop.
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*
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* It also guarantees that if the lookup returns an element it is the 'correct'
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* one. But not returning an element does _NOT_ mean it's not present.
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*
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* NOTE:
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*
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* Stores to __rb_parent_color are not important for simple lookups so those
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* are left undone as of now. Nor did I check for loops involving parent
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* pointers.
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*/
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static inline void rb_set_black(struct rb_node *rb)
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{
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rb->__rb_parent_color |= RB_BLACK;
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}
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static inline struct rb_node *rb_red_parent(struct rb_node *red)
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{
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return (struct rb_node *)red->__rb_parent_color;
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}
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/*
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* Helper function for rotations:
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* - old's parent and color get assigned to new
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* - old gets assigned new as a parent and 'color' as a color.
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*/
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static inline void
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__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
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struct rb_root *root, int color)
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{
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struct rb_node *parent = rb_parent(old);
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new->__rb_parent_color = old->__rb_parent_color;
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rb_set_parent_color(old, new, color);
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__rb_change_child(old, new, parent, root);
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}
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static __always_inline void
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__rb_insert(struct rb_node *node, struct rb_root *root,
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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{
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struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
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while (true) {
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/*
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* Loop invariant: node is red
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*
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* If there is a black parent, we are done.
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* Otherwise, take some corrective action as we don't
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* want a red root or two consecutive red nodes.
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*/
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if (!parent) {
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rb_set_parent_color(node, NULL, RB_BLACK);
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break;
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} else if (rb_is_black(parent))
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break;
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gparent = rb_red_parent(parent);
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tmp = gparent->rb_right;
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if (parent != tmp) { /* parent == gparent->rb_left */
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if (tmp && rb_is_red(tmp)) {
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/*
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* Case 1 - color flips
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*
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* G g
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* / \ / \
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* p u --> P U
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* / /
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* n n
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*
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* However, since g's parent might be red, and
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* 4) does not allow this, we need to recurse
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* at g.
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*/
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rb_set_parent_color(tmp, gparent, RB_BLACK);
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rb_set_parent_color(parent, gparent, RB_BLACK);
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node = gparent;
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parent = rb_parent(node);
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rb_set_parent_color(node, parent, RB_RED);
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continue;
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}
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tmp = parent->rb_right;
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if (node == tmp) {
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/*
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* Case 2 - left rotate at parent
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*
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* G G
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* / \ / \
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* p U --> n U
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* \ /
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* n p
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*
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* This still leaves us in violation of 4), the
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* continuation into Case 3 will fix that.
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*/
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tmp = node->rb_left;
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WRITE_ONCE(parent->rb_right, tmp);
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WRITE_ONCE(node->rb_left, parent);
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if (tmp)
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rb_set_parent_color(tmp, parent,
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RB_BLACK);
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rb_set_parent_color(parent, node, RB_RED);
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augment_rotate(parent, node);
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parent = node;
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tmp = node->rb_right;
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}
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/*
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* Case 3 - right rotate at gparent
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*
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* G P
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* / \ / \
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* p U --> n g
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* / \
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* n U
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*/
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WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
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WRITE_ONCE(parent->rb_right, gparent);
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if (tmp)
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rb_set_parent_color(tmp, gparent, RB_BLACK);
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__rb_rotate_set_parents(gparent, parent, root, RB_RED);
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augment_rotate(gparent, parent);
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break;
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} else {
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tmp = gparent->rb_left;
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if (tmp && rb_is_red(tmp)) {
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/* Case 1 - color flips */
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rb_set_parent_color(tmp, gparent, RB_BLACK);
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rb_set_parent_color(parent, gparent, RB_BLACK);
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node = gparent;
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parent = rb_parent(node);
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rb_set_parent_color(node, parent, RB_RED);
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continue;
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}
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tmp = parent->rb_left;
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if (node == tmp) {
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/* Case 2 - right rotate at parent */
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tmp = node->rb_right;
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WRITE_ONCE(parent->rb_left, tmp);
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WRITE_ONCE(node->rb_right, parent);
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if (tmp)
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rb_set_parent_color(tmp, parent,
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RB_BLACK);
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rb_set_parent_color(parent, node, RB_RED);
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augment_rotate(parent, node);
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parent = node;
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tmp = node->rb_left;
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}
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/* Case 3 - left rotate at gparent */
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WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
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WRITE_ONCE(parent->rb_left, gparent);
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if (tmp)
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rb_set_parent_color(tmp, gparent, RB_BLACK);
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__rb_rotate_set_parents(gparent, parent, root, RB_RED);
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augment_rotate(gparent, parent);
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break;
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}
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}
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}
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/*
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* Inline version for rb_erase() use - we want to be able to inline
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* and eliminate the dummy_rotate callback there
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*/
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static __always_inline void
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____rb_erase_color(struct rb_node *parent, struct rb_root *root,
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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{
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struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
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while (true) {
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/*
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* Loop invariants:
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* - node is black (or NULL on first iteration)
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* - node is not the root (parent is not NULL)
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* - All leaf paths going through parent and node have a
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* black node count that is 1 lower than other leaf paths.
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*/
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sibling = parent->rb_right;
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if (node != sibling) { /* node == parent->rb_left */
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if (rb_is_red(sibling)) {
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/*
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* Case 1 - left rotate at parent
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*
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* P S
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* / \ / \
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* N s --> p Sr
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* / \ / \
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* Sl Sr N Sl
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*/
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tmp1 = sibling->rb_left;
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WRITE_ONCE(parent->rb_right, tmp1);
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WRITE_ONCE(sibling->rb_left, parent);
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rb_set_parent_color(tmp1, parent, RB_BLACK);
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__rb_rotate_set_parents(parent, sibling, root,
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RB_RED);
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augment_rotate(parent, sibling);
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sibling = tmp1;
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}
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tmp1 = sibling->rb_right;
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if (!tmp1 || rb_is_black(tmp1)) {
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tmp2 = sibling->rb_left;
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if (!tmp2 || rb_is_black(tmp2)) {
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/*
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* Case 2 - sibling color flip
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* (p could be either color here)
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*
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* (p) (p)
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* / \ / \
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* N S --> N s
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* / \ / \
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* Sl Sr Sl Sr
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*
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* This leaves us violating 5) which
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* can be fixed by flipping p to black
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* if it was red, or by recursing at p.
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* p is red when coming from Case 1.
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*/
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rb_set_parent_color(sibling, parent,
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RB_RED);
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if (rb_is_red(parent))
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rb_set_black(parent);
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else {
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node = parent;
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parent = rb_parent(node);
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if (parent)
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continue;
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}
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break;
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}
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/*
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* Case 3 - right rotate at sibling
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* (p could be either color here)
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*
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* (p) (p)
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* / \ / \
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* N S --> N Sl
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* / \ \
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* sl Sr s
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* \
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* Sr
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*/
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tmp1 = tmp2->rb_right;
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WRITE_ONCE(sibling->rb_left, tmp1);
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WRITE_ONCE(tmp2->rb_right, sibling);
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WRITE_ONCE(parent->rb_right, tmp2);
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if (tmp1)
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rb_set_parent_color(tmp1, sibling,
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RB_BLACK);
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augment_rotate(sibling, tmp2);
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tmp1 = sibling;
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sibling = tmp2;
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}
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/*
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* Case 4 - left rotate at parent + color flips
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* (p and sl could be either color here.
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* After rotation, p becomes black, s acquires
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* p's color, and sl keeps its color)
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*
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* (p) (s)
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* / \ / \
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* N S --> P Sr
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* / \ / \
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* (sl) sr N (sl)
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*/
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tmp2 = sibling->rb_left;
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WRITE_ONCE(parent->rb_right, tmp2);
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WRITE_ONCE(sibling->rb_left, parent);
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rb_set_parent_color(tmp1, sibling, RB_BLACK);
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if (tmp2)
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rb_set_parent(tmp2, parent);
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__rb_rotate_set_parents(parent, sibling, root,
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RB_BLACK);
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augment_rotate(parent, sibling);
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break;
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} else {
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sibling = parent->rb_left;
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if (rb_is_red(sibling)) {
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/* Case 1 - right rotate at parent */
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tmp1 = sibling->rb_right;
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WRITE_ONCE(parent->rb_left, tmp1);
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WRITE_ONCE(sibling->rb_right, parent);
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rb_set_parent_color(tmp1, parent, RB_BLACK);
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__rb_rotate_set_parents(parent, sibling, root,
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RB_RED);
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augment_rotate(parent, sibling);
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sibling = tmp1;
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}
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tmp1 = sibling->rb_left;
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if (!tmp1 || rb_is_black(tmp1)) {
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tmp2 = sibling->rb_right;
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if (!tmp2 || rb_is_black(tmp2)) {
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/* Case 2 - sibling color flip */
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rb_set_parent_color(sibling, parent,
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RB_RED);
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if (rb_is_red(parent))
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rb_set_black(parent);
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else {
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node = parent;
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parent = rb_parent(node);
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if (parent)
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continue;
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}
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break;
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}
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/* Case 3 - right rotate at sibling */
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tmp1 = tmp2->rb_left;
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WRITE_ONCE(sibling->rb_right, tmp1);
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WRITE_ONCE(tmp2->rb_left, sibling);
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WRITE_ONCE(parent->rb_left, tmp2);
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if (tmp1)
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rb_set_parent_color(tmp1, sibling,
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RB_BLACK);
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augment_rotate(sibling, tmp2);
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tmp1 = sibling;
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sibling = tmp2;
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}
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/* Case 4 - left rotate at parent + color flips */
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tmp2 = sibling->rb_right;
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WRITE_ONCE(parent->rb_left, tmp2);
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WRITE_ONCE(sibling->rb_right, parent);
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rb_set_parent_color(tmp1, sibling, RB_BLACK);
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if (tmp2)
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rb_set_parent(tmp2, parent);
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__rb_rotate_set_parents(parent, sibling, root,
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RB_BLACK);
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augment_rotate(parent, sibling);
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break;
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}
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}
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}
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/* Non-inline version for rb_erase_augmented() use */
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void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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{
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____rb_erase_color(parent, root, augment_rotate);
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}
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EXPORT_SYMBOL(__rb_erase_color);
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/*
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* Non-augmented rbtree manipulation functions.
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*
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* We use dummy augmented callbacks here, and have the compiler optimize them
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* out of the rb_insert_color() and rb_erase() function definitions.
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*/
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static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
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static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
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static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
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static const struct rb_augment_callbacks dummy_callbacks = {
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dummy_propagate, dummy_copy, dummy_rotate
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};
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void rb_insert_color(struct rb_node *node, struct rb_root *root)
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{
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__rb_insert(node, root, dummy_rotate);
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}
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EXPORT_SYMBOL(rb_insert_color);
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void rb_erase(struct rb_node *node, struct rb_root *root)
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{
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struct rb_node *rebalance;
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rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
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if (rebalance)
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____rb_erase_color(rebalance, root, dummy_rotate);
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}
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EXPORT_SYMBOL(rb_erase);
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/*
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* Augmented rbtree manipulation functions.
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*
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* This instantiates the same __always_inline functions as in the non-augmented
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* case, but this time with user-defined callbacks.
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*/
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void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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{
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__rb_insert(node, root, augment_rotate);
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}
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EXPORT_SYMBOL(__rb_insert_augmented);
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/*
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* This function returns the first node (in sort order) of the tree.
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*/
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struct rb_node *rb_first(const struct rb_root *root)
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{
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struct rb_node *n;
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n = root->rb_node;
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if (!n)
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return NULL;
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while (n->rb_left)
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n = n->rb_left;
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return n;
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}
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EXPORT_SYMBOL(rb_first);
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struct rb_node *rb_last(const struct rb_root *root)
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{
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struct rb_node *n;
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n = root->rb_node;
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if (!n)
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return NULL;
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while (n->rb_right)
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n = n->rb_right;
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return n;
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}
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EXPORT_SYMBOL(rb_last);
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struct rb_node *rb_next(const struct rb_node *node)
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{
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struct rb_node *parent;
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if (RB_EMPTY_NODE(node))
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return NULL;
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/*
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* If we have a right-hand child, go down and then left as far
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* as we can.
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*/
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if (node->rb_right) {
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node = node->rb_right;
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while (node->rb_left)
|
|
node=node->rb_left;
|
|
return (struct rb_node *)node;
|
|
}
|
|
|
|
/*
|
|
* No right-hand children. Everything down and left is smaller than us,
|
|
* so any 'next' node must be in the general direction of our parent.
|
|
* Go up the tree; any time the ancestor is a right-hand child of its
|
|
* parent, keep going up. First time it's a left-hand child of its
|
|
* parent, said parent is our 'next' node.
|
|
*/
|
|
while ((parent = rb_parent(node)) && node == parent->rb_right)
|
|
node = parent;
|
|
|
|
return parent;
|
|
}
|
|
EXPORT_SYMBOL(rb_next);
|
|
|
|
struct rb_node *rb_prev(const struct rb_node *node)
|
|
{
|
|
struct rb_node *parent;
|
|
|
|
if (RB_EMPTY_NODE(node))
|
|
return NULL;
|
|
|
|
/*
|
|
* If we have a left-hand child, go down and then right as far
|
|
* as we can.
|
|
*/
|
|
if (node->rb_left) {
|
|
node = node->rb_left;
|
|
while (node->rb_right)
|
|
node=node->rb_right;
|
|
return (struct rb_node *)node;
|
|
}
|
|
|
|
/*
|
|
* No left-hand children. Go up till we find an ancestor which
|
|
* is a right-hand child of its parent.
|
|
*/
|
|
while ((parent = rb_parent(node)) && node == parent->rb_left)
|
|
node = parent;
|
|
|
|
return parent;
|
|
}
|
|
EXPORT_SYMBOL(rb_prev);
|
|
|
|
void rb_replace_node(struct rb_node *victim, struct rb_node *new,
|
|
struct rb_root *root)
|
|
{
|
|
struct rb_node *parent = rb_parent(victim);
|
|
|
|
/* Set the surrounding nodes to point to the replacement */
|
|
__rb_change_child(victim, new, parent, root);
|
|
if (victim->rb_left)
|
|
rb_set_parent(victim->rb_left, new);
|
|
if (victim->rb_right)
|
|
rb_set_parent(victim->rb_right, new);
|
|
|
|
/* Copy the pointers/colour from the victim to the replacement */
|
|
*new = *victim;
|
|
}
|
|
EXPORT_SYMBOL(rb_replace_node);
|
|
|
|
static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
|
|
{
|
|
for (;;) {
|
|
if (node->rb_left)
|
|
node = node->rb_left;
|
|
else if (node->rb_right)
|
|
node = node->rb_right;
|
|
else
|
|
return (struct rb_node *)node;
|
|
}
|
|
}
|
|
|
|
struct rb_node *rb_next_postorder(const struct rb_node *node)
|
|
{
|
|
const struct rb_node *parent;
|
|
if (!node)
|
|
return NULL;
|
|
parent = rb_parent(node);
|
|
|
|
/* If we're sitting on node, we've already seen our children */
|
|
if (parent && node == parent->rb_left && parent->rb_right) {
|
|
/* If we are the parent's left node, go to the parent's right
|
|
* node then all the way down to the left */
|
|
return rb_left_deepest_node(parent->rb_right);
|
|
} else
|
|
/* Otherwise we are the parent's right node, and the parent
|
|
* should be next */
|
|
return (struct rb_node *)parent;
|
|
}
|
|
EXPORT_SYMBOL(rb_next_postorder);
|
|
|
|
struct rb_node *rb_first_postorder(const struct rb_root *root)
|
|
{
|
|
if (!root->rb_node)
|
|
return NULL;
|
|
|
|
return rb_left_deepest_node(root->rb_node);
|
|
}
|
|
EXPORT_SYMBOL(rb_first_postorder);
|