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-rw-r--r--lib/rbtree.c630
1 files changed, 630 insertions, 0 deletions
diff --git a/lib/rbtree.c b/lib/rbtree.c
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+++ b/lib/rbtree.c
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+// SPDX-License-Identifier: GPL-2.0-or-later
+/*
+ Red Black Trees
+ (C) 1999 Andrea Arcangeli <andrea@suse.de>
+ (C) 2002 David Woodhouse <dwmw2@infradead.org>
+ (C) 2012 Michel Lespinasse <walken@google.com>
+
+
+ linux/lib/rbtree.c
+*/
+
+#include <linux/rbtree_augmented.h>
+#include <linux/export.h>
+
+/*
+ * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree
+ *
+ * 1) A node is either red or black
+ * 2) The root is black
+ * 3) All leaves (NULL) are black
+ * 4) Both children of every red node are black
+ * 5) Every simple path from root to leaves contains the same number
+ * of black nodes.
+ *
+ * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
+ * consecutive red nodes in a path and every red node is therefore followed by
+ * a black. So if B is the number of black nodes on every simple path (as per
+ * 5), then the longest possible path due to 4 is 2B.
+ *
+ * We shall indicate color with case, where black nodes are uppercase and red
+ * nodes will be lowercase. Unknown color nodes shall be drawn as red within
+ * parentheses and have some accompanying text comment.
+ */
+
+/*
+ * Notes on lockless lookups:
+ *
+ * All stores to the tree structure (rb_left and rb_right) must be done using
+ * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
+ * tree structure as seen in program order.
+ *
+ * These two requirements will allow lockless iteration of the tree -- not
+ * correct iteration mind you, tree rotations are not atomic so a lookup might
+ * miss entire subtrees.
+ *
+ * But they do guarantee that any such traversal will only see valid elements
+ * and that it will indeed complete -- does not get stuck in a loop.
+ *
+ * It also guarantees that if the lookup returns an element it is the 'correct'
+ * one. But not returning an element does _NOT_ mean it's not present.
+ *
+ * NOTE:
+ *
+ * Stores to __rb_parent_color are not important for simple lookups so those
+ * are left undone as of now. Nor did I check for loops involving parent
+ * pointers.
+ */
+
+static inline void rb_set_black(struct rb_node *rb)
+{
+ rb->__rb_parent_color |= RB_BLACK;
+}
+
+static inline struct rb_node *rb_red_parent(struct rb_node *red)
+{
+ return (struct rb_node *)red->__rb_parent_color;
+}
+
+/*
+ * Helper function for rotations:
+ * - old's parent and color get assigned to new
+ * - old gets assigned new as a parent and 'color' as a color.
+ */
+static inline void
+__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
+ struct rb_root *root, int color)
+{
+ struct rb_node *parent = rb_parent(old);
+ new->__rb_parent_color = old->__rb_parent_color;
+ rb_set_parent_color(old, new, color);
+ __rb_change_child(old, new, parent, root);
+}
+
+static __always_inline void
+__rb_insert(struct rb_node *node, struct rb_root *root,
+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+ struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
+
+ while (true) {
+ /*
+ * Loop invariant: node is red.
+ */
+ if (unlikely(!parent)) {
+ /*
+ * The inserted node is root. Either this is the
+ * first node, or we recursed at Case 1 below and
+ * are no longer violating 4).
+ */
+ rb_set_parent_color(node, NULL, RB_BLACK);
+ break;
+ }
+
+ /*
+ * If there is a black parent, we are done.
+ * Otherwise, take some corrective action as,
+ * per 4), we don't want a red root or two
+ * consecutive red nodes.
+ */
+ if(rb_is_black(parent))
+ break;
+
+ gparent = rb_red_parent(parent);
+
+ tmp = gparent->rb_right;
+ if (parent != tmp) { /* parent == gparent->rb_left */
+ if (tmp && rb_is_red(tmp)) {
+ /*
+ * Case 1 - node's uncle is red (color flips).
+ *
+ * G g
+ * / \ / \
+ * p u --> P U
+ * / /
+ * n n
+ *
+ * However, since g's parent might be red, and
+ * 4) does not allow this, we need to recurse
+ * at g.
+ */
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ rb_set_parent_color(parent, gparent, RB_BLACK);
+ node = gparent;
+ parent = rb_parent(node);
+ rb_set_parent_color(node, parent, RB_RED);
+ continue;
+ }
+
+ tmp = parent->rb_right;
+ if (node == tmp) {
+ /*
+ * Case 2 - node's uncle is black and node is
+ * the parent's right child (left rotate at parent).
+ *
+ * G G
+ * / \ / \
+ * p U --> n U
+ * \ /
+ * n p
+ *
+ * This still leaves us in violation of 4), the
+ * continuation into Case 3 will fix that.
+ */
+ tmp = node->rb_left;
+ WRITE_ONCE(parent->rb_right, tmp);
+ WRITE_ONCE(node->rb_left, parent);
+ if (tmp)
+ rb_set_parent_color(tmp, parent,
+ RB_BLACK);
+ rb_set_parent_color(parent, node, RB_RED);
+ augment_rotate(parent, node);
+ parent = node;
+ tmp = node->rb_right;
+ }
+
+ /*
+ * Case 3 - node's uncle is black and node is
+ * the parent's left child (right rotate at gparent).
+ *
+ * G P
+ * / \ / \
+ * p U --> n g
+ * / \
+ * n U
+ */
+ WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
+ WRITE_ONCE(parent->rb_right, gparent);
+ if (tmp)
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
+ augment_rotate(gparent, parent);
+ break;
+ } else {
+ tmp = gparent->rb_left;
+ if (tmp && rb_is_red(tmp)) {
+ /* Case 1 - color flips */
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ rb_set_parent_color(parent, gparent, RB_BLACK);
+ node = gparent;
+ parent = rb_parent(node);
+ rb_set_parent_color(node, parent, RB_RED);
+ continue;
+ }
+
+ tmp = parent->rb_left;
+ if (node == tmp) {
+ /* Case 2 - right rotate at parent */
+ tmp = node->rb_right;
+ WRITE_ONCE(parent->rb_left, tmp);
+ WRITE_ONCE(node->rb_right, parent);
+ if (tmp)
+ rb_set_parent_color(tmp, parent,
+ RB_BLACK);
+ rb_set_parent_color(parent, node, RB_RED);
+ augment_rotate(parent, node);
+ parent = node;
+ tmp = node->rb_left;
+ }
+
+ /* Case 3 - left rotate at gparent */
+ WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
+ WRITE_ONCE(parent->rb_left, gparent);
+ if (tmp)
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
+ augment_rotate(gparent, parent);
+ break;
+ }
+ }
+}
+
+/*
+ * Inline version for rb_erase() use - we want to be able to inline
+ * and eliminate the dummy_rotate callback there
+ */
+static __always_inline void
+____rb_erase_color(struct rb_node *parent, struct rb_root *root,
+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+ struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
+
+ while (true) {
+ /*
+ * Loop invariants:
+ * - node is black (or NULL on first iteration)
+ * - node is not the root (parent is not NULL)
+ * - All leaf paths going through parent and node have a
+ * black node count that is 1 lower than other leaf paths.
+ */
+ sibling = parent->rb_right;
+ if (node != sibling) { /* node == parent->rb_left */
+ if (rb_is_red(sibling)) {
+ /*
+ * Case 1 - left rotate at parent
+ *
+ * P S
+ * / \ / \
+ * N s --> p Sr
+ * / \ / \
+ * Sl Sr N Sl
+ */
+ tmp1 = sibling->rb_left;
+ WRITE_ONCE(parent->rb_right, tmp1);
+ WRITE_ONCE(sibling->rb_left, parent);
+ rb_set_parent_color(tmp1, parent, RB_BLACK);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_RED);
+ augment_rotate(parent, sibling);
+ sibling = tmp1;
+ }
+ tmp1 = sibling->rb_right;
+ if (!tmp1 || rb_is_black(tmp1)) {
+ tmp2 = sibling->rb_left;
+ if (!tmp2 || rb_is_black(tmp2)) {
+ /*
+ * Case 2 - sibling color flip
+ * (p could be either color here)
+ *
+ * (p) (p)
+ * / \ / \
+ * N S --> N s
+ * / \ / \
+ * Sl Sr Sl Sr
+ *
+ * This leaves us violating 5) which
+ * can be fixed by flipping p to black
+ * if it was red, or by recursing at p.
+ * p is red when coming from Case 1.
+ */
+ rb_set_parent_color(sibling, parent,
+ RB_RED);
+ if (rb_is_red(parent))
+ rb_set_black(parent);
+ else {
+ node = parent;
+ parent = rb_parent(node);
+ if (parent)
+ continue;
+ }
+ break;
+ }
+ /*
+ * Case 3 - right rotate at sibling
+ * (p could be either color here)
+ *
+ * (p) (p)
+ * / \ / \
+ * N S --> N sl
+ * / \ \
+ * sl Sr S
+ * \
+ * Sr
+ *
+ * Note: p might be red, and then both
+ * p and sl are red after rotation(which
+ * breaks property 4). This is fixed in
+ * Case 4 (in __rb_rotate_set_parents()
+ * which set sl the color of p
+ * and set p RB_BLACK)
+ *
+ * (p) (sl)
+ * / \ / \
+ * N sl --> P S
+ * \ / \
+ * S N Sr
+ * \
+ * Sr
+ */
+ tmp1 = tmp2->rb_right;
+ WRITE_ONCE(sibling->rb_left, tmp1);
+ WRITE_ONCE(tmp2->rb_right, sibling);
+ WRITE_ONCE(parent->rb_right, tmp2);
+ if (tmp1)
+ rb_set_parent_color(tmp1, sibling,
+ RB_BLACK);
+ augment_rotate(sibling, tmp2);
+ tmp1 = sibling;
+ sibling = tmp2;
+ }
+ /*
+ * Case 4 - left rotate at parent + color flips
+ * (p and sl could be either color here.
+ * After rotation, p becomes black, s acquires
+ * p's color, and sl keeps its color)
+ *
+ * (p) (s)
+ * / \ / \
+ * N S --> P Sr
+ * / \ / \
+ * (sl) sr N (sl)
+ */
+ tmp2 = sibling->rb_left;
+ WRITE_ONCE(parent->rb_right, tmp2);
+ WRITE_ONCE(sibling->rb_left, parent);
+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
+ if (tmp2)
+ rb_set_parent(tmp2, parent);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_BLACK);
+ augment_rotate(parent, sibling);
+ break;
+ } else {
+ sibling = parent->rb_left;
+ if (rb_is_red(sibling)) {
+ /* Case 1 - right rotate at parent */
+ tmp1 = sibling->rb_right;
+ WRITE_ONCE(parent->rb_left, tmp1);
+ WRITE_ONCE(sibling->rb_right, parent);
+ rb_set_parent_color(tmp1, parent, RB_BLACK);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_RED);
+ augment_rotate(parent, sibling);
+ sibling = tmp1;
+ }
+ tmp1 = sibling->rb_left;
+ if (!tmp1 || rb_is_black(tmp1)) {
+ tmp2 = sibling->rb_right;
+ if (!tmp2 || rb_is_black(tmp2)) {
+ /* Case 2 - sibling color flip */
+ rb_set_parent_color(sibling, parent,
+ RB_RED);
+ if (rb_is_red(parent))
+ rb_set_black(parent);
+ else {
+ node = parent;
+ parent = rb_parent(node);
+ if (parent)
+ continue;
+ }
+ break;
+ }
+ /* Case 3 - left rotate at sibling */
+ tmp1 = tmp2->rb_left;
+ WRITE_ONCE(sibling->rb_right, tmp1);
+ WRITE_ONCE(tmp2->rb_left, sibling);
+ WRITE_ONCE(parent->rb_left, tmp2);
+ if (tmp1)
+ rb_set_parent_color(tmp1, sibling,
+ RB_BLACK);
+ augment_rotate(sibling, tmp2);
+ tmp1 = sibling;
+ sibling = tmp2;
+ }
+ /* Case 4 - right rotate at parent + color flips */
+ tmp2 = sibling->rb_right;
+ WRITE_ONCE(parent->rb_left, tmp2);
+ WRITE_ONCE(sibling->rb_right, parent);
+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
+ if (tmp2)
+ rb_set_parent(tmp2, parent);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_BLACK);
+ augment_rotate(parent, sibling);
+ break;
+ }
+ }
+}
+
+/* Non-inline version for rb_erase_augmented() use */
+void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+ ____rb_erase_color(parent, root, augment_rotate);
+}
+EXPORT_SYMBOL(__rb_erase_color);
+
+/*
+ * Non-augmented rbtree manipulation functions.
+ *
+ * We use dummy augmented callbacks here, and have the compiler optimize them
+ * out of the rb_insert_color() and rb_erase() function definitions.
+ */
+
+static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
+static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
+static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
+
+static const struct rb_augment_callbacks dummy_callbacks = {
+ .propagate = dummy_propagate,
+ .copy = dummy_copy,
+ .rotate = dummy_rotate
+};
+
+void rb_insert_color(struct rb_node *node, struct rb_root *root)
+{
+ __rb_insert(node, root, dummy_rotate);
+}
+EXPORT_SYMBOL(rb_insert_color);
+
+void rb_erase(struct rb_node *node, struct rb_root *root)
+{
+ struct rb_node *rebalance;
+ rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
+ if (rebalance)
+ ____rb_erase_color(rebalance, root, dummy_rotate);
+}
+EXPORT_SYMBOL(rb_erase);
+
+/*
+ * Augmented rbtree manipulation functions.
+ *
+ * This instantiates the same __always_inline functions as in the non-augmented
+ * case, but this time with user-defined callbacks.
+ */
+
+void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+ __rb_insert(node, root, augment_rotate);
+}
+EXPORT_SYMBOL(__rb_insert_augmented);
+
+/*
+ * This function returns the first node (in sort order) of the tree.
+ */
+struct rb_node *rb_first(const struct rb_root *root)
+{
+ struct rb_node *n;
+
+ n = root->rb_node;
+ if (!n)
+ return NULL;
+ while (n->rb_left)
+ n = n->rb_left;
+ return n;
+}
+EXPORT_SYMBOL(rb_first);
+
+struct rb_node *rb_last(const struct rb_root *root)
+{
+ struct rb_node *n;
+
+ n = root->rb_node;
+ if (!n)
+ return NULL;
+ while (n->rb_right)
+ n = n->rb_right;
+ return n;
+}
+EXPORT_SYMBOL(rb_last);
+
+struct rb_node *rb_next(const struct rb_node *node)
+{
+ struct rb_node *parent;
+
+ if (RB_EMPTY_NODE(node))
+ return NULL;
+
+ /*
+ * If we have a right-hand child, go down and then left as far
+ * as we can.
+ */
+ if (node->rb_right) {
+ node = node->rb_right;
+ 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);
+
+ /* Copy the pointers/colour from the victim to the replacement */
+ *new = *victim;
+
+ /* Set the surrounding nodes to point to the replacement */
+ if (victim->rb_left)
+ rb_set_parent(victim->rb_left, new);
+ if (victim->rb_right)
+ rb_set_parent(victim->rb_right, new);
+ __rb_change_child(victim, new, parent, root);
+}
+EXPORT_SYMBOL(rb_replace_node);
+
+void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
+ struct rb_root *root)
+{
+ struct rb_node *parent = rb_parent(victim);
+
+ /* Copy the pointers/colour from the victim to the replacement */
+ *new = *victim;
+
+ /* Set the surrounding nodes to point to the replacement */
+ if (victim->rb_left)
+ rb_set_parent(victim->rb_left, new);
+ if (victim->rb_right)
+ rb_set_parent(victim->rb_right, new);
+
+ /* Set the parent's pointer to the new node last after an RCU barrier
+ * so that the pointers onwards are seen to be set correctly when doing
+ * an RCU walk over the tree.
+ */
+ __rb_change_child_rcu(victim, new, parent, root);
+}
+EXPORT_SYMBOL(rb_replace_node_rcu);
+
+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);
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-01 10:55:36 +0000