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Linux kernel mirror (for testing) git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git
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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);}
/* * 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);}
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);}
/* * 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);}
/* * 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;}
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;}
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;}
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;}
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);}
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;}
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);}