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Diffstat (limited to 'na/lib/rbtree.cc')
| -rw-r--r-- | na/lib/rbtree.cc | 596 |
1 files changed, 0 insertions, 596 deletions
diff --git a/na/lib/rbtree.cc b/na/lib/rbtree.cc deleted file mode 100644 index 6718a1a..0000000 --- a/na/lib/rbtree.cc +++ /dev/null @@ -1,596 +0,0 @@ -// SPDX-License-Identifier: GPL-2.0-only -/* - 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 <lume/rbtree_augmented.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 (nullptr) 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, nullptr, 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 = nullptr, *sibling, *tmp1, *tmp2; - - while (true) { - /* - * Loop invariants: - * - node is black (or nullptr on first iteration) - * - node is not the root (parent is not nullptr) - * - 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); -} - -struct rb_node *rb_next(const struct rb_node *node) -{ - struct rb_node *parent; - - if (RB_EMPTY_NODE(node)) - return nullptr; - - /* - * 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 nullptr; - - /* - * 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 nullptr; - 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 nullptr; - - return rb_left_deepest_node(root->rb_node); -} - -struct rb_node *rb_first(const struct rb_root *root) -{ - struct rb_node *n; - - n = root->rb_node; - if (!n) - return nullptr; - 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 nullptr; - while (n->rb_right) - n = n->rb_right; - return n; -} |