diff options
Diffstat (limited to '')
| -rw-r--r-- | tools/lib/rbtree.c | 597 |
1 files changed, 597 insertions, 0 deletions
diff --git a/tools/lib/rbtree.c b/tools/lib/rbtree.c new file mode 100644 index 000000000..727396de6 --- /dev/null +++ b/tools/lib/rbtree.c @@ -0,0 +1,597 @@ +// 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); +} + +/* + * 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); +} |