/* * Copyright (c) 2018 Intel Corporation * * SPDX-License-Identifier: Apache-2.0 */ /* These assertions are very useful when debugging the tree code * itself, but produce significant performance degradation as they are * checked many times per operation. Leave them off unless you're * working on the rbtree code itself */ #define CHECK(n) /**/ /* #define CHECK(n) __ASSERT_NO_MSG(n) */ #include #include #include enum rb_color { RED = 0U, BLACK = 1U }; static struct rbnode *get_child(struct rbnode *n, uint8_t side) { CHECK(n); if (side != 0U) { return n->children[1]; } uintptr_t l = (uintptr_t) n->children[0]; l &= ~1UL; return (struct rbnode *) l; } static void set_child(struct rbnode *n, uint8_t side, void *val) { CHECK(n); if (side != 0U) { n->children[1] = val; } else { uintptr_t old = (uintptr_t) n->children[0]; uintptr_t new = (uintptr_t) val; n->children[0] = (void *) (new | (old & 1UL)); } } static enum rb_color get_color(struct rbnode *n) { CHECK(n); return ((uintptr_t)n->children[0]) & 1UL; } static bool is_black(struct rbnode *n) { return get_color(n) == BLACK; } static bool is_red(struct rbnode *n) { return get_color(n) == RED; } static void set_color(struct rbnode *n, enum rb_color color) { CHECK(n); uintptr_t *p = (void *) &n->children[0]; *p = (*p & ~1UL) | (uint8_t)color; } /* Searches the tree down to a node that is either identical with the * "node" argument or has an empty/leaf child pointer where "node" * should be, leaving all nodes found in the resulting stack. Note * that tree must not be empty and that stack should be allocated to * contain at least tree->max_depth entries! Returns the number of * entries pushed onto the stack. */ static int find_and_stack(struct rbtree *tree, struct rbnode *node, struct rbnode **stack) { int sz = 0; stack[sz] = tree->root; ++sz; while (stack[sz - 1] != node) { uint8_t side = tree->lessthan_fn(node, stack[sz - 1]) ? 0U : 1U; struct rbnode *ch = get_child(stack[sz - 1], side); if (ch != NULL) { stack[sz] = ch; ++sz; } else { break; } } return sz; } struct rbnode *z_rb_get_minmax(struct rbtree *tree, uint8_t side) { struct rbnode *n; for (n = tree->root; (n != NULL) && (get_child(n, side) != NULL); n = get_child(n, side)) { ; } return n; } static uint8_t get_side(struct rbnode *parent, struct rbnode *child) { CHECK(get_child(parent, 0U) == child || get_child(parent, 1U) == child); return (get_child(parent, 1U) == child) ? 1U : 0U; } /* Swaps the position of the two nodes at the top of the provided * stack, modifying the stack accordingly. Does not change the color * of either node. That is, it effects the following transition (or * its mirror if N is on the other side of P, of course): * * P N * N c --> a P * a b b c * */ static void rotate(struct rbnode **stack, int stacksz) { CHECK(stacksz >= 2); struct rbnode *parent = stack[stacksz - 2]; struct rbnode *child = stack[stacksz - 1]; uint8_t side = get_side(parent, child); struct rbnode *a = get_child(child, side); struct rbnode *b = get_child(child, (side == 0U) ? 1U : 0U); if (stacksz >= 3) { struct rbnode *grandparent = stack[stacksz - 3]; set_child(grandparent, get_side(grandparent, parent), child); } set_child(child, side, a); set_child(child, (side == 0U) ? 1U : 0U, parent); set_child(parent, side, b); stack[stacksz - 2] = child; stack[stacksz - 1] = parent; } /* The node at the top of the provided stack is red, and its parent is * too. Iteratively fix the tree so it becomes a valid red black tree * again */ static void fix_extra_red(struct rbnode **stack, int stacksz) { while (stacksz > 1) { struct rbnode *node = stack[stacksz - 1]; struct rbnode *parent = stack[stacksz - 2]; /* Correct child colors are a precondition of the loop */ CHECK((get_child(node, 0U) == NULL) || is_black(get_child(node, 0U))); CHECK((get_child(node, 1U) == NULL) || is_black(get_child(node, 1U))); if (is_black(parent)) { return; } /* We are guaranteed to have a grandparent if our * parent is red, as red nodes cannot be the root */ CHECK(stacksz >= 2); struct rbnode *grandparent = stack[stacksz - 3]; uint8_t side = get_side(grandparent, parent); struct rbnode *aunt = get_child(grandparent, (side == 0U) ? 1U : 0U); if ((aunt != NULL) && is_red(aunt)) { set_color(grandparent, RED); set_color(parent, BLACK); set_color(aunt, BLACK); /* We colored the grandparent red, which might * have a red parent, so continue iterating * from there. */ stacksz -= 2; continue; } /* We can rotate locally to fix the whole tree. First * make sure that node is on the same side of parent * as parent is of grandparent. */ uint8_t parent_side = get_side(parent, node); if (parent_side != side) { rotate(stack, stacksz); } /* Rotate the grandparent with parent, swapping colors */ rotate(stack, stacksz - 1); set_color(stack[stacksz - 3], BLACK); set_color(stack[stacksz - 2], RED); return; } /* If we exit the loop, it's because our node is now the root, * which must be black. */ set_color(stack[0], BLACK); } void rb_insert(struct rbtree *tree, struct rbnode *node) { set_child(node, 0U, NULL); set_child(node, 1U, NULL); if (tree->root == NULL) { tree->root = node; tree->max_depth = 1; set_color(node, BLACK); return; } #ifdef CONFIG_MISRA_SANE struct rbnode **stack = &tree->iter_stack[0]; #else struct rbnode *stack[tree->max_depth + 1]; #endif int stacksz = find_and_stack(tree, node, stack); struct rbnode *parent = stack[stacksz - 1]; uint8_t side = tree->lessthan_fn(node, parent) ? 0U : 1U; set_child(parent, side, node); set_color(node, RED); stack[stacksz] = node; ++stacksz; fix_extra_red(stack, stacksz); if (stacksz > tree->max_depth) { tree->max_depth = stacksz; } /* We may have rotated up into the root! */ tree->root = stack[0]; CHECK(is_black(tree->root)); } /* Called for a node N (at the top of the stack) which after a * deletion operation is "missing a black" in its subtree. By * construction N must be black (because if it was red it would be * trivially fixed by recoloring and we wouldn't be here). Fixes up * the tree to preserve red/black rules. The "null_node" pointer is * for situations where we are removing a childless black node. The * tree munging needs a real node for simplicity, so we use it and * then clean it up (replace it with a simple NULL child in the * parent) when finished. */ static void fix_missing_black(struct rbnode **stack, int stacksz, struct rbnode *null_node) { /* Loop upward until we reach the root */ while (stacksz > 1) { struct rbnode *c0, *c1, *inner, *outer; struct rbnode *n = stack[stacksz - 1]; struct rbnode *parent = stack[stacksz - 2]; uint8_t n_side = get_side(parent, n); struct rbnode *sib = get_child(parent, (n_side == 0U) ? 1U : 0U); CHECK(is_black(n)); /* Guarantee the sibling is black, rotating N down a * level if needed (after rotate() our parent is the * child of our previous-sibling, so N is lower in the * tree) */ if (!is_black(sib)) { stack[stacksz - 1] = sib; rotate(stack, stacksz); set_color(parent, RED); set_color(sib, BLACK); stack[stacksz] = n; ++stacksz; parent = stack[stacksz - 2]; sib = get_child(parent, (n_side == 0U) ? 1U : 0U); } CHECK(sib); /* Cases where the sibling has only black children * have simple resolutions */ c0 = get_child(sib, 0U); c1 = get_child(sib, 1U); if (((c0 == NULL) || is_black(c0)) && ((c1 == NULL) || is_black(c1))) { if (n == null_node) { set_child(parent, n_side, NULL); } set_color(sib, RED); if (is_black(parent)) { /* Balance the sibling's subtree by * coloring it red, then our parent * has a missing black so iterate * upward */ stacksz--; continue; } else { /* Recoloring makes the whole tree OK */ set_color(parent, BLACK); return; } } CHECK((c0 && is_red(c0)) || (c1 && is_red(c1))); /* We know sibling has at least one red child. Fix it * so that the far/outer position (i.e. on the * opposite side from N) is definitely red. */ outer = get_child(sib, (n_side == 0U) ? 1U : 0U); if (!((outer != NULL) && is_red(outer))) { inner = get_child(sib, n_side); stack[stacksz - 1] = sib; stack[stacksz] = inner; ++stacksz; rotate(stack, stacksz); set_color(sib, RED); set_color(inner, BLACK); /* Restore stack state to have N on the top * and make sib reflect the new sibling */ sib = stack[stacksz - 2]; outer = get_child(sib, (n_side == 0U) ? 1U : 0U); stack[stacksz - 2] = n; stacksz--; } /* Finally, the sibling must have a red child in the * far/outer slot. We can rotate sib with our parent * and recolor to produce a valid tree. */ CHECK(is_red(outer)); set_color(sib, get_color(parent)); set_color(parent, BLACK); set_color(outer, BLACK); stack[stacksz - 1] = sib; rotate(stack, stacksz); if (n == null_node) { set_child(parent, n_side, NULL); } return; } } void rb_remove(struct rbtree *tree, struct rbnode *node) { struct rbnode *tmp; #ifdef CONFIG_MISRA_SANE struct rbnode **stack = &tree->iter_stack[0]; #else struct rbnode *stack[tree->max_depth + 1]; #endif int stacksz = find_and_stack(tree, node, stack); if (node != stack[stacksz - 1]) { return; } /* We can only remove a node with zero or one child, if we * have two then pick the "biggest" child of side 0 (smallest * of 1 would work too) and swap our spot in the tree with * that one */ if ((get_child(node, 0U) != NULL) && (get_child(node, 1U) != NULL)) { int stacksz0 = stacksz; struct rbnode *hiparent, *loparent; struct rbnode *node2 = get_child(node, 0U); hiparent = (stacksz > 1) ? stack[stacksz - 2] : NULL; stack[stacksz] = node2; ++stacksz; while (get_child(node2, 1U) != NULL) { node2 = get_child(node2, 1U); stack[stacksz] = node2; ++stacksz; } loparent = stack[stacksz - 2]; /* Now swap the position of node/node2 in the tree. * Design note: this is a spot where being an * intrusive data structure hurts us fairly badly. * The trees you see in textbooks do this by swapping * the "data" pointers between the two nodes, but we * have a few special cases to check. In principle * this works by swapping the child pointers between * the nodes and retargeting the nodes pointing to * them from their parents, but: (1) the upper node * may be the root of the tree and not have a parent, * and (2) the lower node may be a direct child of the * upper node. Remember to swap the color bits of the * two nodes also. And of course we don't have parent * pointers, so the stack tracking this structure * needs to be swapped too! */ if (hiparent != NULL) { set_child(hiparent, get_side(hiparent, node), node2); } else { tree->root = node2; } if (loparent == node) { set_child(node, 0U, get_child(node2, 0U)); set_child(node2, 0U, node); } else { set_child(loparent, get_side(loparent, node2), node); tmp = get_child(node, 0U); set_child(node, 0U, get_child(node2, 0U)); set_child(node2, 0U, tmp); } set_child(node2, 1U, get_child(node, 1U)); set_child(node, 1U, NULL); tmp = stack[stacksz0 - 1]; stack[stacksz0 - 1] = stack[stacksz - 1]; stack[stacksz - 1] = tmp; enum rb_color ctmp = get_color(node); set_color(node, get_color(node2)); set_color(node2, ctmp); } CHECK((get_child(node, 0U) == NULL) || (get_child(node, 1U) == NULL)); struct rbnode *child = get_child(node, 0U); if (child == NULL) { child = get_child(node, 1U); } /* Removing the root */ if (stacksz < 2) { tree->root = child; if (child != NULL) { set_color(child, BLACK); } else { tree->max_depth = 0; } return; } struct rbnode *parent = stack[stacksz - 2]; /* Special case: if the node to be removed is childless, then * we leave it in place while we do the missing black * rotations, which will replace it with a proper NULL when * they isolate it. */ if (child == NULL) { if (is_black(node)) { fix_missing_black(stack, stacksz, node); } else { /* Red childless nodes can just be dropped */ set_child(parent, get_side(parent, node), NULL); } } else { set_child(parent, get_side(parent, node), child); /* Check colors, if one was red (at least one must have been * black in a valid tree), then we're done. */ __ASSERT(is_black(node) || is_black(child), "both nodes red?!"); if (is_red(node) || is_red(child)) { set_color(child, BLACK); } } /* We may have rotated up into the root! */ tree->root = stack[0]; } #ifndef CONFIG_MISRA_SANE void z_rb_walk(struct rbnode *node, rb_visit_t visit_fn, void *cookie) { if (node != NULL) { z_rb_walk(get_child(node, 0U), visit_fn, cookie); visit_fn(node, cookie); z_rb_walk(get_child(node, 1U), visit_fn, cookie); } } #endif struct rbnode *z_rb_child(struct rbnode *node, uint8_t side) { return get_child(node, side); } int z_rb_is_black(struct rbnode *node) { return is_black(node); } bool rb_contains(struct rbtree *tree, struct rbnode *node) { struct rbnode *n = tree->root; while ((n != NULL) && (n != node)) { n = get_child(n, tree->lessthan_fn(n, node)); } return n == node; } /* Pushes the node and its chain of left-side children onto the stack * in the foreach struct, returning the last node, which is the next * node to iterate. By construction node will always be a right child * or the root, so is_left must be false. */ static inline struct rbnode *stack_left_limb(struct rbnode *n, struct _rb_foreach *f) { f->top++; f->stack[f->top] = n; f->is_left[f->top] = 0U; for (n = get_child(n, 0U); n != NULL; n = get_child(n, 0U)) { f->top++; f->stack[f->top] = n; f->is_left[f->top] = 1; } return f->stack[f->top]; } /* The foreach tracking works via a dynamic stack allocated via * alloca(). The current node is found in stack[top] (and its parent * is thus stack[top-1]). The side of each stacked node from its * parent is stored in is_left[] (i.e. if is_left[top] is true, then * node/stack[top] is the left child of stack[top-1]). The special * case of top == -1 indicates that the stack is uninitialized and we * need to push an initial stack starting at the root. */ struct rbnode *z_rb_foreach_next(struct rbtree *tree, struct _rb_foreach *f) { struct rbnode *n; if (tree->root == NULL) { return NULL; } /* Initialization condition, pick the leftmost child of the * root as our first node, initializing the stack on the way. */ if (f->top == -1) { return stack_left_limb(tree->root, f); } /* The next child from a given node is the leftmost child of * it's right subtree if it has a right child */ n = get_child(f->stack[f->top], 1U); if (n != NULL) { return stack_left_limb(n, f); } /* Otherwise if the node is a left child of its parent, the * next node is the parent (note that the root is stacked * above with is_left set to 0, so this condition still works * even if node has no parent). */ if (f->is_left[f->top] != 0U) { return f->stack[--f->top]; } /* If we had no left tree and are a right child then our * parent was already walked, so walk up the stack looking for * a left child (whose parent is unwalked, and thus next). */ while ((f->top > 0) && (f->is_left[f->top] == 0U)) { f->top--; } f->top--; return (f->top >= 0) ? f->stack[f->top] : NULL; }