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qemu/util/interval-tree.c
Richard Henderson 0d99d37a82 util: Add interval-tree.c 
Copy and simplify the Linux kernel's interval_tree_generic.h,
instantiating for uint64_t.

Reviewed-by: Alex Bennée <alex.bennee@linaro.org>
Signed-off-by: Richard Henderson <richard.henderson@linaro.org>
2022-12-20 17:09:41 -08:00

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/* SPDX-License-Identifier: GPL-2.0-or-later */
#include "qemu/osdep.h"
#include "qemu/interval-tree.h"
#include "qemu/atomic.h"
/*
* Red Black Trees.
*
* For now, don't expose Linux Red-Black Trees separately, but retain the
* separate type definitions to keep the implementation sane, and allow
* the possibility of separating them later.
*
* Derived from include/linux/rbtree_augmented.h and its dependencies.
*/
/*
* 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 [qatomic_set for QEMU]. 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.
*/
typedef enum RBColor
{
RB_RED,
RB_BLACK,
} RBColor;
typedef struct RBAugmentCallbacks {
void (*propagate)(RBNode *node, RBNode *stop);
void (*copy)(RBNode *old, RBNode *new);
void (*rotate)(RBNode *old, RBNode *new);
} RBAugmentCallbacks;
static inline RBNode *rb_parent(const RBNode *n)
{
return (RBNode *)(n->rb_parent_color & ~1);
}
static inline RBNode *rb_red_parent(const RBNode *n)
{
return (RBNode *)n->rb_parent_color;
}
static inline RBColor pc_color(uintptr_t pc)
{
return (RBColor)(pc & 1);
}
static inline bool pc_is_red(uintptr_t pc)
{
return pc_color(pc) == RB_RED;
}
static inline bool pc_is_black(uintptr_t pc)
{
return !pc_is_red(pc);
}
static inline RBColor rb_color(const RBNode *n)
{
return pc_color(n->rb_parent_color);
}
static inline bool rb_is_red(const RBNode *n)
{
return pc_is_red(n->rb_parent_color);
}
static inline bool rb_is_black(const RBNode *n)
{
return pc_is_black(n->rb_parent_color);
}
static inline void rb_set_black(RBNode *n)
{
n->rb_parent_color |= RB_BLACK;
}
static inline void rb_set_parent_color(RBNode *n, RBNode *p, RBColor color)
{
n->rb_parent_color = (uintptr_t)p | color;
}
static inline void rb_set_parent(RBNode *n, RBNode *p)
{
rb_set_parent_color(n, p, rb_color(n));
}
static inline void rb_link_node(RBNode *node, RBNode *parent, RBNode **rb_link)
{
node->rb_parent_color = (uintptr_t)parent;
node->rb_left = node->rb_right = NULL;
qatomic_set(rb_link, node);
}
static RBNode *rb_next(RBNode *node)
{
RBNode *parent;
/* OMIT: if empty 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 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;
}
static inline void rb_change_child(RBNode *old, RBNode *new,
RBNode *parent, RBRoot *root)
{
if (!parent) {
qatomic_set(&root->rb_node, new);
} else if (parent->rb_left == old) {
qatomic_set(&parent->rb_left, new);
} else {
qatomic_set(&parent->rb_right, new);
}
}
static inline void rb_rotate_set_parents(RBNode *old, RBNode *new,
RBRoot *root, RBColor color)
{
RBNode *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 void rb_insert_augmented(RBNode *node, RBRoot *root,
const RBAugmentCallbacks *augment)
{
RBNode *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;
qatomic_set(&parent->rb_right, tmp);
qatomic_set(&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
*/
qatomic_set(&gparent->rb_left, tmp); /* == parent->rb_right */
qatomic_set(&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;
qatomic_set(&parent->rb_left, tmp);
qatomic_set(&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 */
qatomic_set(&gparent->rb_right, tmp); /* == parent->rb_left */
qatomic_set(&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;
}
}
}
static void rb_insert_augmented_cached(RBNode *node,
RBRootLeftCached *root, bool newleft,
const RBAugmentCallbacks *augment)
{
if (newleft) {
root->rb_leftmost = node;
}
rb_insert_augmented(node, &root->rb_root, augment);
}
static void rb_erase_color(RBNode *parent, RBRoot *root,
const RBAugmentCallbacks *augment)
{
RBNode *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;
qatomic_set(&parent->rb_right, tmp1);
qatomic_set(&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 bot
* 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;
qatomic_set(&sibling->rb_left, tmp1);
qatomic_set(&tmp2->rb_right, sibling);
qatomic_set(&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;
qatomic_set(&parent->rb_right, tmp2);
qatomic_set(&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;
qatomic_set(&parent->rb_left, tmp1);
qatomic_set(&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;
qatomic_set(&sibling->rb_right, tmp1);
qatomic_set(&tmp2->rb_left, sibling);
qatomic_set(&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;
qatomic_set(&parent->rb_left, tmp2);
qatomic_set(&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;
}
}
}
static void rb_erase_augmented(RBNode *node, RBRoot *root,
const RBAugmentCallbacks *augment)
{
RBNode *child = node->rb_right;
RBNode *tmp = node->rb_left;
RBNode *parent, *rebalance;
uintptr_t pc;
if (!tmp) {
/*
* Case 1: node to erase has no more than 1 child (easy!)
*
* Note that if there is one child it must be red due to 5)
* and node must be black due to 4). We adjust colors locally
* so as to bypass rb_erase_color() later on.
*/
pc = node->rb_parent_color;
parent = rb_parent(node);
rb_change_child(node, child, parent, root);
if (child) {
child->rb_parent_color = pc;
rebalance = NULL;
} else {
rebalance = pc_is_black(pc) ? parent : NULL;
}
tmp = parent;
} else if (!child) {
/* Still case 1, but this time the child is node->rb_left */
pc = node->rb_parent_color;
parent = rb_parent(node);
tmp->rb_parent_color = pc;
rb_change_child(node, tmp, parent, root);
rebalance = NULL;
tmp = parent;
} else {
RBNode *successor = child, *child2;
tmp = child->rb_left;
if (!tmp) {
/*
* Case 2: node's successor is its right child
*
* (n) (s)
* / \ / \
* (x) (s) -> (x) (c)
* \
* (c)
*/
parent = successor;
child2 = successor->rb_right;
augment->copy(node, successor);
} else {
/*
* Case 3: node's successor is leftmost under
* node's right child subtree
*
* (n) (s)
* / \ / \
* (x) (y) -> (x) (y)
* / /
* (p) (p)
* / /
* (s) (c)
* \
* (c)
*/
do {
parent = successor;
successor = tmp;
tmp = tmp->rb_left;
} while (tmp);
child2 = successor->rb_right;
qatomic_set(&parent->rb_left, child2);
qatomic_set(&successor->rb_right, child);
rb_set_parent(child, successor);
augment->copy(node, successor);
augment->propagate(parent, successor);
}
tmp = node->rb_left;
qatomic_set(&successor->rb_left, tmp);
rb_set_parent(tmp, successor);
pc = node->rb_parent_color;
tmp = rb_parent(node);
rb_change_child(node, successor, tmp, root);
if (child2) {
rb_set_parent_color(child2, parent, RB_BLACK);
rebalance = NULL;
} else {
rebalance = rb_is_black(successor) ? parent : NULL;
}
successor->rb_parent_color = pc;
tmp = successor;
}
augment->propagate(tmp, NULL);
if (rebalance) {
rb_erase_color(rebalance, root, augment);
}
}
static void rb_erase_augmented_cached(RBNode *node, RBRootLeftCached *root,
const RBAugmentCallbacks *augment)
{
if (root->rb_leftmost == node) {
root->rb_leftmost = rb_next(node);
}
rb_erase_augmented(node, &root->rb_root, augment);
}
/*
* Interval trees.
*
* Derived from lib/interval_tree.c and its dependencies,
* especially include/linux/interval_tree_generic.h.
*/
#define rb_to_itree(N) container_of(N, IntervalTreeNode, rb)
static bool interval_tree_compute_max(IntervalTreeNode *node, bool exit)
{
IntervalTreeNode *child;
uint64_t max = node->last;
if (node->rb.rb_left) {
child = rb_to_itree(node->rb.rb_left);
if (child->subtree_last > max) {
max = child->subtree_last;
}
}
if (node->rb.rb_right) {
child = rb_to_itree(node->rb.rb_right);
if (child->subtree_last > max) {
max = child->subtree_last;
}
}
if (exit && node->subtree_last == max) {
return true;
}
node->subtree_last = max;
return false;
}
static void interval_tree_propagate(RBNode *rb, RBNode *stop)
{
while (rb != stop) {
IntervalTreeNode *node = rb_to_itree(rb);
if (interval_tree_compute_max(node, true)) {
break;
}
rb = rb_parent(&node->rb);
}
}
static void interval_tree_copy(RBNode *rb_old, RBNode *rb_new)
{
IntervalTreeNode *old = rb_to_itree(rb_old);
IntervalTreeNode *new = rb_to_itree(rb_new);
new->subtree_last = old->subtree_last;
}
static void interval_tree_rotate(RBNode *rb_old, RBNode *rb_new)
{
IntervalTreeNode *old = rb_to_itree(rb_old);
IntervalTreeNode *new = rb_to_itree(rb_new);
new->subtree_last = old->subtree_last;
interval_tree_compute_max(old, false);
}
static const RBAugmentCallbacks interval_tree_augment = {
.propagate = interval_tree_propagate,
.copy = interval_tree_copy,
.rotate = interval_tree_rotate,
};
/* Insert / remove interval nodes from the tree */
void interval_tree_insert(IntervalTreeNode *node, IntervalTreeRoot *root)
{
RBNode **link = &root->rb_root.rb_node, *rb_parent = NULL;
uint64_t start = node->start, last = node->last;
IntervalTreeNode *parent;
bool leftmost = true;
while (*link) {
rb_parent = *link;
parent = rb_to_itree(rb_parent);
if (parent->subtree_last < last) {
parent->subtree_last = last;
}
if (start < parent->start) {
link = &parent->rb.rb_left;
} else {
link = &parent->rb.rb_right;
leftmost = false;
}
}
node->subtree_last = last;
rb_link_node(&node->rb, rb_parent, link);
rb_insert_augmented_cached(&node->rb, root, leftmost,
&interval_tree_augment);
}
void interval_tree_remove(IntervalTreeNode *node, IntervalTreeRoot *root)
{
rb_erase_augmented_cached(&node->rb, root, &interval_tree_augment);
}
/*
* Iterate over intervals intersecting [start;last]
*
* Note that a node's interval intersects [start;last] iff:
* Cond1: node->start <= last
* and
* Cond2: start <= node->last
*/
static IntervalTreeNode *interval_tree_subtree_search(IntervalTreeNode *node,
uint64_t start,
uint64_t last)
{
while (true) {
/*
* Loop invariant: start <= node->subtree_last
* (Cond2 is satisfied by one of the subtree nodes)
*/
if (node->rb.rb_left) {
IntervalTreeNode *left = rb_to_itree(node->rb.rb_left);
if (start <= left->subtree_last) {
/*
* Some nodes in left subtree satisfy Cond2.
* Iterate to find the leftmost such node N.
* If it also satisfies Cond1, that's the
* match we are looking for. Otherwise, there
* is no matching interval as nodes to the
* right of N can't satisfy Cond1 either.
*/
node = left;
continue;
}
}
if (node->start <= last) { /* Cond1 */
if (start <= node->last) { /* Cond2 */
return node; /* node is leftmost match */
}
if (node->rb.rb_right) {
node = rb_to_itree(node->rb.rb_right);
if (start <= node->subtree_last) {
continue;
}
}
}
return NULL; /* no match */
}
}
IntervalTreeNode *interval_tree_iter_first(IntervalTreeRoot *root,
uint64_t start, uint64_t last)
{
IntervalTreeNode *node, *leftmost;
if (!root->rb_root.rb_node) {
return NULL;
}
/*
* Fastpath range intersection/overlap between A: [a0, a1] and
* B: [b0, b1] is given by:
*
* a0 <= b1 && b0 <= a1
*
* ... where A holds the lock range and B holds the smallest
* 'start' and largest 'last' in the tree. For the later, we
* rely on the root node, which by augmented interval tree
* property, holds the largest value in its last-in-subtree.
* This allows mitigating some of the tree walk overhead for
* for non-intersecting ranges, maintained and consulted in O(1).
*/
node = rb_to_itree(root->rb_root.rb_node);
if (node->subtree_last < start) {
return NULL;
}
leftmost = rb_to_itree(root->rb_leftmost);
if (leftmost->start > last) {
return NULL;
}
return interval_tree_subtree_search(node, start, last);
}
IntervalTreeNode *interval_tree_iter_next(IntervalTreeNode *node,
uint64_t start, uint64_t last)
{
RBNode *rb = node->rb.rb_right, *prev;
while (true) {
/*
* Loop invariants:
* Cond1: node->start <= last
* rb == node->rb.rb_right
*
* First, search right subtree if suitable
*/
if (rb) {
IntervalTreeNode *right = rb_to_itree(rb);
if (start <= right->subtree_last) {
return interval_tree_subtree_search(right, start, last);
}
}
/* Move up the tree until we come from a node's left child */
do {
rb = rb_parent(&node->rb);
if (!rb) {
return NULL;
}
prev = &node->rb;
node = rb_to_itree(rb);
rb = node->rb.rb_right;
} while (prev == rb);
/* Check if the node intersects [start;last] */
if (last < node->start) { /* !Cond1 */
return NULL;
}
if (start <= node->last) { /* Cond2 */
return node;
}
}
}
/* Occasionally useful for calling from within the debugger. */
#if 0
static void debug_interval_tree_int(IntervalTreeNode *node,
const char *dir, int level)
{
printf("%4d %*s %s [%" PRIu64 ",%" PRIu64 "] subtree_last:%" PRIu64 "\n",
level, level + 1, dir, rb_is_red(&node->rb) ? "r" : "b",
node->start, node->last, node->subtree_last);
if (node->rb.rb_left) {
debug_interval_tree_int(rb_to_itree(node->rb.rb_left), "<", level + 1);
}
if (node->rb.rb_right) {
debug_interval_tree_int(rb_to_itree(node->rb.rb_right), ">", level + 1);
}
}
void debug_interval_tree(IntervalTreeNode *node);
void debug_interval_tree(IntervalTreeNode *node)
{
if (node) {
debug_interval_tree_int(node, "*", 0);
} else {
printf("null\n");
}
}
#endif
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