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qemu/util/interval-tree.c
Richard Henderson 79e29851bf util/interval-tree: Use qatomic_read/set for rb_parent_color 
While less susceptible to optimization problems than left and right,
interval_tree_iter_next also reads rb_parent(), so make sure that
stores and loads are atomic.

This goes further than technically required, changing all loads to
be atomic, rather than simply the ones in the iteration side.  But
it doesn't really affect the code generation on the rebalance side
and is cleaner to handle everything the same.

Reviewed-by: Peter Maydell <peter.maydell@linaro.org>
Signed-off-by: Richard Henderson <richard.henderson@linaro.org>
2023-07-31 12:19:13 -07:00

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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.
*/
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 uintptr_t rb_pc(const RBNode *n)
{
return qatomic_read(&n->rb_parent_color);
}
static inline void rb_set_pc(RBNode *n, uintptr_t pc)
{
qatomic_set(&n->rb_parent_color, pc);
}
static inline RBNode *pc_parent(uintptr_t pc)
{
return (RBNode *)(pc & ~1);
}
static inline RBNode *rb_parent(const RBNode *n)
{
return pc_parent(rb_pc(n));
}
static inline RBNode *rb_red_parent(const RBNode *n)
{
return (RBNode *)rb_pc(n);
}
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(rb_pc(n));
}
static inline bool rb_is_red(const RBNode *n)
{
return pc_is_red(rb_pc(n));
}
static inline bool rb_is_black(const RBNode *n)
{
return pc_is_black(rb_pc(n));
}
static inline void rb_set_black(RBNode *n)
{
rb_set_pc(n, rb_pc(n) | RB_BLACK);
}
static inline void rb_set_parent_color(RBNode *n, RBNode *p, RBColor color)
{
rb_set_pc(n, (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;
/*
* Ensure that node is initialized before insertion,
* as viewed by a concurrent search.
*/
qatomic_set_mb(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)
{
uintptr_t pc = rb_pc(old);
RBNode *parent = pc_parent(pc);
rb_set_pc(new, pc);
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 = rb_pc(node);
parent = pc_parent(pc);
rb_change_child(node, child, parent, root);
if (child) {
rb_set_pc(child, 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 = rb_pc(node);
parent = pc_parent(pc);
rb_set_pc(tmp, 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 = rb_pc(node);
tmp = pc_parent(pc);
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;
}
rb_set_pc(successor, 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)
*/
RBNode *tmp = qatomic_read(&node->rb.rb_left);
if (tmp) {
IntervalTreeNode *left = rb_to_itree(tmp);
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 */
}
tmp = qatomic_read(&node->rb.rb_right);
if (tmp) {
node = rb_to_itree(tmp);
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, *prev;
rb = qatomic_read(&node->rb.rb_right);
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 = qatomic_read(&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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