Copy and simplify the Linux kernel's interval_tree_generic.h,
instantiating for uint64_t.
Reviewed-by: Alex Bennée <alex.ben...@linaro.org>
Signed-off-by: Richard Henderson <richard.hender...@linaro.org>
---
include/qemu/interval-tree.h | 99 ++++
tests/unit/test-interval-tree.c | 209 ++++++++
util/interval-tree.c | 882 ++++++++++++++++++++++++++++++++
tests/unit/meson.build | 1 +
util/meson.build | 1 +
5 files changed, 1192 insertions(+)
create mode 100644 include/qemu/interval-tree.h
create mode 100644 tests/unit/test-interval-tree.c
create mode 100644 util/interval-tree.c
diff --git a/include/qemu/interval-tree.h b/include/qemu/interval-tree.h
new file mode 100644
index 0000000000..25006debe8
--- /dev/null
+++ b/include/qemu/interval-tree.h
@@ -0,0 +1,99 @@
+/* SPDX-License-Identifier: GPL-2.0-or-later */
+/*
+ * Interval trees.
+ *
+ * Derived from include/linux/interval_tree.h and its dependencies.
+ */
+
+#ifndef QEMU_INTERVAL_TREE_H
+#define QEMU_INTERVAL_TREE_H
+
+/*
+ * 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 disentangling them later.
+ */
+typedef struct RBNode
+{
+ /* Encodes parent with color in the lsb. */
+ uintptr_t rb_parent_color;
+ struct RBNode *rb_right;
+ struct RBNode *rb_left;
+} RBNode;
+
+typedef struct RBRoot
+{
+ RBNode *rb_node;
+} RBRoot;
+
+typedef struct RBRootLeftCached {
+ RBRoot rb_root;
+ RBNode *rb_leftmost;
+} RBRootLeftCached;
+
+typedef struct IntervalTreeNode
+{
+ RBNode rb;
+
+ uint64_t start; /* Start of interval */
+ uint64_t last; /* Last location _in_ interval */
+ uint64_t subtree_last;
+} IntervalTreeNode;
+
+typedef RBRootLeftCached IntervalTreeRoot;
+
+/**
+ * interval_tree_is_empty
+ * @root: root of the tree.
+ *
+ * Returns true if the tree contains no nodes.
+ */
+static inline bool interval_tree_is_empty(const IntervalTreeRoot *root)
+{
+ return root->rb_root.rb_node == NULL;
+}
+
+/**
+ * interval_tree_insert
+ * @node: node to insert,
+ * @root: root of the tree.
+ *
+ * Insert @node into @root, and rebalance.
+ */
+void interval_tree_insert(IntervalTreeNode *node, IntervalTreeRoot *root);
+
+/**
+ * interval_tree_remove
+ * @node: node to remove,
+ * @root: root of the tree.
+ *
+ * Remove @node from @root, and rebalance.
+ */
+void interval_tree_remove(IntervalTreeNode *node, IntervalTreeRoot *root);
+
+/**
+ * interval_tree_iter_first:
+ * @root: root of the tree,
+ * @start, @last: the inclusive interval [start, last].
+ *
+ * Locate the "first" of a set of nodes within the tree at @root
+ * that overlap the interval, where "first" is sorted by start.
+ * Returns NULL if no overlap found.
+ */
+IntervalTreeNode *interval_tree_iter_first(IntervalTreeRoot *root,
+ uint64_t start, uint64_t last);
+
+/**
+ * interval_tree_iter_next:
+ * @node: previous search result
+ * @start, @last: the inclusive interval [start, last].
+ *
+ * Locate the "next" of a set of nodes within the tree that overlap the
+ * interval; @next is the result of a previous call to
+ * interval_tree_iter_{first,next}. Returns NULL if @next was the last
+ * node in the set.
+ */
+IntervalTreeNode *interval_tree_iter_next(IntervalTreeNode *node,
+ uint64_t start, uint64_t last);
+
+#endif /* QEMU_INTERVAL_TREE_H */
diff --git a/tests/unit/test-interval-tree.c b/tests/unit/test-interval-tree.c
new file mode 100644
index 0000000000..119817a019
--- /dev/null
+++ b/tests/unit/test-interval-tree.c
@@ -0,0 +1,209 @@
+/*
+ * Test interval trees
+ *
+ * This work is licensed under the terms of the GNU LGPL, version 2 or later.
+ * See the COPYING.LIB file in the top-level directory.
+ *
+ */
+
+#include "qemu/osdep.h"
+#include "qemu/interval-tree.h"
+
+static IntervalTreeNode nodes[20];
+static IntervalTreeRoot root;
+
+static void rand_interval(IntervalTreeNode *n, uint64_t start, uint64_t last)
+{
+ gint32 s_ofs, l_ofs, l_max;
+
+ if (last - start > INT32_MAX) {
+ l_max = INT32_MAX;
+ } else {
+ l_max = last - start;
+ }
+ s_ofs = g_test_rand_int_range(0, l_max);
+ l_ofs = g_test_rand_int_range(s_ofs, l_max);
+
+ n->start = start + s_ofs;
+ n->last = start + l_ofs;
+}
+
+static void test_empty(void)
+{
+ g_assert(root.rb_root.rb_node == NULL);
+ g_assert(root.rb_leftmost == NULL);
+ g_assert(interval_tree_iter_first(&root, 0, UINT64_MAX) == NULL);
+}
+
+static void test_find_one_point(void)
+{
+ /* Create a tree of a single node, which is the point [1,1]. */
+ nodes[0].start = 1;
+ nodes[0].last = 1;
+
+ interval_tree_insert(&nodes[0], &root);
+
+ g_assert(interval_tree_iter_first(&root, 0, 9) == &nodes[0]);
+ g_assert(interval_tree_iter_next(&nodes[0], 0, 9) == NULL);
+ g_assert(interval_tree_iter_first(&root, 0, 0) == NULL);
+ g_assert(interval_tree_iter_next(&nodes[0], 0, 0) == NULL);
+ g_assert(interval_tree_iter_first(&root, 0, 1) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 1, 1) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 1, 2) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 2, 2) == NULL);
+
+ interval_tree_remove(&nodes[0], &root);
+ g_assert(root.rb_root.rb_node == NULL);
+ g_assert(root.rb_leftmost == NULL);
+}
+
+static void test_find_two_point(void)
+{
+ IntervalTreeNode *find0, *find1;
+
+ /* Create a tree of a two nodes, which are both the point [1,1]. */
+ nodes[0].start = 1;
+ nodes[0].last = 1;
+ nodes[1] = nodes[0];
+
+ interval_tree_insert(&nodes[0], &root);
+ interval_tree_insert(&nodes[1], &root);
+
+ find0 = interval_tree_iter_first(&root, 0, 9);
+ g_assert(find0 == &nodes[0] || find0 == &nodes[1]);
+
+ find1 = interval_tree_iter_next(find0, 0, 9);
+ g_assert(find1 == &nodes[0] || find1 == &nodes[1]);
+ g_assert(find0 != find1);
+
+ interval_tree_remove(&nodes[1], &root);
+
+ g_assert(interval_tree_iter_first(&root, 0, 9) == &nodes[0]);
+ g_assert(interval_tree_iter_next(&nodes[0], 0, 9) == NULL);
+
+ interval_tree_remove(&nodes[0], &root);
+}
+
+static void test_find_one_range(void)
+{
+ /* Create a tree of a single node, which is the range [1,8]. */
+ nodes[0].start = 1;
+ nodes[0].last = 8;
+
+ interval_tree_insert(&nodes[0], &root);
+
+ g_assert(interval_tree_iter_first(&root, 0, 9) == &nodes[0]);
+ g_assert(interval_tree_iter_next(&nodes[0], 0, 9) == NULL);
+ g_assert(interval_tree_iter_first(&root, 0, 0) == NULL);
+ g_assert(interval_tree_iter_first(&root, 0, 1) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 1, 1) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 4, 6) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 8, 8) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 9, 9) == NULL);
+
+ interval_tree_remove(&nodes[0], &root);
+}
+
+static void test_find_one_range_many(void)
+{
+ int i;
+
+ /*
+ * Create a tree of many nodes in [0,99] and [200,299],
+ * but only one node with exactly [110,190].
+ */
+ nodes[0].start = 110;
+ nodes[0].last = 190;
+
+ for (i = 1; i < ARRAY_SIZE(nodes) / 2; ++i) {
+ rand_interval(&nodes[i], 0, 99);
+ }
+ for (; i < ARRAY_SIZE(nodes); ++i) {
+ rand_interval(&nodes[i], 200, 299);
+ }
+
+ for (i = 0; i < ARRAY_SIZE(nodes); ++i) {
+ interval_tree_insert(&nodes[i], &root);
+ }
+
+ /* Test that we find exactly the one node. */
+ g_assert(interval_tree_iter_first(&root, 100, 199) == &nodes[0]);
+ g_assert(interval_tree_iter_next(&nodes[0], 100, 199) == NULL);
+ g_assert(interval_tree_iter_first(&root, 100, 109) == NULL);
+ g_assert(interval_tree_iter_first(&root, 100, 110) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 111, 120) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 111, 199) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 190, 199) == &nodes[0]);
+ g_assert(interval_tree_iter_first(&root, 192, 199) == NULL);
+
+ /*
+ * Test that if there are multiple matches, we return the one
+ * with the minimal start.
+ */
+ g_assert(interval_tree_iter_first(&root, 100, 300) == &nodes[0]);
+
+ /* Test that we don't find it after it is removed. */
+ interval_tree_remove(&nodes[0], &root);
+ g_assert(interval_tree_iter_first(&root, 100, 199) == NULL);
+
+ for (i = 1; i < ARRAY_SIZE(nodes); ++i) {
+ interval_tree_remove(&nodes[i], &root);
+ }
+}
+
+static void test_find_many_range(void)
+{
+ IntervalTreeNode *find;
+ int i, n;
+
+ n = g_test_rand_int_range(ARRAY_SIZE(nodes) / 3, ARRAY_SIZE(nodes) / 2);
+
+ /*
+ * Create a fair few nodes in [2000,2999], with the others
+ * distributed around.
+ */
+ for (i = 0; i < n; ++i) {
+ rand_interval(&nodes[i], 2000, 2999);
+ }
+ for (; i < ARRAY_SIZE(nodes) * 2 / 3; ++i) {
+ rand_interval(&nodes[i], 1000, 1899);
+ }
+ for (; i < ARRAY_SIZE(nodes); ++i) {
+ rand_interval(&nodes[i], 3100, 3999);
+ }
+
+ for (i = 0; i < ARRAY_SIZE(nodes); ++i) {
+ interval_tree_insert(&nodes[i], &root);
+ }
+
+ /* Test that we find all of the nodes. */
+ find = interval_tree_iter_first(&root, 2000, 2999);
+ for (i = 0; find != NULL; i++) {
+ find = interval_tree_iter_next(find, 2000, 2999);
+ }
+ g_assert_cmpint(i, ==, n);
+
+ g_assert(interval_tree_iter_first(&root, 0, 999) == NULL);
+ g_assert(interval_tree_iter_first(&root, 1900, 1999) == NULL);
+ g_assert(interval_tree_iter_first(&root, 3000, 3099) == NULL);
+ g_assert(interval_tree_iter_first(&root, 4000, UINT64_MAX) == NULL);
+
+ for (i = 0; i < ARRAY_SIZE(nodes); ++i) {
+ interval_tree_remove(&nodes[i], &root);
+ }
+}
+
+int main(int argc, char **argv)
+{
+ g_test_init(&argc, &argv, NULL);
+
+ g_test_add_func("/interval-tree/empty", test_empty);
+ g_test_add_func("/interval-tree/find-one-point", test_find_one_point);
+ g_test_add_func("/interval-tree/find-two-point", test_find_two_point);
+ g_test_add_func("/interval-tree/find-one-range", test_find_one_range);
+ g_test_add_func("/interval-tree/find-one-range-many",
+ test_find_one_range_many);
+ g_test_add_func("/interval-tree/find-many-range", test_find_many_range);
+
+ return g_test_run();
+}
diff --git a/util/interval-tree.c b/util/interval-tree.c
new file mode 100644
index 0000000000..4c0baf108f
--- /dev/null
+++ b/util/interval-tree.c
@@ -0,0 +1,882 @@
+/* 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
diff --git a/tests/unit/meson.build b/tests/unit/meson.build
index b497a41378..ffa444f432 100644
--- a/tests/unit/meson.build
+++ b/tests/unit/meson.build
@@ -47,6 +47,7 @@ tests = {
'ptimer-test': ['ptimer-test-stubs.c', meson.project_source_root() /
'hw/core/ptimer.c'],
'test-qapi-util': [],
'test-smp-parse': [qom, meson.project_source_root() /
'hw/core/machine-smp.c'],
+ 'test-interval-tree': [],
}
if have_system or have_tools
diff --git a/util/meson.build b/util/meson.build
index 25b9b61f98..d8d109ff84 100644
--- a/util/meson.build
+++ b/util/meson.build
@@ -57,6 +57,7 @@ util_ss.add(files('guest-random.c'))
util_ss.add(files('yank.c'))
util_ss.add(files('int128.c'))
util_ss.add(files('memalign.c'))
+util_ss.add(files('interval-tree.c'))
if have_user
util_ss.add(files('selfmap.c'))
--
2.34.1
