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>

2 files changed, 883 insertions, 0 deletions

diff --git a/util/interval-tree.c b/util/interval-tree.c
new file mode 100644
index 0000000..4c0baf1
--- /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/util/meson.build b/util/meson.build
index 25b9b61..d8d109f 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'))