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+/*
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+ Interval Trees
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+ (C) 2012 Michel Lespinasse <walken@google.com>
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+
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+ This program is free software; you can redistribute it and/or modify
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+ it under the terms of the GNU General Public License as published by
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+ the Free Software Foundation; either version 2 of the License, or
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+ (at your option) any later version.
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+
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+ This program is distributed in the hope that it will be useful,
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+ but WITHOUT ANY WARRANTY; without even the implied warranty of
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+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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+ GNU General Public License for more details.
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+
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+ You should have received a copy of the GNU General Public License
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+ along with this program; if not, write to the Free Software
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+ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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+
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+ include/linux/interval_tree_tmpl.h
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+*/
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+
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+/*
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+ * Template for implementing interval trees
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+ *
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+ * ITSTRUCT: struct type of the interval tree nodes
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+ * ITRB: name of struct rb_node field within ITSTRUCT
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+ * ITTYPE: type of the interval endpoints
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+ * ITSUBTREE: name of ITTYPE field within ITSTRUCT holding last-in-subtree
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+ * ITSTART(n): start endpoint of ITSTRUCT node n
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+ * ITLAST(n): last endpoing of ITSTRUCT node n
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+ * ITSTATIC: 'static' or empty
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+ * ITPREFIX: prefix to use for the inline tree definitions
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+ */
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+
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+/* IT(name) -> ITPREFIX_name */
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+#define _ITNAME(prefix, name) prefix ## _ ## name
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+#define ITNAME(prefix, name) _ITNAME(prefix, name)
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+#define IT(name) ITNAME(ITPREFIX, name)
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+
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+/* Callbacks for augmented rbtree insert and remove */
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+
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+static inline ITTYPE IT(compute_subtree_last)(ITSTRUCT *node)
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+{
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+ ITTYPE max = ITLAST(node), subtree_last;
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+ if (node->ITRB.rb_left) {
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+ subtree_last = rb_entry(node->ITRB.rb_left,
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+ ITSTRUCT, ITRB)->ITSUBTREE;
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+ if (max < subtree_last)
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+ max = subtree_last;
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+ }
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+ if (node->ITRB.rb_right) {
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+ subtree_last = rb_entry(node->ITRB.rb_right,
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+ ITSTRUCT, ITRB)->ITSUBTREE;
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+ if (max < subtree_last)
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+ max = subtree_last;
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+ }
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+ return max;
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+}
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+
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+static void IT(augment_propagate)(struct rb_node *rb, struct rb_node *stop)
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+{
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+ while (rb != stop) {
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+ ITSTRUCT *node = rb_entry(rb, ITSTRUCT, ITRB);
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+ ITTYPE subtree_last = IT(compute_subtree_last)(node);
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+ if (node->ITSUBTREE == subtree_last)
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+ break;
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+ node->ITSUBTREE = subtree_last;
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+ rb = rb_parent(&node->ITRB);
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+ }
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+}
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+
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+static void IT(augment_copy)(struct rb_node *rb_old, struct rb_node *rb_new)
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+{
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+ ITSTRUCT *old = rb_entry(rb_old, ITSTRUCT, ITRB);
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+ ITSTRUCT *new = rb_entry(rb_new, ITSTRUCT, ITRB);
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+
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+ new->ITSUBTREE = old->ITSUBTREE;
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+}
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+
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+static void IT(augment_rotate)(struct rb_node *rb_old, struct rb_node *rb_new)
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+{
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+ ITSTRUCT *old = rb_entry(rb_old, ITSTRUCT, ITRB);
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+ ITSTRUCT *new = rb_entry(rb_new, ITSTRUCT, ITRB);
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+
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+ new->ITSUBTREE = old->ITSUBTREE;
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+ old->ITSUBTREE = IT(compute_subtree_last)(old);
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+}
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+
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+static const struct rb_augment_callbacks IT(augment_callbacks) = {
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+ IT(augment_propagate), IT(augment_copy), IT(augment_rotate)
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+};
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+
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+/* Insert / remove interval nodes from the tree */
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+
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+ITSTATIC void IT(insert)(ITSTRUCT *node, struct rb_root *root)
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+{
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+ struct rb_node **link = &root->rb_node, *rb_parent = NULL;
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+ ITTYPE start = ITSTART(node), last = ITLAST(node);
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+ ITSTRUCT *parent;
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+
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+ while (*link) {
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+ rb_parent = *link;
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+ parent = rb_entry(rb_parent, ITSTRUCT, ITRB);
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+ if (parent->ITSUBTREE < last)
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+ parent->ITSUBTREE = last;
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+ if (start < ITSTART(parent))
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+ link = &parent->ITRB.rb_left;
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+ else
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+ link = &parent->ITRB.rb_right;
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+ }
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+
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+ node->ITSUBTREE = last;
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+ rb_link_node(&node->ITRB, rb_parent, link);
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+ rb_insert_augmented(&node->ITRB, root, &IT(augment_callbacks));
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+}
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+
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+ITSTATIC void IT(remove)(ITSTRUCT *node, struct rb_root *root)
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+{
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+ rb_erase_augmented(&node->ITRB, root, &IT(augment_callbacks));
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+}
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+
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+/*
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+ * Iterate over intervals intersecting [start;last]
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+ *
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+ * Note that a node's interval intersects [start;last] iff:
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+ * Cond1: ITSTART(node) <= last
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+ * and
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+ * Cond2: start <= ITLAST(node)
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+ */
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+
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+static ITSTRUCT *IT(subtree_search)(ITSTRUCT *node, ITTYPE start, ITTYPE last)
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+{
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+ while (true) {
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+ /*
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+ * Loop invariant: start <= node->ITSUBTREE
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+ * (Cond2 is satisfied by one of the subtree nodes)
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+ */
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+ if (node->ITRB.rb_left) {
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+ ITSTRUCT *left = rb_entry(node->ITRB.rb_left,
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+ ITSTRUCT, ITRB);
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+ if (start <= left->ITSUBTREE) {
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+ /*
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+ * Some nodes in left subtree satisfy Cond2.
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+ * Iterate to find the leftmost such node N.
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+ * If it also satisfies Cond1, that's the match
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+ * we are looking for. Otherwise, there is no
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+ * matching interval as nodes to the right of N
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+ * can't satisfy Cond1 either.
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+ */
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+ node = left;
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+ continue;
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+ }
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+ }
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+ if (ITSTART(node) <= last) { /* Cond1 */
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+ if (start <= ITLAST(node)) /* Cond2 */
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+ return node; /* node is leftmost match */
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+ if (node->ITRB.rb_right) {
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+ node = rb_entry(node->ITRB.rb_right,
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+ ITSTRUCT, ITRB);
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+ if (start <= node->ITSUBTREE)
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+ continue;
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+ }
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+ }
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+ return NULL; /* No match */
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+ }
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+}
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+
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+ITSTATIC ITSTRUCT *IT(iter_first)(struct rb_root *root,
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+ ITTYPE start, ITTYPE last)
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+{
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+ ITSTRUCT *node;
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+
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+ if (!root->rb_node)
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+ return NULL;
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+ node = rb_entry(root->rb_node, ITSTRUCT, ITRB);
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+ if (node->ITSUBTREE < start)
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+ return NULL;
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+ return IT(subtree_search)(node, start, last);
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+}
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+
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+ITSTATIC ITSTRUCT *IT(iter_next)(ITSTRUCT *node, ITTYPE start, ITTYPE last)
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+{
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+ struct rb_node *rb = node->ITRB.rb_right, *prev;
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+
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+ while (true) {
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+ /*
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+ * Loop invariants:
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+ * Cond1: ITSTART(node) <= last
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+ * rb == node->ITRB.rb_right
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+ *
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+ * First, search right subtree if suitable
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+ */
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+ if (rb) {
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+ ITSTRUCT *right = rb_entry(rb, ITSTRUCT, ITRB);
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+ if (start <= right->ITSUBTREE)
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+ return IT(subtree_search)(right, start, last);
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+ }
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+
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+ /* Move up the tree until we come from a node's left child */
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+ do {
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+ rb = rb_parent(&node->ITRB);
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+ if (!rb)
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+ return NULL;
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+ prev = &node->ITRB;
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+ node = rb_entry(rb, ITSTRUCT, ITRB);
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+ rb = node->ITRB.rb_right;
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+ } while (prev == rb);
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+
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+ /* Check if the node intersects [start;last] */
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+ if (last < ITSTART(node)) /* !Cond1 */
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+ return NULL;
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+ else if (start <= ITLAST(node)) /* Cond2 */
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+ return node;
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+ }
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+}
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