lustre/obdclass/interval_tree.c

   1 /*
   2  * GPL HEADER START
   3  *
   4  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU General Public License version 2 only,
   8  * as published by the Free Software Foundation.
   9  *
  10  * This program is distributed in the hope that it will be useful, but
  11  * WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13  * General Public License version 2 for more details (a copy is included
  14  * in the LICENSE file that accompanied this code).
  15  *
  16  * You should have received a copy of the GNU General Public License
  17  * version 2 along with this program; If not, see
  18  * http://www.gnu.org/licenses/gpl-2.0.html
  19  *
  20  * GPL HEADER END
  21  */
  22 /*
  23  * Copyright (c) 2008, 2010, Oracle and/or its affiliates. All rights reserved.
  24  * Use is subject to license terms.
  25  *
  26  * Copyright (c) 2014, Intel Corporation.
  27  */
  28 /*
  29  * This file is part of Lustre, http://www.lustre.org/
  30  *
  31  * lustre/ldlm/interval_tree.c
  32  *
  33  * Interval tree library used by ldlm extent lock code
  34  *
  35  * Author: Huang Wei <huangwei@clusterfs.com>
  36  * Author: Jay Xiong <jinshan.xiong@sun.com>
  37  */
  38
  39 #include <lustre_dlm.h>
  40 #include <interval_tree.h>
  41
  42 enum {
  43         INTERVAL_RED = 0,
  44         INTERVAL_BLACK = 1
  45 };
  46
  47 static inline int node_is_left_child(struct interval_node *node)
  48 {
  49         LASSERT(node->in_parent != NULL);
  50         return node == node->in_parent->in_left;
  51 }
  52
  53 static inline int node_is_right_child(struct interval_node *node)
  54 {
  55         LASSERT(node->in_parent != NULL);
  56         return node == node->in_parent->in_right;
  57 }
  58
  59 static inline int node_is_red(struct interval_node *node)
  60 {
  61         return node->in_color == INTERVAL_RED;
  62 }
  63
  64 static inline int node_is_black(struct interval_node *node)
  65 {
  66         return node->in_color == INTERVAL_BLACK;
  67 }
  68
  69 static inline int extent_compare(struct interval_node_extent *e1,
  70                                  struct interval_node_extent *e2)
  71 {
  72         int rc;
  73
  74         if (e1->start == e2->start) {
  75                 if (e1->end < e2->end)
  76                         rc = -1;
  77                 else if (e1->end > e2->end)
  78                         rc = 1;
  79                 else
  80                         rc = 0;
  81         } else {
  82                 if (e1->start < e2->start)
  83                         rc = -1;
  84                 else
  85                         rc = 1;
  86         }
  87         return rc;
  88 }
  89
  90 static inline int extent_equal(struct interval_node_extent *e1,
  91                                struct interval_node_extent *e2)
  92 {
  93         return (e1->start == e2->start) && (e1->end == e2->end);
  94 }
  95
  96 static inline int extent_overlapped(struct interval_node_extent *e1,
  97                                     struct interval_node_extent *e2)
  98 {
  99         return (e1->start <= e2->end) && (e2->start <= e1->end);
 100 }
 101
 102 static inline int node_compare(struct interval_node *n1,
 103                                struct interval_node *n2)
 104 {
 105         return extent_compare(&n1->in_extent, &n2->in_extent);
 106 }
 107
 108 #define interval_for_each(node, root)                   \
 109 for (node = interval_first(root); node != NULL;         \
 110         node = interval_next(node))
 111
 112 #define interval_for_each_reverse(node, root)           \
 113 for (node = interval_last(root); node != NULL;          \
 114         node = interval_prev(node))
 115
 116 static struct interval_node *interval_first(struct interval_node *node)
 117 {
 118         ENTRY;
 119
 120         if (!node)
 121                 RETURN(NULL);
 122         while (node->in_left)
 123                 node = node->in_left;
 124         RETURN(node);
 125 }
 126
 127 static struct interval_node *interval_last(struct interval_node *node)
 128 {
 129         ENTRY;
 130
 131         if (!node)
 132                 RETURN(NULL);
 133         while (node->in_right)
 134                 node = node->in_right;
 135         RETURN(node);
 136 }
 137
 138 static struct interval_node *interval_next(struct interval_node *node)
 139 {
 140         ENTRY;
 141
 142         if (!node)
 143                 RETURN(NULL);
 144         if (node->in_right)
 145                 RETURN(interval_first(node->in_right));
 146         while (node->in_parent && node_is_right_child(node))
 147                 node = node->in_parent;
 148         RETURN(node->in_parent);
 149 }
 150
 151 static struct interval_node *interval_prev(struct interval_node *node)
 152 {
 153         ENTRY;
 154
 155         if (!node)
 156                 RETURN(NULL);
 157
 158         if (node->in_left)
 159                 RETURN(interval_last(node->in_left));
 160
 161         while (node->in_parent && node_is_left_child(node))
 162                 node = node->in_parent;
 163
 164         RETURN(node->in_parent);
 165 }
 166
 167 enum interval_iter interval_iterate(struct interval_node *root,
 168                                     interval_callback_t func,
 169                                     void *data)
 170 {
 171         struct interval_node *node;
 172         enum interval_iter rc = INTERVAL_ITER_CONT;
 173
 174         ENTRY;
 175
 176         interval_for_each(node, root) {
 177                 rc = func(node, data);
 178                 if (rc == INTERVAL_ITER_STOP)
 179                         break;
 180         }
 181
 182         RETURN(rc);
 183 }
 184 EXPORT_SYMBOL(interval_iterate);
 185
 186 enum interval_iter interval_iterate_reverse(struct interval_node *root,
 187                                             interval_callback_t func,
 188                                             void *data)
 189 {
 190         struct interval_node *node;
 191         enum interval_iter rc = INTERVAL_ITER_CONT;
 192
 193         ENTRY;
 194
 195         interval_for_each_reverse(node, root) {
 196                 rc = func(node, data);
 197                 if (rc == INTERVAL_ITER_STOP)
 198                         break;
 199         }
 200
 201         RETURN(rc);
 202 }
 203 EXPORT_SYMBOL(interval_iterate_reverse);
 204
 205 /* try to find a node with same interval in the tree,
 206  * if found, return the pointer to the node, otherwise return NULL
 207  */
 208 struct interval_node *interval_find(struct interval_node *root,
 209                                     struct interval_node_extent *ex)
 210 {
 211         struct interval_node *walk = root;
 212         int rc;
 213
 214         ENTRY;
 215
 216         while (walk) {
 217                 rc = extent_compare(ex, &walk->in_extent);
 218                 if (rc == 0)
 219                         break;
 220                 else if (rc < 0)
 221                         walk = walk->in_left;
 222                 else
 223                         walk = walk->in_right;
 224         }
 225
 226         RETURN(walk);
 227 }
 228 EXPORT_SYMBOL(interval_find);
 229
 230 static void __rotate_change_maxhigh(struct interval_node *node,
 231                                     struct interval_node *rotate)
 232 {
 233         __u64 left_max, right_max;
 234
 235         rotate->in_max_high = node->in_max_high;
 236         left_max = node->in_left ? node->in_left->in_max_high : 0;
 237         right_max = node->in_right ? node->in_right->in_max_high : 0;
 238         node->in_max_high  = max3(interval_high(node),
 239                                   left_max, right_max);
 240 }
 241
 242 /* The left rotation "pivots" around the link from node to node->right, and
 243  * - node will be linked to node->right's left child, and
 244  * - node->right's left child will be linked to node's right child.
 245  */
 246 static void __rotate_left(struct interval_node *node,
 247                           struct interval_node **root)
 248 {
 249         struct interval_node *right = node->in_right;
 250         struct interval_node *parent = node->in_parent;
 251
 252         node->in_right = right->in_left;
 253         if (node->in_right)
 254                 right->in_left->in_parent = node;
 255
 256         right->in_left = node;
 257         right->in_parent = parent;
 258         if (parent) {
 259                 if (node_is_left_child(node))
 260                         parent->in_left = right;
 261                 else
 262                         parent->in_right = right;
 263         } else {
 264                 *root = right;
 265         }
 266         node->in_parent = right;
 267
 268         /* update max_high for node and right */
 269         __rotate_change_maxhigh(node, right);
 270 }
 271
 272 /* The right rotation "pivots" around the link from node to node->left, and
 273  * - node will be linked to node->left's right child, and
 274  * - node->left's right child will be linked to node's left child.
 275  */
 276 static void __rotate_right(struct interval_node *node,
 277                            struct interval_node **root)
 278 {
 279         struct interval_node *left = node->in_left;
 280         struct interval_node *parent = node->in_parent;
 281
 282         node->in_left = left->in_right;
 283         if (node->in_left)
 284                 left->in_right->in_parent = node;
 285         left->in_right = node;
 286
 287         left->in_parent = parent;
 288         if (parent) {
 289                 if (node_is_right_child(node))
 290                         parent->in_right = left;
 291                 else
 292                         parent->in_left = left;
 293         } else {
 294                 *root = left;
 295         }
 296         node->in_parent = left;
 297
 298         /* update max_high for node and left */
 299         __rotate_change_maxhigh(node, left);
 300 }
 301
 302 #define interval_swap(a, b) do {                        \
 303         struct interval_node *c = a; a = b; b = c;      \
 304 } while (0)
 305
 306 /*
 307  * Operations INSERT and DELETE, when run on a tree with n keys,
 308  * take O(logN) time.Because they modify the tree, the result
 309  * may violate the red-black properties.To restore these properties,
 310  * we must change the colors of some of the nodes in the tree
 311  * and also change the pointer structure.
 312  */
 313 static void interval_insert_color(struct interval_node *node,
 314                                   struct interval_node **root)
 315 {
 316         struct interval_node *parent, *gparent;
 317
 318         ENTRY;
 319
 320         while ((parent = node->in_parent) && node_is_red(parent)) {
 321                 gparent = parent->in_parent;
 322                 /* Parent is RED, so gparent must not be NULL */
 323                 if (node_is_left_child(parent)) {
 324                         struct interval_node *uncle;
 325
 326                         uncle = gparent->in_right;
 327                         if (uncle && node_is_red(uncle)) {
 328                                 uncle->in_color = INTERVAL_BLACK;
 329                                 parent->in_color = INTERVAL_BLACK;
 330                                 gparent->in_color = INTERVAL_RED;
 331                                 node = gparent;
 332                                 continue;
 333                         }
 334
 335                         if (parent->in_right == node) {
 336                                 __rotate_left(parent, root);
 337                                 interval_swap(node, parent);
 338                         }
 339
 340                         parent->in_color = INTERVAL_BLACK;
 341                         gparent->in_color = INTERVAL_RED;
 342                         __rotate_right(gparent, root);
 343                 } else {
 344                         struct interval_node *uncle;
 345
 346                         uncle = gparent->in_left;
 347                         if (uncle && node_is_red(uncle)) {
 348                                 uncle->in_color = INTERVAL_BLACK;
 349                                 parent->in_color = INTERVAL_BLACK;
 350                                 gparent->in_color = INTERVAL_RED;
 351                                 node = gparent;
 352                                 continue;
 353                         }
 354
 355                         if (node_is_left_child(node)) {
 356                                 __rotate_right(parent, root);
 357                                 interval_swap(node, parent);
 358                         }
 359
 360                         parent->in_color = INTERVAL_BLACK;
 361                         gparent->in_color = INTERVAL_RED;
 362                         __rotate_left(gparent, root);
 363                 }
 364         }
 365
 366         (*root)->in_color = INTERVAL_BLACK;
 367         EXIT;
 368 }
 369
 370 struct interval_node *interval_insert(struct interval_node *node,
 371                                       struct interval_node **root)
 372 {
 373         struct interval_node **p, *parent = NULL;
 374
 375         ENTRY;
 376
 377         LASSERT(!interval_is_intree(node));
 378         p = root;
 379         while (*p) {
 380                 parent = *p;
 381
 382                 /* max_high field must be updated after each iteration */
 383                 if (parent->in_max_high < interval_high(node))
 384                         parent->in_max_high = interval_high(node);
 385
 386                 if (node_compare(node, parent) < 0)
 387                         p = &parent->in_left;
 388                 else
 389                         p = &parent->in_right;
 390         }
 391
 392         /* link node into the tree */
 393         node->in_parent = parent;
 394         node->in_color = INTERVAL_RED;
 395         node->in_left = node->in_right = NULL;
 396         *p = node;
 397
 398         interval_insert_color(node, root);
 399         node->in_intree = 1;
 400
 401         RETURN(NULL);
 402 }
 403 EXPORT_SYMBOL(interval_insert);
 404
 405 static inline int node_is_black_or_0(struct interval_node *node)
 406 {
 407         return !node || node_is_black(node);
 408 }
 409
 410 static void interval_erase_color(struct interval_node *node,
 411                                  struct interval_node *parent,
 412                                  struct interval_node **root)
 413 {
 414         struct interval_node *tmp;
 415
 416         ENTRY;
 417
 418         while (node_is_black_or_0(node) && node != *root) {
 419                 if (parent->in_left == node) {
 420                         tmp = parent->in_right;
 421                         if (node_is_red(tmp)) {
 422                                 tmp->in_color = INTERVAL_BLACK;
 423                                 parent->in_color = INTERVAL_RED;
 424                                 __rotate_left(parent, root);
 425                                 tmp = parent->in_right;
 426                         }
 427                         if (node_is_black_or_0(tmp->in_left) &&
 428                             node_is_black_or_0(tmp->in_right)) {
 429                                 tmp->in_color = INTERVAL_RED;
 430                                 node = parent;
 431                                 parent = node->in_parent;
 432                         } else {
 433                                 if (node_is_black_or_0(tmp->in_right)) {
 434                                         struct interval_node *o_left;
 435
 436                                         if ((o_left = tmp->in_left))
 437                                                 o_left->in_color =
 438                                                         INTERVAL_BLACK;
 439                                         tmp->in_color = INTERVAL_RED;
 440                                         __rotate_right(tmp, root);
 441                                         tmp = parent->in_right;
 442                                 }
 443                                 tmp->in_color = parent->in_color;
 444                                 parent->in_color = INTERVAL_BLACK;
 445                                 if (tmp->in_right)
 446                                         tmp->in_right->in_color =
 447                                                 INTERVAL_BLACK;
 448                                 __rotate_left(parent, root);
 449                                 node = *root;
 450                                 break;
 451                         }
 452                 } else {
 453                         tmp = parent->in_left;
 454                         if (node_is_red(tmp)) {
 455                                 tmp->in_color = INTERVAL_BLACK;
 456                                 parent->in_color = INTERVAL_RED;
 457                                 __rotate_right(parent, root);
 458                                 tmp = parent->in_left;
 459                         }
 460                         if (node_is_black_or_0(tmp->in_left) &&
 461                             node_is_black_or_0(tmp->in_right)) {
 462                                 tmp->in_color = INTERVAL_RED;
 463                                 node = parent;
 464                                 parent = node->in_parent;
 465                         } else {
 466                                 if (node_is_black_or_0(tmp->in_left)) {
 467                                         struct interval_node *o_right;
 468
 469                                         if ((o_right = tmp->in_right))
 470                                                 o_right->in_color =
 471                                                         INTERVAL_BLACK;
 472                                         tmp->in_color = INTERVAL_RED;
 473                                         __rotate_left(tmp, root);
 474                                         tmp = parent->in_left;
 475                                 }
 476                                 tmp->in_color = parent->in_color;
 477                                 parent->in_color = INTERVAL_BLACK;
 478                                 if (tmp->in_left)
 479                                         tmp->in_left->in_color = INTERVAL_BLACK;
 480                                 __rotate_right(parent, root);
 481                                 node = *root;
 482                                 break;
 483                         }
 484                 }
 485         }
 486         if (node)
 487                 node->in_color = INTERVAL_BLACK;
 488         EXIT;
 489 }
 490
 491 /*
 492  * if the @max_high value of @node is changed, this function traverse a path
 493  * from node  up to the root to update max_high for the whole tree.
 494  */
 495 static void update_maxhigh(struct interval_node *node,
 496                            __u64  old_maxhigh)
 497 {
 498         __u64 left_max, right_max;
 499
 500         ENTRY;
 501
 502         while (node) {
 503                 left_max = node->in_left ? node->in_left->in_max_high : 0;
 504                 right_max = node->in_right ? node->in_right->in_max_high : 0;
 505                 node->in_max_high = max3(interval_high(node),
 506                                          left_max, right_max);
 507
 508                 if (node->in_max_high >= old_maxhigh)
 509                         break;
 510                 node = node->in_parent;
 511         }
 512         EXIT;
 513 }
 514
 515 void interval_erase(struct interval_node *node,
 516                     struct interval_node **root)
 517 {
 518         struct interval_node *child, *parent;
 519         int color;
 520
 521         ENTRY;
 522
 523         LASSERT(interval_is_intree(node));
 524         node->in_intree = 0;
 525         if (!node->in_left) {
 526                 child = node->in_right;
 527         } else if (!node->in_right) {
 528                 child = node->in_left;
 529         } else { /* Both left and right child are not NULL */
 530                 struct interval_node *old = node;
 531
 532                 node = interval_next(node);
 533                 child = node->in_right;
 534                 parent = node->in_parent;
 535                 color = node->in_color;
 536
 537                 if (child)
 538                         child->in_parent = parent;
 539                 if (parent == old)
 540                         parent->in_right = child;
 541                 else
 542                         parent->in_left = child;
 543
 544                 node->in_color = old->in_color;
 545                 node->in_right = old->in_right;
 546                 node->in_left = old->in_left;
 547                 node->in_parent = old->in_parent;
 548
 549                 if (old->in_parent) {
 550                         if (node_is_left_child(old))
 551                                 old->in_parent->in_left = node;
 552                         else
 553                                 old->in_parent->in_right = node;
 554                 } else {
 555                         *root = node;
 556                 }
 557
 558                 old->in_left->in_parent = node;
 559                 if (old->in_right)
 560                         old->in_right->in_parent = node;
 561                 update_maxhigh(child ? : parent, node->in_max_high);
 562                 update_maxhigh(node, old->in_max_high);
 563                 if (parent == old)
 564                         parent = node;
 565                 goto color;
 566         }
 567         parent = node->in_parent;
 568         color = node->in_color;
 569
 570         if (child)
 571                 child->in_parent = parent;
 572         if (parent) {
 573                 if (node_is_left_child(node))
 574                         parent->in_left = child;
 575                 else
 576                         parent->in_right = child;
 577         } else {
 578                 *root = child;
 579         }
 580
 581         update_maxhigh(child ? : parent, node->in_max_high);
 582
 583 color:
 584         if (color == INTERVAL_BLACK)
 585                 interval_erase_color(child, parent, root);
 586         EXIT;
 587 }
 588 EXPORT_SYMBOL(interval_erase);
 589
 590 static inline int interval_may_overlap(struct interval_node *node,
 591                                        struct interval_node_extent *ext)
 592 {
 593         return (ext->start <= node->in_max_high &&
 594                 ext->end >= interval_low(node));
 595 }
 596
 597 /*
 598  * This function finds all intervals that overlap interval ext,
 599  * and calls func to handle resulted intervals one by one.
 600  * in lustre, this function will find all conflicting locks in
 601  * the granted queue and add these locks to the ast work list.
 602  *
 603  * {
 604  *       if (node == NULL)
 605  *               return 0;
 606  *       if (ext->end < interval_low(node)) {
 607  *               interval_search(node->in_left, ext, func, data);
 608  *       } else if (interval_may_overlap(node, ext)) {
 609  *               if (extent_overlapped(ext, &node->in_extent))
 610  *                       func(node, data);
 611  *               interval_search(node->in_left, ext, func, data);
 612  *               interval_search(node->in_right, ext, func, data);
 613  *       }
 614  *       return 0;
 615  * }
 616  *
 617  */
 618 enum interval_iter interval_search(struct interval_node *node,
 619                                    struct interval_node_extent *ext,
 620                                    interval_callback_t func,
 621                                    void *data)
 622 {
 623         struct interval_node *parent;
 624         enum interval_iter rc = INTERVAL_ITER_CONT;
 625
 626         ENTRY;
 627
 628         LASSERT(ext != NULL);
 629         LASSERT(func != NULL);
 630
 631         while (node) {
 632                 if (ext->end < interval_low(node)) {
 633                         if (node->in_left) {
 634                                 node = node->in_left;
 635                                 continue;
 636                         }
 637                 } else if (interval_may_overlap(node, ext)) {
 638                         if (extent_overlapped(ext, &node->in_extent)) {
 639                                 rc = func(node, data);
 640                                 if (rc == INTERVAL_ITER_STOP)
 641                                         break;
 642                         }
 643
 644                         if (node->in_left) {
 645                                 node = node->in_left;
 646                                 continue;
 647                         }
 648                         if (node->in_right) {
 649                                 node = node->in_right;
 650                                 continue;
 651                         }
 652                 }
 653
 654                 parent = node->in_parent;
 655                 while (parent) {
 656                         if (node_is_left_child(node) &&
 657                             parent->in_right) {
 658                                 /* If we ever got the left, it means that the
 659                                  * parent met ext->end<interval_low(parent), or
 660                                  * may_overlap(parent). If the former is true,
 661                                  * we needn't go back. So stop early and check
 662                                  * may_overlap(parent) after this loop.
 663                                  */
 664                                 node = parent->in_right;
 665                                 break;
 666                         }
 667                         node = parent;
 668                         parent = parent->in_parent;
 669                 }
 670                 if (parent == NULL || !interval_may_overlap(parent, ext))
 671                         break;
 672         }
 673
 674         RETURN(rc);
 675 }
 676 EXPORT_SYMBOL(interval_search);
 677
 678 static enum interval_iter interval_overlap_cb(struct interval_node *n,
 679                                               void *args)
 680 {
 681         *(int *)args = 1;
 682         return INTERVAL_ITER_STOP;
 683 }
 684
 685 int interval_is_overlapped(struct interval_node *root,
 686                            struct interval_node_extent *ext)
 687 {
 688         int has = 0;
 689         (void)interval_search(root, ext, interval_overlap_cb, &has);
 690         return has;
 691 }
 692 EXPORT_SYMBOL(interval_is_overlapped);
 693
 694 /* Don't expand to low. Expanding downwards is expensive, and meaningless to
 695  * some extents, because programs seldom do IO backward.
 696  *
 697  * The recursive algorithm of expanding low:
 698  * expand_low {
 699  *        struct interval_node *tmp;
 700  *        static __u64 res = 0;
 701  *
 702  *        if (root == NULL)
 703  *                return res;
 704  *        if (root->in_max_high < low) {
 705  *                res = max(root->in_max_high + 1, res);
 706  *                return res;
 707  *        } else if (low < interval_low(root)) {
 708  *                interval_expand_low(root->in_left, low);
 709  *                return res;
 710  *        }
 711  *
 712  *        if (interval_high(root) < low)
 713  *                res = max(interval_high(root) + 1, res);
 714  *        interval_expand_low(root->in_left, low);
 715  *        interval_expand_low(root->in_right, low);
 716  *
 717  *        return res;
 718  * }
 719  *
 720  * It's much easy to eliminate the recursion, see interval_search for
 721  * an example. -jay
 722  */
 723 static inline __u64 interval_expand_low(struct interval_node *root, __u64 low)
 724 {
 725         /* we only concern the empty tree right now. */
 726         if (root == NULL)
 727                 return 0;
 728         return low;
 729 }
 730
 731 static inline __u64 interval_expand_high(struct interval_node *node, __u64 high)
 732 {
 733         __u64 result = ~0;
 734
 735         while (node != NULL) {
 736                 if (node->in_max_high < high)
 737                         break;
 738
 739                 if (interval_low(node) > high) {
 740                         result = interval_low(node) - 1;
 741                         node = node->in_left;
 742                 } else {
 743                         node = node->in_right;
 744                 }
 745         }
 746
 747         return result;
 748 }
 749
 750 /* expanding the extent based on @ext. */
 751 void interval_expand(struct interval_node *root,
 752                      struct interval_node_extent *ext,
 753                      struct interval_node_extent *limiter)
 754 {
 755         /* The assertion of interval_is_overlapped is expensive because we may
 756          * travel many nodes to find the overlapped node.
 757          */
 758         LASSERT(interval_is_overlapped(root, ext) == 0);
 759         if (!limiter || limiter->start < ext->start)
 760                 ext->start = interval_expand_low(root, ext->start);
 761         if (!limiter || limiter->end > ext->end)
 762                 ext->end = interval_expand_high(root, ext->end);
 763         LASSERT(interval_is_overlapped(root, ext) == 0);
 764 }
 765 EXPORT_SYMBOL(interval_expand);