drivers/staging/lustre/lustre/ldlm/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.sun.com/software/products/lustre/docs/GPLv2.pdf
  19  *
  20  * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
  21  * CA 95054 USA or visit www.sun.com if you need additional information or
  22  * have any questions.
  23  *
  24  * GPL HEADER END
  25  */
  26 /*
  27  * Copyright (c) 2008, 2010, Oracle and/or its affiliates. All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 /*
  31  * This file is part of Lustre, http://www.lustre.org/
  32  * Lustre is a trademark of Sun Microsystems, Inc.
  33  *
  34  * lustre/ldlm/interval_tree.c
  35  *
  36  * Interval tree library used by ldlm extent lock code
  37  *
  38  * Author: Huang Wei <huangwei@clusterfs.com>
  39  * Author: Jay Xiong <jinshan.xiong@sun.com>
  40  */
  41 # include <lustre_dlm.h>
  42 #include <obd_support.h>
  43 #include <interval_tree.h>
  44
  45 enum {
  46         INTERVAL_RED = 0,
  47         INTERVAL_BLACK = 1
  48 };
  49
  50 static inline int node_is_left_child(struct interval_node *node)
  51 {
  52         LASSERT(node->in_parent != NULL);
  53         return node == node->in_parent->in_left;
  54 }
  55
  56 static inline int node_is_right_child(struct interval_node *node)
  57 {
  58         LASSERT(node->in_parent != NULL);
  59         return node == node->in_parent->in_right;
  60 }
  61
  62 static inline int node_is_red(struct interval_node *node)
  63 {
  64         return node->in_color == INTERVAL_RED;
  65 }
  66
  67 static inline int node_is_black(struct interval_node *node)
  68 {
  69         return node->in_color == INTERVAL_BLACK;
  70 }
  71
  72 static inline int extent_compare(struct interval_node_extent *e1,
  73                                  struct interval_node_extent *e2)
  74 {
  75         int rc;
  76         if (e1->start == e2->start) {
  77                 if (e1->end < e2->end)
  78                         rc = -1;
  79                 else if (e1->end > e2->end)
  80                         rc = 1;
  81                 else
  82                         rc = 0;
  83         } else {
  84                 if (e1->start < e2->start)
  85                         rc = -1;
  86                 else
  87                         rc = 1;
  88         }
  89         return rc;
  90 }
  91
  92 static inline int extent_equal(struct interval_node_extent *e1,
  93                                struct interval_node_extent *e2)
  94 {
  95         return (e1->start == e2->start) && (e1->end == e2->end);
  96 }
  97
  98 static inline int extent_overlapped(struct interval_node_extent *e1,
  99                                     struct interval_node_extent *e2)
 100 {
 101         return (e1->start <= e2->end) && (e2->start <= e1->end);
 102 }
 103
 104 static inline int node_compare(struct interval_node *n1,
 105                                struct interval_node *n2)
 106 {
 107         return extent_compare(&n1->in_extent, &n2->in_extent);
 108 }
 109
 110 static inline int node_equal(struct interval_node *n1,
 111                              struct interval_node *n2)
 112 {
 113         return extent_equal(&n1->in_extent, &n2->in_extent);
 114 }
 115
 116 static inline __u64 max_u64(__u64 x, __u64 y)
 117 {
 118         return x > y ? x : y;
 119 }
 120
 121 static inline __u64 min_u64(__u64 x, __u64 y)
 122 {
 123         return x < y ? x : y;
 124 }
 125
 126 #define interval_for_each(node, root)              \
 127 for (node = interval_first(root); node != NULL;  \
 128      node = interval_next(node))
 129
 130 #define interval_for_each_reverse(node, root)      \
 131 for (node = interval_last(root); node != NULL;    \
 132      node = interval_prev(node))
 133
 134 static struct interval_node *interval_first(struct interval_node *node)
 135 {
 136         if (!node)
 137                 return NULL;
 138         while (node->in_left)
 139                 node = node->in_left;
 140         return node;
 141 }
 142
 143 static struct interval_node *interval_last(struct interval_node *node)
 144 {
 145         if (!node)
 146                 return NULL;
 147         while (node->in_right)
 148                 node = node->in_right;
 149         return node;
 150 }
 151
 152 static struct interval_node *interval_next(struct interval_node *node)
 153 {
 154         if (!node)
 155                 return NULL;
 156         if (node->in_right)
 157                 return interval_first(node->in_right);
 158         while (node->in_parent && node_is_right_child(node))
 159                 node = node->in_parent;
 160         return node->in_parent;
 161 }
 162
 163 static struct interval_node *interval_prev(struct interval_node *node)
 164 {
 165         if (!node)
 166                 return NULL;
 167
 168         if (node->in_left)
 169                 return interval_last(node->in_left);
 170
 171         while (node->in_parent && node_is_left_child(node))
 172                 node = node->in_parent;
 173
 174         return node->in_parent;
 175 }
 176
 177 enum interval_iter interval_iterate(struct interval_node *root,
 178                                     interval_callback_t func,
 179                                     void *data)
 180 {
 181         struct interval_node *node;
 182         enum interval_iter rc = INTERVAL_ITER_CONT;
 183
 184         interval_for_each(node, root) {
 185                 rc = func(node, data);
 186                 if (rc == INTERVAL_ITER_STOP)
 187                         break;
 188         }
 189
 190         return rc;
 191 }
 192 EXPORT_SYMBOL(interval_iterate);
 193
 194 enum interval_iter interval_iterate_reverse(struct interval_node *root,
 195                                             interval_callback_t func,
 196                                             void *data)
 197 {
 198         struct interval_node *node;
 199         enum interval_iter rc = INTERVAL_ITER_CONT;
 200
 201         interval_for_each_reverse(node, root) {
 202                 rc = func(node, data);
 203                 if (rc == INTERVAL_ITER_STOP)
 204                         break;
 205         }
 206
 207         return rc;
 208 }
 209 EXPORT_SYMBOL(interval_iterate_reverse);
 210
 211 /* try to find a node with same interval in the tree,
 212  * if found, return the pointer to the node, otherwise return NULL*/
 213 struct interval_node *interval_find(struct interval_node *root,
 214                                     struct interval_node_extent *ex)
 215 {
 216         struct interval_node *walk = root;
 217         int rc;
 218
 219         while (walk) {
 220                 rc = extent_compare(ex, &walk->in_extent);
 221                 if (rc == 0)
 222                         break;
 223                 else if (rc < 0)
 224                         walk = walk->in_left;
 225                 else
 226                         walk = walk->in_right;
 227         }
 228
 229         return walk;
 230 }
 231 EXPORT_SYMBOL(interval_find);
 232
 233 static void __rotate_change_maxhigh(struct interval_node *node,
 234                                     struct interval_node *rotate)
 235 {
 236         __u64 left_max, right_max;
 237
 238         rotate->in_max_high = node->in_max_high;
 239         left_max = node->in_left ? node->in_left->in_max_high : 0;
 240         right_max = node->in_right ? node->in_right->in_max_high : 0;
 241         node->in_max_high  = max_u64(interval_high(node),
 242                                      max_u64(left_max,right_max));
 243 }
 244
 245 /* The left rotation "pivots" around the link from node to node->right, and
 246  * - node will be linked to node->right's left child, and
 247  * - node->right's left child will be linked to node's right child.  */
 248 static void __rotate_left(struct interval_node *node,
 249                           struct interval_node **root)
 250 {
 251         struct interval_node *right = node->in_right;
 252         struct interval_node *parent = node->in_parent;
 253
 254         node->in_right = right->in_left;
 255         if (node->in_right)
 256                 right->in_left->in_parent = node;
 257
 258         right->in_left = node;
 259         right->in_parent = parent;
 260         if (parent) {
 261                 if (node_is_left_child(node))
 262                         parent->in_left = right;
 263                 else
 264                         parent->in_right = right;
 265         } else {
 266                 *root = right;
 267         }
 268         node->in_parent = right;
 269
 270         /* update max_high for node and right */
 271         __rotate_change_maxhigh(node, right);
 272 }
 273
 274 /* The right rotation "pivots" around the link from node to node->left, and
 275  * - node will be linked to node->left's right child, and
 276  * - node->left's right child will be linked to node's left child.  */
 277 static void __rotate_right(struct interval_node *node,
 278                            struct interval_node **root)
 279 {
 280         struct interval_node *left = node->in_left;
 281         struct interval_node *parent = node->in_parent;
 282
 283         node->in_left = left->in_right;
 284         if (node->in_left)
 285                 left->in_right->in_parent = node;
 286         left->in_right = node;
 287
 288         left->in_parent = parent;
 289         if (parent) {
 290                 if (node_is_right_child(node))
 291                         parent->in_right = left;
 292                 else
 293                         parent->in_left = left;
 294         } else {
 295                 *root = left;
 296         }
 297         node->in_parent = left;
 298
 299         /* update max_high for node and left */
 300         __rotate_change_maxhigh(node, left);
 301 }
 302
 303 #define interval_swap(a, b) do {                        \
 304         struct interval_node *c = a; a = b; b = c;      \
 305 } while (0)
 306
 307 /*
 308  * Operations INSERT and DELETE, when run on a tree with n keys,
 309  * take O(logN) time.Because they modify the tree, the result
 310  * may violate the red-black properties.To restore these properties,
 311  * we must change the colors of some of the nodes in the tree
 312  * and also change the pointer structure.
 313  */
 314 static void interval_insert_color(struct interval_node *node,
 315                                   struct interval_node **root)
 316 {
 317         struct interval_node *parent, *gparent;
 318
 319         while ((parent = node->in_parent) && node_is_red(parent)) {
 320                 gparent = parent->in_parent;
 321                 /* Parent is RED, so gparent must not be NULL */
 322                 if (node_is_left_child(parent)) {
 323                         struct interval_node *uncle;
 324                         uncle = gparent->in_right;
 325                         if (uncle && node_is_red(uncle)) {
 326                                 uncle->in_color = INTERVAL_BLACK;
 327                                 parent->in_color = INTERVAL_BLACK;
 328                                 gparent->in_color = INTERVAL_RED;
 329                                 node = gparent;
 330                                 continue;
 331                         }
 332
 333                         if (parent->in_right == node) {
 334                                 __rotate_left(parent, root);
 335                                 interval_swap(node, parent);
 336                         }
 337
 338                         parent->in_color = INTERVAL_BLACK;
 339                         gparent->in_color = INTERVAL_RED;
 340                         __rotate_right(gparent, root);
 341                 } else {
 342                         struct interval_node *uncle;
 343                         uncle = gparent->in_left;
 344                         if (uncle && node_is_red(uncle)) {
 345                                 uncle->in_color = INTERVAL_BLACK;
 346                                 parent->in_color = INTERVAL_BLACK;
 347                                 gparent->in_color = INTERVAL_RED;
 348                                 node = gparent;
 349                                 continue;
 350                         }
 351
 352                         if (node_is_left_child(node)) {
 353                                 __rotate_right(parent, root);
 354                                 interval_swap(node, parent);
 355                         }
 356
 357                         parent->in_color = INTERVAL_BLACK;
 358                         gparent->in_color = INTERVAL_RED;
 359                         __rotate_left(gparent, root);
 360                 }
 361         }
 362
 363         (*root)->in_color = INTERVAL_BLACK;
 364 }
 365
 366 struct interval_node *interval_insert(struct interval_node *node,
 367                                       struct interval_node **root)
 368
 369 {
 370         struct interval_node **p, *parent = NULL;
 371
 372         LASSERT(!interval_is_intree(node));
 373         p = root;
 374         while (*p) {
 375                 parent = *p;
 376                 if (node_equal(parent, node))
 377                         return parent;
 378
 379                 /* max_high field must be updated after each iteration */
 380                 if (parent->in_max_high < interval_high(node))
 381                         parent->in_max_high = interval_high(node);
 382
 383                 if (node_compare(node, parent) < 0)
 384                         p = &parent->in_left;
 385                 else
 386                         p = &parent->in_right;
 387         }
 388
 389         /* link node into the tree */
 390         node->in_parent = parent;
 391         node->in_color = INTERVAL_RED;
 392         node->in_left = node->in_right = NULL;
 393         *p = node;
 394
 395         interval_insert_color(node, root);
 396         node->in_intree = 1;
 397
 398         return NULL;
 399 }
 400 EXPORT_SYMBOL(interval_insert);
 401
 402 static inline int node_is_black_or_0(struct interval_node *node)
 403 {
 404         return !node || node_is_black(node);
 405 }
 406
 407 static void interval_erase_color(struct interval_node *node,
 408                                  struct interval_node *parent,
 409                                  struct interval_node **root)
 410 {
 411         struct interval_node *tmp;
 412
 413         while (node_is_black_or_0(node) && node != *root) {
 414                 if (parent->in_left == node) {
 415                         tmp = parent->in_right;
 416                         if (node_is_red(tmp)) {
 417                                 tmp->in_color = INTERVAL_BLACK;
 418                                 parent->in_color = INTERVAL_RED;
 419                                 __rotate_left(parent, root);
 420                                 tmp = parent->in_right;
 421                         }
 422                         if (node_is_black_or_0(tmp->in_left) &&
 423                             node_is_black_or_0(tmp->in_right)) {
 424                                 tmp->in_color = INTERVAL_RED;
 425                                 node = parent;
 426                                 parent = node->in_parent;
 427                         } else {
 428                                 if (node_is_black_or_0(tmp->in_right)) {
 429                                         struct interval_node *o_left;
 430                                         if ((o_left = tmp->in_left))
 431                                              o_left->in_color = INTERVAL_BLACK;
 432                                         tmp->in_color = INTERVAL_RED;
 433                                         __rotate_right(tmp, root);
 434                                         tmp = parent->in_right;
 435                                 }
 436                                 tmp->in_color = parent->in_color;
 437                                 parent->in_color = INTERVAL_BLACK;
 438                                 if (tmp->in_right)
 439                                     tmp->in_right->in_color = INTERVAL_BLACK;
 440                                 __rotate_left(parent, root);
 441                                 node = *root;
 442                                 break;
 443                         }
 444                 } else {
 445                         tmp = parent->in_left;
 446                         if (node_is_red(tmp)) {
 447                                 tmp->in_color = INTERVAL_BLACK;
 448                                 parent->in_color = INTERVAL_RED;
 449                                 __rotate_right(parent, root);
 450                                 tmp = parent->in_left;
 451                         }
 452                         if (node_is_black_or_0(tmp->in_left) &&
 453                             node_is_black_or_0(tmp->in_right)) {
 454                                 tmp->in_color = INTERVAL_RED;
 455                                 node = parent;
 456                                 parent = node->in_parent;
 457                         } else {
 458                                 if (node_is_black_or_0(tmp->in_left)) {
 459                                         struct interval_node *o_right;
 460                                         if ((o_right = tmp->in_right))
 461                                             o_right->in_color = INTERVAL_BLACK;
 462                                         tmp->in_color = INTERVAL_RED;
 463                                         __rotate_left(tmp, root);
 464                                         tmp = parent->in_left;
 465                                 }
 466                                 tmp->in_color = parent->in_color;
 467                                 parent->in_color = INTERVAL_BLACK;
 468                                 if (tmp->in_left)
 469                                         tmp->in_left->in_color = INTERVAL_BLACK;
 470                                 __rotate_right(parent, root);
 471                                 node = *root;
 472                                 break;
 473                         }
 474                 }
 475         }
 476         if (node)
 477                 node->in_color = INTERVAL_BLACK;
 478 }
 479
 480 /*
 481  * if the @max_high value of @node is changed, this function traverse  a path
 482  * from node  up to the root to update max_high for the whole tree.
 483  */
 484 static void update_maxhigh(struct interval_node *node,
 485                            __u64  old_maxhigh)
 486 {
 487         __u64 left_max, right_max;
 488
 489         while (node) {
 490                 left_max = node->in_left ? node->in_left->in_max_high : 0;
 491                 right_max = node->in_right ? node->in_right->in_max_high : 0;
 492                 node->in_max_high = max_u64(interval_high(node),
 493                                             max_u64(left_max, right_max));
 494
 495                 if (node->in_max_high >= old_maxhigh)
 496                         break;
 497                 node = node->in_parent;
 498         }
 499 }
 500
 501 void interval_erase(struct interval_node *node,
 502                     struct interval_node **root)
 503 {
 504         struct interval_node *child, *parent;
 505         int color;
 506
 507         LASSERT(interval_is_intree(node));
 508         node->in_intree = 0;
 509         if (!node->in_left) {
 510                 child = node->in_right;
 511         } else if (!node->in_right) {
 512                 child = node->in_left;
 513         } else { /* Both left and right child are not NULL */
 514                 struct interval_node *old = node;
 515
 516                 node = interval_next(node);
 517                 child = node->in_right;
 518                 parent = node->in_parent;
 519                 color = node->in_color;
 520
 521                 if (child)
 522                         child->in_parent = parent;
 523                 if (parent == old)
 524                         parent->in_right = child;
 525                 else
 526                         parent->in_left = child;
 527
 528                 node->in_color = old->in_color;
 529                 node->in_right = old->in_right;
 530                 node->in_left = old->in_left;
 531                 node->in_parent = old->in_parent;
 532
 533                 if (old->in_parent) {
 534                         if (node_is_left_child(old))
 535                                 old->in_parent->in_left = node;
 536                         else
 537                                 old->in_parent->in_right = node;
 538                 } else {
 539                         *root = node;
 540                 }
 541
 542                 old->in_left->in_parent = node;
 543                 if (old->in_right)
 544                         old->in_right->in_parent = node;
 545                 update_maxhigh(child ? : parent, node->in_max_high);
 546                 update_maxhigh(node, old->in_max_high);
 547                 if (parent == old)
 548                          parent = node;
 549                 goto color;
 550         }
 551         parent = node->in_parent;
 552         color = node->in_color;
 553
 554         if (child)
 555                 child->in_parent = parent;
 556         if (parent) {
 557                 if (node_is_left_child(node))
 558                         parent->in_left = child;
 559                 else
 560                         parent->in_right = child;
 561         } else {
 562                 *root = child;
 563         }
 564
 565         update_maxhigh(child ? : parent, node->in_max_high);
 566
 567 color:
 568         if (color == INTERVAL_BLACK)
 569                 interval_erase_color(child, parent, root);
 570 }
 571 EXPORT_SYMBOL(interval_erase);
 572
 573 static inline int interval_may_overlap(struct interval_node *node,
 574                                           struct interval_node_extent *ext)
 575 {
 576         return (ext->start <= node->in_max_high &&
 577                 ext->end >= interval_low(node));
 578 }
 579
 580 /*
 581  * This function finds all intervals that overlap interval ext,
 582  * and calls func to handle resulted intervals one by one.
 583  * in lustre, this function will find all conflicting locks in
 584  * the granted queue and add these locks to the ast work list.
 585  *
 586  * {
 587  *       if (node == NULL)
 588  *             return 0;
 589  *       if (ext->end < interval_low(node)) {
 590  *             interval_search(node->in_left, ext, func, data);
 591  *       } else if (interval_may_overlap(node, ext)) {
 592  *             if (extent_overlapped(ext, &node->in_extent))
 593  *                     func(node, data);
 594  *             interval_search(node->in_left, ext, func, data);
 595  *             interval_search(node->in_right, ext, func, data);
 596  *       }
 597  *       return 0;
 598  * }
 599  *
 600  */
 601 enum interval_iter interval_search(struct interval_node *node,
 602                                    struct interval_node_extent *ext,
 603                                    interval_callback_t func,
 604                                    void *data)
 605 {
 606         struct interval_node *parent;
 607         enum interval_iter rc = INTERVAL_ITER_CONT;
 608
 609         LASSERT(ext != NULL);
 610         LASSERT(func != NULL);
 611
 612         while (node) {
 613                 if (ext->end < interval_low(node)) {
 614                         if (node->in_left) {
 615                                 node = node->in_left;
 616                                 continue;
 617                         }
 618                 } else if (interval_may_overlap(node, ext)) {
 619                         if (extent_overlapped(ext, &node->in_extent)) {
 620                                 rc = func(node, data);
 621                                 if (rc == INTERVAL_ITER_STOP)
 622                                         break;
 623                         }
 624
 625                         if (node->in_left) {
 626                                 node = node->in_left;
 627                                 continue;
 628                         }
 629                         if (node->in_right) {
 630                                 node = node->in_right;
 631                                 continue;
 632                         }
 633                 }
 634
 635                 parent = node->in_parent;
 636                 while (parent) {
 637                         if (node_is_left_child(node) &&
 638                             parent->in_right) {
 639                                 /* If we ever got the left, it means that the
 640                                  * parent met ext->end<interval_low(parent), or
 641                                  * may_overlap(parent). If the former is true,
 642                                  * we needn't go back. So stop early and check
 643                                  * may_overlap(parent) after this loop.  */
 644                                 node = parent->in_right;
 645                                 break;
 646                         }
 647                         node = parent;
 648                         parent = parent->in_parent;
 649                 }
 650                 if (parent == NULL || !interval_may_overlap(parent, ext))
 651                         break;
 652         }
 653
 654         return rc;
 655 }
 656 EXPORT_SYMBOL(interval_search);
 657
 658 static enum interval_iter interval_overlap_cb(struct interval_node *n,
 659                                               void *args)
 660 {
 661         *(int *)args = 1;
 662         return INTERVAL_ITER_STOP;
 663 }
 664
 665 int interval_is_overlapped(struct interval_node *root,
 666                            struct interval_node_extent *ext)
 667 {
 668         int has = 0;
 669         (void)interval_search(root, ext, interval_overlap_cb, &has);
 670         return has;
 671 }
 672 EXPORT_SYMBOL(interval_is_overlapped);
 673
 674 /* Don't expand to low. Expanding downwards is expensive, and meaningless to
 675  * some extents, because programs seldom do IO backward.
 676  *
 677  * The recursive algorithm of expanding low:
 678  * expand_low {
 679  *      struct interval_node *tmp;
 680  *      static __u64 res = 0;
 681  *
 682  *      if (root == NULL)
 683  *              return res;
 684  *      if (root->in_max_high < low) {
 685  *              res = max_u64(root->in_max_high + 1, res);
 686  *              return res;
 687  *      } else if (low < interval_low(root)) {
 688  *              interval_expand_low(root->in_left, low);
 689  *              return res;
 690  *      }
 691  *
 692  *      if (interval_high(root) < low)
 693  *              res = max_u64(interval_high(root) + 1, res);
 694  *      interval_expand_low(root->in_left, low);
 695  *      interval_expand_low(root->in_right, low);
 696  *
 697  *      return res;
 698  * }
 699  *
 700  * It's much easy to eliminate the recursion, see interval_search for
 701  * an example. -jay
 702  */
 703 static inline __u64 interval_expand_low(struct interval_node *root, __u64 low)
 704 {
 705         /* we only concern the empty tree right now. */
 706         if (root == NULL)
 707                 return 0;
 708         return low;
 709 }
 710
 711 static inline __u64 interval_expand_high(struct interval_node *node, __u64 high)
 712 {
 713         __u64 result = ~0;
 714
 715         while (node != NULL) {
 716                 if (node->in_max_high < high)
 717                         break;
 718
 719                 if (interval_low(node) > high) {
 720                         result = interval_low(node) - 1;
 721                         node = node->in_left;
 722                 } else {
 723                         node = node->in_right;
 724                 }
 725         }
 726
 727         return result;
 728 }
 729
 730 /* expanding the extent based on @ext. */
 731 void interval_expand(struct interval_node *root,
 732                      struct interval_node_extent *ext,
 733                      struct interval_node_extent *limiter)
 734 {
 735         /* The assertion of interval_is_overlapped is expensive because we may
 736          * travel many nodes to find the overlapped node. */
 737         LASSERT(interval_is_overlapped(root, ext) == 0);
 738         if (!limiter || limiter->start < ext->start)
 739                 ext->start = interval_expand_low(root, ext->start);
 740         if (!limiter || limiter->end > ext->end)
 741                 ext->end = interval_expand_high(root, ext->end);
 742         LASSERT(interval_is_overlapped(root, ext) == 0);
 743 }
 744 EXPORT_SYMBOL(interval_expand);