lustre/ldlm/interval_tree.c

   1 /* -*- mode: c; c-basic-offset: 8; indent-tabs-mode: nil; -*-
   2  * vim:expandtab:shiftwidth=8:tabstop=8:
   3  *
   4  * GPL HEADER START
   5  *
   6  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   7  *
   8  * This program is free software; you can redistribute it and/or modify
   9  * it under the terms of the GNU General Public License version 2 only,
  10  * as published by the Free Software Foundation.
  11  *
  12  * This program is distributed in the hope that it will be useful, but
  13  * WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * General Public License version 2 for more details (a copy is included
  16  * in the LICENSE file that accompanied this code).
  17  *
  18  * You should have received a copy of the GNU General Public License
  19  * version 2 along with this program; If not, see
  20  * http://www.sun.com/software/products/lustre/docs/GPLv2.pdf
  21  *
  22  * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
  23  * CA 95054 USA or visit www.sun.com if you need additional information or
  24  * have any questions.
  25  *
  26  * GPL HEADER END
  27  */
  28 /*
  29  * Copyright  2008 Sun Microsystems, Inc. All rights reserved
  30  * Use is subject to license terms.
  31  */
  32 /*
  33  * This file is part of Lustre, http://www.lustre.org/
  34  * Lustre is a trademark of Sun Microsystems, Inc.
  35  *
  36  * lustre/ldlm/interval_tree.c
  37  *
  38  * Interval tree library used by ldlm extent lock code
  39  *
  40  * Author: Huang Wei <huangwei@clusterfs.com>
  41  * Author: Jay Xiong <jinshan.xiong@sun.com>
  42  */
  43 #ifdef __KERNEL__
  44 # include <lustre_dlm.h>
  45 #else
  46 # include <liblustre.h>
  47 # include <libcfs/kp30.h>
  48 #endif
  49 #include <obd_support.h>
  50 #include <interval_tree.h>
  51
  52 enum {
  53         INTERVAL_RED = 0,
  54         INTERVAL_BLACK = 1
  55 };
  56
  57 static inline int node_is_left_child(struct interval_node *node)
  58 {
  59         LASSERT(node->in_parent != NULL);
  60         return node == node->in_parent->in_left;
  61 }
  62
  63 static inline int node_is_right_child(struct interval_node *node)
  64 {
  65         LASSERT(node->in_parent != NULL);
  66         return node == node->in_parent->in_right;
  67 }
  68
  69 static inline int node_is_red(struct interval_node *node)
  70 {
  71         return node->in_color == INTERVAL_RED;
  72 }
  73
  74 static inline int node_is_black(struct interval_node *node)
  75 {
  76         return node->in_color == INTERVAL_BLACK;
  77 }
  78
  79 static inline int extent_compare(struct interval_node_extent *e1,
  80                                  struct interval_node_extent *e2)
  81 {
  82         int rc;
  83         if (e1->start == e2->start) {
  84                 if (e1->end < e2->end)
  85                         rc = -1;
  86                 else if (e1->end > e2->end)
  87                         rc = 1;
  88                 else
  89                         rc = 0;
  90         } else {
  91                 if (e1->start < e2->start)
  92                         rc = -1;
  93                 else
  94                         rc = 1;
  95         }
  96         return rc;
  97 }
  98
  99 static inline int extent_equal(struct interval_node_extent *e1,
 100                                struct interval_node_extent *e2)
 101 {
 102         return (e1->start == e2->start) && (e1->end == e2->end);
 103 }
 104
 105 static inline int extent_overlapped(struct interval_node_extent *e1,
 106                                     struct interval_node_extent *e2)
 107 {
 108         return (e1->start <= e2->end) && (e2->start <= e1->end);
 109 }
 110
 111 static inline int node_compare(struct interval_node *n1,
 112                                struct interval_node *n2)
 113 {
 114         return extent_compare(&n1->in_extent, &n2->in_extent);
 115 }
 116
 117 static inline int node_equal(struct interval_node *n1,
 118                              struct interval_node *n2)
 119 {
 120         return extent_equal(&n1->in_extent, &n2->in_extent);
 121 }
 122
 123 static inline __u64 max_u64(__u64 x, __u64 y)
 124 {
 125         return x > y ? x : y;
 126 }
 127
 128 static inline __u64 min_u64(__u64 x, __u64 y)
 129 {
 130         return x < y ? x : y;
 131 }
 132
 133 #define interval_for_each(node, root)                   \
 134 for (node = interval_first(root); node != NULL;         \
 135      node = interval_next(node))
 136
 137 #define interval_for_each_reverse(node, root)           \
 138 for (node = interval_last(root); node != NULL;          \
 139      node = interval_prev(node))
 140
 141 static struct interval_node *interval_first(struct interval_node *node)
 142 {
 143         ENTRY;
 144
 145         if (!node)
 146                 RETURN(NULL);
 147         while (node->in_left)
 148                 node = node->in_left;
 149         RETURN(node);
 150 }
 151
 152 static struct interval_node *interval_last(struct interval_node *node)
 153 {
 154         ENTRY;
 155
 156         if (!node)
 157                 RETURN(NULL);
 158         while (node->in_right)
 159                 node = node->in_right;
 160         RETURN(node);
 161 }
 162
 163 static struct interval_node *interval_next(struct interval_node *node)
 164 {
 165         ENTRY;
 166
 167         if (!node)
 168                 RETURN(NULL);
 169         if (node->in_right)
 170                 RETURN(interval_first(node->in_right));
 171         while (node->in_parent && node_is_right_child(node))
 172                 node = node->in_parent;
 173         RETURN(node->in_parent);
 174 }
 175
 176 static struct interval_node *interval_prev(struct interval_node *node)
 177 {
 178         ENTRY;
 179
 180         if (!node)
 181                 RETURN(NULL);
 182
 183         if (node->in_left)
 184                 RETURN(interval_last(node->in_left));
 185
 186         while (node->in_parent && node_is_left_child(node))
 187                 node = node->in_parent;
 188
 189         RETURN(node->in_parent);
 190 }
 191
 192 enum interval_iter interval_iterate(struct interval_node *root,
 193                                     interval_callback_t func,
 194                                     void *data)
 195 {
 196         struct interval_node *node;
 197         enum interval_iter rc = INTERVAL_ITER_CONT;
 198         ENTRY;
 199
 200         interval_for_each(node, root) {
 201                 rc = func(node, data);
 202                 if (rc == INTERVAL_ITER_STOP)
 203                         break;
 204         }
 205
 206         RETURN(rc);
 207 }
 208 EXPORT_SYMBOL(interval_iterate);
 209
 210 enum interval_iter interval_iterate_reverse(struct interval_node *root,
 211                                             interval_callback_t func,
 212                                             void *data)
 213 {
 214         struct interval_node *node;
 215         enum interval_iter rc = INTERVAL_ITER_CONT;
 216         ENTRY;
 217
 218         interval_for_each_reverse(node, root) {
 219                 rc = func(node, data);
 220                 if (rc == INTERVAL_ITER_STOP)
 221                         break;
 222         }
 223
 224         RETURN(rc);
 225 }
 226 EXPORT_SYMBOL(interval_iterate_reverse);
 227
 228 /* try to find a node with same interval in the tree,
 229  * if found, return the pointer to the node, otherwise return NULL*/
 230 struct interval_node *interval_find(struct interval_node *root,
 231                                     struct interval_node_extent *ex)
 232 {
 233         struct interval_node *walk = root;
 234         int rc;
 235         ENTRY;
 236
 237         while (walk) {
 238                 rc = extent_compare(ex, &walk->in_extent);
 239                 if (rc == 0)
 240                         break;
 241                 else if (rc < 0)
 242                         walk = walk->in_left;
 243                 else
 244                         walk = walk->in_right;
 245         }
 246
 247         RETURN(walk);
 248 }
 249 EXPORT_SYMBOL(interval_find);
 250
 251 static void __rotate_change_maxhigh(struct interval_node *node,
 252                                     struct interval_node *rotate)
 253 {
 254         __u64 left_max, right_max;
 255
 256         rotate->in_max_high = node->in_max_high;
 257         left_max = node->in_left ? node->in_left->in_max_high : 0;
 258         right_max = node->in_right ? node->in_right->in_max_high : 0;
 259         node->in_max_high  = max_u64(interval_high(node),
 260                                      max_u64(left_max,right_max));
 261 }
 262
 263 /* The left rotation "pivots" around the link from node to node->right, and
 264  * - node will be linked to node->right's left child, and
 265  * - node->right's left child will be linked to node's right child.  */
 266 static void __rotate_left(struct interval_node *node,
 267                           struct interval_node **root)
 268 {
 269         struct interval_node *right = node->in_right;
 270         struct interval_node *parent = node->in_parent;
 271
 272         node->in_right = right->in_left;
 273         if (node->in_right)
 274                 right->in_left->in_parent = node;
 275
 276         right->in_left = node;
 277         right->in_parent = parent;
 278         if (parent) {
 279                 if (node_is_left_child(node))
 280                         parent->in_left = right;
 281                 else
 282                         parent->in_right = right;
 283         } else {
 284                 *root = right;
 285         }
 286         node->in_parent = right;
 287
 288         /* update max_high for node and right */
 289         __rotate_change_maxhigh(node, right);
 290 }
 291
 292 /* The right rotation "pivots" around the link from node to node->left, and
 293  * - node will be linked to node->left's right child, and
 294  * - node->left's right child will be linked to node's left child.  */
 295 static void __rotate_right(struct interval_node *node,
 296                            struct interval_node **root)
 297 {
 298         struct interval_node *left = node->in_left;
 299         struct interval_node *parent = node->in_parent;
 300
 301         node->in_left = left->in_right;
 302         if (node->in_left)
 303                 left->in_right->in_parent = node;
 304         left->in_right = node;
 305
 306         left->in_parent = parent;
 307         if (parent) {
 308                 if (node_is_right_child(node))
 309                         parent->in_right = left;
 310                 else
 311                         parent->in_left = left;
 312         } else {
 313                 *root = left;
 314         }
 315         node->in_parent = left;
 316
 317         /* update max_high for node and left */
 318         __rotate_change_maxhigh(node, left);
 319 }
 320
 321 #define interval_swap(a, b) do {                        \
 322         struct interval_node *c = a; a = b; b = c;      \
 323 } while (0)
 324
 325 /*
 326  * Operations INSERT and DELETE, when run on a tree with n keys,
 327  * take O(logN) time.Because they modify the tree, the result
 328  * may violate the red-black properties.To restore these properties,
 329  * we must change the colors of some of the nodes in the tree
 330  * and also change the pointer structure.
 331  */
 332 static void interval_insert_color(struct interval_node *node,
 333                                   struct interval_node **root)
 334 {
 335         struct interval_node *parent, *gparent;
 336         ENTRY;
 337
 338         while ((parent = node->in_parent) && node_is_red(parent)) {
 339                 gparent = parent->in_parent;
 340                 /* Parent is RED, so gparent must not be NULL */
 341                 if (node_is_left_child(parent)) {
 342                         struct interval_node *uncle;
 343                         uncle = gparent->in_right;
 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 (parent->in_right == node) {
 353                                 __rotate_left(parent, root);
 354                                 interval_swap(node, parent);
 355                         }
 356
 357                         parent->in_color = INTERVAL_BLACK;
 358                         gparent->in_color = INTERVAL_RED;
 359                         __rotate_right(gparent, root);
 360                 } else {
 361                         struct interval_node *uncle;
 362                         uncle = gparent->in_left;
 363                         if (uncle && node_is_red(uncle)) {
 364                                 uncle->in_color = INTERVAL_BLACK;
 365                                 parent->in_color = INTERVAL_BLACK;
 366                                 gparent->in_color = INTERVAL_RED;
 367                                 node = gparent;
 368                                 continue;
 369                         }
 370
 371                         if (node_is_left_child(node)) {
 372                                 __rotate_right(parent, root);
 373                                 interval_swap(node, parent);
 374                         }
 375
 376                         parent->in_color = INTERVAL_BLACK;
 377                         gparent->in_color = INTERVAL_RED;
 378                         __rotate_left(gparent, root);
 379                 }
 380         }
 381
 382         (*root)->in_color = INTERVAL_BLACK;
 383         EXIT;
 384 }
 385
 386 struct interval_node *interval_insert(struct interval_node *node,
 387                                       struct interval_node **root)
 388
 389 {
 390         struct interval_node **p, *parent = NULL;
 391         ENTRY;
 392
 393         LASSERT(!interval_is_intree(node));
 394         p = root;
 395         while (*p) {
 396                 parent = *p;
 397                 if (node_equal(parent, node))
 398                         RETURN(parent);
 399
 400                 /* max_high field must be updated after each iteration */
 401                 if (parent->in_max_high < interval_high(node))
 402                         parent->in_max_high = interval_high(node);
 403
 404                 if (node_compare(node, parent) < 0)
 405                         p = &parent->in_left;
 406                 else
 407                         p = &parent->in_right;
 408         }
 409
 410         /* link node into the tree */
 411         node->in_parent = parent;
 412         node->in_color = INTERVAL_RED;
 413         node->in_left = node->in_right = NULL;
 414         *p = node;
 415
 416         interval_insert_color(node, root);
 417         node->in_intree = 1;
 418
 419         RETURN(NULL);
 420 }
 421 EXPORT_SYMBOL(interval_insert);
 422
 423 static inline int node_is_black_or_0(struct interval_node *node)
 424 {
 425         return !node || node_is_black(node);
 426 }
 427
 428 static void interval_erase_color(struct interval_node *node,
 429                                  struct interval_node *parent,
 430                                  struct interval_node **root)
 431 {
 432         struct interval_node *tmp;
 433         ENTRY;
 434
 435         while (node_is_black_or_0(node) && node != *root) {
 436                 if (parent->in_left == node) {
 437                         tmp = parent->in_right;
 438                         if (node_is_red(tmp)) {
 439                                 tmp->in_color = INTERVAL_BLACK;
 440                                 parent->in_color = INTERVAL_RED;
 441                                 __rotate_left(parent, root);
 442                                 tmp = parent->in_right;
 443                         }
 444                         if (node_is_black_or_0(tmp->in_left) &&
 445                             node_is_black_or_0(tmp->in_right)) {
 446                                 tmp->in_color = INTERVAL_RED;
 447                                 node = parent;
 448                                 parent = node->in_parent;
 449                         } else {
 450                                 if (node_is_black_or_0(tmp->in_right)) {
 451                                         struct interval_node *o_left;
 452                                         if ((o_left = tmp->in_left))
 453                                              o_left->in_color = INTERVAL_BLACK;
 454                                         tmp->in_color = INTERVAL_RED;
 455                                         __rotate_right(tmp, root);
 456                                         tmp = parent->in_right;
 457                                 }
 458                                 tmp->in_color = parent->in_color;
 459                                 parent->in_color = INTERVAL_BLACK;
 460                                 if (tmp->in_right)
 461                                     tmp->in_right->in_color = INTERVAL_BLACK;
 462                                 __rotate_left(parent, root);
 463                                 node = *root;
 464                                 break;
 465                         }
 466                 } else {
 467                         tmp = parent->in_left;
 468                         if (node_is_red(tmp)) {
 469                                 tmp->in_color = INTERVAL_BLACK;
 470                                 parent->in_color = INTERVAL_RED;
 471                                 __rotate_right(parent, root);
 472                                 tmp = parent->in_left;
 473                         }
 474                         if (node_is_black_or_0(tmp->in_left) &&
 475                             node_is_black_or_0(tmp->in_right)) {
 476                                 tmp->in_color = INTERVAL_RED;
 477                                 node = parent;
 478                                 parent = node->in_parent;
 479                         } else {
 480                                 if (node_is_black_or_0(tmp->in_left)) {
 481                                         struct interval_node *o_right;
 482                                         if ((o_right = tmp->in_right))
 483                                             o_right->in_color = INTERVAL_BLACK;
 484                                         tmp->in_color = INTERVAL_RED;
 485                                         __rotate_left(tmp, root);
 486                                         tmp = parent->in_left;
 487                                 }
 488                                 tmp->in_color = parent->in_color;
 489                                 parent->in_color = INTERVAL_BLACK;
 490                                 if (tmp->in_left)
 491                                         tmp->in_left->in_color = INTERVAL_BLACK;
 492                                 __rotate_right(parent, root);
 493                                 node = *root;
 494                                 break;
 495                         }
 496                 }
 497         }
 498         if (node)
 499                 node->in_color = INTERVAL_BLACK;
 500         EXIT;
 501 }
 502
 503 /*
 504  * if the @max_high value of @node is changed, this function traverse  a path
 505  * from node  up to the root to update max_high for the whole tree.
 506  */
 507 static void update_maxhigh(struct interval_node *node,
 508                            __u64  old_maxhigh)
 509 {
 510         __u64 left_max, right_max;
 511         ENTRY;
 512
 513         while (node) {
 514                 left_max = node->in_left ? node->in_left->in_max_high : 0;
 515                 right_max = node->in_right ? node->in_right->in_max_high : 0;
 516                 node->in_max_high = max_u64(interval_high(node),
 517                                             max_u64(left_max, right_max));
 518
 519                 if (node->in_max_high >= old_maxhigh)
 520                         break;
 521                 node = node->in_parent;
 522         }
 523         EXIT;
 524 }
 525
 526 void interval_erase(struct interval_node *node,
 527                     struct interval_node **root)
 528 {
 529         struct interval_node *child, *parent;
 530         int color;
 531         ENTRY;
 532
 533         LASSERT(interval_is_intree(node));
 534         node->in_intree = 0;
 535         if (!node->in_left) {
 536                 child = node->in_right;
 537         } else if (!node->in_right) {
 538                 child = node->in_left;
 539         } else { /* Both left and right child are not NULL */
 540                 struct interval_node *old = node;
 541
 542                 node = interval_next(node);
 543                 child = node->in_right;
 544                 parent = node->in_parent;
 545                 color = node->in_color;
 546
 547                 if (child)
 548                         child->in_parent = parent;
 549                 if (parent == old) {
 550                         parent->in_right = child;
 551                         parent = node;
 552                 } else {
 553                         parent->in_left = child;
 554                 }
 555
 556                 node->in_color = old->in_color;
 557                 node->in_right = old->in_right;
 558                 node->in_left = old->in_left;
 559                 node->in_parent = old->in_parent;
 560
 561                 if (old->in_parent) {
 562                         if (node_is_left_child(old))
 563                                 old->in_parent->in_left = node;
 564                         else
 565                                 old->in_parent->in_right = node;
 566                 } else {
 567                         *root = node;
 568                 }
 569
 570                 old->in_left->in_parent = node;
 571                 if (old->in_right)
 572                         old->in_right->in_parent = node;
 573                 update_maxhigh(child, node->in_max_high);
 574                 update_maxhigh(node, old->in_max_high);
 575                 goto color;
 576         }
 577         parent = node->in_parent;
 578         color = node->in_color;
 579
 580         if (child)
 581                 child->in_parent = parent;
 582         if (parent) {
 583                 if (node_is_left_child(node))
 584                         parent->in_left = child;
 585                 else
 586                         parent->in_right = child;
 587         } else {
 588                 *root = child;
 589         }
 590
 591         update_maxhigh(child, node->in_max_high);
 592
 593 color:
 594         if (color == INTERVAL_BLACK)
 595                 interval_erase_color(child, parent, root);
 596         EXIT;
 597 }
 598 EXPORT_SYMBOL(interval_erase);
 599
 600 static inline int interval_may_overlap(struct interval_node *node,
 601                                           struct interval_node_extent *ext)
 602 {
 603         return (ext->start <= node->in_max_high &&
 604                 ext->end >= interval_low(node));
 605 }
 606
 607 /*
 608  * This function finds all intervals that overlap interval ext,
 609  * and calls func to handle resulted intervals one by one.
 610  * in lustre, this function will find all conflicting locks in
 611  * the granted queue and add these locks to the ast work list.
 612  *
 613  * {
 614  *       if (node == NULL)
 615  *               return 0;
 616  *       if (ext->end < interval_low(node)) {
 617  *               interval_search(node->in_left, ext, func, data);
 618  *       } else if (interval_may_overlap(node, ext)) {
 619  *               if (extent_overlapped(ext, &node->in_extent))
 620  *                       func(node, data);
 621  *               interval_search(node->in_left, ext, func, data);
 622  *               interval_search(node->in_right, ext, func, data);
 623  *       }
 624  *       return 0;
 625  * }
 626  *
 627  */
 628 enum interval_iter interval_search(struct interval_node *node,
 629                                    struct interval_node_extent *ext,
 630                                    interval_callback_t func,
 631                                    void *data)
 632 {
 633         struct interval_node *parent;
 634         enum interval_iter rc = INTERVAL_ITER_CONT;
 635
 636         LASSERT(ext != NULL);
 637         LASSERT(func != NULL);
 638
 639         while (node) {
 640                 if (ext->end < interval_low(node)) {
 641                         if (node->in_left) {
 642                                 node = node->in_left;
 643                                 continue;
 644                         }
 645                 } else if (interval_may_overlap(node, ext)) {
 646                         if (extent_overlapped(ext, &node->in_extent)) {
 647                                 rc = func(node, data);
 648                                 if (rc == INTERVAL_ITER_STOP)
 649                                         break;
 650                         }
 651
 652                         if (node->in_left) {
 653                                 node = node->in_left;
 654                                 continue;
 655                         }
 656                         if (node->in_right) {
 657                                 node = node->in_right;
 658                                 continue;
 659                         }
 660                 }
 661
 662                 parent = node->in_parent;
 663                 while (parent) {
 664                         if (node_is_left_child(node) &&
 665                             parent->in_right) {
 666                                 /* If we ever got the left, it means that the
 667                                  * parent met ext->end<interval_low(parent), or
 668                                  * may_overlap(parent). If the former is true,
 669                                  * we needn't go back. So stop early and check
 670                                  * may_overlap(parent) after this loop.  */
 671                                 node = parent->in_right;
 672                                 break;
 673                         }
 674                         node = parent;
 675                         parent = parent->in_parent;
 676                 }
 677                 if (parent == NULL || !interval_may_overlap(parent, ext))
 678                         break;
 679         }
 680
 681         return rc;
 682 }
 683 EXPORT_SYMBOL(interval_search);
 684
 685 static enum interval_iter interval_overlap_cb(struct interval_node *n,
 686                                               void *args)
 687 {
 688         *(int *)args = 1;
 689         return INTERVAL_ITER_STOP;
 690 }
 691
 692 int interval_is_overlapped(struct interval_node *root,
 693                            struct interval_node_extent *ext)
 694 {
 695         int has = 0;
 696         (void)interval_search(root, ext, interval_overlap_cb, &has);
 697         return has;
 698 }
 699 EXPORT_SYMBOL(interval_is_overlapped);
 700
 701 /* Don't expand to low. Expanding downwards is expensive, and meaningless to
 702  * some extents, because programs seldom do IO backward.
 703  *
 704  * The recursive algorithm of expanding low:
 705  * expand_low {
 706  *        struct interval_node *tmp;
 707  *        static __u64 res = 0;
 708  *
 709  *        if (root == NULL)
 710  *                return res;
 711  *        if (root->in_max_high < low) {
 712  *                res = max_u64(root->in_max_high + 1, res);
 713  *                return res;
 714  *        } else if (low < interval_low(root)) {
 715  *                interval_expand_low(root->in_left, low);
 716  *                return res;
 717  *        }
 718  *
 719  *        if (interval_high(root) < low)
 720  *                res = max_u64(interval_high(root) + 1, res);
 721  *        interval_expand_low(root->in_left, low);
 722  *        interval_expand_low(root->in_right, low);
 723  *
 724  *        return res;
 725  * }
 726  *
 727  * It's much easy to eliminate the recursion, see interval_search for
 728  * an example. -jay
 729  */
 730 static inline __u64 interval_expand_low(struct interval_node *root, __u64 low)
 731 {
 732         /* we only concern the empty tree right now. */
 733         if (root == NULL)
 734                 return 0;
 735         return low;
 736 }
 737
 738 static inline __u64 interval_expand_high(struct interval_node *node, __u64 high)
 739 {
 740         __u64 result = ~0;
 741
 742         while (node != NULL) {
 743                 if (node->in_max_high < high)
 744                         break;
 745
 746                 if (interval_low(node) > high) {
 747                         result = interval_low(node) - 1;
 748                         node = node->in_left;
 749                 } else {
 750                         node = node->in_right;
 751                 }
 752         }
 753
 754         return result;
 755 }
 756
 757 /* expanding the extent based on @ext. */
 758 void interval_expand(struct interval_node *root,
 759                      struct interval_node_extent *ext,
 760                      struct interval_node_extent *limiter)
 761 {
 762         /* The assertion of interval_is_overlapped is expensive because we may
 763          * travel many nodes to find the overlapped node. */
 764         LASSERT(interval_is_overlapped(root, ext) == 0);
 765         if (!limiter || limiter->start < ext->start)
 766                 ext->start = interval_expand_low(root, ext->start);
 767         if (!limiter || limiter->end > ext->end)
 768                 ext->end = interval_expand_high(root, ext->end);
 769         LASSERT(interval_is_overlapped(root, ext) == 0);
 770 }
 771 EXPORT_SYMBOL(interval_expand);