lib/prio_tree.c

   1 /*
   2  * lib/prio_tree.c - priority search tree
   3  *
   4  * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
   5  *
   6  * This file is released under the GPL v2.
   7  *
   8  * Based on the radix priority search tree proposed by Edward M. McCreight
   9  * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
  10  *
  11  * 02Feb2004    Initial version
  12  */
  13
  14 #include <stdlib.h>
  15 #include <limits.h>
  16 #include "../fio.h"
  17 #include "prio_tree.h"
  18
  19 /*
  20  * A clever mix of heap and radix trees forms a radix priority search tree (PST)
  21  * which is useful for storing intervals, e.g, we can consider a vma as a closed
  22  * interval of file pages [offset_begin, offset_end], and store all vmas that
  23  * map a file in a PST. Then, using the PST, we can answer a stabbing query,
  24  * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
  25  * given input interval X (a set of consecutive file pages), in "O(log n + m)"
  26  * time where 'log n' is the height of the PST, and 'm' is the number of stored
  27  * intervals (vmas) that overlap (map) with the input interval X (the set of
  28  * consecutive file pages).
  29  *
  30  * In our implementation, we store closed intervals of the form [radix_index,
  31  * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
  32  * is designed for storing intervals with unique radix indices, i.e., each
  33  * interval have different radix_index. However, this limitation can be easily
  34  * overcome by using the size, i.e., heap_index - radix_index, as part of the
  35  * index, so we index the tree using [(radix_index,size), heap_index].
  36  *
  37  * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
  38  * machine, the maximum height of a PST can be 64. We can use a balanced version
  39  * of the priority search tree to optimize the tree height, but the balanced
  40  * tree proposed by McCreight is too complex and memory-hungry for our purpose.
  41  */
  42
  43 static void get_index(const struct prio_tree_node *node,
  44                       unsigned long *radix, unsigned long *heap)
  45 {
  46         *radix = node->start;
  47         *heap = node->last;
  48 }
  49
  50 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  51
  52 static void fio_init prio_tree_init(void)
  53 {
  54         unsigned int i;
  55
  56         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  57                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  58         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  59 }
  60
  61 /*
  62  * Maximum heap_index that can be stored in a PST with index_bits bits
  63  */
  64 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  65 {
  66         return index_bits_to_maxindex[bits - 1];
  67 }
  68
  69 /*
  70  * Extend a priority search tree so that it can store a node with heap_index
  71  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
  72  * However, this function is used rarely and the common case performance is
  73  * not bad.
  74  */
  75 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
  76                 struct prio_tree_node *node, unsigned long max_heap_index)
  77 {
  78         struct prio_tree_node *first = NULL, *prev, *last = NULL;
  79
  80         if (max_heap_index > prio_tree_maxindex(root->index_bits))
  81                 root->index_bits++;
  82
  83         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
  84                 root->index_bits++;
  85
  86                 if (prio_tree_empty(root))
  87                         continue;
  88
  89                 if (first == NULL) {
  90                         first = root->prio_tree_node;
  91                         prio_tree_remove(root, root->prio_tree_node);
  92                         INIT_PRIO_TREE_NODE(first);
  93                         last = first;
  94                 } else {
  95                         prev = last;
  96                         last = root->prio_tree_node;
  97                         prio_tree_remove(root, root->prio_tree_node);
  98                         INIT_PRIO_TREE_NODE(last);
  99                         prev->left = last;
 100                         last->parent = prev;
 101                 }
 102         }
 103
 104         INIT_PRIO_TREE_NODE(node);
 105
 106         if (first) {
 107                 node->left = first;
 108                 first->parent = node;
 109         } else
 110                 last = node;
 111
 112         if (!prio_tree_empty(root)) {
 113                 last->left = root->prio_tree_node;
 114                 last->left->parent = last;
 115         }
 116
 117         root->prio_tree_node = node;
 118         return node;
 119 }
 120
 121 /*
 122  * Replace a prio_tree_node with a new node and return the old node
 123  */
 124 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 125                 struct prio_tree_node *old, struct prio_tree_node *node)
 126 {
 127         INIT_PRIO_TREE_NODE(node);
 128
 129         if (prio_tree_root(old)) {
 130                 assert(root->prio_tree_node == old);
 131                 /*
 132                  * We can reduce root->index_bits here. However, it is complex
 133                  * and does not help much to improve performance (IMO).
 134                  */
 135                 node->parent = node;
 136                 root->prio_tree_node = node;
 137         } else {
 138                 node->parent = old->parent;
 139                 if (old->parent->left == old)
 140                         old->parent->left = node;
 141                 else
 142                         old->parent->right = node;
 143         }
 144
 145         if (!prio_tree_left_empty(old)) {
 146                 node->left = old->left;
 147                 old->left->parent = node;
 148         }
 149
 150         if (!prio_tree_right_empty(old)) {
 151                 node->right = old->right;
 152                 old->right->parent = node;
 153         }
 154
 155         return old;
 156 }
 157
 158 /*
 159  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 160  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 161  * required to represent the maximum heap_index. In the worst case, the algo
 162  * can take O((log n)^2) - check prio_tree_expand.
 163  *
 164  * If a prior node with same radix_index and heap_index is already found in
 165  * the tree, then returns the address of the prior node. Otherwise, inserts
 166  * @node into the tree and returns @node.
 167  */
 168 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 169                 struct prio_tree_node *node)
 170 {
 171         struct prio_tree_node *cur, *res = node;
 172         unsigned long radix_index, heap_index;
 173         unsigned long r_index, h_index, index, mask;
 174         int size_flag = 0;
 175
 176         get_index(node, &radix_index, &heap_index);
 177
 178         if (prio_tree_empty(root) ||
 179                         heap_index > prio_tree_maxindex(root->index_bits))
 180                 return prio_tree_expand(root, node, heap_index);
 181
 182         cur = root->prio_tree_node;
 183         mask = 1UL << (root->index_bits - 1);
 184
 185         while (mask) {
 186                 get_index(cur, &r_index, &h_index);
 187
 188                 if (r_index == radix_index && h_index == heap_index)
 189                         return cur;
 190
 191                 if (h_index < heap_index ||
 192                     (h_index == heap_index && r_index > radix_index)) {
 193                         struct prio_tree_node *tmp = node;
 194                         node = prio_tree_replace(root, cur, node);
 195                         cur = tmp;
 196                         /* swap indices */
 197                         index = r_index;
 198                         r_index = radix_index;
 199                         radix_index = index;
 200                         index = h_index;
 201                         h_index = heap_index;
 202                         heap_index = index;
 203                 }
 204
 205                 if (size_flag)
 206                         index = heap_index - radix_index;
 207                 else
 208                         index = radix_index;
 209
 210                 if (index & mask) {
 211                         if (prio_tree_right_empty(cur)) {
 212                                 INIT_PRIO_TREE_NODE(node);
 213                                 cur->right = node;
 214                                 node->parent = cur;
 215                                 return res;
 216                         } else
 217                                 cur = cur->right;
 218                 } else {
 219                         if (prio_tree_left_empty(cur)) {
 220                                 INIT_PRIO_TREE_NODE(node);
 221                                 cur->left = node;
 222                                 node->parent = cur;
 223                                 return res;
 224                         } else
 225                                 cur = cur->left;
 226                 }
 227
 228                 mask >>= 1;
 229
 230                 if (!mask) {
 231                         mask = 1UL << (BITS_PER_LONG - 1);
 232                         size_flag = 1;
 233                 }
 234         }
 235         /* Should not reach here */
 236         assert(0);
 237         return NULL;
 238 }
 239
 240 /*
 241  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 242  * algorithm takes O(log n) time where 'log n' is the number of bits required
 243  * to represent the maximum heap_index.
 244  */
 245 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 246 {
 247         struct prio_tree_node *cur;
 248         unsigned long r_index, h_index_right, h_index_left;
 249
 250         cur = node;
 251
 252         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 253                 if (!prio_tree_left_empty(cur))
 254                         get_index(cur->left, &r_index, &h_index_left);
 255                 else {
 256                         cur = cur->right;
 257                         continue;
 258                 }
 259
 260                 if (!prio_tree_right_empty(cur))
 261                         get_index(cur->right, &r_index, &h_index_right);
 262                 else {
 263                         cur = cur->left;
 264                         continue;
 265                 }
 266
 267                 /* both h_index_left and h_index_right cannot be 0 */
 268                 if (h_index_left >= h_index_right)
 269                         cur = cur->left;
 270                 else
 271                         cur = cur->right;
 272         }
 273
 274         if (prio_tree_root(cur)) {
 275                 assert(root->prio_tree_node == cur);
 276                 INIT_PRIO_TREE_ROOT(root);
 277                 return;
 278         }
 279
 280         if (cur->parent->right == cur)
 281                 cur->parent->right = cur->parent;
 282         else
 283                 cur->parent->left = cur->parent;
 284
 285         while (cur != node)
 286                 cur = prio_tree_replace(root, cur->parent, cur);
 287 }
 288
 289 /*
 290  * Following functions help to enumerate all prio_tree_nodes in the tree that
 291  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 292  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 293  * proportional to # of bits required to represent the maximum heap_index) and
 294  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 295  */
 296
 297 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 298                 unsigned long *r_index, unsigned long *h_index)
 299 {
 300         if (prio_tree_left_empty(iter->cur))
 301                 return NULL;
 302
 303         get_index(iter->cur->left, r_index, h_index);
 304
 305         if (iter->r_index <= *h_index) {
 306                 iter->cur = iter->cur->left;
 307                 iter->mask >>= 1;
 308                 if (iter->mask) {
 309                         if (iter->size_level)
 310                                 iter->size_level++;
 311                 } else {
 312                         if (iter->size_level) {
 313                                 assert(prio_tree_left_empty(iter->cur));
 314                                 assert(prio_tree_right_empty(iter->cur));
 315                                 iter->size_level++;
 316                                 iter->mask = ULONG_MAX;
 317                         } else {
 318                                 iter->size_level = 1;
 319                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 320                         }
 321                 }
 322                 return iter->cur;
 323         }
 324
 325         return NULL;
 326 }
 327
 328 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 329                 unsigned long *r_index, unsigned long *h_index)
 330 {
 331         unsigned long value;
 332
 333         if (prio_tree_right_empty(iter->cur))
 334                 return NULL;
 335
 336         if (iter->size_level)
 337                 value = iter->value;
 338         else
 339                 value = iter->value | iter->mask;
 340
 341         if (iter->h_index < value)
 342                 return NULL;
 343
 344         get_index(iter->cur->right, r_index, h_index);
 345
 346         if (iter->r_index <= *h_index) {
 347                 iter->cur = iter->cur->right;
 348                 iter->mask >>= 1;
 349                 iter->value = value;
 350                 if (iter->mask) {
 351                         if (iter->size_level)
 352                                 iter->size_level++;
 353                 } else {
 354                         if (iter->size_level) {
 355                                 assert(prio_tree_left_empty(iter->cur));
 356                                 assert(prio_tree_right_empty(iter->cur));
 357                                 iter->size_level++;
 358                                 iter->mask = ULONG_MAX;
 359                         } else {
 360                                 iter->size_level = 1;
 361                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 362                         }
 363                 }
 364                 return iter->cur;
 365         }
 366
 367         return NULL;
 368 }
 369
 370 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 371 {
 372         iter->cur = iter->cur->parent;
 373         if (iter->mask == ULONG_MAX)
 374                 iter->mask = 1UL;
 375         else if (iter->size_level == 1)
 376                 iter->mask = 1UL;
 377         else
 378                 iter->mask <<= 1;
 379         if (iter->size_level)
 380                 iter->size_level--;
 381         if (!iter->size_level && (iter->value & iter->mask))
 382                 iter->value ^= iter->mask;
 383         return iter->cur;
 384 }
 385
 386 static inline int overlap(struct prio_tree_iter *iter,
 387                 unsigned long r_index, unsigned long h_index)
 388 {
 389         return iter->h_index >= r_index && iter->r_index <= h_index;
 390 }
 391
 392 /*
 393  * prio_tree_first:
 394  *
 395  * Get the first prio_tree_node that overlaps with the interval [radix_index,
 396  * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 397  * traversal of the tree.
 398  */
 399 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 400 {
 401         struct prio_tree_root *root;
 402         unsigned long r_index, h_index;
 403
 404         INIT_PRIO_TREE_ITER(iter);
 405
 406         root = iter->root;
 407         if (prio_tree_empty(root))
 408                 return NULL;
 409
 410         get_index(root->prio_tree_node, &r_index, &h_index);
 411
 412         if (iter->r_index > h_index)
 413                 return NULL;
 414
 415         iter->mask = 1UL << (root->index_bits - 1);
 416         iter->cur = root->prio_tree_node;
 417
 418         while (1) {
 419                 if (overlap(iter, r_index, h_index))
 420                         return iter->cur;
 421
 422                 if (prio_tree_left(iter, &r_index, &h_index))
 423                         continue;
 424
 425                 if (prio_tree_right(iter, &r_index, &h_index))
 426                         continue;
 427
 428                 break;
 429         }
 430         return NULL;
 431 }
 432
 433 /*
 434  * prio_tree_next:
 435  *
 436  * Get the next prio_tree_node that overlaps with the input interval in iter
 437  */
 438 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 439 {
 440         unsigned long r_index, h_index;
 441
 442         if (iter->cur == NULL)
 443                 return prio_tree_first(iter);
 444
 445 repeat:
 446         while (prio_tree_left(iter, &r_index, &h_index))
 447                 if (overlap(iter, r_index, h_index))
 448                         return iter->cur;
 449
 450         while (!prio_tree_right(iter, &r_index, &h_index)) {
 451                 while (!prio_tree_root(iter->cur) &&
 452                                 iter->cur->parent->right == iter->cur)
 453                         prio_tree_parent(iter);
 454
 455                 if (prio_tree_root(iter->cur))
 456                         return NULL;
 457
 458                 prio_tree_parent(iter);
 459         }
 460
 461         if (overlap(iter, r_index, h_index))
 462                 return iter->cur;
 463
 464         goto repeat;
 465 }