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
  17 #include "../compiler/compiler.h"
  18 #include "prio_tree.h"
  19
  20 #define ARRAY_SIZE(x)    (sizeof((x)) / (sizeof((x)[0])))
  21
  22 /*
  23  * A clever mix of heap and radix trees forms a radix priority search tree (PST)
  24  * which is useful for storing intervals, e.g, we can consider a vma as a closed
  25  * interval of file pages [offset_begin, offset_end], and store all vmas that
  26  * map a file in a PST. Then, using the PST, we can answer a stabbing query,
  27  * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
  28  * given input interval X (a set of consecutive file pages), in "O(log n + m)"
  29  * time where 'log n' is the height of the PST, and 'm' is the number of stored
  30  * intervals (vmas) that overlap (map) with the input interval X (the set of
  31  * consecutive file pages).
  32  *
  33  * In our implementation, we store closed intervals of the form [radix_index,
  34  * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
  35  * is designed for storing intervals with unique radix indices, i.e., each
  36  * interval have different radix_index. However, this limitation can be easily
  37  * overcome by using the size, i.e., heap_index - radix_index, as part of the
  38  * index, so we index the tree using [(radix_index,size), heap_index].
  39  *
  40  * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
  41  * machine, the maximum height of a PST can be 64. We can use a balanced version
  42  * of the priority search tree to optimize the tree height, but the balanced
  43  * tree proposed by McCreight is too complex and memory-hungry for our purpose.
  44  */
  45
  46 static void get_index(const struct prio_tree_node *node,
  47                       unsigned long *radix, unsigned long *heap)
  48 {
  49         *radix = node->start;
  50         *heap = node->last;
  51 }
  52
  53 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  54
  55 static void fio_init prio_tree_init(void)
  56 {
  57         unsigned int i;
  58
  59         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  60                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  61         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  62 }
  63
  64 /*
  65  * Maximum heap_index that can be stored in a PST with index_bits bits
  66  */
  67 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  68 {
  69         return index_bits_to_maxindex[bits - 1];
  70 }
  71
  72 /*
  73  * Extend a priority search tree so that it can store a node with heap_index
  74  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
  75  * However, this function is used rarely and the common case performance is
  76  * not bad.
  77  */
  78 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
  79                 struct prio_tree_node *node, unsigned long max_heap_index)
  80 {
  81         struct prio_tree_node *first = NULL, *prev, *last = NULL;
  82
  83         if (max_heap_index > prio_tree_maxindex(root->index_bits))
  84                 root->index_bits++;
  85
  86         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
  87                 root->index_bits++;
  88
  89                 if (prio_tree_empty(root))
  90                         continue;
  91
  92                 if (first == NULL) {
  93                         first = root->prio_tree_node;
  94                         prio_tree_remove(root, root->prio_tree_node);
  95                         INIT_PRIO_TREE_NODE(first);
  96                         last = first;
  97                 } else {
  98                         prev = last;
  99                         last = root->prio_tree_node;
 100                         prio_tree_remove(root, root->prio_tree_node);
 101                         INIT_PRIO_TREE_NODE(last);
 102                         prev->left = last;
 103                         last->parent = prev;
 104                 }
 105         }
 106
 107         INIT_PRIO_TREE_NODE(node);
 108
 109         if (first) {
 110                 node->left = first;
 111                 first->parent = node;
 112         } else
 113                 last = node;
 114
 115         if (!prio_tree_empty(root)) {
 116                 last->left = root->prio_tree_node;
 117                 last->left->parent = last;
 118         }
 119
 120         root->prio_tree_node = node;
 121         return node;
 122 }
 123
 124 /*
 125  * Replace a prio_tree_node with a new node and return the old node
 126  */
 127 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 128                 struct prio_tree_node *old, struct prio_tree_node *node)
 129 {
 130         INIT_PRIO_TREE_NODE(node);
 131
 132         if (prio_tree_root(old)) {
 133                 assert(root->prio_tree_node == old);
 134                 /*
 135                  * We can reduce root->index_bits here. However, it is complex
 136                  * and does not help much to improve performance (IMO).
 137                  */
 138                 node->parent = node;
 139                 root->prio_tree_node = node;
 140         } else {
 141                 node->parent = old->parent;
 142                 if (old->parent->left == old)
 143                         old->parent->left = node;
 144                 else
 145                         old->parent->right = node;
 146         }
 147
 148         if (!prio_tree_left_empty(old)) {
 149                 node->left = old->left;
 150                 old->left->parent = node;
 151         }
 152
 153         if (!prio_tree_right_empty(old)) {
 154                 node->right = old->right;
 155                 old->right->parent = node;
 156         }
 157
 158         return old;
 159 }
 160
 161 /*
 162  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 163  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 164  * required to represent the maximum heap_index. In the worst case, the algo
 165  * can take O((log n)^2) - check prio_tree_expand.
 166  *
 167  * If a prior node with same radix_index and heap_index is already found in
 168  * the tree, then returns the address of the prior node. Otherwise, inserts
 169  * @node into the tree and returns @node.
 170  */
 171 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 172                 struct prio_tree_node *node)
 173 {
 174         struct prio_tree_node *cur, *res = node;
 175         unsigned long radix_index, heap_index;
 176         unsigned long r_index, h_index, index, mask;
 177         int size_flag = 0;
 178
 179         get_index(node, &radix_index, &heap_index);
 180
 181         if (prio_tree_empty(root) ||
 182                         heap_index > prio_tree_maxindex(root->index_bits))
 183                 return prio_tree_expand(root, node, heap_index);
 184
 185         cur = root->prio_tree_node;
 186         mask = 1UL << (root->index_bits - 1);
 187
 188         while (mask) {
 189                 get_index(cur, &r_index, &h_index);
 190
 191                 if (r_index == radix_index && h_index == heap_index)
 192                         return cur;
 193
 194                 if (h_index < heap_index ||
 195                     (h_index == heap_index && r_index > radix_index)) {
 196                         struct prio_tree_node *tmp = node;
 197                         node = prio_tree_replace(root, cur, node);
 198                         cur = tmp;
 199                         /* swap indices */
 200                         index = r_index;
 201                         r_index = radix_index;
 202                         radix_index = index;
 203                         index = h_index;
 204                         h_index = heap_index;
 205                         heap_index = index;
 206                 }
 207
 208                 if (size_flag)
 209                         index = heap_index - radix_index;
 210                 else
 211                         index = radix_index;
 212
 213                 if (index & mask) {
 214                         if (prio_tree_right_empty(cur)) {
 215                                 INIT_PRIO_TREE_NODE(node);
 216                                 cur->right = node;
 217                                 node->parent = cur;
 218                                 return res;
 219                         } else
 220                                 cur = cur->right;
 221                 } else {
 222                         if (prio_tree_left_empty(cur)) {
 223                                 INIT_PRIO_TREE_NODE(node);
 224                                 cur->left = node;
 225                                 node->parent = cur;
 226                                 return res;
 227                         } else
 228                                 cur = cur->left;
 229                 }
 230
 231                 mask >>= 1;
 232
 233                 if (!mask) {
 234                         mask = 1UL << (BITS_PER_LONG - 1);
 235                         size_flag = 1;
 236                 }
 237         }
 238         /* Should not reach here */
 239         assert(0);
 240         return NULL;
 241 }
 242
 243 /*
 244  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 245  * algorithm takes O(log n) time where 'log n' is the number of bits required
 246  * to represent the maximum heap_index.
 247  */
 248 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 249 {
 250         struct prio_tree_node *cur;
 251         unsigned long r_index, h_index_right, h_index_left;
 252
 253         cur = node;
 254
 255         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 256                 if (!prio_tree_left_empty(cur))
 257                         get_index(cur->left, &r_index, &h_index_left);
 258                 else {
 259                         cur = cur->right;
 260                         continue;
 261                 }
 262
 263                 if (!prio_tree_right_empty(cur))
 264                         get_index(cur->right, &r_index, &h_index_right);
 265                 else {
 266                         cur = cur->left;
 267                         continue;
 268                 }
 269
 270                 /* both h_index_left and h_index_right cannot be 0 */
 271                 if (h_index_left >= h_index_right)
 272                         cur = cur->left;
 273                 else
 274                         cur = cur->right;
 275         }
 276
 277         if (prio_tree_root(cur)) {
 278                 assert(root->prio_tree_node == cur);
 279                 INIT_PRIO_TREE_ROOT(root);
 280                 return;
 281         }
 282
 283         if (cur->parent->right == cur)
 284                 cur->parent->right = cur->parent;
 285         else
 286                 cur->parent->left = cur->parent;
 287
 288         while (cur != node)
 289                 cur = prio_tree_replace(root, cur->parent, cur);
 290 }
 291
 292 /*
 293  * Following functions help to enumerate all prio_tree_nodes in the tree that
 294  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 295  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 296  * proportional to # of bits required to represent the maximum heap_index) and
 297  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 298  */
 299
 300 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 301                 unsigned long *r_index, unsigned long *h_index)
 302 {
 303         if (prio_tree_left_empty(iter->cur))
 304                 return NULL;
 305
 306         get_index(iter->cur->left, r_index, h_index);
 307
 308         if (iter->r_index <= *h_index) {
 309                 iter->cur = iter->cur->left;
 310                 iter->mask >>= 1;
 311                 if (iter->mask) {
 312                         if (iter->size_level)
 313                                 iter->size_level++;
 314                 } else {
 315                         if (iter->size_level) {
 316                                 assert(prio_tree_left_empty(iter->cur));
 317                                 assert(prio_tree_right_empty(iter->cur));
 318                                 iter->size_level++;
 319                                 iter->mask = ULONG_MAX;
 320                         } else {
 321                                 iter->size_level = 1;
 322                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 323                         }
 324                 }
 325                 return iter->cur;
 326         }
 327
 328         return NULL;
 329 }
 330
 331 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 332                 unsigned long *r_index, unsigned long *h_index)
 333 {
 334         unsigned long value;
 335
 336         if (prio_tree_right_empty(iter->cur))
 337                 return NULL;
 338
 339         if (iter->size_level)
 340                 value = iter->value;
 341         else
 342                 value = iter->value | iter->mask;
 343
 344         if (iter->h_index < value)
 345                 return NULL;
 346
 347         get_index(iter->cur->right, r_index, h_index);
 348
 349         if (iter->r_index <= *h_index) {
 350                 iter->cur = iter->cur->right;
 351                 iter->mask >>= 1;
 352                 iter->value = value;
 353                 if (iter->mask) {
 354                         if (iter->size_level)
 355                                 iter->size_level++;
 356                 } else {
 357                         if (iter->size_level) {
 358                                 assert(prio_tree_left_empty(iter->cur));
 359                                 assert(prio_tree_right_empty(iter->cur));
 360                                 iter->size_level++;
 361                                 iter->mask = ULONG_MAX;
 362                         } else {
 363                                 iter->size_level = 1;
 364                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 365                         }
 366                 }
 367                 return iter->cur;
 368         }
 369
 370         return NULL;
 371 }
 372
 373 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 374 {
 375         iter->cur = iter->cur->parent;
 376         if (iter->mask == ULONG_MAX)
 377                 iter->mask = 1UL;
 378         else if (iter->size_level == 1)
 379                 iter->mask = 1UL;
 380         else
 381                 iter->mask <<= 1;
 382         if (iter->size_level)
 383                 iter->size_level--;
 384         if (!iter->size_level && (iter->value & iter->mask))
 385                 iter->value ^= iter->mask;
 386         return iter->cur;
 387 }
 388
 389 static inline int overlap(struct prio_tree_iter *iter,
 390                 unsigned long r_index, unsigned long h_index)
 391 {
 392         return iter->h_index >= r_index && iter->r_index <= h_index;
 393 }
 394
 395 /*
 396  * prio_tree_first:
 397  *
 398  * Get the first prio_tree_node that overlaps with the interval [radix_index,
 399  * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 400  * traversal of the tree.
 401  */
 402 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 403 {
 404         struct prio_tree_root *root;
 405         unsigned long r_index, h_index;
 406
 407         INIT_PRIO_TREE_ITER(iter);
 408
 409         root = iter->root;
 410         if (prio_tree_empty(root))
 411                 return NULL;
 412
 413         get_index(root->prio_tree_node, &r_index, &h_index);
 414
 415         if (iter->r_index > h_index)
 416                 return NULL;
 417
 418         iter->mask = 1UL << (root->index_bits - 1);
 419         iter->cur = root->prio_tree_node;
 420
 421         while (1) {
 422                 if (overlap(iter, r_index, h_index))
 423                         return iter->cur;
 424
 425                 if (prio_tree_left(iter, &r_index, &h_index))
 426                         continue;
 427
 428                 if (prio_tree_right(iter, &r_index, &h_index))
 429                         continue;
 430
 431                 break;
 432         }
 433         return NULL;
 434 }
 435
 436 /*
 437  * prio_tree_next:
 438  *
 439  * Get the next prio_tree_node that overlaps with the input interval in iter
 440  */
 441 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 442 {
 443         unsigned long r_index, h_index;
 444
 445         if (iter->cur == NULL)
 446                 return prio_tree_first(iter);
 447
 448 repeat:
 449         while (prio_tree_left(iter, &r_index, &h_index))
 450                 if (overlap(iter, r_index, h_index))
 451                         return iter->cur;
 452
 453         while (!prio_tree_right(iter, &r_index, &h_index)) {
 454                 while (!prio_tree_root(iter->cur) &&
 455                                 iter->cur->parent->right == iter->cur)
 456                         prio_tree_parent(iter);
 457
 458                 if (prio_tree_root(iter->cur))
 459                         return NULL;
 460
 461                 prio_tree_parent(iter);
 462         }
 463
 464         if (overlap(iter, r_index, h_index))
 465                 return iter->cur;
 466
 467         goto repeat;
 468 }