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 <assert.h>
  15 #include <stdlib.h>
  16 #include <limits.h>
  17
  18 #include "../compiler/compiler.h"
  19 #include "prio_tree.h"
  20
  21 #define ARRAY_SIZE(x)    (sizeof((x)) / (sizeof((x)[0])))
  22
  23 /*
  24  * A clever mix of heap and radix trees forms a radix priority search tree (PST)
  25  * which is useful for storing intervals, e.g, we can consider a vma as a closed
  26  * interval of file pages [offset_begin, offset_end], and store all vmas that
  27  * map a file in a PST. Then, using the PST, we can answer a stabbing query,
  28  * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
  29  * given input interval X (a set of consecutive file pages), in "O(log n + m)"
  30  * time where 'log n' is the height of the PST, and 'm' is the number of stored
  31  * intervals (vmas) that overlap (map) with the input interval X (the set of
  32  * consecutive file pages).
  33  *
  34  * In our implementation, we store closed intervals of the form [radix_index,
  35  * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
  36  * is designed for storing intervals with unique radix indices, i.e., each
  37  * interval have different radix_index. However, this limitation can be easily
  38  * overcome by using the size, i.e., heap_index - radix_index, as part of the
  39  * index, so we index the tree using [(radix_index,size), heap_index].
  40  *
  41  * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
  42  * machine, the maximum height of a PST can be 64. We can use a balanced version
  43  * of the priority search tree to optimize the tree height, but the balanced
  44  * tree proposed by McCreight is too complex and memory-hungry for our purpose.
  45  */
  46
  47 static void get_index(const struct prio_tree_node *node,
  48                       unsigned long *radix, unsigned long *heap)
  49 {
  50         *radix = node->start;
  51         *heap = node->last;
  52 }
  53
  54 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  55
  56 static void fio_init prio_tree_init(void)
  57 {
  58         unsigned int i;
  59
  60         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  61                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  62         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  63 }
  64
  65 /*
  66  * Maximum heap_index that can be stored in a PST with index_bits bits
  67  */
  68 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  69 {
  70         return index_bits_to_maxindex[bits - 1];
  71 }
  72
  73 /*
  74  * Extend a priority search tree so that it can store a node with heap_index
  75  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
  76  * However, this function is used rarely and the common case performance is
  77  * not bad.
  78  */
  79 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
  80                 struct prio_tree_node *node, unsigned long max_heap_index)
  81 {
  82         struct prio_tree_node *first = NULL, *prev, *last = NULL;
  83
  84         if (max_heap_index > prio_tree_maxindex(root->index_bits))
  85                 root->index_bits++;
  86
  87         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
  88                 root->index_bits++;
  89
  90                 if (prio_tree_empty(root))
  91                         continue;
  92
  93                 if (first == NULL) {
  94                         first = root->prio_tree_node;
  95                         prio_tree_remove(root, root->prio_tree_node);
  96                         INIT_PRIO_TREE_NODE(first);
  97                         last = first;
  98                 } else {
  99                         prev = last;
 100                         last = root->prio_tree_node;
 101                         prio_tree_remove(root, root->prio_tree_node);
 102                         INIT_PRIO_TREE_NODE(last);
 103                         prev->left = last;
 104                         last->parent = prev;
 105                 }
 106         }
 107
 108         INIT_PRIO_TREE_NODE(node);
 109
 110         if (first) {
 111                 node->left = first;
 112                 first->parent = node;
 113         } else
 114                 last = node;
 115
 116         if (!prio_tree_empty(root)) {
 117                 last->left = root->prio_tree_node;
 118                 last->left->parent = last;
 119         }
 120
 121         root->prio_tree_node = node;
 122         return node;
 123 }
 124
 125 /*
 126  * Replace a prio_tree_node with a new node and return the old node
 127  */
 128 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 129                 struct prio_tree_node *old, struct prio_tree_node *node)
 130 {
 131         INIT_PRIO_TREE_NODE(node);
 132
 133         if (prio_tree_root(old)) {
 134                 assert(root->prio_tree_node == old);
 135                 /*
 136                  * We can reduce root->index_bits here. However, it is complex
 137                  * and does not help much to improve performance (IMO).
 138                  */
 139                 node->parent = node;
 140                 root->prio_tree_node = node;
 141         } else {
 142                 node->parent = old->parent;
 143                 if (old->parent->left == old)
 144                         old->parent->left = node;
 145                 else
 146                         old->parent->right = node;
 147         }
 148
 149         if (!prio_tree_left_empty(old)) {
 150                 node->left = old->left;
 151                 old->left->parent = node;
 152         }
 153
 154         if (!prio_tree_right_empty(old)) {
 155                 node->right = old->right;
 156                 old->right->parent = node;
 157         }
 158
 159         return old;
 160 }
 161
 162 /*
 163  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 164  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 165  * required to represent the maximum heap_index. In the worst case, the algo
 166  * can take O((log n)^2) - check prio_tree_expand.
 167  *
 168  * If a prior node with same radix_index and heap_index is already found in
 169  * the tree, then returns the address of the prior node. Otherwise, inserts
 170  * @node into the tree and returns @node.
 171  */
 172 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 173                 struct prio_tree_node *node)
 174 {
 175         struct prio_tree_node *cur, *res = node;
 176         unsigned long radix_index, heap_index;
 177         unsigned long r_index, h_index, index, mask;
 178         int size_flag = 0;
 179
 180         get_index(node, &radix_index, &heap_index);
 181
 182         if (prio_tree_empty(root) ||
 183                         heap_index > prio_tree_maxindex(root->index_bits))
 184                 return prio_tree_expand(root, node, heap_index);
 185
 186         cur = root->prio_tree_node;
 187         mask = 1UL << (root->index_bits - 1);
 188
 189         while (mask) {
 190                 get_index(cur, &r_index, &h_index);
 191
 192                 if (r_index == radix_index && h_index == heap_index)
 193                         return cur;
 194
 195                 if (h_index < heap_index ||
 196                     (h_index == heap_index && r_index > radix_index)) {
 197                         struct prio_tree_node *tmp = node;
 198                         node = prio_tree_replace(root, cur, node);
 199                         cur = tmp;
 200                         /* swap indices */
 201                         index = r_index;
 202                         r_index = radix_index;
 203                         radix_index = index;
 204                         index = h_index;
 205                         h_index = heap_index;
 206                         heap_index = index;
 207                 }
 208
 209                 if (size_flag)
 210                         index = heap_index - radix_index;
 211                 else
 212                         index = radix_index;
 213
 214                 if (index & mask) {
 215                         if (prio_tree_right_empty(cur)) {
 216                                 INIT_PRIO_TREE_NODE(node);
 217                                 cur->right = node;
 218                                 node->parent = cur;
 219                                 return res;
 220                         } else
 221                                 cur = cur->right;
 222                 } else {
 223                         if (prio_tree_left_empty(cur)) {
 224                                 INIT_PRIO_TREE_NODE(node);
 225                                 cur->left = node;
 226                                 node->parent = cur;
 227                                 return res;
 228                         } else
 229                                 cur = cur->left;
 230                 }
 231
 232                 mask >>= 1;
 233
 234                 if (!mask) {
 235                         mask = 1UL << (BITS_PER_LONG - 1);
 236                         size_flag = 1;
 237                 }
 238         }
 239         /* Should not reach here */
 240         assert(0);
 241         return NULL;
 242 }
 243
 244 /*
 245  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 246  * algorithm takes O(log n) time where 'log n' is the number of bits required
 247  * to represent the maximum heap_index.
 248  */
 249 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 250 {
 251         struct prio_tree_node *cur;
 252         unsigned long r_index, h_index_right, h_index_left;
 253
 254         cur = node;
 255
 256         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 257                 if (!prio_tree_left_empty(cur))
 258                         get_index(cur->left, &r_index, &h_index_left);
 259                 else {
 260                         cur = cur->right;
 261                         continue;
 262                 }
 263
 264                 if (!prio_tree_right_empty(cur))
 265                         get_index(cur->right, &r_index, &h_index_right);
 266                 else {
 267                         cur = cur->left;
 268                         continue;
 269                 }
 270
 271                 /* both h_index_left and h_index_right cannot be 0 */
 272                 if (h_index_left >= h_index_right)
 273                         cur = cur->left;
 274                 else
 275                         cur = cur->right;
 276         }
 277
 278         if (prio_tree_root(cur)) {
 279                 assert(root->prio_tree_node == cur);
 280                 INIT_PRIO_TREE_ROOT(root);
 281                 return;
 282         }
 283
 284         if (cur->parent->right == cur)
 285                 cur->parent->right = cur->parent;
 286         else
 287                 cur->parent->left = cur->parent;
 288
 289         while (cur != node)
 290                 cur = prio_tree_replace(root, cur->parent, cur);
 291 }
 292
 293 /*
 294  * Following functions help to enumerate all prio_tree_nodes in the tree that
 295  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 296  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 297  * proportional to # of bits required to represent the maximum heap_index) and
 298  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 299  */
 300
 301 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 302                 unsigned long *r_index, unsigned long *h_index)
 303 {
 304         if (prio_tree_left_empty(iter->cur))
 305                 return NULL;
 306
 307         get_index(iter->cur->left, r_index, h_index);
 308
 309         if (iter->r_index <= *h_index) {
 310                 iter->cur = iter->cur->left;
 311                 iter->mask >>= 1;
 312                 if (iter->mask) {
 313                         if (iter->size_level)
 314                                 iter->size_level++;
 315                 } else {
 316                         if (iter->size_level) {
 317                                 assert(prio_tree_left_empty(iter->cur));
 318                                 assert(prio_tree_right_empty(iter->cur));
 319                                 iter->size_level++;
 320                                 iter->mask = ULONG_MAX;
 321                         } else {
 322                                 iter->size_level = 1;
 323                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 324                         }
 325                 }
 326                 return iter->cur;
 327         }
 328
 329         return NULL;
 330 }
 331
 332 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 333                 unsigned long *r_index, unsigned long *h_index)
 334 {
 335         unsigned long value;
 336
 337         if (prio_tree_right_empty(iter->cur))
 338                 return NULL;
 339
 340         if (iter->size_level)
 341                 value = iter->value;
 342         else
 343                 value = iter->value | iter->mask;
 344
 345         if (iter->h_index < value)
 346                 return NULL;
 347
 348         get_index(iter->cur->right, r_index, h_index);
 349
 350         if (iter->r_index <= *h_index) {
 351                 iter->cur = iter->cur->right;
 352                 iter->mask >>= 1;
 353                 iter->value = value;
 354                 if (iter->mask) {
 355                         if (iter->size_level)
 356                                 iter->size_level++;
 357                 } else {
 358                         if (iter->size_level) {
 359                                 assert(prio_tree_left_empty(iter->cur));
 360                                 assert(prio_tree_right_empty(iter->cur));
 361                                 iter->size_level++;
 362                                 iter->mask = ULONG_MAX;
 363                         } else {
 364                                 iter->size_level = 1;
 365                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 366                         }
 367                 }
 368                 return iter->cur;
 369         }
 370
 371         return NULL;
 372 }
 373
 374 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 375 {
 376         iter->cur = iter->cur->parent;
 377         if (iter->mask == ULONG_MAX)
 378                 iter->mask = 1UL;
 379         else if (iter->size_level == 1)
 380                 iter->mask = 1UL;
 381         else
 382                 iter->mask <<= 1;
 383         if (iter->size_level)
 384                 iter->size_level--;
 385         if (!iter->size_level && (iter->value & iter->mask))
 386                 iter->value ^= iter->mask;
 387         return iter->cur;
 388 }
 389
 390 static inline int overlap(struct prio_tree_iter *iter,
 391                 unsigned long r_index, unsigned long h_index)
 392 {
 393         return iter->h_index >= r_index && iter->r_index <= h_index;
 394 }
 395
 396 /*
 397  * prio_tree_first:
 398  *
 399  * Get the first prio_tree_node that overlaps with the interval [radix_index,
 400  * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 401  * traversal of the tree.
 402  */
 403 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 404 {
 405         struct prio_tree_root *root;
 406         unsigned long r_index, h_index;
 407
 408         INIT_PRIO_TREE_ITER(iter);
 409
 410         root = iter->root;
 411         if (prio_tree_empty(root))
 412                 return NULL;
 413
 414         get_index(root->prio_tree_node, &r_index, &h_index);
 415
 416         if (iter->r_index > h_index)
 417                 return NULL;
 418
 419         iter->mask = 1UL << (root->index_bits - 1);
 420         iter->cur = root->prio_tree_node;
 421
 422         while (1) {
 423                 if (overlap(iter, r_index, h_index))
 424                         return iter->cur;
 425
 426                 if (prio_tree_left(iter, &r_index, &h_index))
 427                         continue;
 428
 429                 if (prio_tree_right(iter, &r_index, &h_index))
 430                         continue;
 431
 432                 break;
 433         }
 434         return NULL;
 435 }
 436
 437 /*
 438  * prio_tree_next:
 439  *
 440  * Get the next prio_tree_node that overlaps with the input interval in iter
 441  */
 442 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 443 {
 444         unsigned long r_index, h_index;
 445
 446         if (iter->cur == NULL)
 447                 return prio_tree_first(iter);
 448
 449 repeat:
 450         while (prio_tree_left(iter, &r_index, &h_index))
 451                 if (overlap(iter, r_index, h_index))
 452                         return iter->cur;
 453
 454         while (!prio_tree_right(iter, &r_index, &h_index)) {
 455                 while (!prio_tree_root(iter->cur) &&
 456                                 iter->cur->parent->right == iter->cur)
 457                         prio_tree_parent(iter);
 458
 459                 if (prio_tree_root(iter->cur))
 460                         return NULL;
 461
 462                 prio_tree_parent(iter);
 463         }
 464
 465         if (overlap(iter, r_index, h_index))
 466                 return iter->cur;
 467
 468         goto repeat;
 469 }