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 <linux/init.h>
  15 #include <linux/mm.h>
  16 #include <linux/prio_tree.h>
  17 #include <linux/export.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 /*
  44  * The following macros are used for implementing prio_tree for i_mmap
  45  */
  46
  47 #define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
  48 #define VMA_SIZE(vma)     (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
  49 /* avoid overflow */
  50 #define HEAP_INDEX(vma)   ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
  51
  52
  53 static void get_index(const struct prio_tree_root *root,
  54     const struct prio_tree_node *node,
  55     unsigned long *radix, unsigned long *heap)
  56 {
  57         if (root->raw) {
  58                 struct vm_area_struct *vma = prio_tree_entry(
  59                     node, struct vm_area_struct, shared.prio_tree_node);
  60
  61                 *radix = RADIX_INDEX(vma);
  62                 *heap = HEAP_INDEX(vma);
  63         }
  64         else {
  65                 *radix = node->start;
  66                 *heap = node->last;
  67         }
  68 }
  69
  70 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  71
  72 void __init prio_tree_init(void)
  73 {
  74         unsigned int i;
  75
  76         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  77                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  78         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  79 }
  80
  81 /*
  82  * Maximum heap_index that can be stored in a PST with index_bits bits
  83  */
  84 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  85 {
  86         return index_bits_to_maxindex[bits - 1];
  87 }
  88
  89 static void prio_set_parent(struct prio_tree_node *parent,
  90                             struct prio_tree_node *child, bool left)
  91 {
  92         if (left)
  93                 parent->left = child;
  94         else
  95                 parent->right = child;
  96
  97         child->parent = parent;
  98 }
  99
 100 /*
 101  * Extend a priority search tree so that it can store a node with heap_index
 102  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 103  * However, this function is used rarely and the common case performance is
 104  * not bad.
 105  */
 106 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
 107                 struct prio_tree_node *node, unsigned long max_heap_index)
 108 {
 109         struct prio_tree_node *prev;
 110
 111         if (max_heap_index > prio_tree_maxindex(root->index_bits))
 112                 root->index_bits++;
 113
 114         prev = node;
 115         INIT_PRIO_TREE_NODE(node);
 116
 117         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
 118                 struct prio_tree_node *tmp = root->prio_tree_node;
 119
 120                 root->index_bits++;
 121
 122                 if (prio_tree_empty(root))
 123                         continue;
 124
 125                 prio_tree_remove(root, root->prio_tree_node);
 126                 INIT_PRIO_TREE_NODE(tmp);
 127
 128                 prio_set_parent(prev, tmp, true);
 129                 prev = tmp;
 130         }
 131
 132         if (!prio_tree_empty(root))
 133                 prio_set_parent(prev, root->prio_tree_node, true);
 134
 135         root->prio_tree_node = node;
 136         return node;
 137 }
 138
 139 /*
 140  * Replace a prio_tree_node with a new node and return the old node
 141  */
 142 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 143                 struct prio_tree_node *old, struct prio_tree_node *node)
 144 {
 145         INIT_PRIO_TREE_NODE(node);
 146
 147         if (prio_tree_root(old)) {
 148                 BUG_ON(root->prio_tree_node != old);
 149                 /*
 150                  * We can reduce root->index_bits here. However, it is complex
 151                  * and does not help much to improve performance (IMO).
 152                  */
 153                 root->prio_tree_node = node;
 154         } else
 155                 prio_set_parent(old->parent, node, old->parent->left == old);
 156
 157         if (!prio_tree_left_empty(old))
 158                 prio_set_parent(node, old->left, true);
 159
 160         if (!prio_tree_right_empty(old))
 161                 prio_set_parent(node, old->right, false);
 162
 163         return old;
 164 }
 165
 166 /*
 167  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 168  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 169  * required to represent the maximum heap_index. In the worst case, the algo
 170  * can take O((log n)^2) - check prio_tree_expand.
 171  *
 172  * If a prior node with same radix_index and heap_index is already found in
 173  * the tree, then returns the address of the prior node. Otherwise, inserts
 174  * @node into the tree and returns @node.
 175  */
 176 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 177                 struct prio_tree_node *node)
 178 {
 179         struct prio_tree_node *cur, *res = node;
 180         unsigned long radix_index, heap_index;
 181         unsigned long r_index, h_index, index, mask;
 182         int size_flag = 0;
 183
 184         get_index(root, node, &radix_index, &heap_index);
 185
 186         if (prio_tree_empty(root) ||
 187                         heap_index > prio_tree_maxindex(root->index_bits))
 188                 return prio_tree_expand(root, node, heap_index);
 189
 190         cur = root->prio_tree_node;
 191         mask = 1UL << (root->index_bits - 1);
 192
 193         while (mask) {
 194                 get_index(root, cur, &r_index, &h_index);
 195
 196                 if (r_index == radix_index && h_index == heap_index)
 197                         return cur;
 198
 199                 if (h_index < heap_index ||
 200                     (h_index == heap_index && r_index > radix_index)) {
 201                         struct prio_tree_node *tmp = node;
 202                         node = prio_tree_replace(root, cur, node);
 203                         cur = tmp;
 204                         /* swap indices */
 205                         index = r_index;
 206                         r_index = radix_index;
 207                         radix_index = index;
 208                         index = h_index;
 209                         h_index = heap_index;
 210                         heap_index = index;
 211                 }
 212
 213                 if (size_flag)
 214                         index = heap_index - radix_index;
 215                 else
 216                         index = radix_index;
 217
 218                 if (index & mask) {
 219                         if (prio_tree_right_empty(cur)) {
 220                                 INIT_PRIO_TREE_NODE(node);
 221                                 prio_set_parent(cur, node, false);
 222                                 return res;
 223                         } else
 224                                 cur = cur->right;
 225                 } else {
 226                         if (prio_tree_left_empty(cur)) {
 227                                 INIT_PRIO_TREE_NODE(node);
 228                                 prio_set_parent(cur, node, true);
 229                                 return res;
 230                         } else
 231                                 cur = cur->left;
 232                 }
 233
 234                 mask >>= 1;
 235
 236                 if (!mask) {
 237                         mask = 1UL << (BITS_PER_LONG - 1);
 238                         size_flag = 1;
 239                 }
 240         }
 241         /* Should not reach here */
 242         BUG();
 243         return NULL;
 244 }
 245 EXPORT_SYMBOL(prio_tree_insert);
 246
 247 /*
 248  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 249  * algorithm takes O(log n) time where 'log n' is the number of bits required
 250  * to represent the maximum heap_index.
 251  */
 252 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 253 {
 254         struct prio_tree_node *cur;
 255         unsigned long r_index, h_index_right, h_index_left;
 256
 257         cur = node;
 258
 259         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 260                 if (!prio_tree_left_empty(cur))
 261                         get_index(root, cur->left, &r_index, &h_index_left);
 262                 else {
 263                         cur = cur->right;
 264                         continue;
 265                 }
 266
 267                 if (!prio_tree_right_empty(cur))
 268                         get_index(root, cur->right, &r_index, &h_index_right);
 269                 else {
 270                         cur = cur->left;
 271                         continue;
 272                 }
 273
 274                 /* both h_index_left and h_index_right cannot be 0 */
 275                 if (h_index_left >= h_index_right)
 276                         cur = cur->left;
 277                 else
 278                         cur = cur->right;
 279         }
 280
 281         if (prio_tree_root(cur)) {
 282                 BUG_ON(root->prio_tree_node != cur);
 283                 __INIT_PRIO_TREE_ROOT(root, root->raw);
 284                 return;
 285         }
 286
 287         if (cur->parent->right == cur)
 288                 cur->parent->right = cur->parent;
 289         else
 290                 cur->parent->left = cur->parent;
 291
 292         while (cur != node)
 293                 cur = prio_tree_replace(root, cur->parent, cur);
 294 }
 295 EXPORT_SYMBOL(prio_tree_remove);
 296
 297 static void iter_walk_down(struct prio_tree_iter *iter)
 298 {
 299         iter->mask >>= 1;
 300         if (iter->mask) {
 301                 if (iter->size_level)
 302                         iter->size_level++;
 303                 return;
 304         }
 305
 306         if (iter->size_level) {
 307                 BUG_ON(!prio_tree_left_empty(iter->cur));
 308                 BUG_ON(!prio_tree_right_empty(iter->cur));
 309                 iter->size_level++;
 310                 iter->mask = ULONG_MAX;
 311         } else {
 312                 iter->size_level = 1;
 313                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 314         }
 315 }
 316
 317 static void iter_walk_up(struct prio_tree_iter *iter)
 318 {
 319         if (iter->mask == ULONG_MAX)
 320                 iter->mask = 1UL;
 321         else if (iter->size_level == 1)
 322                 iter->mask = 1UL;
 323         else
 324                 iter->mask <<= 1;
 325         if (iter->size_level)
 326                 iter->size_level--;
 327         if (!iter->size_level && (iter->value & iter->mask))
 328                 iter->value ^= iter->mask;
 329 }
 330
 331 /*
 332  * Following functions help to enumerate all prio_tree_nodes in the tree that
 333  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 334  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 335  * proportional to # of bits required to represent the maximum heap_index) and
 336  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 337  */
 338
 339 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 340                 unsigned long *r_index, unsigned long *h_index)
 341 {
 342         if (prio_tree_left_empty(iter->cur))
 343                 return NULL;
 344
 345         get_index(iter->root, iter->cur->left, r_index, h_index);
 346
 347         if (iter->r_index <= *h_index) {
 348                 iter->cur = iter->cur->left;
 349                 iter_walk_down(iter);
 350                 return iter->cur;
 351         }
 352
 353         return NULL;
 354 }
 355
 356 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 357                 unsigned long *r_index, unsigned long *h_index)
 358 {
 359         unsigned long value;
 360
 361         if (prio_tree_right_empty(iter->cur))
 362                 return NULL;
 363
 364         if (iter->size_level)
 365                 value = iter->value;
 366         else
 367                 value = iter->value | iter->mask;
 368
 369         if (iter->h_index < value)
 370                 return NULL;
 371
 372         get_index(iter->root, iter->cur->right, r_index, h_index);
 373
 374         if (iter->r_index <= *h_index) {
 375                 iter->cur = iter->cur->right;
 376                 iter_walk_down(iter);
 377                 return iter->cur;
 378         }
 379
 380         return NULL;
 381 }
 382
 383 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 384 {
 385         iter->cur = iter->cur->parent;
 386         iter_walk_up(iter);
 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, 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 }
 470 EXPORT_SYMBOL(prio_tree_next);