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
  18 /*
  19  * A clever mix of heap and radix trees forms a radix priority search tree (PST)
  20  * which is useful for storing intervals, e.g, we can consider a vma as a closed
  21  * interval of file pages [offset_begin, offset_end], and store all vmas that
  22  * map a file in a PST. Then, using the PST, we can answer a stabbing query,
  23  * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
  24  * given input interval X (a set of consecutive file pages), in "O(log n + m)"
  25  * time where 'log n' is the height of the PST, and 'm' is the number of stored
  26  * intervals (vmas) that overlap (map) with the input interval X (the set of
  27  * consecutive file pages).
  28  *
  29  * In our implementation, we store closed intervals of the form [radix_index,
  30  * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
  31  * is designed for storing intervals with unique radix indices, i.e., each
  32  * interval have different radix_index. However, this limitation can be easily
  33  * overcome by using the size, i.e., heap_index - radix_index, as part of the
  34  * index, so we index the tree using [(radix_index,size), heap_index].
  35  *
  36  * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
  37  * machine, the maximum height of a PST can be 64. We can use a balanced version
  38  * of the priority search tree to optimize the tree height, but the balanced
  39  * tree proposed by McCreight is too complex and memory-hungry for our purpose.
  40  */
  41
  42 /*
  43  * The following macros are used for implementing prio_tree for i_mmap
  44  */
  45
  46 #define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
  47 #define VMA_SIZE(vma)     (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
  48 /* avoid overflow */
  49 #define HEAP_INDEX(vma)   ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
  50
  51
  52 static void get_index(const struct prio_tree_root *root,
  53     const struct prio_tree_node *node,
  54     unsigned long *radix, unsigned long *heap)
  55 {
  56         if (root->raw) {
  57                 struct vm_area_struct *vma = prio_tree_entry(
  58                     node, struct vm_area_struct, shared.prio_tree_node);
  59
  60                 *radix = RADIX_INDEX(vma);
  61                 *heap = HEAP_INDEX(vma);
  62         }
  63         else {
  64                 *radix = node->start;
  65                 *heap = node->last;
  66         }
  67 }
  68
  69 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  70
  71 void __init prio_tree_init(void)
  72 {
  73         unsigned int i;
  74
  75         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  76                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  77         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  78 }
  79
  80 /*
  81  * Maximum heap_index that can be stored in a PST with index_bits bits
  82  */
  83 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  84 {
  85         return index_bits_to_maxindex[bits - 1];
  86 }
  87
  88 /*
  89  * Extend a priority search tree so that it can store a node with heap_index
  90  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
  91  * However, this function is used rarely and the common case performance is
  92  * not bad.
  93  */
  94 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
  95                 struct prio_tree_node *node, unsigned long max_heap_index)
  96 {
  97         struct prio_tree_node *first = NULL, *prev, *last = NULL;
  98
  99         if (max_heap_index > prio_tree_maxindex(root->index_bits))
 100                 root->index_bits++;
 101
 102         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
 103                 root->index_bits++;
 104
 105                 if (prio_tree_empty(root))
 106                         continue;
 107
 108                 if (first == NULL) {
 109                         first = root->prio_tree_node;
 110                         prio_tree_remove(root, root->prio_tree_node);
 111                         INIT_PRIO_TREE_NODE(first);
 112                         last = first;
 113                 } else {
 114                         prev = last;
 115                         last = root->prio_tree_node;
 116                         prio_tree_remove(root, root->prio_tree_node);
 117                         INIT_PRIO_TREE_NODE(last);
 118                         prev->left = last;
 119                         last->parent = prev;
 120                 }
 121         }
 122
 123         INIT_PRIO_TREE_NODE(node);
 124
 125         if (first) {
 126                 node->left = first;
 127                 first->parent = node;
 128         } else
 129                 last = node;
 130
 131         if (!prio_tree_empty(root)) {
 132                 last->left = root->prio_tree_node;
 133                 last->left->parent = last;
 134         }
 135
 136         root->prio_tree_node = node;
 137         return node;
 138 }
 139
 140 /*
 141  * Replace a prio_tree_node with a new node and return the old node
 142  */
 143 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 144                 struct prio_tree_node *old, struct prio_tree_node *node)
 145 {
 146         INIT_PRIO_TREE_NODE(node);
 147
 148         if (prio_tree_root(old)) {
 149                 BUG_ON(root->prio_tree_node != old);
 150                 /*
 151                  * We can reduce root->index_bits here. However, it is complex
 152                  * and does not help much to improve performance (IMO).
 153                  */
 154                 node->parent = node;
 155                 root->prio_tree_node = node;
 156         } else {
 157                 node->parent = old->parent;
 158                 if (old->parent->left == old)
 159                         old->parent->left = node;
 160                 else
 161                         old->parent->right = node;
 162         }
 163
 164         if (!prio_tree_left_empty(old)) {
 165                 node->left = old->left;
 166                 old->left->parent = node;
 167         }
 168
 169         if (!prio_tree_right_empty(old)) {
 170                 node->right = old->right;
 171                 old->right->parent = node;
 172         }
 173
 174         return old;
 175 }
 176
 177 /*
 178  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 179  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 180  * required to represent the maximum heap_index. In the worst case, the algo
 181  * can take O((log n)^2) - check prio_tree_expand.
 182  *
 183  * If a prior node with same radix_index and heap_index is already found in
 184  * the tree, then returns the address of the prior node. Otherwise, inserts
 185  * @node into the tree and returns @node.
 186  */
 187 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 188                 struct prio_tree_node *node)
 189 {
 190         struct prio_tree_node *cur, *res = node;
 191         unsigned long radix_index, heap_index;
 192         unsigned long r_index, h_index, index, mask;
 193         int size_flag = 0;
 194
 195         get_index(root, node, &radix_index, &heap_index);
 196
 197         if (prio_tree_empty(root) ||
 198                         heap_index > prio_tree_maxindex(root->index_bits))
 199                 return prio_tree_expand(root, node, heap_index);
 200
 201         cur = root->prio_tree_node;
 202         mask = 1UL << (root->index_bits - 1);
 203
 204         while (mask) {
 205                 get_index(root, cur, &r_index, &h_index);
 206
 207                 if (r_index == radix_index && h_index == heap_index)
 208                         return cur;
 209
 210                 if (h_index < heap_index ||
 211                     (h_index == heap_index && r_index > radix_index)) {
 212                         struct prio_tree_node *tmp = node;
 213                         node = prio_tree_replace(root, cur, node);
 214                         cur = tmp;
 215                         /* swap indices */
 216                         index = r_index;
 217                         r_index = radix_index;
 218                         radix_index = index;
 219                         index = h_index;
 220                         h_index = heap_index;
 221                         heap_index = index;
 222                 }
 223
 224                 if (size_flag)
 225                         index = heap_index - radix_index;
 226                 else
 227                         index = radix_index;
 228
 229                 if (index & mask) {
 230                         if (prio_tree_right_empty(cur)) {
 231                                 INIT_PRIO_TREE_NODE(node);
 232                                 cur->right = node;
 233                                 node->parent = cur;
 234                                 return res;
 235                         } else
 236                                 cur = cur->right;
 237                 } else {
 238                         if (prio_tree_left_empty(cur)) {
 239                                 INIT_PRIO_TREE_NODE(node);
 240                                 cur->left = node;
 241                                 node->parent = cur;
 242                                 return res;
 243                         } else
 244                                 cur = cur->left;
 245                 }
 246
 247                 mask >>= 1;
 248
 249                 if (!mask) {
 250                         mask = 1UL << (BITS_PER_LONG - 1);
 251                         size_flag = 1;
 252                 }
 253         }
 254         /* Should not reach here */
 255         BUG();
 256         return NULL;
 257 }
 258
 259 /*
 260  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 261  * algorithm takes O(log n) time where 'log n' is the number of bits required
 262  * to represent the maximum heap_index.
 263  */
 264 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 265 {
 266         struct prio_tree_node *cur;
 267         unsigned long r_index, h_index_right, h_index_left;
 268
 269         cur = node;
 270
 271         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 272                 if (!prio_tree_left_empty(cur))
 273                         get_index(root, cur->left, &r_index, &h_index_left);
 274                 else {
 275                         cur = cur->right;
 276                         continue;
 277                 }
 278
 279                 if (!prio_tree_right_empty(cur))
 280                         get_index(root, cur->right, &r_index, &h_index_right);
 281                 else {
 282                         cur = cur->left;
 283                         continue;
 284                 }
 285
 286                 /* both h_index_left and h_index_right cannot be 0 */
 287                 if (h_index_left >= h_index_right)
 288                         cur = cur->left;
 289                 else
 290                         cur = cur->right;
 291         }
 292
 293         if (prio_tree_root(cur)) {
 294                 BUG_ON(root->prio_tree_node != cur);
 295                 __INIT_PRIO_TREE_ROOT(root, root->raw);
 296                 return;
 297         }
 298
 299         if (cur->parent->right == cur)
 300                 cur->parent->right = cur->parent;
 301         else
 302                 cur->parent->left = cur->parent;
 303
 304         while (cur != node)
 305                 cur = prio_tree_replace(root, cur->parent, cur);
 306 }
 307
 308 /*
 309  * Following functions help to enumerate all prio_tree_nodes in the tree that
 310  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 311  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 312  * proportional to # of bits required to represent the maximum heap_index) and
 313  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 314  */
 315
 316 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 317                 unsigned long *r_index, unsigned long *h_index)
 318 {
 319         if (prio_tree_left_empty(iter->cur))
 320                 return NULL;
 321
 322         get_index(iter->root, iter->cur->left, r_index, h_index);
 323
 324         if (iter->r_index <= *h_index) {
 325                 iter->cur = iter->cur->left;
 326                 iter->mask >>= 1;
 327                 if (iter->mask) {
 328                         if (iter->size_level)
 329                                 iter->size_level++;
 330                 } else {
 331                         if (iter->size_level) {
 332                                 BUG_ON(!prio_tree_left_empty(iter->cur));
 333                                 BUG_ON(!prio_tree_right_empty(iter->cur));
 334                                 iter->size_level++;
 335                                 iter->mask = ULONG_MAX;
 336                         } else {
 337                                 iter->size_level = 1;
 338                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 339                         }
 340                 }
 341                 return iter->cur;
 342         }
 343
 344         return NULL;
 345 }
 346
 347 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 348                 unsigned long *r_index, unsigned long *h_index)
 349 {
 350         unsigned long value;
 351
 352         if (prio_tree_right_empty(iter->cur))
 353                 return NULL;
 354
 355         if (iter->size_level)
 356                 value = iter->value;
 357         else
 358                 value = iter->value | iter->mask;
 359
 360         if (iter->h_index < value)
 361                 return NULL;
 362
 363         get_index(iter->root, iter->cur->right, r_index, h_index);
 364
 365         if (iter->r_index <= *h_index) {
 366                 iter->cur = iter->cur->right;
 367                 iter->mask >>= 1;
 368                 iter->value = value;
 369                 if (iter->mask) {
 370                         if (iter->size_level)
 371                                 iter->size_level++;
 372                 } else {
 373                         if (iter->size_level) {
 374                                 BUG_ON(!prio_tree_left_empty(iter->cur));
 375                                 BUG_ON(!prio_tree_right_empty(iter->cur));
 376                                 iter->size_level++;
 377                                 iter->mask = ULONG_MAX;
 378                         } else {
 379                                 iter->size_level = 1;
 380                                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 381                         }
 382                 }
 383                 return iter->cur;
 384         }
 385
 386         return NULL;
 387 }
 388
 389 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 390 {
 391         iter->cur = iter->cur->parent;
 392         if (iter->mask == ULONG_MAX)
 393                 iter->mask = 1UL;
 394         else if (iter->size_level == 1)
 395                 iter->mask = 1UL;
 396         else
 397                 iter->mask <<= 1;
 398         if (iter->size_level)
 399                 iter->size_level--;
 400         if (!iter->size_level && (iter->value & iter->mask))
 401                 iter->value ^= iter->mask;
 402         return iter->cur;
 403 }
 404
 405 static inline int overlap(struct prio_tree_iter *iter,
 406                 unsigned long r_index, unsigned long h_index)
 407 {
 408         return iter->h_index >= r_index && iter->r_index <= h_index;
 409 }
 410
 411 /*
 412  * prio_tree_first:
 413  *
 414  * Get the first prio_tree_node that overlaps with the interval [radix_index,
 415  * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 416  * traversal of the tree.
 417  */
 418 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 419 {
 420         struct prio_tree_root *root;
 421         unsigned long r_index, h_index;
 422
 423         INIT_PRIO_TREE_ITER(iter);
 424
 425         root = iter->root;
 426         if (prio_tree_empty(root))
 427                 return NULL;
 428
 429         get_index(root, root->prio_tree_node, &r_index, &h_index);
 430
 431         if (iter->r_index > h_index)
 432                 return NULL;
 433
 434         iter->mask = 1UL << (root->index_bits - 1);
 435         iter->cur = root->prio_tree_node;
 436
 437         while (1) {
 438                 if (overlap(iter, r_index, h_index))
 439                         return iter->cur;
 440
 441                 if (prio_tree_left(iter, &r_index, &h_index))
 442                         continue;
 443
 444                 if (prio_tree_right(iter, &r_index, &h_index))
 445                         continue;
 446
 447                 break;
 448         }
 449         return NULL;
 450 }
 451
 452 /*
 453  * prio_tree_next:
 454  *
 455  * Get the next prio_tree_node that overlaps with the input interval in iter
 456  */
 457 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 458 {
 459         unsigned long r_index, h_index;
 460
 461         if (iter->cur == NULL)
 462                 return prio_tree_first(iter);
 463
 464 repeat:
 465         while (prio_tree_left(iter, &r_index, &h_index))
 466                 if (overlap(iter, r_index, h_index))
 467                         return iter->cur;
 468
 469         while (!prio_tree_right(iter, &r_index, &h_index)) {
 470                 while (!prio_tree_root(iter->cur) &&
 471                                 iter->cur->parent->right == iter->cur)
 472                         prio_tree_parent(iter);
 473
 474                 if (prio_tree_root(iter->cur))
 475                         return NULL;
 476
 477                 prio_tree_parent(iter);
 478         }
 479
 480         if (overlap(iter, r_index, h_index))
 481                 return iter->cur;
 482
 483         goto repeat;
 484 }