linux/lib/prio_tree.c
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   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
  52static 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
  69static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  70
  71void __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 */
  83static inline unsigned long prio_tree_maxindex(unsigned int bits)
  84{
  85        return index_bits_to_maxindex[bits - 1];
  86}
  87
  88static void prio_set_parent(struct prio_tree_node *parent,
  89                            struct prio_tree_node *child, bool left)
  90{
  91        if (left)
  92                parent->left = child;
  93        else
  94                parent->right = child;
  95
  96        child->parent = parent;
  97}
  98
  99/*
 100 * Extend a priority search tree so that it can store a node with heap_index
 101 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 102 * However, this function is used rarely and the common case performance is
 103 * not bad.
 104 */
 105static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
 106                struct prio_tree_node *node, unsigned long max_heap_index)
 107{
 108        struct prio_tree_node *prev;
 109
 110        if (max_heap_index > prio_tree_maxindex(root->index_bits))
 111                root->index_bits++;
 112
 113        prev = node;
 114        INIT_PRIO_TREE_NODE(node);
 115
 116        while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
 117                struct prio_tree_node *tmp = root->prio_tree_node;
 118
 119                root->index_bits++;
 120
 121                if (prio_tree_empty(root))
 122                        continue;
 123
 124                prio_tree_remove(root, root->prio_tree_node);
 125                INIT_PRIO_TREE_NODE(tmp);
 126
 127                prio_set_parent(prev, tmp, true);
 128                prev = tmp;
 129        }
 130
 131        if (!prio_tree_empty(root))
 132                prio_set_parent(prev, root->prio_tree_node, true);
 133
 134        root->prio_tree_node = node;
 135        return node;
 136}
 137
 138/*
 139 * Replace a prio_tree_node with a new node and return the old node
 140 */
 141struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 142                struct prio_tree_node *old, struct prio_tree_node *node)
 143{
 144        INIT_PRIO_TREE_NODE(node);
 145
 146        if (prio_tree_root(old)) {
 147                BUG_ON(root->prio_tree_node != old);
 148                /*
 149                 * We can reduce root->index_bits here. However, it is complex
 150                 * and does not help much to improve performance (IMO).
 151                 */
 152                root->prio_tree_node = node;
 153        } else
 154                prio_set_parent(old->parent, node, old->parent->left == old);
 155
 156        if (!prio_tree_left_empty(old))
 157                prio_set_parent(node, old->left, true);
 158
 159        if (!prio_tree_right_empty(old))
 160                prio_set_parent(node, old->right, false);
 161
 162        return old;
 163}
 164
 165/*
 166 * Insert a prio_tree_node @node into a radix priority search tree @root. The
 167 * algorithm typically takes O(log n) time where 'log n' is the number of bits
 168 * required to represent the maximum heap_index. In the worst case, the algo
 169 * can take O((log n)^2) - check prio_tree_expand.
 170 *
 171 * If a prior node with same radix_index and heap_index is already found in
 172 * the tree, then returns the address of the prior node. Otherwise, inserts
 173 * @node into the tree and returns @node.
 174 */
 175struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 176                struct prio_tree_node *node)
 177{
 178        struct prio_tree_node *cur, *res = node;
 179        unsigned long radix_index, heap_index;
 180        unsigned long r_index, h_index, index, mask;
 181        int size_flag = 0;
 182
 183        get_index(root, node, &radix_index, &heap_index);
 184
 185        if (prio_tree_empty(root) ||
 186                        heap_index > prio_tree_maxindex(root->index_bits))
 187                return prio_tree_expand(root, node, heap_index);
 188
 189        cur = root->prio_tree_node;
 190        mask = 1UL << (root->index_bits - 1);
 191
 192        while (mask) {
 193                get_index(root, cur, &r_index, &h_index);
 194
 195                if (r_index == radix_index && h_index == heap_index)
 196                        return cur;
 197
 198                if (h_index < heap_index ||
 199                    (h_index == heap_index && r_index > radix_index)) {
 200                        struct prio_tree_node *tmp = node;
 201                        node = prio_tree_replace(root, cur, node);
 202                        cur = tmp;
 203                        /* swap indices */
 204                        index = r_index;
 205                        r_index = radix_index;
 206                        radix_index = index;
 207                        index = h_index;
 208                        h_index = heap_index;
 209                        heap_index = index;
 210                }
 211
 212                if (size_flag)
 213                        index = heap_index - radix_index;
 214                else
 215                        index = radix_index;
 216
 217                if (index & mask) {
 218                        if (prio_tree_right_empty(cur)) {
 219                                INIT_PRIO_TREE_NODE(node);
 220                                prio_set_parent(cur, node, false);
 221                                return res;
 222                        } else
 223                                cur = cur->right;
 224                } else {
 225                        if (prio_tree_left_empty(cur)) {
 226                                INIT_PRIO_TREE_NODE(node);
 227                                prio_set_parent(cur, node, true);
 228                                return res;
 229                        } else
 230                                cur = cur->left;
 231                }
 232
 233                mask >>= 1;
 234
 235                if (!mask) {
 236                        mask = 1UL << (BITS_PER_LONG - 1);
 237                        size_flag = 1;
 238                }
 239        }
 240        /* Should not reach here */
 241        BUG();
 242        return NULL;
 243}
 244
 245/*
 246 * Remove a prio_tree_node @node from a radix priority search tree @root. The
 247 * algorithm takes O(log n) time where 'log n' is the number of bits required
 248 * to represent the maximum heap_index.
 249 */
 250void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 251{
 252        struct prio_tree_node *cur;
 253        unsigned long r_index, h_index_right, h_index_left;
 254
 255        cur = node;
 256
 257        while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 258                if (!prio_tree_left_empty(cur))
 259                        get_index(root, cur->left, &r_index, &h_index_left);
 260                else {
 261                        cur = cur->right;
 262                        continue;
 263                }
 264
 265                if (!prio_tree_right_empty(cur))
 266                        get_index(root, cur->right, &r_index, &h_index_right);
 267                else {
 268                        cur = cur->left;
 269                        continue;
 270                }
 271
 272                /* both h_index_left and h_index_right cannot be 0 */
 273                if (h_index_left >= h_index_right)
 274                        cur = cur->left;
 275                else
 276                        cur = cur->right;
 277        }
 278
 279        if (prio_tree_root(cur)) {
 280                BUG_ON(root->prio_tree_node != cur);
 281                __INIT_PRIO_TREE_ROOT(root, root->raw);
 282                return;
 283        }
 284
 285        if (cur->parent->right == cur)
 286                cur->parent->right = cur->parent;
 287        else
 288                cur->parent->left = cur->parent;
 289
 290        while (cur != node)
 291                cur = prio_tree_replace(root, cur->parent, cur);
 292}
 293
 294static void iter_walk_down(struct prio_tree_iter *iter)
 295{
 296        iter->mask >>= 1;
 297        if (iter->mask) {
 298                if (iter->size_level)
 299                        iter->size_level++;
 300                return;
 301        }
 302
 303        if (iter->size_level) {
 304                BUG_ON(!prio_tree_left_empty(iter->cur));
 305                BUG_ON(!prio_tree_right_empty(iter->cur));
 306                iter->size_level++;
 307                iter->mask = ULONG_MAX;
 308        } else {
 309                iter->size_level = 1;
 310                iter->mask = 1UL << (BITS_PER_LONG - 1);
 311        }
 312}
 313
 314static void iter_walk_up(struct prio_tree_iter *iter)
 315{
 316        if (iter->mask == ULONG_MAX)
 317                iter->mask = 1UL;
 318        else if (iter->size_level == 1)
 319                iter->mask = 1UL;
 320        else
 321                iter->mask <<= 1;
 322        if (iter->size_level)
 323                iter->size_level--;
 324        if (!iter->size_level && (iter->value & iter->mask))
 325                iter->value ^= iter->mask;
 326}
 327
 328/*
 329 * Following functions help to enumerate all prio_tree_nodes in the tree that
 330 * overlap with the input interval X [radix_index, heap_index]. The enumeration
 331 * takes O(log n + m) time where 'log n' is the height of the tree (which is
 332 * proportional to # of bits required to represent the maximum heap_index) and
 333 * 'm' is the number of prio_tree_nodes that overlap the interval X.
 334 */
 335
 336static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 337                unsigned long *r_index, unsigned long *h_index)
 338{
 339        if (prio_tree_left_empty(iter->cur))
 340                return NULL;
 341
 342        get_index(iter->root, iter->cur->left, r_index, h_index);
 343
 344        if (iter->r_index <= *h_index) {
 345                iter->cur = iter->cur->left;
 346                iter_walk_down(iter);
 347                return iter->cur;
 348        }
 349
 350        return NULL;
 351}
 352
 353static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 354                unsigned long *r_index, unsigned long *h_index)
 355{
 356        unsigned long value;
 357
 358        if (prio_tree_right_empty(iter->cur))
 359                return NULL;
 360
 361        if (iter->size_level)
 362                value = iter->value;
 363        else
 364                value = iter->value | iter->mask;
 365
 366        if (iter->h_index < value)
 367                return NULL;
 368
 369        get_index(iter->root, iter->cur->right, r_index, h_index);
 370
 371        if (iter->r_index <= *h_index) {
 372                iter->cur = iter->cur->right;
 373                iter_walk_down(iter);
 374                return iter->cur;
 375        }
 376
 377        return NULL;
 378}
 379
 380static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 381{
 382        iter->cur = iter->cur->parent;
 383        iter_walk_up(iter);
 384        return iter->cur;
 385}
 386
 387static inline int overlap(struct prio_tree_iter *iter,
 388                unsigned long r_index, unsigned long h_index)
 389{
 390        return iter->h_index >= r_index && iter->r_index <= h_index;
 391}
 392
 393/*
 394 * prio_tree_first:
 395 *
 396 * Get the first prio_tree_node that overlaps with the interval [radix_index,
 397 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 398 * traversal of the tree.
 399 */
 400static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 401{
 402        struct prio_tree_root *root;
 403        unsigned long r_index, h_index;
 404
 405        INIT_PRIO_TREE_ITER(iter);
 406
 407        root = iter->root;
 408        if (prio_tree_empty(root))
 409                return NULL;
 410
 411        get_index(root, root->prio_tree_node, &r_index, &h_index);
 412
 413        if (iter->r_index > h_index)
 414                return NULL;
 415
 416        iter->mask = 1UL << (root->index_bits - 1);
 417        iter->cur = root->prio_tree_node;
 418
 419        while (1) {
 420                if (overlap(iter, r_index, h_index))
 421                        return iter->cur;
 422
 423                if (prio_tree_left(iter, &r_index, &h_index))
 424                        continue;
 425
 426                if (prio_tree_right(iter, &r_index, &h_index))
 427                        continue;
 428
 429                break;
 430        }
 431        return NULL;
 432}
 433
 434/*
 435 * prio_tree_next:
 436 *
 437 * Get the next prio_tree_node that overlaps with the input interval in iter
 438 */
 439struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 440{
 441        unsigned long r_index, h_index;
 442
 443        if (iter->cur == NULL)
 444                return prio_tree_first(iter);
 445
 446repeat:
 447        while (prio_tree_left(iter, &r_index, &h_index))
 448                if (overlap(iter, r_index, h_index))
 449                        return iter->cur;
 450
 451        while (!prio_tree_right(iter, &r_index, &h_index)) {
 452                while (!prio_tree_root(iter->cur) &&
 453                                iter->cur->parent->right == iter->cur)
 454                        prio_tree_parent(iter);
 455
 456                if (prio_tree_root(iter->cur))
 457                        return NULL;
 458
 459                prio_tree_parent(iter);
 460        }
 461
 462        if (overlap(iter, r_index, h_index))
 463                return iter->cur;
 464
 465        goto repeat;
 466}
 467
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