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 
   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 }
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sys/lib/prio_tree.c
