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