1 /* 2 * lib/prio_tree.c - priority search tree 3 * 4 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh (at) 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 } 466
