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