| 1 | /* |
| 2 | * Flexible B-tree implementation. Supports reference counting for |
| 3 | * copy-on-write, user-defined node properties, and variable |
| 4 | * degree. |
| 5 | * |
| 6 | * This file is copyright 2001,2004 Simon Tatham. |
| 7 | * |
| 8 | * Permission is hereby granted, free of charge, to any person |
| 9 | * obtaining a copy of this software and associated documentation |
| 10 | * files (the "Software"), to deal in the Software without |
| 11 | * restriction, including without limitation the rights to use, |
| 12 | * copy, modify, merge, publish, distribute, sublicense, and/or |
| 13 | * sell copies of the Software, and to permit persons to whom the |
| 14 | * Software is furnished to do so, subject to the following |
| 15 | * conditions: |
| 16 | * |
| 17 | * The above copyright notice and this permission notice shall be |
| 18 | * included in all copies or substantial portions of the Software. |
| 19 | * |
| 20 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
| 21 | * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES |
| 22 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
| 23 | * NONINFRINGEMENT. IN NO EVENT SHALL SIMON TATHAM BE LIABLE FOR |
| 24 | * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF |
| 25 | * CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN |
| 26 | * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| 27 | * SOFTWARE. |
| 28 | */ |
| 29 | |
| 30 | /* |
| 31 | * TODO: |
| 32 | * |
| 33 | * Possibly TODO in future, but may not be sensible in this code |
| 34 | * architecture: |
| 35 | * |
| 36 | * - user write properties. |
| 37 | * * this all happens during write_unlock(), I think. Except |
| 38 | * that we'll now need an _internal_ write_unlock() which |
| 39 | * does everything except user write properties. Sigh. |
| 40 | * * note that we also need a transform function for elements |
| 41 | * (rot13 will certainly require this, and reverse will |
| 42 | * require it if the elements themselves are in some way |
| 43 | * reversible). |
| 44 | * |
| 45 | * Still untested: |
| 46 | * - searching on user read properties. |
| 47 | * - user-supplied copy function. |
| 48 | * - bt_add when element already exists. |
| 49 | * - bt_del when element doesn't. |
| 50 | * - splitpos with before==TRUE. |
| 51 | * - split() on sorted elements (but it should be fine). |
| 52 | * - bt_replace, at all (it won't be useful until we get user read |
| 53 | * properties). |
| 54 | * - bt_index_w (won't make much sense until we start using |
| 55 | * user-supplied copy fn). |
| 56 | */ |
| 57 | |
| 58 | #include <stdlib.h> |
| 59 | #include <string.h> |
| 60 | #include <assert.h> |
| 61 | |
| 62 | #ifdef TEST |
| 63 | #include <stdio.h> |
| 64 | #include <stdarg.h> |
| 65 | #endif |
| 66 | |
| 67 | #include "btree.h" |
| 68 | |
| 69 | #ifdef TEST |
| 70 | static void set_invalid_property(void *prop); |
| 71 | #endif |
| 72 | |
| 73 | /* ---------------------------------------------------------------------- |
| 74 | * Type definitions. |
| 75 | */ |
| 76 | |
| 77 | typedef union nodecomponent nodecomponent; |
| 78 | typedef nodecomponent *nodeptr; |
| 79 | |
| 80 | /* |
| 81 | * For type-checking purposes, and to ensure I don't accidentally |
| 82 | * confuse node_addr with node_ptr during implementation, I'll |
| 83 | * define node_addr for the in-memory case as being a struct |
| 84 | * containing only a nodeptr. |
| 85 | * |
| 86 | * This unfortunately needs to go in btree.h so that clients |
| 87 | * writing user properties can know about the nodecomponent |
| 88 | * structure. |
| 89 | */ |
| 90 | typedef struct { |
| 91 | nodeptr p; |
| 92 | } node_addr; |
| 93 | |
| 94 | /* |
| 95 | * A B-tree node is a horrible thing when you're trying to be |
| 96 | * flexible. It is of variable size, and it contains a variety of |
| 97 | * distinct types of thing: nodes, elements, some counters, some |
| 98 | * user-defined properties ... it's a horrible thing. So we define |
| 99 | * it as an array of unions, each union being either an `int' or a |
| 100 | * `bt_element_t' or a `node_addr'... |
| 101 | */ |
| 102 | |
| 103 | union nodecomponent { |
| 104 | int i; |
| 105 | node_addr na; |
| 106 | bt_element_t ep; |
| 107 | }; |
| 108 | |
| 109 | static const node_addr NODE_ADDR_NULL = { NULL }; |
| 110 | |
| 111 | /* |
| 112 | * The array of nodecomponents will take the following form: |
| 113 | * |
| 114 | * - (maxdegree) child pointers. |
| 115 | * - (maxdegree-1) element pointers. |
| 116 | * - one subtree count (current number of child pointers that are |
| 117 | * valid; note that `valid' doesn't imply non-NULL). |
| 118 | * - one element count. |
| 119 | * - one reference count. |
| 120 | */ |
| 121 | |
| 122 | struct btree { |
| 123 | int mindegree; /* min number of subtrees */ |
| 124 | int maxdegree; /* max number of subtrees */ |
| 125 | int depth; /* helps to store this explicitly */ |
| 126 | node_addr root; |
| 127 | cmpfn_t cmp; |
| 128 | copyfn_t copy; |
| 129 | freefn_t freeelt; |
| 130 | int propsize, propalign, propoffset; |
| 131 | propmakefn_t propmake; |
| 132 | propmergefn_t propmerge; |
| 133 | void *userstate; /* passed to all user functions */ |
| 134 | }; |
| 135 | |
| 136 | /* ---------------------------------------------------------------------- |
| 137 | * Memory management routines and other housekeeping. |
| 138 | */ |
| 139 | #ifdef HAVE_ALLOCA |
| 140 | # define ialloc(x) alloca(x) |
| 141 | # define ifree(x) |
| 142 | #else |
| 143 | # define ialloc(x) smalloc(x) |
| 144 | # define ifree(x) sfree(x) |
| 145 | #endif |
| 146 | |
| 147 | #define new1(t) ( (t *) smalloc(sizeof(t)) ) |
| 148 | #define newn(t, n) ( (t *) smalloc((n) * sizeof(t)) ) |
| 149 | #define inew1(t) ( (t *) ialloc(sizeof(t)) ) |
| 150 | #define inewn(t, n) ( (t *) ialloc((n) * sizeof(t)) ) |
| 151 | |
| 152 | static void *smalloc(size_t size) |
| 153 | { |
| 154 | void *ret = malloc(size); |
| 155 | if (!ret) |
| 156 | abort(); |
| 157 | return ret; |
| 158 | } |
| 159 | |
| 160 | static void sfree(void *p) |
| 161 | { |
| 162 | free(p); |
| 163 | } |
| 164 | |
| 165 | #ifndef FALSE |
| 166 | #define FALSE 0 |
| 167 | #endif |
| 168 | #ifndef TRUE |
| 169 | #define TRUE 1 |
| 170 | #endif |
| 171 | |
| 172 | /* We could probably do with more compiler-specific branches of this #if. */ |
| 173 | #if defined(__GNUC__) |
| 174 | #define INLINE __inline |
| 175 | #else |
| 176 | #define INLINE |
| 177 | #endif |
| 178 | |
| 179 | /* Hooks into the low-level code for test purposes. */ |
| 180 | #ifdef TEST |
| 181 | void testlock(int write, int set, nodeptr n); |
| 182 | #else |
| 183 | #define testlock(w,s,n) |
| 184 | #endif |
| 185 | |
| 186 | /* ---------------------------------------------------------------------- |
| 187 | * Low-level helper routines, which understand the in-memory format |
| 188 | * of a node and know how to read-lock and write-lock. |
| 189 | */ |
| 190 | |
| 191 | /* |
| 192 | * Read and write the node_addr of a child. |
| 193 | */ |
| 194 | static INLINE node_addr bt_child(btree *bt, nodeptr n, int index) |
| 195 | { |
| 196 | return n[index].na; |
| 197 | } |
| 198 | static INLINE void bt_set_child(btree *bt, nodeptr n, |
| 199 | int index, node_addr value) |
| 200 | { |
| 201 | n[index].na = value; |
| 202 | } |
| 203 | |
| 204 | /* |
| 205 | * Read and write the address of an element. |
| 206 | */ |
| 207 | static INLINE bt_element_t bt_element(btree *bt, nodeptr n, int index) |
| 208 | { |
| 209 | return n[bt->maxdegree + index].ep; |
| 210 | } |
| 211 | static INLINE void bt_set_element(btree *bt, nodeptr n, |
| 212 | int index, bt_element_t value) |
| 213 | { |
| 214 | n[bt->maxdegree + index].ep = value; |
| 215 | } |
| 216 | |
| 217 | /* |
| 218 | * Give the number of subtrees currently present in an element. |
| 219 | */ |
| 220 | static INLINE int bt_subtrees(btree *bt, nodeptr n) |
| 221 | { |
| 222 | return n[bt->maxdegree*2-1].i; |
| 223 | } |
| 224 | #define bt_elements(bt,n) (bt_subtrees(bt,n) - 1) |
| 225 | |
| 226 | /* |
| 227 | * Give the minimum and maximum number of subtrees allowed in a |
| 228 | * node. |
| 229 | */ |
| 230 | static INLINE int bt_min_subtrees(btree *bt) |
| 231 | { |
| 232 | return bt->mindegree; |
| 233 | } |
| 234 | static INLINE int bt_max_subtrees(btree *bt) |
| 235 | { |
| 236 | return bt->maxdegree; |
| 237 | } |
| 238 | |
| 239 | /* |
| 240 | * Return the count of items, and the user properties, in a |
| 241 | * particular subtree of a node. |
| 242 | * |
| 243 | * Note that in the in-memory form of the tree, this breaks the |
| 244 | * read-locking semantics, by reading the counts out of the child |
| 245 | * nodes without bothering to lock them. We're allowed to do this |
| 246 | * because this function is implemented at the same very low level |
| 247 | * as the implementation of bt_read_lock(), so we're allowed to |
| 248 | * know that read locking actually doesn't do anything. |
| 249 | */ |
| 250 | static INLINE int bt_child_count(btree *bt, nodeptr n, int index) |
| 251 | { |
| 252 | if (n[index].na.p) |
| 253 | return n[index].na.p[bt->maxdegree*2].i; |
| 254 | else |
| 255 | return 0; |
| 256 | } |
| 257 | |
| 258 | static INLINE void *bt_child_prop(btree *bt, nodeptr n, int index) |
| 259 | { |
| 260 | if (n[index].na.p) |
| 261 | return (char *)n[index].na.p + bt->propoffset; |
| 262 | else |
| 263 | return NULL; |
| 264 | } |
| 265 | |
| 266 | /* |
| 267 | * Return the count of items in a whole node. |
| 268 | */ |
| 269 | static INLINE int bt_node_count(btree *bt, nodeptr n) |
| 270 | { |
| 271 | return n[bt->maxdegree*2].i; |
| 272 | } |
| 273 | |
| 274 | /* |
| 275 | * Determine whether a node is a leaf node or not. |
| 276 | */ |
| 277 | static INLINE int bt_is_leaf(btree *bt, nodeptr n) |
| 278 | { |
| 279 | return n[0].na.p == NULL; |
| 280 | } |
| 281 | |
| 282 | /* |
| 283 | * Create a new write-locked node, and return a pointer to it. |
| 284 | */ |
| 285 | static INLINE nodeptr bt_new_node(btree *bt, int nsubtrees) |
| 286 | { |
| 287 | nodeptr ret = (nodecomponent *)smalloc(bt->propoffset + bt->propsize); |
| 288 | ret[bt->maxdegree*2-1].i = nsubtrees; |
| 289 | ret[bt->maxdegree*2+1].i = 1; /* reference count 1 */ |
| 290 | #ifdef TEST |
| 291 | set_invalid_property(ret + bt->maxdegree * 2 + 2); |
| 292 | #else |
| 293 | memset((char *)ret + bt->propoffset, 0, bt->propsize); |
| 294 | #endif |
| 295 | testlock(TRUE, TRUE, ret); |
| 296 | return ret; |
| 297 | } |
| 298 | |
| 299 | /* |
| 300 | * Destroy a node (must be write-locked). |
| 301 | */ |
| 302 | static INLINE void bt_destroy_node(btree *bt, nodeptr n) |
| 303 | { |
| 304 | testlock(TRUE, FALSE, n); |
| 305 | /* Free the property. */ |
| 306 | bt->propmerge(bt->userstate, NULL, NULL, n + bt->maxdegree * 2 + 2); |
| 307 | sfree(n); |
| 308 | } |
| 309 | |
| 310 | /* |
| 311 | * Take an existing node and prepare to re-use it in a new context. |
| 312 | */ |
| 313 | static INLINE nodeptr bt_reuse_node(btree *bt, nodeptr n, int nsubtrees) |
| 314 | { |
| 315 | testlock(TRUE, FALSE, n); |
| 316 | testlock(TRUE, TRUE, n); |
| 317 | n[bt->maxdegree*2-1].i = nsubtrees; |
| 318 | return n; |
| 319 | } |
| 320 | |
| 321 | /* |
| 322 | * Return an extra reference to a node, for purposes of cloning. So |
| 323 | * we have to update its reference count as well. |
| 324 | */ |
| 325 | static INLINE node_addr bt_ref_node(btree *bt, node_addr n) |
| 326 | { |
| 327 | if (n.p) |
| 328 | n.p[bt->maxdegree*2+1].i++; |
| 329 | return n; |
| 330 | } |
| 331 | |
| 332 | /* |
| 333 | * Drop a node's reference count, for purposes of freeing. Returns |
| 334 | * the new reference count. Typically this will be tested against |
| 335 | * zero to see if the node needs to be physically freed; hence a |
| 336 | * NULL node_addr causes a return of 1 (because this isn't |
| 337 | * necessary). |
| 338 | */ |
| 339 | static INLINE int bt_unref_node(btree *bt, node_addr n) |
| 340 | { |
| 341 | if (n.p) { |
| 342 | n.p[bt->maxdegree*2+1].i--; |
| 343 | return n.p[bt->maxdegree*2+1].i; |
| 344 | } else |
| 345 | return 1; /* a NULL node is considered OK */ |
| 346 | } |
| 347 | |
| 348 | /* |
| 349 | * Clone a node during write unlocking, if its reference count is |
| 350 | * more than one. |
| 351 | */ |
| 352 | static nodeptr bt_clone_node(btree *bt, nodeptr n) |
| 353 | { |
| 354 | int i; |
| 355 | nodeptr ret = (nodecomponent *)smalloc(bt->propoffset + bt->propsize); |
| 356 | memcpy(ret, n, (bt->maxdegree*2+1) * sizeof(nodecomponent)); |
| 357 | if (bt->copy) { |
| 358 | for (i = 0; i < bt_elements(bt, ret); i++) { |
| 359 | bt_element_t *e = bt_element(bt, ret, i); |
| 360 | bt_set_element(bt, ret, i, bt->copy(bt->userstate, e)); |
| 361 | } |
| 362 | } |
| 363 | ret[bt->maxdegree*2+1].i = 1; /* clone has reference count 1 */ |
| 364 | n[bt->maxdegree*2+1].i--; /* drop original's ref count by one */ |
| 365 | /* |
| 366 | * At this low level, we're allowed to reach directly into the |
| 367 | * subtrees to fiddle with their reference counts without |
| 368 | * having to lock them. |
| 369 | */ |
| 370 | for (i = 0; i < bt_subtrees(bt, ret); i++) { |
| 371 | node_addr na = bt_child(bt, ret, i); |
| 372 | if (na.p) |
| 373 | na.p[bt->maxdegree*2+1].i++; /* inc ref count of each child */ |
| 374 | } |
| 375 | /* |
| 376 | * Copy the user property explicitly (in case it contains a |
| 377 | * pointer to an allocated area). |
| 378 | */ |
| 379 | memset((char *)ret + bt->propoffset, 0, bt->propsize); |
| 380 | bt->propmerge(bt->userstate, NULL, n + bt->maxdegree * 2 + 2, |
| 381 | ret + bt->maxdegree * 2 + 2); |
| 382 | return ret; |
| 383 | } |
| 384 | |
| 385 | /* |
| 386 | * Return the node_addr for a currently locked node. NB that this |
| 387 | * means node movement must take place during _locking_ rather than |
| 388 | * unlocking! |
| 389 | */ |
| 390 | static INLINE node_addr bt_node_addr(btree *bt, nodeptr n) |
| 391 | { |
| 392 | node_addr ret; |
| 393 | ret.p = n; |
| 394 | return ret; |
| 395 | } |
| 396 | |
| 397 | /* |
| 398 | * The bt_write_lock and bt_read_lock functions should gracefully |
| 399 | * handle being asked to write-lock a null node pointer, and just |
| 400 | * return a null nodeptr. |
| 401 | */ |
| 402 | static INLINE nodeptr bt_write_lock_child(btree *bt, nodeptr a, int index) |
| 403 | { |
| 404 | node_addr addr = bt_child(bt, a, index); |
| 405 | if (addr.p && addr.p[bt->maxdegree*2+1].i > 1) { |
| 406 | nodeptr clone = bt_clone_node(bt, addr.p); |
| 407 | bt_set_child(bt, a, index, bt_node_addr(bt, clone)); |
| 408 | testlock(TRUE, TRUE, clone); |
| 409 | return clone; |
| 410 | } |
| 411 | testlock(TRUE, TRUE, addr.p); |
| 412 | return addr.p; |
| 413 | } |
| 414 | static INLINE nodeptr bt_write_lock_root(btree *bt) |
| 415 | { |
| 416 | node_addr addr = bt->root; |
| 417 | if (addr.p && addr.p[bt->maxdegree*2+1].i > 1) { |
| 418 | nodeptr clone = bt_clone_node(bt, addr.p); |
| 419 | bt->root = bt_node_addr(bt, clone); |
| 420 | testlock(TRUE, TRUE, clone); |
| 421 | return clone; |
| 422 | } |
| 423 | testlock(TRUE, TRUE, addr.p); |
| 424 | return addr.p; |
| 425 | } |
| 426 | static INLINE nodeptr bt_read_lock(btree *bt, node_addr a) |
| 427 | { |
| 428 | testlock(FALSE, TRUE, a.p); |
| 429 | return a.p; |
| 430 | } |
| 431 | #define bt_read_lock_root(bt) (bt_read_lock(bt, (bt)->root)) |
| 432 | #define bt_read_lock_child(bt,a,index) (bt_read_lock(bt,bt_child(bt,a,index))) |
| 433 | |
| 434 | static INLINE void bt_write_relock(btree *bt, nodeptr n, int props) |
| 435 | { |
| 436 | int i, ns, count; |
| 437 | |
| 438 | /* |
| 439 | * Update the count in the node. |
| 440 | */ |
| 441 | ns = bt_subtrees(bt, n); |
| 442 | count = ns-1; /* count the elements */ |
| 443 | for (i = 0; i < ns; i++) |
| 444 | count += bt_child_count(bt, n, i); |
| 445 | n[bt->maxdegree*2].i = count; |
| 446 | testlock(TRUE, FALSE, n); |
| 447 | testlock(TRUE, TRUE, n); |
| 448 | |
| 449 | /* |
| 450 | * Update user read properties. |
| 451 | */ |
| 452 | if (props && bt->propsize) { |
| 453 | void *prevprop, *eltprop, *thisprop, *childprop; |
| 454 | |
| 455 | prevprop = NULL; |
| 456 | eltprop = ialloc(bt->propsize); |
| 457 | thisprop = (void *)((char *)n + bt->propoffset); |
| 458 | |
| 459 | for (i = 0; i < ns; i++) { |
| 460 | /* Merge a subtree's property into this one. |
| 461 | * Initially prevprop==NULL, meaning to just copy. */ |
| 462 | if ( (childprop = bt_child_prop(bt, n, i)) != NULL ) { |
| 463 | bt->propmerge(bt->userstate, prevprop, childprop, thisprop); |
| 464 | prevprop = thisprop; |
| 465 | } |
| 466 | |
| 467 | if (i < ns-1) { |
| 468 | /* Now merge in the separating element. */ |
| 469 | bt->propmake(bt->userstate, bt_element(bt, n, i), eltprop); |
| 470 | bt->propmerge(bt->userstate, prevprop, eltprop, thisprop); |
| 471 | prevprop = thisprop; |
| 472 | } |
| 473 | } |
| 474 | |
| 475 | ifree(eltprop); |
| 476 | } |
| 477 | } |
| 478 | |
| 479 | static INLINE node_addr bt_write_unlock_internal(btree *bt, nodeptr n, |
| 480 | int props) |
| 481 | { |
| 482 | node_addr ret; |
| 483 | |
| 484 | bt_write_relock(bt, n, props); |
| 485 | |
| 486 | testlock(TRUE, FALSE, n); |
| 487 | |
| 488 | ret.p = n; |
| 489 | return ret; |
| 490 | } |
| 491 | |
| 492 | static INLINE node_addr bt_write_unlock(btree *bt, nodeptr n) |
| 493 | { |
| 494 | return bt_write_unlock_internal(bt, n, TRUE); |
| 495 | } |
| 496 | |
| 497 | static INLINE void bt_read_unlock(btree *bt, nodeptr n) |
| 498 | { |
| 499 | /* |
| 500 | * For trees in memory, we do nothing here, except run some |
| 501 | * optional testing. |
| 502 | */ |
| 503 | testlock(FALSE, FALSE, n); |
| 504 | } |
| 505 | |
| 506 | /* ---------------------------------------------------------------------- |
| 507 | * Higher-level helper functions, which should be independent of |
| 508 | * the knowledge of precise node structure in the above code. |
| 509 | */ |
| 510 | |
| 511 | /* |
| 512 | * Return the count of items below a node that appear before the |
| 513 | * start of a given subtree. |
| 514 | */ |
| 515 | static int bt_child_startpos(btree *bt, nodeptr n, int index) |
| 516 | { |
| 517 | int pos = 0; |
| 518 | |
| 519 | while (index > 0) { |
| 520 | index--; |
| 521 | pos += bt_child_count(bt, n, index) + 1; /* 1 for separating elt */ |
| 522 | } |
| 523 | return pos; |
| 524 | } |
| 525 | |
| 526 | /* |
| 527 | * Create a new root node for a tree. |
| 528 | */ |
| 529 | static void bt_new_root(btree *bt, node_addr left, node_addr right, |
| 530 | bt_element_t element) |
| 531 | { |
| 532 | nodeptr n; |
| 533 | n = bt_new_node(bt, 2); |
| 534 | bt_set_child(bt, n, 0, left); |
| 535 | bt_set_child(bt, n, 1, right); |
| 536 | bt_set_element(bt, n, 0, element); |
| 537 | bt->root = bt_write_unlock(bt, n); |
| 538 | bt->depth++; |
| 539 | } |
| 540 | |
| 541 | /* |
| 542 | * Discard the root node of a tree, and enshrine a new node as the |
| 543 | * root. Expects to be passed a write-locked nodeptr to the old |
| 544 | * root. |
| 545 | */ |
| 546 | static void bt_shift_root(btree *bt, nodeptr n, node_addr na) |
| 547 | { |
| 548 | bt_destroy_node(bt, n); |
| 549 | bt->root = na; |
| 550 | bt->depth--; |
| 551 | } |
| 552 | |
| 553 | /* |
| 554 | * Given a numeric index within a node, find which subtree we would |
| 555 | * descend to in order to find that index. |
| 556 | * |
| 557 | * Updates `pos' to give the numeric index within the subtree |
| 558 | * found. Also returns `ends' (if non-NULL), which has bit 0 set if |
| 559 | * the index is at the very left edge of the subtree, and/or bit 1 |
| 560 | * if it's at the very right edge. |
| 561 | * |
| 562 | * Return value is the number of the subtree (0 upwards). |
| 563 | */ |
| 564 | #define ENDS_NONE 0 |
| 565 | #define ENDS_LEFT 1 |
| 566 | #define ENDS_RIGHT 2 |
| 567 | #define ENDS_BOTH 3 |
| 568 | static int bt_lookup_pos(btree *bt, nodeptr n, int *pos, int *ends) |
| 569 | { |
| 570 | int child = 0; |
| 571 | int nchildren = bt_subtrees(bt, n); |
| 572 | |
| 573 | while (child < nchildren) { |
| 574 | int count = bt_child_count(bt, n, child); |
| 575 | if (*pos <= count) { |
| 576 | if (ends) { |
| 577 | *ends = 0; |
| 578 | if (*pos == count) |
| 579 | *ends |= ENDS_RIGHT; |
| 580 | if (*pos == 0) |
| 581 | *ends |= ENDS_LEFT; |
| 582 | } |
| 583 | return child; |
| 584 | } |
| 585 | *pos -= count + 1; /* 1 for the separating element */ |
| 586 | child++; |
| 587 | } |
| 588 | return -1; /* ran off the end; shouldn't happen */ |
| 589 | } |
| 590 | |
| 591 | /* |
| 592 | * Given an element to search for within a node, find either the |
| 593 | * element, or which subtree we would descend to to continue |
| 594 | * searching for that element. |
| 595 | * |
| 596 | * Return value is either the index of the element, or the index of |
| 597 | * the subtree (both 0 upwards). `is_elt' returns FALSE or TRUE |
| 598 | * respectively. |
| 599 | * |
| 600 | * Since this may be used by bt_find() with an alternative cmpfn_t, |
| 601 | * we always pass the input element as the first argument to cmp. |
| 602 | */ |
| 603 | static int bt_lookup_cmp(btree *bt, nodeptr n, bt_element_t element, |
| 604 | cmpfn_t cmp, int *is_elt) |
| 605 | { |
| 606 | int mintree = 0, maxtree = bt_subtrees(bt, n)-1; |
| 607 | |
| 608 | while (mintree < maxtree) { |
| 609 | int elt = (maxtree + mintree) / 2; |
| 610 | int c = cmp(bt->userstate, element, bt_element(bt, n, elt)); |
| 611 | |
| 612 | if (c == 0) { |
| 613 | *is_elt = TRUE; |
| 614 | return elt; |
| 615 | } else if (c < 0) { |
| 616 | /* |
| 617 | * `element' is less than element `elt'. So it can be |
| 618 | * in subtree number `elt' at the highest. |
| 619 | */ |
| 620 | maxtree = elt; |
| 621 | } else { /* c > 0 */ |
| 622 | /* |
| 623 | * `element' is greater than element `elt'. So it can |
| 624 | * be in subtree number (elt+1) at the lowest. |
| 625 | */ |
| 626 | mintree = elt+1; |
| 627 | } |
| 628 | } |
| 629 | |
| 630 | /* |
| 631 | * If we reach here without returning, we must have narrowed |
| 632 | * our search to the point where mintree = maxtree. So the |
| 633 | * element is not in the node itself and we know which subtree |
| 634 | * to search next. |
| 635 | */ |
| 636 | assert(mintree == maxtree); |
| 637 | *is_elt = FALSE; |
| 638 | return mintree; |
| 639 | } |
| 640 | |
| 641 | /* |
| 642 | * Generic transformations on B-tree nodes. |
| 643 | * |
| 644 | * This function divides essentially into an input side and an |
| 645 | * output side. The input side accumulates a list of items |
| 646 | * node,element,node,element,...,element,node; the output side |
| 647 | * writes those items into either one or two nodes. |
| 648 | * |
| 649 | * `intype' can be: |
| 650 | * |
| 651 | * - NODE_AS_IS. The input list is the contents of in1, followed |
| 652 | * by inelt, followed by the contents of in2. The `extra' |
| 653 | * parameters are unused, as is `inaux'. |
| 654 | * |
| 655 | * - NODE_ADD_ELT. `in2' is unused. The input list is the contents |
| 656 | * of `in1', but with subtree pointer number `inaux' replaced by |
| 657 | * extra1/inelt/extra2. |
| 658 | * |
| 659 | * - NODE_DEL_ELT. `in2' and `inelt' are unused, as is `extra2'. |
| 660 | * The input list is the contents of `in1', but with element |
| 661 | * pointer number `inaux' and its surrounding two subtrees |
| 662 | * replaced by extra1. |
| 663 | * |
| 664 | * Having obtained the input list, it is then written to one or two |
| 665 | * output nodes. If `splitpos' is NODE_JOIN, everything is written |
| 666 | * into one output node `out1'. Otherwise, `splitpos' is treated as |
| 667 | * an element index within the input list; that element is returned |
| 668 | * in `outelt', and the contents of the list is divided there and |
| 669 | * returned in nodes `out1' and `out2'. |
| 670 | * |
| 671 | * This function will re-use nodes in the `obvious' order. If two |
| 672 | * nodes are passed in and two nodes are output, they'll be the |
| 673 | * same nodes; if one node is passed in and one node output, it |
| 674 | * will be the same node too. If two are passed in and only one |
| 675 | * output, the first one will be used and the second destroyed; if |
| 676 | * one node is passed in and two are output, the one passed in will |
| 677 | * be the first of those returned, and the second will be new. |
| 678 | */ |
| 679 | #define NODE_AS_IS 1 |
| 680 | #define NODE_ADD_ELT 2 |
| 681 | #define NODE_DEL_ELT 3 |
| 682 | #define NODE_JOIN -1 |
| 683 | static void bt_xform(btree *bt, int intype, int inaux, |
| 684 | nodeptr in1, nodeptr in2, bt_element_t inelt, |
| 685 | node_addr extra1, node_addr extra2, |
| 686 | int splitpos, nodeptr *out1, nodeptr *out2, |
| 687 | bt_element_t *outelt) |
| 688 | { |
| 689 | node_addr *nodes; |
| 690 | bt_element_t *elements; |
| 691 | nodeptr ret1, ret2; |
| 692 | int n1, n2, off2, i, j; |
| 693 | |
| 694 | nodes = inewn(node_addr, 2 * bt_max_subtrees(bt)); |
| 695 | elements = inewn(bt_element_t, 2 * bt_max_subtrees(bt)); |
| 696 | |
| 697 | /* |
| 698 | * Accumulate the input list. |
| 699 | */ |
| 700 | switch(intype) { |
| 701 | case NODE_AS_IS: |
| 702 | n1 = bt_subtrees(bt, in1); |
| 703 | n2 = bt_subtrees(bt, in2); |
| 704 | off2 = 0; |
| 705 | break; |
| 706 | case NODE_ADD_ELT: |
| 707 | in2 = in1; |
| 708 | n1 = inaux+1; |
| 709 | n2 = bt_subtrees(bt, in1) - inaux; |
| 710 | off2 = inaux; |
| 711 | break; |
| 712 | case NODE_DEL_ELT: |
| 713 | in2 = in1; |
| 714 | n1 = inaux+1; |
| 715 | n2 = bt_subtrees(bt, in1) - inaux - 1; |
| 716 | off2 = inaux+1; |
| 717 | break; |
| 718 | } |
| 719 | i = j = 0; |
| 720 | while (j < n1) { |
| 721 | nodes[i] = bt_child(bt, in1, j); |
| 722 | if (j+1 < n1) |
| 723 | elements[i] = bt_element(bt, in1, j); |
| 724 | i++, j++; |
| 725 | } |
| 726 | if (intype == NODE_DEL_ELT) { |
| 727 | i--; |
| 728 | } |
| 729 | j = 0; |
| 730 | while (j < n2) { |
| 731 | nodes[i] = bt_child(bt, in2, off2+j); |
| 732 | if (j+1 < n2) |
| 733 | elements[i] = bt_element(bt, in2, off2+j); |
| 734 | i++, j++; |
| 735 | } |
| 736 | switch (intype) { |
| 737 | case NODE_AS_IS: |
| 738 | elements[n1-1] = inelt; |
| 739 | break; |
| 740 | case NODE_ADD_ELT: |
| 741 | nodes[n1-1] = extra1; |
| 742 | nodes[n1] = extra2; |
| 743 | elements[n1-1] = inelt; |
| 744 | break; |
| 745 | case NODE_DEL_ELT: |
| 746 | nodes[n1-1] = extra1; |
| 747 | break; |
| 748 | } |
| 749 | |
| 750 | /* |
| 751 | * Now determine how many subtrees go in each output node, and |
| 752 | * actually create the nodes to be returned. |
| 753 | */ |
| 754 | if (splitpos != NODE_JOIN) { |
| 755 | n1 = splitpos+1, n2 = i - splitpos - 1; |
| 756 | if (outelt) |
| 757 | *outelt = elements[splitpos]; |
| 758 | } else { |
| 759 | n1 = i, n2 = 0; |
| 760 | } |
| 761 | |
| 762 | ret1 = bt_reuse_node(bt, in1, n1); |
| 763 | if (intype == NODE_AS_IS && in2) { |
| 764 | /* We have a second input node. */ |
| 765 | if (n2) |
| 766 | ret2 = bt_reuse_node(bt, in2, n2); |
| 767 | else |
| 768 | bt_destroy_node(bt, in2); |
| 769 | } else { |
| 770 | /* We have no second input node. */ |
| 771 | if (n2) |
| 772 | ret2 = bt_new_node(bt, n2); |
| 773 | else |
| 774 | ret2 = NULL; |
| 775 | } |
| 776 | |
| 777 | if (out1) *out1 = ret1; |
| 778 | if (out2) *out2 = ret2; |
| 779 | |
| 780 | for (i = 0; i < n1; i++) { |
| 781 | bt_set_child(bt, ret1, i, nodes[i]); |
| 782 | if (i+1 < n1) |
| 783 | bt_set_element(bt, ret1, i, elements[i]); |
| 784 | } |
| 785 | if (n2) { |
| 786 | if (outelt) *outelt = elements[n1-1]; |
| 787 | for (i = 0; i < n2; i++) { |
| 788 | bt_set_child(bt, ret2, i, nodes[n1+i]); |
| 789 | if (i+1 < n2) |
| 790 | bt_set_element(bt, ret2, i, elements[n1+i]); |
| 791 | } |
| 792 | } |
| 793 | |
| 794 | ifree(nodes); |
| 795 | ifree(elements); |
| 796 | } |
| 797 | |
| 798 | /* |
| 799 | * Fiddly little compare functions for use in special cases of |
| 800 | * findrelpos. One always returns +1 (a > b), the other always |
| 801 | * returns -1 (a < b). |
| 802 | */ |
| 803 | static int bt_cmp_greater(void *state, |
| 804 | const bt_element_t a, const bt_element_t b) |
| 805 | { |
| 806 | return +1; |
| 807 | } |
| 808 | static int bt_cmp_less(void *state, |
| 809 | const bt_element_t a, const bt_element_t b) |
| 810 | { |
| 811 | return -1; |
| 812 | } |
| 813 | |
| 814 | /* ---------------------------------------------------------------------- |
| 815 | * User-visible administration routines. |
| 816 | */ |
| 817 | |
| 818 | btree *bt_new(cmpfn_t cmp, copyfn_t copy, freefn_t freeelt, |
| 819 | int propsize, int propalign, propmakefn_t propmake, |
| 820 | propmergefn_t propmerge, void *state, int mindegree) |
| 821 | { |
| 822 | btree *ret; |
| 823 | |
| 824 | ret = new1(btree); |
| 825 | ret->mindegree = mindegree; |
| 826 | ret->maxdegree = 2*mindegree; |
| 827 | ret->depth = 0; /* not even a root right now */ |
| 828 | ret->root = NODE_ADDR_NULL; |
| 829 | ret->cmp = cmp; |
| 830 | ret->copy = copy; |
| 831 | ret->freeelt = freeelt; |
| 832 | ret->propsize = propsize; |
| 833 | ret->propalign = propalign; |
| 834 | ret->propoffset = sizeof(nodecomponent) * (ret->maxdegree*2 + 2); |
| 835 | if (propalign > 0) { |
| 836 | ret->propoffset += propalign - 1; |
| 837 | ret->propoffset -= ret->propoffset % propalign; |
| 838 | } |
| 839 | ret->propmake = propmake; |
| 840 | ret->propmerge = propmerge; |
| 841 | ret->userstate = state; |
| 842 | |
| 843 | return ret; |
| 844 | } |
| 845 | |
| 846 | static void bt_free_node(btree *bt, nodeptr n) |
| 847 | { |
| 848 | int i; |
| 849 | |
| 850 | for (i = 0; i < bt_subtrees(bt, n); i++) { |
| 851 | node_addr na; |
| 852 | nodeptr n2; |
| 853 | |
| 854 | na = bt_child(bt, n, i); |
| 855 | if (!bt_unref_node(bt, na)) { |
| 856 | n2 = bt_write_lock_child(bt, n, i); |
| 857 | bt_free_node(bt, n2); |
| 858 | } |
| 859 | } |
| 860 | |
| 861 | if (bt->freeelt) { |
| 862 | for (i = 0; i < bt_subtrees(bt, n)-1; i++) |
| 863 | bt->freeelt(bt->userstate, bt_element(bt, n, i)); |
| 864 | } |
| 865 | |
| 866 | bt_destroy_node(bt, n); |
| 867 | } |
| 868 | |
| 869 | void bt_free(btree *bt) |
| 870 | { |
| 871 | nodeptr n; |
| 872 | |
| 873 | if (!bt_unref_node(bt, bt->root)) { |
| 874 | n = bt_write_lock_root(bt); |
| 875 | bt_free_node(bt, n); |
| 876 | } |
| 877 | |
| 878 | sfree(bt); |
| 879 | } |
| 880 | |
| 881 | btree *bt_clone(btree *bt) |
| 882 | { |
| 883 | btree *bt2; |
| 884 | |
| 885 | bt2 = bt_new(bt->cmp, bt->copy, bt->freeelt, bt->propsize, bt->propalign, |
| 886 | bt->propmake, bt->propmerge, bt->userstate, bt->mindegree); |
| 887 | bt2->depth = bt->depth; |
| 888 | bt2->root = bt_ref_node(bt, bt->root); |
| 889 | return bt2; |
| 890 | } |
| 891 | |
| 892 | /* |
| 893 | * Nice simple function to count the size of a tree. |
| 894 | */ |
| 895 | int bt_count(btree *bt) |
| 896 | { |
| 897 | int count; |
| 898 | nodeptr n; |
| 899 | |
| 900 | n = bt_read_lock_root(bt); |
| 901 | if (n) { |
| 902 | count = bt_node_count(bt, n); |
| 903 | bt_read_unlock(bt, n); |
| 904 | return count; |
| 905 | } else { |
| 906 | return 0; |
| 907 | } |
| 908 | } |
| 909 | |
| 910 | /* ---------------------------------------------------------------------- |
| 911 | * Actual B-tree algorithms. |
| 912 | */ |
| 913 | |
| 914 | /* |
| 915 | * Find an element by numeric index. bt_index_w is the same, but |
| 916 | * works with write locks instead of read locks, so it guarantees |
| 917 | * to return an element with only one reference to it. (You'd use |
| 918 | * this if you were using tree cloning, and wanted to modify the |
| 919 | * element once you'd found it.) |
| 920 | */ |
| 921 | bt_element_t bt_index(btree *bt, int index) |
| 922 | { |
| 923 | nodeptr n, n2; |
| 924 | int child, ends; |
| 925 | |
| 926 | n = bt_read_lock_root(bt); |
| 927 | |
| 928 | if (index < 0 || index >= bt_node_count(bt, n)) { |
| 929 | bt_read_unlock(bt, n); |
| 930 | return NULL; |
| 931 | } |
| 932 | |
| 933 | while (1) { |
| 934 | child = bt_lookup_pos(bt, n, &index, &ends); |
| 935 | if (ends & ENDS_RIGHT) { |
| 936 | bt_element_t ret = bt_element(bt, n, child); |
| 937 | bt_read_unlock(bt, n); |
| 938 | return ret; |
| 939 | } |
| 940 | n2 = bt_read_lock_child(bt, n, child); |
| 941 | bt_read_unlock(bt, n); |
| 942 | n = n2; |
| 943 | assert(n != NULL); |
| 944 | } |
| 945 | } |
| 946 | |
| 947 | bt_element_t bt_index_w(btree *bt, int index) |
| 948 | { |
| 949 | nodeptr n, n2; |
| 950 | int nnodes, child, ends; |
| 951 | nodeptr *nodes; |
| 952 | bt_element_t ret; |
| 953 | |
| 954 | nodes = inewn(nodeptr, bt->depth+1); |
| 955 | nnodes = 0; |
| 956 | |
| 957 | n = bt_write_lock_root(bt); |
| 958 | |
| 959 | if (index < 0 || index >= bt_node_count(bt, n)) { |
| 960 | bt_write_unlock(bt, n); |
| 961 | return NULL; |
| 962 | } |
| 963 | |
| 964 | while (1) { |
| 965 | nodes[nnodes++] = n; |
| 966 | child = bt_lookup_pos(bt, n, &index, &ends); |
| 967 | if (ends & ENDS_RIGHT) { |
| 968 | ret = bt_element(bt, n, child); |
| 969 | break; |
| 970 | } |
| 971 | n2 = bt_write_lock_child(bt, n, child); |
| 972 | n = n2; |
| 973 | assert(n != NULL); |
| 974 | } |
| 975 | |
| 976 | while (nnodes-- > 0) |
| 977 | bt_write_unlock(bt, nodes[nnodes]); |
| 978 | |
| 979 | return ret; |
| 980 | } |
| 981 | |
| 982 | /* |
| 983 | * Search for an element by sorted order. |
| 984 | */ |
| 985 | bt_element_t bt_findrelpos(btree *bt, bt_element_t element, cmpfn_t cmp, |
| 986 | int relation, int *index) |
| 987 | { |
| 988 | nodeptr n, n2; |
| 989 | int child, is_elt; |
| 990 | bt_element_t gotit; |
| 991 | int pos = 0; |
| 992 | int count; |
| 993 | |
| 994 | if (!cmp) cmp = bt->cmp; |
| 995 | |
| 996 | /* |
| 997 | * Special case: relation LT/GT and element NULL means get an |
| 998 | * extreme element of the tree. We do this by fudging the |
| 999 | * compare function so that our NULL element will be considered |
| 1000 | * infinitely large or infinitely small. |
| 1001 | */ |
| 1002 | if (element == NULL) { |
| 1003 | assert(relation == BT_REL_LT || relation == BT_REL_GT); |
| 1004 | if (relation == BT_REL_LT) |
| 1005 | cmp = bt_cmp_greater; /* always returns a > b */ |
| 1006 | else |
| 1007 | cmp = bt_cmp_less; /* always returns a < b */ |
| 1008 | } |
| 1009 | |
| 1010 | gotit = NULL; |
| 1011 | n = bt_read_lock_root(bt); |
| 1012 | if (!n) |
| 1013 | return NULL; |
| 1014 | count = bt_node_count(bt, n); |
| 1015 | while (n) { |
| 1016 | child = bt_lookup_cmp(bt, n, element, cmp, &is_elt); |
| 1017 | if (is_elt) { |
| 1018 | pos += bt_child_startpos(bt, n, child+1) - 1; |
| 1019 | gotit = bt_element(bt, n, child); |
| 1020 | bt_read_unlock(bt, n); |
| 1021 | break; |
| 1022 | } else { |
| 1023 | pos += bt_child_startpos(bt, n, child); |
| 1024 | n2 = bt_read_lock_child(bt, n, child); |
| 1025 | bt_read_unlock(bt, n); |
| 1026 | n = n2; |
| 1027 | } |
| 1028 | } |
| 1029 | |
| 1030 | /* |
| 1031 | * Now all nodes are unlocked, and we are _either_ (a) holding |
| 1032 | * an element in `gotit' whose index we have in `pos', _or_ (b) |
| 1033 | * holding nothing in `gotit' but we know the index of the |
| 1034 | * next-higher element. |
| 1035 | */ |
| 1036 | if (gotit) { |
| 1037 | /* |
| 1038 | * We have the real element. For EQ, LE and GE relations we |
| 1039 | * can now just return it; otherwise we must return the |
| 1040 | * next element down or up. |
| 1041 | */ |
| 1042 | if (relation == BT_REL_LT) |
| 1043 | gotit = bt_index(bt, --pos); |
| 1044 | else if (relation == BT_REL_GT) |
| 1045 | gotit = bt_index(bt, ++pos); |
| 1046 | } else { |
| 1047 | /* |
| 1048 | * We don't have the real element. For EQ relation we now |
| 1049 | * just give up; for everything else we return the next |
| 1050 | * element down or up. |
| 1051 | */ |
| 1052 | if (relation == BT_REL_LT || relation == BT_REL_LE) |
| 1053 | gotit = bt_index(bt, --pos); |
| 1054 | else if (relation == BT_REL_GT || relation == BT_REL_GE) |
| 1055 | gotit = bt_index(bt, pos); |
| 1056 | } |
| 1057 | |
| 1058 | if (gotit && index) *index = pos; |
| 1059 | return gotit; |
| 1060 | } |
| 1061 | bt_element_t bt_findrel(btree *bt, bt_element_t element, cmpfn_t cmp, |
| 1062 | int relation) |
| 1063 | { |
| 1064 | return bt_findrelpos(bt, element, cmp, relation, NULL); |
| 1065 | } |
| 1066 | bt_element_t bt_findpos(btree *bt, bt_element_t element, cmpfn_t cmp, |
| 1067 | int *index) |
| 1068 | { |
| 1069 | return bt_findrelpos(bt, element, cmp, BT_REL_EQ, index); |
| 1070 | } |
| 1071 | bt_element_t bt_find(btree *bt, bt_element_t element, cmpfn_t cmp) |
| 1072 | { |
| 1073 | return bt_findrelpos(bt, element, cmp, BT_REL_EQ, NULL); |
| 1074 | } |
| 1075 | |
| 1076 | /* |
| 1077 | * Find an element by property-based search. Returns the element |
| 1078 | * (if one is selected - the search can also terminate by |
| 1079 | * descending to a nonexistent subtree of a leaf node, equivalent |
| 1080 | * to selecting the _gap_ between two elements); also returns the |
| 1081 | * index of either the element or the gap in `*index' if `index' is |
| 1082 | * non-NULL. |
| 1083 | */ |
| 1084 | bt_element_t bt_propfind(btree *bt, searchfn_t search, void *sstate, |
| 1085 | int *index) |
| 1086 | { |
| 1087 | nodeptr n, n2; |
| 1088 | int i, j, count, is_elt; |
| 1089 | void **props; |
| 1090 | int *counts; |
| 1091 | bt_element_t *elts; |
| 1092 | bt_element_t *e = NULL; |
| 1093 | |
| 1094 | props = inewn(void *, bt->maxdegree); |
| 1095 | counts = inewn(int, bt->maxdegree); |
| 1096 | elts = inewn(bt_element_t, bt->maxdegree); |
| 1097 | |
| 1098 | n = bt_read_lock_root(bt); |
| 1099 | |
| 1100 | count = 0; |
| 1101 | |
| 1102 | while (n) { |
| 1103 | int ntrees = bt_subtrees(bt, n); |
| 1104 | |
| 1105 | /* |
| 1106 | * Prepare the arguments to the search function. |
| 1107 | */ |
| 1108 | for (i = 0; i < ntrees; i++) { |
| 1109 | props[i] = bt_child_prop(bt, n, i); |
| 1110 | counts[i] = bt_child_count(bt, n, i); |
| 1111 | if (i < ntrees-1) |
| 1112 | elts[i] = bt_element(bt, n, i); |
| 1113 | } |
| 1114 | |
| 1115 | /* |
| 1116 | * Call the search function. |
| 1117 | */ |
| 1118 | i = search(bt->userstate, sstate, ntrees, |
| 1119 | props, counts, elts, &is_elt); |
| 1120 | |
| 1121 | if (!is_elt) { |
| 1122 | /* |
| 1123 | * Descend to subtree i. Update `count' to consider |
| 1124 | * everything (both subtrees and elements) before that |
| 1125 | * subtree. |
| 1126 | */ |
| 1127 | for (j = 0; j < i; j++) |
| 1128 | count += 1 + bt_child_count(bt, n, j); |
| 1129 | n2 = bt_read_lock_child(bt, n, i); |
| 1130 | bt_read_unlock(bt, n); |
| 1131 | n = n2; |
| 1132 | } else { |
| 1133 | /* |
| 1134 | * Return element i. Update `count' to consider |
| 1135 | * everything (both subtrees and elements) before that |
| 1136 | * element. |
| 1137 | */ |
| 1138 | for (j = 0; j <= i; j++) |
| 1139 | count += 1 + bt_child_count(bt, n, j); |
| 1140 | count--; /* don't count element i itself */ |
| 1141 | e = bt_element(bt, n, i); |
| 1142 | bt_read_unlock(bt, n); |
| 1143 | break; |
| 1144 | } |
| 1145 | } |
| 1146 | |
| 1147 | ifree(props); |
| 1148 | ifree(counts); |
| 1149 | ifree(elts); |
| 1150 | |
| 1151 | if (index) *index = count; |
| 1152 | return e; |
| 1153 | } |
| 1154 | |
| 1155 | /* |
| 1156 | * Replace the element at a numeric index by a new element. Returns |
| 1157 | * the old element. |
| 1158 | * |
| 1159 | * Can also be used when the new element is the _same_ as the old |
| 1160 | * element, but has changed in some way that will affect user |
| 1161 | * properties. |
| 1162 | */ |
| 1163 | bt_element_t bt_replace(btree *bt, bt_element_t element, int index) |
| 1164 | { |
| 1165 | nodeptr n; |
| 1166 | nodeptr *nodes; |
| 1167 | bt_element_t ret; |
| 1168 | int nnodes, child, ends; |
| 1169 | |
| 1170 | nodes = inewn(nodeptr, bt->depth+1); |
| 1171 | nnodes = 0; |
| 1172 | |
| 1173 | n = bt_write_lock_root(bt); |
| 1174 | |
| 1175 | if (index < 0 || index >= bt_node_count(bt, n)) { |
| 1176 | bt_write_unlock(bt, n); |
| 1177 | return NULL; |
| 1178 | } |
| 1179 | |
| 1180 | while (1) { |
| 1181 | nodes[nnodes++] = n; |
| 1182 | child = bt_lookup_pos(bt, n, &index, &ends); |
| 1183 | if (ends & ENDS_RIGHT) { |
| 1184 | ret = bt_element(bt, n, child); |
| 1185 | bt_set_element(bt, n, child, element); |
| 1186 | break; |
| 1187 | } |
| 1188 | n = bt_write_lock_child(bt, n, child); |
| 1189 | assert(n != NULL); |
| 1190 | } |
| 1191 | |
| 1192 | while (nnodes-- > 0) |
| 1193 | bt_write_unlock(bt, nodes[nnodes]); |
| 1194 | |
| 1195 | return ret; |
| 1196 | } |
| 1197 | |
| 1198 | /* |
| 1199 | * Add at a specific position. As we search down the tree we must |
| 1200 | * write-lock every node we meet, since otherwise we might fail to |
| 1201 | * clone nodes that will end up pointing to different things. |
| 1202 | */ |
| 1203 | void bt_addpos(btree *bt, bt_element_t element, int pos) |
| 1204 | { |
| 1205 | nodeptr n; |
| 1206 | node_addr left, right, single; |
| 1207 | nodeptr *nodes; |
| 1208 | int *childposns; |
| 1209 | int nnodes, child; |
| 1210 | |
| 1211 | /* |
| 1212 | * Since in a reference-counted tree we can't have parent |
| 1213 | * links, we will have to use O(depth) space to store the list |
| 1214 | * of nodeptrs we have gone through, so we can un-write-lock |
| 1215 | * them when we've finished. We also store the subtree index we |
| 1216 | * descended to at each stage. |
| 1217 | */ |
| 1218 | nodes = inewn(nodeptr, bt->depth+1); |
| 1219 | childposns = inewn(int, bt->depth+1); |
| 1220 | nnodes = 0; |
| 1221 | |
| 1222 | n = bt_write_lock_root(bt); |
| 1223 | |
| 1224 | assert(pos >= 0 && pos <= (n ? bt_node_count(bt, n) : 0)); |
| 1225 | |
| 1226 | /* |
| 1227 | * Scan down the tree, write-locking nodes, until we find the |
| 1228 | * empty subtree where we want to insert the item. |
| 1229 | */ |
| 1230 | while (n) { |
| 1231 | nodes[nnodes] = n; |
| 1232 | child = bt_lookup_pos(bt, n, &pos, NULL); |
| 1233 | childposns[nnodes] = child; |
| 1234 | nnodes++; |
| 1235 | n = bt_write_lock_child(bt, n, child); |
| 1236 | } |
| 1237 | |
| 1238 | left = right = NODE_ADDR_NULL; |
| 1239 | |
| 1240 | /* |
| 1241 | * Now nodes[nnodes-1] wants to have subtree index |
| 1242 | * childposns[nnodes-1] replaced by the node/element/node triple |
| 1243 | * (left,element,right). Propagate this up the tree until we |
| 1244 | * can stop. |
| 1245 | */ |
| 1246 | while (nnodes-- > 0) { |
| 1247 | n = nodes[nnodes]; |
| 1248 | if (bt_subtrees(bt, n) == bt_max_subtrees(bt)) { |
| 1249 | nodeptr lptr, rptr; |
| 1250 | /* Split the node and carry on up. */ |
| 1251 | bt_xform(bt, NODE_ADD_ELT, childposns[nnodes], |
| 1252 | n, NULL, element, left, right, |
| 1253 | bt_min_subtrees(bt), &lptr, &rptr, &element); |
| 1254 | left = bt_write_unlock(bt, lptr); |
| 1255 | right = bt_write_unlock(bt, rptr); |
| 1256 | } else { |
| 1257 | bt_xform(bt, NODE_ADD_ELT, childposns[nnodes], |
| 1258 | n, NULL, element, left, right, |
| 1259 | NODE_JOIN, &n, NULL, NULL); |
| 1260 | single = bt_write_unlock(bt, n); |
| 1261 | break; |
| 1262 | } |
| 1263 | } |
| 1264 | |
| 1265 | /* |
| 1266 | * If nnodes < 0, we have just split the root and we need to |
| 1267 | * build a new root node. |
| 1268 | */ |
| 1269 | if (nnodes < 0) { |
| 1270 | bt_new_root(bt, left, right, element); |
| 1271 | } else { |
| 1272 | /* |
| 1273 | * Now nodes[nnodes-1] just wants to have child pointer |
| 1274 | * child[nnodes-1] replaced by `single', in case the |
| 1275 | * subtree was moved. Propagate this back up to the root, |
| 1276 | * unlocking all nodes. |
| 1277 | */ |
| 1278 | while (nnodes-- > 0) { |
| 1279 | bt_set_child(bt, nodes[nnodes], childposns[nnodes], single); |
| 1280 | single = bt_write_unlock(bt, nodes[nnodes]); |
| 1281 | } |
| 1282 | } |
| 1283 | |
| 1284 | ifree(nodes); |
| 1285 | ifree(childposns); |
| 1286 | } |
| 1287 | |
| 1288 | /* |
| 1289 | * Add an element in sorted order. This is a wrapper on bt_addpos() |
| 1290 | * which finds the numeric index to add the item at and then calls |
| 1291 | * addpos. This isn't an optimal use of time, but it saves space by |
| 1292 | * avoiding starting to clone multiply-linked nodes until it's |
| 1293 | * known that the item _can_ be added to the tree (and isn't |
| 1294 | * duplicated in it already). |
| 1295 | */ |
| 1296 | bt_element_t bt_add(btree *bt, bt_element_t element) |
| 1297 | { |
| 1298 | nodeptr n, n2; |
| 1299 | int child, is_elt; |
| 1300 | int pos = 0; |
| 1301 | |
| 1302 | n = bt_read_lock_root(bt); |
| 1303 | while (n) { |
| 1304 | child = bt_lookup_cmp(bt, n, element, bt->cmp, &is_elt); |
| 1305 | if (is_elt) { |
| 1306 | bt_read_unlock(bt, n); |
| 1307 | return bt_element(bt, n, child); /* element exists already */ |
| 1308 | } else { |
| 1309 | pos += bt_child_startpos(bt, n, child); |
| 1310 | n2 = bt_read_lock_child(bt, n, child); |
| 1311 | bt_read_unlock(bt, n); |
| 1312 | n = n2; |
| 1313 | } |
| 1314 | } |
| 1315 | bt_addpos(bt, element, pos); |
| 1316 | return element; |
| 1317 | } |
| 1318 | |
| 1319 | /* |
| 1320 | * Delete an element given its numeric position. Returns the |
| 1321 | * element deleted. |
| 1322 | */ |
| 1323 | bt_element_t bt_delpos(btree *bt, int pos) |
| 1324 | { |
| 1325 | nodeptr n, c, c2, saved_n; |
| 1326 | nodeptr *nodes; |
| 1327 | int nnodes, child, nroot, pos2, ends, st, splitpoint, saved_pos; |
| 1328 | bt_element_t e, ret; |
| 1329 | |
| 1330 | /* |
| 1331 | * Just like in bt_add, we store the set of nodeptrs we |
| 1332 | * write-locked on the way down, so we can unlock them on the |
| 1333 | * way back up. |
| 1334 | */ |
| 1335 | nodes = inewn(nodeptr, bt->depth+1); |
| 1336 | nnodes = 0; |
| 1337 | |
| 1338 | n = bt_write_lock_root(bt); |
| 1339 | nroot = TRUE; |
| 1340 | saved_n = NULL; |
| 1341 | |
| 1342 | if (!n || pos < 0 || pos >= bt_node_count(bt, n)) { |
| 1343 | if (n) |
| 1344 | bt_write_unlock(bt, n); |
| 1345 | return NULL; |
| 1346 | } |
| 1347 | |
| 1348 | while (1) { |
| 1349 | nodes[nnodes++] = n; |
| 1350 | |
| 1351 | /* |
| 1352 | * Find out which subtree to descend to. |
| 1353 | */ |
| 1354 | pos2 = pos; |
| 1355 | child = bt_lookup_pos(bt, n, &pos, &ends); |
| 1356 | c = bt_write_lock_child(bt, n, child); |
| 1357 | if (c && bt_subtrees(bt, c) == bt_min_subtrees(bt)) { |
| 1358 | /* |
| 1359 | * We're trying to descend to a subtree that's of |
| 1360 | * minimum size. Do something! |
| 1361 | */ |
| 1362 | if (child > 0) { |
| 1363 | /* |
| 1364 | * Either move a subtree from the left sibling, or |
| 1365 | * merge with it. (Traditionally we would only |
| 1366 | * merge if we can't move a subtree from _either_ |
| 1367 | * sibling, but this way avoids too many extra |
| 1368 | * write locks.) |
| 1369 | */ |
| 1370 | c2 = c; |
| 1371 | c = bt_write_lock_child(bt, n, child-1); |
| 1372 | e = bt_element(bt, n, child-1); |
| 1373 | st = bt_subtrees(bt, c); |
| 1374 | if (st > bt_min_subtrees(bt)) |
| 1375 | splitpoint = st - 2; |
| 1376 | else |
| 1377 | splitpoint = NODE_JOIN; |
| 1378 | child--; |
| 1379 | } else { |
| 1380 | /* |
| 1381 | * Likewise on the right-hand side. |
| 1382 | */ |
| 1383 | c2 = bt_write_lock_child(bt, n, child+1); |
| 1384 | e = bt_element(bt, n, child); |
| 1385 | st = bt_subtrees(bt, c2); |
| 1386 | if (st > bt_min_subtrees(bt)) |
| 1387 | splitpoint = bt_min_subtrees(bt); |
| 1388 | else |
| 1389 | splitpoint = NODE_JOIN; |
| 1390 | } |
| 1391 | |
| 1392 | if (splitpoint == NODE_JOIN) { |
| 1393 | /* |
| 1394 | * So if we're merging nodes, go to it... |
| 1395 | */ |
| 1396 | bt_xform(bt, NODE_AS_IS, 0, |
| 1397 | c, c2, e, NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1398 | NODE_JOIN, &c, NULL, NULL); |
| 1399 | bt_xform(bt, NODE_DEL_ELT, child, |
| 1400 | n, NULL, NULL, bt_node_addr(bt, c), NODE_ADDR_NULL, |
| 1401 | NODE_JOIN, &n, NULL, NULL); |
| 1402 | if (nroot && bt_subtrees(bt, n) == 1) { |
| 1403 | /* |
| 1404 | * Whoops, we just merged the last two children |
| 1405 | * of the root. Better relocate the root. |
| 1406 | */ |
| 1407 | bt_shift_root(bt, n, bt_node_addr(bt, c)); |
| 1408 | nnodes--; /* don't leave it in nodes[]! */ |
| 1409 | n = NULL; |
| 1410 | bt_write_relock(bt, c, TRUE); |
| 1411 | } else |
| 1412 | bt_write_unlock(bt, c); |
| 1413 | } else { |
| 1414 | /* |
| 1415 | * Or if we're redistributing subtrees, go to that. |
| 1416 | */ |
| 1417 | bt_xform(bt, NODE_AS_IS, 0, |
| 1418 | c, c2, e, NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1419 | splitpoint, &c, &c2, &e); |
| 1420 | bt_set_element(bt, n, child, e); |
| 1421 | bt_write_unlock(bt, c); |
| 1422 | bt_write_unlock(bt, c2); |
| 1423 | } |
| 1424 | |
| 1425 | if (n) { |
| 1426 | /* Recompute the counts in n so we can do lookups again. */ |
| 1427 | bt_write_relock(bt, n, TRUE); |
| 1428 | |
| 1429 | /* Having done the transform, redo the position lookup. */ |
| 1430 | pos = pos2; |
| 1431 | child = bt_lookup_pos(bt, n, &pos, &ends); |
| 1432 | c = bt_write_lock_child(bt, n, child); |
| 1433 | } else { |
| 1434 | pos = pos2; |
| 1435 | } |
| 1436 | } |
| 1437 | |
| 1438 | /* |
| 1439 | * Now see if this node contains the element we're |
| 1440 | * looking for. |
| 1441 | */ |
| 1442 | if (n && (ends & ENDS_RIGHT)) { |
| 1443 | /* |
| 1444 | * It does. Element number `child' is the element we |
| 1445 | * want to delete. See if this is a leaf node... |
| 1446 | */ |
| 1447 | if (!bt_is_leaf(bt, n)) { |
| 1448 | /* |
| 1449 | * It's not a leaf node. So we save the nodeptr and |
| 1450 | * element index for later reference, and decrement |
| 1451 | * `pos' so that we're searching for the element to its |
| 1452 | * left, which _will_ be in a leaf node. |
| 1453 | */ |
| 1454 | saved_n = n; |
| 1455 | saved_pos = child; |
| 1456 | pos--; |
| 1457 | } else { |
| 1458 | /* |
| 1459 | * We've reached a leaf node. Check to see if an |
| 1460 | * internal-node position was stored in saved_n and |
| 1461 | * saved_pos, and move this element there if so. |
| 1462 | */ |
| 1463 | if (saved_n) { |
| 1464 | ret = bt_element(bt, saved_n, saved_pos); |
| 1465 | bt_set_element(bt, saved_n, saved_pos, |
| 1466 | bt_element(bt, n, child)); |
| 1467 | } else { |
| 1468 | ret = bt_element(bt, n, child); |
| 1469 | } |
| 1470 | /* Then delete it from the leaf node. */ |
| 1471 | bt_xform(bt, NODE_DEL_ELT, child, |
| 1472 | n, NULL, NULL, NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1473 | NODE_JOIN, &n, NULL, NULL); |
| 1474 | /* |
| 1475 | * Final special case: if this is the root node and |
| 1476 | * we've just deleted its last element, we should |
| 1477 | * destroy it and leave a completely empty tree. |
| 1478 | */ |
| 1479 | if (nroot && bt_subtrees(bt, n) == 1) { |
| 1480 | bt_shift_root(bt, n, NODE_ADDR_NULL); |
| 1481 | nnodes--; /* and take it out of nodes[] */ |
| 1482 | } |
| 1483 | /* Now we're done */ |
| 1484 | break; |
| 1485 | } |
| 1486 | } |
| 1487 | |
| 1488 | /* Descend to the child and go round again. */ |
| 1489 | n = c; |
| 1490 | nroot = FALSE; |
| 1491 | } |
| 1492 | |
| 1493 | /* |
| 1494 | * All done. Zip back up the tree un-write-locking nodes. |
| 1495 | */ |
| 1496 | while (nnodes-- > 0) |
| 1497 | bt_write_unlock(bt, nodes[nnodes]); |
| 1498 | |
| 1499 | ifree(nodes); |
| 1500 | |
| 1501 | return ret; |
| 1502 | } |
| 1503 | |
| 1504 | /* |
| 1505 | * Delete an element in sorted order. |
| 1506 | */ |
| 1507 | bt_element_t bt_del(btree *bt, bt_element_t element) |
| 1508 | { |
| 1509 | int index; |
| 1510 | if (!bt_findrelpos(bt, element, NULL, BT_REL_EQ, &index)) |
| 1511 | return NULL; /* wasn't there */ |
| 1512 | return bt_delpos(bt, index); |
| 1513 | } |
| 1514 | |
| 1515 | /* |
| 1516 | * Join two trees together, given their respective depths and a |
| 1517 | * middle element. Puts the resulting tree in the root of `bt'. |
| 1518 | * |
| 1519 | * This internal routine assumes that the trees have the same |
| 1520 | * degree. |
| 1521 | * |
| 1522 | * The input nodeptrs are assumed to be write-locked, but none of |
| 1523 | * their children are yet write-locked. |
| 1524 | */ |
| 1525 | static void bt_join_internal(btree *bt, nodeptr lp, nodeptr rp, |
| 1526 | bt_element_t sep, int ld, int rd) |
| 1527 | { |
| 1528 | nodeptr *nodes; |
| 1529 | int *childposns; |
| 1530 | int nnodes, nodessize; |
| 1531 | int lsub, rsub; |
| 1532 | |
| 1533 | /* |
| 1534 | * We will need to store parent nodes up to the difference |
| 1535 | * between ld and rd. |
| 1536 | */ |
| 1537 | nodessize = (ld < rd ? rd-ld : ld-rd); |
| 1538 | if (nodessize) { /* we may not need _any_! */ |
| 1539 | nodes = inewn(nodeptr, nodessize); |
| 1540 | childposns = inewn(int, nodessize); |
| 1541 | } |
| 1542 | nnodes = 0; |
| 1543 | |
| 1544 | if (ld > rd) { |
| 1545 | bt->root = bt_node_addr(bt, lp); |
| 1546 | bt->depth = ld; |
| 1547 | /* If the left tree is taller, search down its right-hand edge. */ |
| 1548 | while (ld > rd) { |
| 1549 | int child = bt_subtrees(bt, lp) - 1; |
| 1550 | nodeptr n = bt_write_lock_child(bt, lp, child); |
| 1551 | nodes[nnodes] = lp; |
| 1552 | childposns[nnodes] = child; |
| 1553 | nnodes++; |
| 1554 | lp = n; |
| 1555 | ld--; |
| 1556 | } |
| 1557 | } else { |
| 1558 | bt->root = bt_node_addr(bt, rp); |
| 1559 | bt->depth = rd; |
| 1560 | /* If the right tree is taller, search down its left-hand edge. */ |
| 1561 | while (rd > ld) { |
| 1562 | nodeptr n = bt_write_lock_child(bt, rp, 0); |
| 1563 | nodes[nnodes] = rp; |
| 1564 | childposns[nnodes] = 0; |
| 1565 | nnodes++; |
| 1566 | rp = n; |
| 1567 | rd--; |
| 1568 | } |
| 1569 | } |
| 1570 | |
| 1571 | /* |
| 1572 | * So we now want to combine nodes lp and rp into either one or |
| 1573 | * two plausibly-sized nodes, whichever is feasible. We have a |
| 1574 | * joining element `sep'. |
| 1575 | */ |
| 1576 | lsub = (lp ? bt_subtrees(bt, lp) : 0); |
| 1577 | rsub = (rp ? bt_subtrees(bt, rp) : 0); |
| 1578 | if (lp && rp && lsub + rsub <= bt_max_subtrees(bt)) { |
| 1579 | node_addr la; |
| 1580 | /* Join the nodes into one. */ |
| 1581 | bt_xform(bt, NODE_AS_IS, 0, lp, rp, sep, |
| 1582 | NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1583 | NODE_JOIN, &lp, NULL, NULL); |
| 1584 | /* Unlock the node. */ |
| 1585 | la = bt_write_unlock(bt, lp); |
| 1586 | /* Update the child pointer in the next node up. */ |
| 1587 | if (nnodes > 0) |
| 1588 | bt_set_child(bt, nodes[nnodes-1], childposns[nnodes-1], la); |
| 1589 | else |
| 1590 | bt->root = la; |
| 1591 | } else { |
| 1592 | node_addr la, ra; |
| 1593 | if (!lp || !rp) { |
| 1594 | la = NODE_ADDR_NULL; |
| 1595 | ra = NODE_ADDR_NULL; |
| 1596 | } else { |
| 1597 | int lsize, rsize; |
| 1598 | /* Re-split the nodes into two plausibly sized ones. */ |
| 1599 | lsize = lsub + rsub; |
| 1600 | rsize = lsize / 2; |
| 1601 | lsize -= rsize; |
| 1602 | bt_xform(bt, NODE_AS_IS, 0, lp, rp, sep, |
| 1603 | NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1604 | lsize-1, &lp, &rp, &sep); |
| 1605 | /* Unlock the nodes. */ |
| 1606 | la = bt_write_unlock(bt, lp); |
| 1607 | ra = bt_write_unlock(bt, rp); |
| 1608 | } |
| 1609 | |
| 1610 | /* |
| 1611 | * Now we have to do the addition thing: progress up the |
| 1612 | * tree replacing a single subtree pointer with the |
| 1613 | * la/sep/ra assembly, until no more nodes have to split as |
| 1614 | * a result. |
| 1615 | */ |
| 1616 | while (nnodes-- > 0) { |
| 1617 | nodeptr n = nodes[nnodes]; |
| 1618 | if (bt_subtrees(bt, n) == bt_max_subtrees(bt)) { |
| 1619 | /* Split the node and carry on up. */ |
| 1620 | bt_xform(bt, NODE_ADD_ELT, childposns[nnodes], |
| 1621 | n, NULL, sep, la, ra, |
| 1622 | bt_min_subtrees(bt), &lp, &rp, &sep); |
| 1623 | la = bt_write_unlock(bt, lp); |
| 1624 | ra = bt_write_unlock(bt, rp); |
| 1625 | } else { |
| 1626 | bt_xform(bt, NODE_ADD_ELT, childposns[nnodes], |
| 1627 | n, NULL, sep, la, ra, |
| 1628 | NODE_JOIN, &n, NULL, NULL); |
| 1629 | bt_write_unlock(bt, n); |
| 1630 | break; |
| 1631 | } |
| 1632 | } |
| 1633 | |
| 1634 | /* |
| 1635 | * If nnodes < 0, we have just split the root and we need |
| 1636 | * to build a new root node. |
| 1637 | */ |
| 1638 | if (nnodes < 0) |
| 1639 | bt_new_root(bt, la, ra, sep); |
| 1640 | } |
| 1641 | |
| 1642 | /* |
| 1643 | * Now we just need to go back up and unlock any remaining |
| 1644 | * nodes. Also here we ensure the root points where it should. |
| 1645 | */ |
| 1646 | while (nnodes-- > 0) { |
| 1647 | node_addr na; |
| 1648 | na = bt_write_unlock(bt, nodes[nnodes]); |
| 1649 | if (nnodes == 0) |
| 1650 | bt->root = na; |
| 1651 | } |
| 1652 | |
| 1653 | if (nodessize) { |
| 1654 | ifree(nodes); |
| 1655 | ifree(childposns); |
| 1656 | } |
| 1657 | } |
| 1658 | |
| 1659 | /* |
| 1660 | * External interfaces to the join functionality: join and joinr |
| 1661 | * (differing only in which B-tree structure they leave without any |
| 1662 | * elements, and which they return the combined tree in). |
| 1663 | */ |
| 1664 | btree *bt_join(btree *bt1, btree *bt2) |
| 1665 | { |
| 1666 | nodeptr root1, root2; |
| 1667 | int size2; |
| 1668 | |
| 1669 | size2 = bt_count(bt2); |
| 1670 | if (size2 > 0) { |
| 1671 | bt_element_t sep; |
| 1672 | |
| 1673 | if (bt1->cmp) { |
| 1674 | /* |
| 1675 | * The trees are ordered, so verify the ordering |
| 1676 | * condition: ensure nothing in bt1 is greater than or |
| 1677 | * equal to the minimum element in bt2. |
| 1678 | */ |
| 1679 | sep = bt_index(bt2, 0); |
| 1680 | sep = bt_findrelpos(bt1, sep, NULL, BT_REL_GE, NULL); |
| 1681 | if (sep) |
| 1682 | return NULL; |
| 1683 | } |
| 1684 | |
| 1685 | sep = bt_delpos(bt2, 0); |
| 1686 | root1 = bt_write_lock_root(bt1); |
| 1687 | root2 = bt_write_lock_root(bt2); |
| 1688 | bt_join_internal(bt1, root1, root2, sep, bt1->depth, bt2->depth); |
| 1689 | bt2->root = NODE_ADDR_NULL; |
| 1690 | bt2->depth = 0; |
| 1691 | } |
| 1692 | return bt1; |
| 1693 | } |
| 1694 | |
| 1695 | btree *bt_joinr(btree *bt1, btree *bt2) |
| 1696 | { |
| 1697 | nodeptr root1, root2; |
| 1698 | int size1; |
| 1699 | |
| 1700 | size1 = bt_count(bt1); |
| 1701 | if (size1 > 0) { |
| 1702 | bt_element_t sep; |
| 1703 | |
| 1704 | if (bt2->cmp) { |
| 1705 | /* |
| 1706 | * The trees are ordered, so verify the ordering |
| 1707 | * condition: ensure nothing in bt2 is less than or |
| 1708 | * equal to the maximum element in bt1. |
| 1709 | */ |
| 1710 | sep = bt_index(bt1, size1-1); |
| 1711 | sep = bt_findrelpos(bt2, sep, NULL, BT_REL_LE, NULL); |
| 1712 | if (sep) |
| 1713 | return NULL; |
| 1714 | } |
| 1715 | |
| 1716 | sep = bt_delpos(bt1, size1-1); |
| 1717 | root1 = bt_write_lock_root(bt1); |
| 1718 | root2 = bt_write_lock_root(bt2); |
| 1719 | bt_join_internal(bt2, root1, root2, sep, bt1->depth, bt2->depth); |
| 1720 | bt1->root = NODE_ADDR_NULL; |
| 1721 | bt1->depth = 0; |
| 1722 | } |
| 1723 | return bt2; |
| 1724 | } |
| 1725 | |
| 1726 | /* |
| 1727 | * Perform the healing process after a tree has been split. `rhs' |
| 1728 | * is set if the cut edge is the one on the right. |
| 1729 | */ |
| 1730 | static void bt_split_heal(btree *bt, int rhs) |
| 1731 | { |
| 1732 | nodeptr n; |
| 1733 | nodeptr *nodes; |
| 1734 | int nnodes; |
| 1735 | |
| 1736 | nodes = inewn(nodeptr, bt->depth); |
| 1737 | nnodes = 0; |
| 1738 | |
| 1739 | n = bt_write_lock_root(bt); |
| 1740 | |
| 1741 | /* |
| 1742 | * First dispense with completely trivial cases: a root node |
| 1743 | * containing only one subtree can be thrown away instantly. |
| 1744 | */ |
| 1745 | while (n && bt_subtrees(bt, n) == 1) { |
| 1746 | nodeptr n2 = bt_write_lock_child(bt, n, 0); |
| 1747 | bt_shift_root(bt, n, bt_node_addr(bt, n2)); |
| 1748 | n = n2; |
| 1749 | } |
| 1750 | |
| 1751 | /* |
| 1752 | * Now we have a plausible root node. Start going down the cut |
| 1753 | * edge looking for undersized or minimum nodes, and arranging |
| 1754 | * for them to be above minimum size. |
| 1755 | */ |
| 1756 | while (n) { |
| 1757 | int edge, next, elt, size_e, size_n, size_total; |
| 1758 | nodeptr ne, nn, nl, nr; |
| 1759 | bt_element_t el; |
| 1760 | |
| 1761 | nodes[nnodes++] = n; |
| 1762 | |
| 1763 | if (rhs) { |
| 1764 | edge = bt_subtrees(bt, n) - 1; |
| 1765 | next = edge - 1; |
| 1766 | elt = next; |
| 1767 | } else { |
| 1768 | edge = 0; |
| 1769 | next = 1; |
| 1770 | elt = edge; |
| 1771 | } |
| 1772 | |
| 1773 | ne = bt_write_lock_child(bt, n, edge); |
| 1774 | if (!ne) |
| 1775 | break; |
| 1776 | |
| 1777 | size_e = bt_subtrees(bt, ne); |
| 1778 | |
| 1779 | if (size_e <= bt_min_subtrees(bt)) { |
| 1780 | nn = bt_write_lock_child(bt, n, next); |
| 1781 | el = bt_element(bt, n, elt); |
| 1782 | size_n = bt_subtrees(bt, nn); |
| 1783 | if (edge < next) |
| 1784 | nl = ne, nr = nn; |
| 1785 | else |
| 1786 | nl = nn, nr = ne; |
| 1787 | size_total = size_e + size_n; |
| 1788 | if (size_e + size_n <= bt_max_subtrees(bt)) { |
| 1789 | /* |
| 1790 | * Merge the edge node and its sibling together. |
| 1791 | */ |
| 1792 | bt_xform(bt, NODE_AS_IS, 0, nl, nr, el, |
| 1793 | NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1794 | NODE_JOIN, &ne, NULL, NULL); |
| 1795 | bt_xform(bt, NODE_DEL_ELT, elt, n, NULL, NULL, |
| 1796 | bt_node_addr(bt, ne), NODE_ADDR_NULL, |
| 1797 | NODE_JOIN, &n, NULL, NULL); |
| 1798 | /* |
| 1799 | * It's possible we've just trashed the root of the |
| 1800 | * tree, again. |
| 1801 | */ |
| 1802 | if (bt_subtrees(bt, n) == 1) { |
| 1803 | bt_shift_root(bt, n, bt_node_addr(bt, ne)); |
| 1804 | nnodes--; /* and take it out of nodes[] */ |
| 1805 | } |
| 1806 | } else { |
| 1807 | /* |
| 1808 | * Redistribute subtrees between the edge node and |
| 1809 | * its sibling. |
| 1810 | */ |
| 1811 | int split; |
| 1812 | size_e = (size_total + 1) / 2; |
| 1813 | assert(size_e > bt_min_subtrees(bt)); |
| 1814 | if (next < edge) |
| 1815 | split = size_total - size_e - 1; |
| 1816 | else |
| 1817 | split = size_e - 1; |
| 1818 | bt_xform(bt, NODE_AS_IS, 0, nl, nr, el, |
| 1819 | NODE_ADDR_NULL, NODE_ADDR_NULL, |
| 1820 | split, &nl, &nr, &el); |
| 1821 | bt_write_unlock(bt, nn); |
| 1822 | bt_set_element(bt, n, elt, el); |
| 1823 | } |
| 1824 | } |
| 1825 | |
| 1826 | n = ne; |
| 1827 | } |
| 1828 | |
| 1829 | /* |
| 1830 | * Now we just need to go back up and unlock any remaining |
| 1831 | * nodes. |
| 1832 | */ |
| 1833 | while (nnodes-- > 0) |
| 1834 | bt_write_unlock(bt, nodes[nnodes]); |
| 1835 | |
| 1836 | ifree(nodes); |
| 1837 | } |
| 1838 | |
| 1839 | /* |
| 1840 | * Split a tree by numeric position. The new tree returned is the |
| 1841 | * one on the right; the original tree contains the stuff on the |
| 1842 | * left. |
| 1843 | */ |
| 1844 | static btree *bt_split_internal(btree *bt1, int index) |
| 1845 | { |
| 1846 | btree *bt2; |
| 1847 | nodeptr *lnodes, *rnodes; |
| 1848 | nodeptr n1, n2, n; |
| 1849 | int nnodes, child; |
| 1850 | |
| 1851 | bt2 = bt_new(bt1->cmp, bt1->copy, bt1->freeelt, bt1->propsize, |
| 1852 | bt1->propalign, bt1->propmake, bt1->propmerge, |
| 1853 | bt1->userstate, bt1->mindegree); |
| 1854 | bt2->depth = bt1->depth; |
| 1855 | |
| 1856 | lnodes = inewn(nodeptr, bt1->depth); |
| 1857 | rnodes = inewn(nodeptr, bt2->depth); |
| 1858 | nnodes = 0; |
| 1859 | |
| 1860 | n1 = bt_write_lock_root(bt1); |
| 1861 | while (n1) { |
| 1862 | child = bt_lookup_pos(bt1, n1, &index, NULL); |
| 1863 | n = bt_write_lock_child(bt1, n1, child); |
| 1864 | bt_xform(bt1, NODE_ADD_ELT, child, n1, NULL, NULL, |
| 1865 | bt_node_addr(bt1, n), NODE_ADDR_NULL, |
| 1866 | child, &n1, &n2, NULL); |
| 1867 | lnodes[nnodes] = n1; |
| 1868 | rnodes[nnodes] = n2; |
| 1869 | if (nnodes > 0) |
| 1870 | bt_set_child(bt2, rnodes[nnodes-1], 0, bt_node_addr(bt2, n2)); |
| 1871 | else |
| 1872 | bt2->root = bt_node_addr(bt2, n2); |
| 1873 | nnodes++; |
| 1874 | n1 = n; |
| 1875 | } |
| 1876 | |
| 1877 | /* |
| 1878 | * Now we go back up and unlock all the nodes. At this point we |
| 1879 | * don't mess with user properties, because there's the danger |
| 1880 | * of a node containing no subtrees _or_ elements and hence us |
| 1881 | * having to invent a notation for an empty property. We're |
| 1882 | * going to make a second healing pass in a moment anyway, |
| 1883 | * which will sort all that out for us. |
| 1884 | */ |
| 1885 | while (nnodes-- > 0) { |
| 1886 | bt_write_unlock_internal(bt1, lnodes[nnodes], FALSE); |
| 1887 | bt_write_unlock_internal(bt2, rnodes[nnodes], FALSE); |
| 1888 | } |
| 1889 | |
| 1890 | /* |
| 1891 | * Then we make a healing pass down each side of the tree. |
| 1892 | */ |
| 1893 | bt_split_heal(bt1, TRUE); |
| 1894 | bt_split_heal(bt2, FALSE); |
| 1895 | |
| 1896 | ifree(lnodes); |
| 1897 | ifree(rnodes); |
| 1898 | |
| 1899 | return bt2; |
| 1900 | } |
| 1901 | |
| 1902 | /* |
| 1903 | * Split a tree at a numeric index. |
| 1904 | */ |
| 1905 | btree *bt_splitpos(btree *bt, int index, int before) |
| 1906 | { |
| 1907 | btree *ret; |
| 1908 | node_addr na; |
| 1909 | int count, nd; |
| 1910 | nodeptr n; |
| 1911 | |
| 1912 | n = bt_read_lock_root(bt); |
| 1913 | count = (n ? bt_node_count(bt, n) : 0); |
| 1914 | bt_read_unlock(bt, n); |
| 1915 | |
| 1916 | if (index < 0 || index > count) |
| 1917 | return NULL; |
| 1918 | |
| 1919 | ret = bt_split_internal(bt, index); |
| 1920 | if (before) { |
| 1921 | na = bt->root; |
| 1922 | bt->root = ret->root; |
| 1923 | ret->root = na; |
| 1924 | |
| 1925 | nd = bt->depth; |
| 1926 | bt->depth = ret->depth; |
| 1927 | ret->depth = nd; |
| 1928 | } |
| 1929 | return ret; |
| 1930 | } |
| 1931 | |
| 1932 | /* |
| 1933 | * Split a tree at a position dictated by the sorting order. |
| 1934 | */ |
| 1935 | btree *bt_split(btree *bt, bt_element_t element, cmpfn_t cmp, int rel) |
| 1936 | { |
| 1937 | int before, index; |
| 1938 | |
| 1939 | assert(rel != BT_REL_EQ); /* has to be an inequality */ |
| 1940 | |
| 1941 | if (rel == BT_REL_GT || rel == BT_REL_GE) { |
| 1942 | before = TRUE; |
| 1943 | rel = (rel == BT_REL_GT ? BT_REL_LE : BT_REL_LT); |
| 1944 | } else { |
| 1945 | before = FALSE; |
| 1946 | } |
| 1947 | if (!bt_findrelpos(bt, element, cmp, rel, &index)) |
| 1948 | index = -1; |
| 1949 | return bt_splitpos(bt, index+1, before); |
| 1950 | } |
| 1951 | |
| 1952 | #ifdef TEST |
| 1953 | |
| 1954 | #define TEST_DEGREE 4 |
| 1955 | #define BT_COPY bt_clone |
| 1956 | #define MAXTREESIZE 10000 |
| 1957 | #define MAXLOCKS 100 |
| 1958 | |
| 1959 | int errors; |
| 1960 | |
| 1961 | /* |
| 1962 | * Error reporting function. |
| 1963 | */ |
| 1964 | void error(char *fmt, ...) { |
| 1965 | va_list ap; |
| 1966 | fprintf(stderr, "ERROR: "); |
| 1967 | va_start(ap, fmt); |
| 1968 | vfprintf(stderr, fmt, ap); |
| 1969 | va_end(ap); |
| 1970 | fprintf(stderr, "\n"); |
| 1971 | errors++; |
| 1972 | } |
| 1973 | |
| 1974 | /* |
| 1975 | * See if a tree has a 2-element root node. |
| 1976 | */ |
| 1977 | static int bt_tworoot(btree *bt) |
| 1978 | { |
| 1979 | nodeptr n; |
| 1980 | int i; |
| 1981 | n = bt_read_lock_root(bt); |
| 1982 | i = bt_subtrees(bt, n); |
| 1983 | bt_read_unlock(bt, n); |
| 1984 | return (i == 2 ? TRUE : FALSE); |
| 1985 | } |
| 1986 | |
| 1987 | /* |
| 1988 | * Physically copy an entire B-tree. (NB this appears as a test |
| 1989 | * routine rather than a production one, since reference counting |
| 1990 | * and bt_clone() provide a better way to do this for real code. If |
| 1991 | * anyone really needs a genuine physical copy for anything other |
| 1992 | * than testing reasons, I suppose they could always lift this into |
| 1993 | * the admin section above.) |
| 1994 | */ |
| 1995 | |
| 1996 | static nodeptr bt_copy_node(btree *bt, nodeptr n) |
| 1997 | { |
| 1998 | int i, children; |
| 1999 | nodeptr ret; |
| 2000 | |
| 2001 | children = bt_subtrees(bt, n); |
| 2002 | ret = bt_new_node(bt, children); |
| 2003 | |
| 2004 | for (i = 0; i < children; i++) { |
| 2005 | nodeptr n2 = bt_read_lock_child(bt, n, i); |
| 2006 | nodeptr n3; |
| 2007 | if (n2) { |
| 2008 | n3 = bt_copy_node(bt, n2); |
| 2009 | bt_set_child(bt, ret, i, bt_write_unlock(bt, n3)); |
| 2010 | } else { |
| 2011 | bt_set_child(bt, ret, i, NODE_ADDR_NULL); |
| 2012 | } |
| 2013 | bt_read_unlock(bt, n2); |
| 2014 | |
| 2015 | if (i < children-1) { |
| 2016 | bt_element_t e = bt_element(bt, n, i); |
| 2017 | if (bt->copy) |
| 2018 | e = bt->copy(bt->userstate, e); |
| 2019 | bt_set_element(bt, ret, i, e); |
| 2020 | } |
| 2021 | } |
| 2022 | |
| 2023 | return ret; |
| 2024 | } |
| 2025 | |
| 2026 | btree *bt_copy(btree *bt) |
| 2027 | { |
| 2028 | nodeptr n; |
| 2029 | btree *bt2; |
| 2030 | |
| 2031 | bt2 = bt_new(bt->cmp, bt->copy, bt->freeelt, bt->propsize, bt->propalign, |
| 2032 | bt->propmake, bt->propmerge, bt->userstate, bt->mindegree); |
| 2033 | bt2->depth = bt->depth; |
| 2034 | |
| 2035 | n = bt_read_lock_root(bt); |
| 2036 | if (n) |
| 2037 | bt2->root = bt_write_unlock(bt2, bt_copy_node(bt, n)); |
| 2038 | bt_read_unlock(bt, n); |
| 2039 | |
| 2040 | return bt2; |
| 2041 | } |
| 2042 | |
| 2043 | /* |
| 2044 | * This function is intended to be called from gdb when debugging |
| 2045 | * things. |
| 2046 | */ |
| 2047 | void bt_dump_nodes(btree *bt, ...) |
| 2048 | { |
| 2049 | int i, children; |
| 2050 | va_list ap; |
| 2051 | nodeptr n; |
| 2052 | |
| 2053 | va_start(ap, bt); |
| 2054 | while (1) { |
| 2055 | n = va_arg(ap, nodeptr); |
| 2056 | if (!n) |
| 2057 | break; |
| 2058 | printf("%p [%d]:", n, n[bt->maxdegree*2+1].i); |
| 2059 | children = bt_subtrees(bt, n); |
| 2060 | for (i = 0; i < children; i++) { |
| 2061 | printf(" %p", bt_child(bt, n, i).p); |
| 2062 | if (i < children-1) |
| 2063 | printf(" %s", (char *)bt_element(bt, n, i)); |
| 2064 | } |
| 2065 | printf("\n"); |
| 2066 | } |
| 2067 | va_end(ap); |
| 2068 | } |
| 2069 | |
| 2070 | /* |
| 2071 | * Verify a tree against an array. Checks that: |
| 2072 | * |
| 2073 | * - every node has a valid number of subtrees |
| 2074 | * - subtrees are either all present (internal node) or all absent |
| 2075 | * (leaf) |
| 2076 | * - elements are all present |
| 2077 | * - every leaf is at exactly the depth claimed by the tree |
| 2078 | * - the tree represents the correct list of elements in the |
| 2079 | * correct order. (This also tests the ordering constraint, |
| 2080 | * assuming the array is correctly constructed.) |
| 2081 | */ |
| 2082 | |
| 2083 | void verifynode(btree *bt, nodeptr n, bt_element_t *array, int *arraypos, |
| 2084 | int depth) |
| 2085 | { |
| 2086 | int subtrees, min, max, i, before, after, count; |
| 2087 | |
| 2088 | /* Check the subtree count. The root can have as few as 2 subtrees. */ |
| 2089 | subtrees = bt_subtrees(bt, n); |
| 2090 | max = bt_max_subtrees(bt); |
| 2091 | min = (depth == 1) ? 2 : bt_min_subtrees(bt); |
| 2092 | if (subtrees > max) |
| 2093 | error("node %p has too many subtrees (%d > %d)", n, subtrees, max); |
| 2094 | if (subtrees < min) |
| 2095 | error("node %p has too few subtrees (%d < %d)", n, subtrees, min); |
| 2096 | |
| 2097 | /* Check that subtrees are present or absent as required. */ |
| 2098 | for (i = 0; i < subtrees; i++) { |
| 2099 | node_addr child = bt_child(bt, n, i); |
| 2100 | if (depth == bt->depth && child.p != NULL) |
| 2101 | error("leaf node %p child %d is %p not NULL\n", n, i, child); |
| 2102 | if (depth != bt->depth && child.p == NULL) |
| 2103 | error("non-leaf node %p child %d is NULL\n", n, i); |
| 2104 | } |
| 2105 | |
| 2106 | /* Check that elements are all present. */ |
| 2107 | for (i = 0; i < subtrees-1; i++) { |
| 2108 | bt_element_t elt = bt_element(bt, n, i); |
| 2109 | if (elt == NULL) |
| 2110 | error("node %p element %d is NULL\n", n, i); |
| 2111 | } |
| 2112 | |
| 2113 | before = *arraypos; |
| 2114 | |
| 2115 | /* Now verify the subtrees, and simultaneously check the ordering. */ |
| 2116 | for (i = 0; i < subtrees; i++) { |
| 2117 | if (depth < bt->depth) { |
| 2118 | nodeptr child = bt_read_lock_child(bt, n, i); |
| 2119 | verifynode(bt, child, array, arraypos, depth+1); |
| 2120 | bt_read_unlock(bt, child); |
| 2121 | } |
| 2122 | if (i < subtrees-1) { |
| 2123 | bt_element_t elt = bt_element(bt, n, i); |
| 2124 | if (array[*arraypos] != elt) { |
| 2125 | error("node %p element %d is \"%s\", but array[%d]=\"%s\"", |
| 2126 | n, i, elt, *arraypos, array[*arraypos]); |
| 2127 | } |
| 2128 | (*arraypos)++; |
| 2129 | } |
| 2130 | } |
| 2131 | |
| 2132 | after = *arraypos; |
| 2133 | |
| 2134 | /* Check the node count. */ |
| 2135 | count = bt_node_count(bt, n); |
| 2136 | if (count != after - before) |
| 2137 | error("node %p count is %d, should be %d", n, count, after - before); |
| 2138 | |
| 2139 | /* |
| 2140 | * Check the user properties. |
| 2141 | */ |
| 2142 | { |
| 2143 | nodecomponent *prop; |
| 2144 | int i; |
| 2145 | int max = 0, total = 0; |
| 2146 | |
| 2147 | prop = n + bt->maxdegree * 2 + 2; |
| 2148 | |
| 2149 | for (i = before; i < after; i++) { |
| 2150 | int c = (unsigned char)*(char *)array[i]; |
| 2151 | |
| 2152 | if (max < c) max = c; |
| 2153 | total += c; |
| 2154 | } |
| 2155 | |
| 2156 | if (prop[0].i != total) |
| 2157 | error("node %p total prop is %d, should be %d", n, |
| 2158 | prop[0].i, total); |
| 2159 | if (prop[1].i != max) |
| 2160 | error("node %p max prop is %d, should be %d", n, |
| 2161 | prop[1].i, max); |
| 2162 | } |
| 2163 | } |
| 2164 | |
| 2165 | void verifytree(btree *bt, bt_element_t *array, int arraylen) |
| 2166 | { |
| 2167 | nodeptr n; |
| 2168 | int i = 0; |
| 2169 | n = bt_read_lock_root(bt); |
| 2170 | if (n) { |
| 2171 | verifynode(bt, n, array, &i, 1); |
| 2172 | bt_read_unlock(bt, n); |
| 2173 | } else { |
| 2174 | if (bt->depth != 0) { |
| 2175 | error("tree has null root but depth is %d not zero", bt->depth); |
| 2176 | } |
| 2177 | } |
| 2178 | if (i != arraylen) |
| 2179 | error("tree contains %d elements, array contains %d", |
| 2180 | i, arraylen); |
| 2181 | testlock(-1, 0, NULL); |
| 2182 | } |
| 2183 | |
| 2184 | int mycmp(void *state, void *av, void *bv) { |
| 2185 | char const *a = (char const *)av; |
| 2186 | char const *b = (char const *)bv; |
| 2187 | return strcmp(a, b); |
| 2188 | } |
| 2189 | |
| 2190 | static void set_invalid_property(void *propv) |
| 2191 | { |
| 2192 | int *prop = (int *)propv; |
| 2193 | prop[0] = prop[1] = -1; |
| 2194 | } |
| 2195 | |
| 2196 | void mypropmake(void *state, void *av, void *destv) |
| 2197 | { |
| 2198 | char const *a = (char const *)av; |
| 2199 | int *dest = (int *)destv; |
| 2200 | dest[0] = dest[1] = (unsigned char)*a; |
| 2201 | } |
| 2202 | |
| 2203 | void mypropmerge(void *state, void *s1v, void *s2v, void *destv) |
| 2204 | { |
| 2205 | int *s1 = (int *)s1v; |
| 2206 | int *s2 = (int *)s2v; |
| 2207 | int *dest = (int *)destv; |
| 2208 | if (!s1v && !s2v) { |
| 2209 | /* Special `destroy' case. */ |
| 2210 | set_invalid_property(destv); |
| 2211 | return; |
| 2212 | } |
| 2213 | assert(s2[0] >= 0 && s2[1] >= 0); |
| 2214 | assert(s1 == NULL || (s1[0] >= 0 && s1[1] >= 0)); |
| 2215 | dest[0] = s2[0] + (s1 ? s1[0] : 0); |
| 2216 | dest[1] = (s1 && s1[1] > s2[1] ? s1[1] : s2[1]); |
| 2217 | } |
| 2218 | |
| 2219 | void array_addpos(bt_element_t *array, int *arraylen, bt_element_t e, int i) |
| 2220 | { |
| 2221 | bt_element_t e2; |
| 2222 | int len = *arraylen; |
| 2223 | |
| 2224 | assert(len < MAXTREESIZE); |
| 2225 | |
| 2226 | while (i < len) { |
| 2227 | e2 = array[i]; |
| 2228 | array[i] = e; |
| 2229 | e = e2; |
| 2230 | i++; |
| 2231 | } |
| 2232 | array[len] = e; |
| 2233 | *arraylen = len+1; |
| 2234 | } |
| 2235 | |
| 2236 | void array_add(bt_element_t *array, int *arraylen, bt_element_t e) |
| 2237 | { |
| 2238 | int i; |
| 2239 | int len = *arraylen; |
| 2240 | |
| 2241 | for (i = 0; i < len; i++) |
| 2242 | if (mycmp(NULL, array[i], e) >= 0) |
| 2243 | break; |
| 2244 | assert(i == len || mycmp(NULL, array[i], e) != 0); |
| 2245 | array_addpos(array, arraylen, e, i); |
| 2246 | } |
| 2247 | |
| 2248 | void array_delpos(bt_element_t *array, int *arraylen, int i) |
| 2249 | { |
| 2250 | int len = *arraylen; |
| 2251 | |
| 2252 | while (i < len-1) { |
| 2253 | array[i] = array[i+1]; |
| 2254 | i++; |
| 2255 | } |
| 2256 | *arraylen = len-1; |
| 2257 | } |
| 2258 | |
| 2259 | bt_element_t array_del(bt_element_t *array, int *arraylen, bt_element_t e) |
| 2260 | { |
| 2261 | int i; |
| 2262 | int len = *arraylen; |
| 2263 | bt_element_t ret; |
| 2264 | |
| 2265 | for (i = 0; i < len; i++) |
| 2266 | if (mycmp(NULL, array[i], e) >= 0) |
| 2267 | break; |
| 2268 | if (i < len && mycmp(NULL, array[i], e) == 0) { |
| 2269 | ret = array[i]; |
| 2270 | array_delpos(array, arraylen, i); |
| 2271 | } else |
| 2272 | ret = NULL; |
| 2273 | return ret; |
| 2274 | } |
| 2275 | |
| 2276 | /* A sample data set and test utility. Designed for pseudo-randomness, |
| 2277 | * and yet repeatability. */ |
| 2278 | |
| 2279 | /* |
| 2280 | * This random number generator uses the `portable implementation' |
| 2281 | * given in ANSI C99 draft N869. It assumes `unsigned' is 32 bits; |
| 2282 | * change it if not. |
| 2283 | */ |
| 2284 | int randomnumber(unsigned *seed) { |
| 2285 | *seed *= 1103515245; |
| 2286 | *seed += 12345; |
| 2287 | return ((*seed) / 65536) % 32768; |
| 2288 | } |
| 2289 | |
| 2290 | #define lenof(x) ( sizeof((x)) / sizeof(*(x)) ) |
| 2291 | |
| 2292 | char *strings[] = { |
| 2293 | "0", "2", "3", "I", "K", "d", "H", "J", "Q", "N", "n", "q", "j", "i", |
| 2294 | "7", "G", "F", "D", "b", "x", "g", "B", "e", "v", "V", "T", "f", "E", |
| 2295 | "S", "8", "A", "k", "X", "p", "C", "R", "a", "o", "r", "O", "Z", "u", |
| 2296 | "6", "1", "w", "L", "P", "M", "c", "U", "h", "9", "t", "5", "W", "Y", |
| 2297 | "m", "s", "l", "4", |
| 2298 | }; |
| 2299 | |
| 2300 | #define NSTR lenof(strings) |
| 2301 | |
| 2302 | void findtest(btree *tree, bt_element_t *array, int arraylen) |
| 2303 | { |
| 2304 | static const int rels[] = { |
| 2305 | BT_REL_EQ, BT_REL_GE, BT_REL_LE, BT_REL_LT, BT_REL_GT |
| 2306 | }; |
| 2307 | static const char *const relnames[] = { |
| 2308 | "EQ", "GE", "LE", "LT", "GT" |
| 2309 | }; |
| 2310 | int i, j, rel, index; |
| 2311 | char *p, *ret, *realret, *realret2; |
| 2312 | int lo, hi, mid, c; |
| 2313 | |
| 2314 | for (i = 0; i < (int)NSTR; i++) { |
| 2315 | p = strings[i]; |
| 2316 | for (j = 0; j < (int)(sizeof(rels)/sizeof(*rels)); j++) { |
| 2317 | rel = rels[j]; |
| 2318 | |
| 2319 | lo = 0; hi = arraylen-1; |
| 2320 | while (lo <= hi) { |
| 2321 | mid = (lo + hi) / 2; |
| 2322 | c = strcmp(p, array[mid]); |
| 2323 | if (c < 0) |
| 2324 | hi = mid-1; |
| 2325 | else if (c > 0) |
| 2326 | lo = mid+1; |
| 2327 | else |
| 2328 | break; |
| 2329 | } |
| 2330 | |
| 2331 | if (c == 0) { |
| 2332 | if (rel == BT_REL_LT) |
| 2333 | ret = (mid > 0 ? array[--mid] : NULL); |
| 2334 | else if (rel == BT_REL_GT) |
| 2335 | ret = (mid < arraylen-1 ? array[++mid] : NULL); |
| 2336 | else |
| 2337 | ret = array[mid]; |
| 2338 | } else { |
| 2339 | assert(lo == hi+1); |
| 2340 | if (rel == BT_REL_LT || rel == BT_REL_LE) { |
| 2341 | mid = hi; |
| 2342 | ret = (hi >= 0 ? array[hi] : NULL); |
| 2343 | } else if (rel == BT_REL_GT || rel == BT_REL_GE) { |
| 2344 | mid = lo; |
| 2345 | ret = (lo < arraylen ? array[lo] : NULL); |
| 2346 | } else |
| 2347 | ret = NULL; |
| 2348 | } |
| 2349 | |
| 2350 | realret = bt_findrelpos(tree, p, NULL, rel, &index); |
| 2351 | testlock(-1, 0, NULL); |
| 2352 | if (realret != ret) { |
| 2353 | error("find(\"%s\",%s) gave %s should be %s", |
| 2354 | p, relnames[j], realret, ret); |
| 2355 | } |
| 2356 | if (realret && index != mid) { |
| 2357 | error("find(\"%s\",%s) gave %d should be %d", |
| 2358 | p, relnames[j], index, mid); |
| 2359 | } |
| 2360 | if (realret && rel == BT_REL_EQ) { |
| 2361 | realret2 = bt_index(tree, index); |
| 2362 | if (realret2 != realret) { |
| 2363 | error("find(\"%s\",%s) gave %s(%d) but %d -> %s", |
| 2364 | p, relnames[j], realret, index, index, realret2); |
| 2365 | } |
| 2366 | } |
| 2367 | } |
| 2368 | } |
| 2369 | |
| 2370 | realret = bt_findrelpos(tree, NULL, NULL, BT_REL_GT, &index); |
| 2371 | testlock(-1, 0, NULL); |
| 2372 | if (arraylen && (realret != array[0] || index != 0)) { |
| 2373 | error("find(NULL,GT) gave %s(%d) should be %s(0)", |
| 2374 | realret, index, array[0]); |
| 2375 | } else if (!arraylen && (realret != NULL)) { |
| 2376 | error("find(NULL,GT) gave %s(%d) should be NULL", |
| 2377 | realret, index); |
| 2378 | } |
| 2379 | |
| 2380 | realret = bt_findrelpos(tree, NULL, NULL, BT_REL_LT, &index); |
| 2381 | testlock(-1, 0, NULL); |
| 2382 | if (arraylen && (realret != array[arraylen-1] || index != arraylen-1)) { |
| 2383 | error("find(NULL,LT) gave %s(%d) should be %s(0)", |
| 2384 | realret, index, array[arraylen-1]); |
| 2385 | } else if (!arraylen && (realret != NULL)) { |
| 2386 | error("find(NULL,LT) gave %s(%d) should be NULL", |
| 2387 | realret, index); |
| 2388 | } |
| 2389 | } |
| 2390 | |
| 2391 | void splittest(btree *tree, bt_element_t *array, int arraylen) |
| 2392 | { |
| 2393 | int i; |
| 2394 | btree *tree3, *tree4; |
| 2395 | for (i = 0; i <= arraylen; i++) { |
| 2396 | printf("splittest: %d\n", i); |
| 2397 | tree3 = BT_COPY(tree); |
| 2398 | testlock(-1, 0, NULL); |
| 2399 | tree4 = bt_splitpos(tree3, i, 0); |
| 2400 | testlock(-1, 0, NULL); |
| 2401 | verifytree(tree3, array, i); |
| 2402 | verifytree(tree4, array+i, arraylen-i); |
| 2403 | bt_join(tree3, tree4); |
| 2404 | testlock(-1, 0, NULL); |
| 2405 | verifytree(tree4, NULL, 0); |
| 2406 | bt_free(tree4); /* left empty by join */ |
| 2407 | testlock(-1, 0, NULL); |
| 2408 | verifytree(tree3, array, arraylen); |
| 2409 | bt_free(tree3); |
| 2410 | testlock(-1, 0, NULL); |
| 2411 | } |
| 2412 | } |
| 2413 | |
| 2414 | /* |
| 2415 | * Called to track read and write locks on nodes. |
| 2416 | */ |
| 2417 | void testlock(int write, int set, nodeptr n) |
| 2418 | { |
| 2419 | static nodeptr readlocks[MAXLOCKS], writelocks[MAXLOCKS]; |
| 2420 | static int nreadlocks = 0, nwritelocks = 0; |
| 2421 | |
| 2422 | int i, rp, wp; |
| 2423 | |
| 2424 | if (write == -1) { |
| 2425 | /* Called after an operation to ensure all locks are unlocked. */ |
| 2426 | if (nreadlocks != 0 || nwritelocks != 0) |
| 2427 | error("at least one left-behind lock exists!"); |
| 2428 | return; |
| 2429 | } |
| 2430 | |
| 2431 | /* Locking NULL does nothing. Unlocking it is an error. */ |
| 2432 | if (n == NULL) { |
| 2433 | if (!set) |
| 2434 | error("attempting to %s-unlock NULL", write ? "write" : "read"); |
| 2435 | return; |
| 2436 | } |
| 2437 | |
| 2438 | assert(nreadlocks < MAXLOCKS && nwritelocks < MAXLOCKS); |
| 2439 | |
| 2440 | /* First look for the node in both lock lists. */ |
| 2441 | rp = wp = -1; |
| 2442 | for (i = 0; i < nreadlocks; i++) |
| 2443 | if (readlocks[i] == n) |
| 2444 | rp = i; |
| 2445 | for (i = 0; i < nwritelocks; i++) |
| 2446 | if (writelocks[i] == n) |
| 2447 | wp = i; |
| 2448 | |
| 2449 | /* Now diverge based on what we're supposed to be up to. */ |
| 2450 | if (set) { |
| 2451 | /* Setting a lock. Should not already be locked in either list. */ |
| 2452 | if (rp != -1 || wp != -1) { |
| 2453 | error("attempt to %s-lock node %p, already %s-locked", |
| 2454 | (write ? "write" : "read"), n, (rp==-1 ? "write" : "read")); |
| 2455 | } |
| 2456 | if (write) |
| 2457 | writelocks[nwritelocks++] = n; |
| 2458 | else |
| 2459 | readlocks[nreadlocks++] = n; |
| 2460 | } else { |
| 2461 | /* Clearing a lock. Should exist in exactly the correct list. */ |
| 2462 | if (write && rp != -1) |
| 2463 | error("attempt to write-unlock node %p which is read-locked", n); |
| 2464 | if (!write && wp != -1) |
| 2465 | error("attempt to read-unlock node %p which is write-locked", n); |
| 2466 | if (wp != -1) { |
| 2467 | nwritelocks--; |
| 2468 | for (i = wp; i < nwritelocks; i++) |
| 2469 | writelocks[i] = writelocks[i+1]; |
| 2470 | } |
| 2471 | if (rp != -1) { |
| 2472 | nreadlocks--; |
| 2473 | for (i = rp; i < nreadlocks; i++) |
| 2474 | readlocks[i] = readlocks[i+1]; |
| 2475 | } |
| 2476 | } |
| 2477 | } |
| 2478 | |
| 2479 | int main(void) { |
| 2480 | int in[NSTR]; |
| 2481 | int i, j, k; |
| 2482 | int tworoot, tmplen; |
| 2483 | unsigned seed = 0; |
| 2484 | bt_element_t *array; |
| 2485 | int arraylen; |
| 2486 | bt_element_t ret, ret2, item; |
| 2487 | btree *tree, *tree2, *tree3, *tree4; |
| 2488 | |
| 2489 | setvbuf(stdout, NULL, _IOLBF, 0); |
| 2490 | setvbuf(stderr, NULL, _IOLBF, 0); |
| 2491 | errors = 0; |
| 2492 | |
| 2493 | for (i = 0; i < (int)NSTR; i++) in[i] = 0; |
| 2494 | array = newn(bt_element_t, MAXTREESIZE); |
| 2495 | arraylen = 0; |
| 2496 | tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2497 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2498 | |
| 2499 | verifytree(tree, array, arraylen); |
| 2500 | for (i = 0; i < 10000; i++) { |
| 2501 | j = randomnumber(&seed); |
| 2502 | j %= NSTR; |
| 2503 | printf("trial: %d\n", i); |
| 2504 | if (in[j]) { |
| 2505 | printf("deleting %s (%d)\n", strings[j], j); |
| 2506 | ret2 = array_del(array, &arraylen, strings[j]); |
| 2507 | ret = bt_del(tree, strings[j]); |
| 2508 | testlock(-1, 0, NULL); |
| 2509 | assert((bt_element_t)strings[j] == ret && ret == ret2); |
| 2510 | verifytree(tree, array, arraylen); |
| 2511 | in[j] = 0; |
| 2512 | } else { |
| 2513 | printf("adding %s (%d)\n", strings[j], j); |
| 2514 | array_add(array, &arraylen, strings[j]); |
| 2515 | ret = bt_add(tree, strings[j]); |
| 2516 | testlock(-1, 0, NULL); |
| 2517 | assert(strings[j] == ret); |
| 2518 | verifytree(tree, array, arraylen); |
| 2519 | in[j] = 1; |
| 2520 | } |
| 2521 | /* disptree(tree); */ |
| 2522 | findtest(tree, array, arraylen); |
| 2523 | } |
| 2524 | |
| 2525 | while (arraylen > 0) { |
| 2526 | j = randomnumber(&seed); |
| 2527 | j %= arraylen; |
| 2528 | item = array[j]; |
| 2529 | ret2 = array_del(array, &arraylen, item); |
| 2530 | ret = bt_del(tree, item); |
| 2531 | testlock(-1, 0, NULL); |
| 2532 | assert(ret2 == ret); |
| 2533 | verifytree(tree, array, arraylen); |
| 2534 | } |
| 2535 | |
| 2536 | bt_free(tree); |
| 2537 | testlock(-1, 0, NULL); |
| 2538 | |
| 2539 | /* |
| 2540 | * Now try an unsorted tree. We don't really need to test |
| 2541 | * delpos because we know del is based on it, so it's already |
| 2542 | * been tested in the above sorted-tree code; but for |
| 2543 | * completeness we'll use it to tear down our unsorted tree |
| 2544 | * once we've built it. |
| 2545 | */ |
| 2546 | tree = bt_new(NULL, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2547 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2548 | verifytree(tree, array, arraylen); |
| 2549 | for (i = 0; i < 1000; i++) { |
| 2550 | printf("trial: %d\n", i); |
| 2551 | j = randomnumber(&seed); |
| 2552 | j %= NSTR; |
| 2553 | k = randomnumber(&seed); |
| 2554 | k %= bt_count(tree)+1; |
| 2555 | testlock(-1, 0, NULL); |
| 2556 | printf("adding string %s at index %d\n", strings[j], k); |
| 2557 | array_addpos(array, &arraylen, strings[j], k); |
| 2558 | bt_addpos(tree, strings[j], k); |
| 2559 | testlock(-1, 0, NULL); |
| 2560 | verifytree(tree, array, arraylen); |
| 2561 | } |
| 2562 | |
| 2563 | /* |
| 2564 | * While we have this tree in its full form, we'll take a copy |
| 2565 | * of it to use in split and join testing. |
| 2566 | */ |
| 2567 | tree2 = BT_COPY(tree); |
| 2568 | testlock(-1, 0, NULL); |
| 2569 | verifytree(tree2, array, arraylen);/* check the copy is accurate */ |
| 2570 | /* |
| 2571 | * Split tests. Split the tree at every possible point and |
| 2572 | * check the resulting subtrees. |
| 2573 | */ |
| 2574 | tworoot = bt_tworoot(tree2); /* see if it has a 2-root */ |
| 2575 | testlock(-1, 0, NULL); |
| 2576 | splittest(tree2, array, arraylen); |
| 2577 | /* |
| 2578 | * Now do the split test again, but on a tree that has a 2-root |
| 2579 | * (if the previous one didn't) or doesn't (if the previous one |
| 2580 | * did). |
| 2581 | */ |
| 2582 | tmplen = arraylen; |
| 2583 | while (bt_tworoot(tree2) == tworoot) { |
| 2584 | bt_delpos(tree2, --tmplen); |
| 2585 | testlock(-1, 0, NULL); |
| 2586 | } |
| 2587 | printf("now trying splits on second tree\n"); |
| 2588 | splittest(tree2, array, tmplen); |
| 2589 | bt_free(tree2); |
| 2590 | testlock(-1, 0, NULL); |
| 2591 | |
| 2592 | /* |
| 2593 | * Back to the main testing of uncounted trees. |
| 2594 | */ |
| 2595 | while (bt_count(tree) > 0) { |
| 2596 | printf("cleanup: tree size %d\n", bt_count(tree)); |
| 2597 | j = randomnumber(&seed); |
| 2598 | j %= bt_count(tree); |
| 2599 | printf("deleting string %s from index %d\n", (char *)array[j], j); |
| 2600 | ret = bt_delpos(tree, j); |
| 2601 | testlock(-1, 0, NULL); |
| 2602 | assert((bt_element_t)array[j] == ret); |
| 2603 | array_delpos(array, &arraylen, j); |
| 2604 | verifytree(tree, array, arraylen); |
| 2605 | } |
| 2606 | bt_free(tree); |
| 2607 | testlock(-1, 0, NULL); |
| 2608 | |
| 2609 | /* |
| 2610 | * Finally, do some testing on split/join on _sorted_ trees. At |
| 2611 | * the same time, we'll be testing split on very small trees. |
| 2612 | */ |
| 2613 | tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2614 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2615 | arraylen = 0; |
| 2616 | for (i = 0; i < 16; i++) { |
| 2617 | array_add(array, &arraylen, strings[i]); |
| 2618 | ret = bt_add(tree, strings[i]); |
| 2619 | testlock(-1, 0, NULL); |
| 2620 | assert(strings[i] == ret); |
| 2621 | verifytree(tree, array, arraylen); |
| 2622 | tree2 = BT_COPY(tree); |
| 2623 | splittest(tree2, array, arraylen); |
| 2624 | testlock(-1, 0, NULL); |
| 2625 | bt_free(tree2); |
| 2626 | testlock(-1, 0, NULL); |
| 2627 | } |
| 2628 | bt_free(tree); |
| 2629 | testlock(-1, 0, NULL); |
| 2630 | |
| 2631 | /* |
| 2632 | * Test silly cases of join: join(emptytree, emptytree), and |
| 2633 | * also ensure join correctly spots when sorted trees fail the |
| 2634 | * ordering constraint. |
| 2635 | */ |
| 2636 | tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2637 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2638 | tree2 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2639 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2640 | tree3 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2641 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2642 | tree4 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int), |
| 2643 | mypropmake, mypropmerge, NULL, TEST_DEGREE); |
| 2644 | assert(mycmp(NULL, strings[0], strings[1]) < 0); /* just in case :-) */ |
| 2645 | bt_add(tree2, strings[1]); |
| 2646 | testlock(-1, 0, NULL); |
| 2647 | bt_add(tree4, strings[0]); |
| 2648 | testlock(-1, 0, NULL); |
| 2649 | array[0] = strings[0]; |
| 2650 | array[1] = strings[1]; |
| 2651 | verifytree(tree, array, 0); |
| 2652 | verifytree(tree2, array+1, 1); |
| 2653 | verifytree(tree3, array, 0); |
| 2654 | verifytree(tree4, array, 1); |
| 2655 | |
| 2656 | /* |
| 2657 | * So: |
| 2658 | * - join(tree,tree3) should leave both tree and tree3 unchanged. |
| 2659 | * - joinr(tree,tree2) should leave both tree and tree2 unchanged. |
| 2660 | * - join(tree4,tree3) should leave both tree3 and tree4 unchanged. |
| 2661 | * - join(tree, tree2) should move the element from tree2 to tree. |
| 2662 | * - joinr(tree4, tree3) should move the element from tree4 to tree3. |
| 2663 | * - join(tree,tree3) should return NULL and leave both unchanged. |
| 2664 | * - join(tree3,tree) should work and create a bigger tree in tree3. |
| 2665 | */ |
| 2666 | assert(tree == bt_join(tree, tree3)); |
| 2667 | testlock(-1, 0, NULL); |
| 2668 | verifytree(tree, array, 0); |
| 2669 | verifytree(tree3, array, 0); |
| 2670 | assert(tree2 == bt_joinr(tree, tree2)); |
| 2671 | testlock(-1, 0, NULL); |
| 2672 | verifytree(tree, array, 0); |
| 2673 | verifytree(tree2, array+1, 1); |
| 2674 | assert(tree4 == bt_join(tree4, tree3)); |
| 2675 | testlock(-1, 0, NULL); |
| 2676 | verifytree(tree3, array, 0); |
| 2677 | verifytree(tree4, array, 1); |
| 2678 | assert(tree == bt_join(tree, tree2)); |
| 2679 | testlock(-1, 0, NULL); |
| 2680 | verifytree(tree, array+1, 1); |
| 2681 | verifytree(tree2, array, 0); |
| 2682 | assert(tree3 == bt_joinr(tree4, tree3)); |
| 2683 | testlock(-1, 0, NULL); |
| 2684 | verifytree(tree3, array, 1); |
| 2685 | verifytree(tree4, array, 0); |
| 2686 | assert(NULL == bt_join(tree, tree3)); |
| 2687 | testlock(-1, 0, NULL); |
| 2688 | verifytree(tree, array+1, 1); |
| 2689 | verifytree(tree3, array, 1); |
| 2690 | assert(tree3 == bt_join(tree3, tree)); |
| 2691 | testlock(-1, 0, NULL); |
| 2692 | verifytree(tree3, array, 2); |
| 2693 | verifytree(tree, array, 0); |
| 2694 | |
| 2695 | bt_free(tree); |
| 2696 | testlock(-1, 0, NULL); |
| 2697 | bt_free(tree2); |
| 2698 | testlock(-1, 0, NULL); |
| 2699 | bt_free(tree3); |
| 2700 | testlock(-1, 0, NULL); |
| 2701 | bt_free(tree4); |
| 2702 | testlock(-1, 0, NULL); |
| 2703 | |
| 2704 | sfree(array); |
| 2705 | |
| 2706 | if (errors) |
| 2707 | fprintf(stderr, "%d errors!\n", errors); |
| 2708 | return (errors != 0 ? 1 : 0); |
| 2709 | } |
| 2710 | |
| 2711 | #endif |