1 // SPDX-License-Identifier: GPL-2.0+ 2 /* 3 Red Black Trees 4 (C) 1999 Andrea Arcangeli <andrea (at) suse.de> 5 (C) 2002 David Woodhouse <dwmw2 (at) infradead.org> 6 (C) 2012 Michel Lespinasse <walken (at) google.com> 7 8 linux/lib/rbtree.c 9 */ 10 11 #include <linux/rbtree_augmented.h> 12 #ifndef __UBOOT__ 13 #include <linux/export.h> 14 #else 15 #include <ubi_uboot.h> 16 #endif 17 /* 18 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree 19 * 20 * 1) A node is either red or black 21 * 2) The root is black 22 * 3) All leaves (NULL) are black 23 * 4) Both children of every red node are black 24 * 5) Every simple path from root to leaves contains the same number 25 * of black nodes. 26 * 27 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two 28 * consecutive red nodes in a path and every red node is therefore followed by 29 * a black. So if B is the number of black nodes on every simple path (as per 30 * 5), then the longest possible path due to 4 is 2B. 31 * 32 * We shall indicate color with case, where black nodes are uppercase and red 33 * nodes will be lowercase. Unknown color nodes shall be drawn as red within 34 * parentheses and have some accompanying text comment. 35 */ 36 37 static inline void rb_set_black(struct rb_node *rb) 38 { 39 rb->__rb_parent_color |= RB_BLACK; 40 } 41 42 static inline struct rb_node *rb_red_parent(struct rb_node *red) 43 { 44 return (struct rb_node *)red->__rb_parent_color; 45 } 46 47 /* 48 * Helper function for rotations: 49 * - old's parent and color get assigned to new 50 * - old gets assigned new as a parent and 'color' as a color. 51 */ 52 static inline void 53 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 54 struct rb_root *root, int color) 55 { 56 struct rb_node *parent = rb_parent(old); 57 new->__rb_parent_color = old->__rb_parent_color; 58 rb_set_parent_color(old, new, color); 59 __rb_change_child(old, new, parent, root); 60 } 61 62 static __always_inline void 63 __rb_insert(struct rb_node *node, struct rb_root *root, 64 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 65 { 66 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; 67 68 while (true) { 69 /* 70 * Loop invariant: node is red 71 * 72 * If there is a black parent, we are done. 73 * Otherwise, take some corrective action as we don't 74 * want a red root or two consecutive red nodes. 75 */ 76 if (!parent) { 77 rb_set_parent_color(node, NULL, RB_BLACK); 78 break; 79 } else if (rb_is_black(parent)) 80 break; 81 82 gparent = rb_red_parent(parent); 83 84 tmp = gparent->rb_right; 85 if (parent != tmp) { /* parent == gparent->rb_left */ 86 if (tmp && rb_is_red(tmp)) { 87 /* 88 * Case 1 - color flips 89 * 90 * G g 91 * / \ / \ 92 * p u --> P U 93 * / / 94 * n N 95 * 96 * However, since g's parent might be red, and 97 * 4) does not allow this, we need to recurse 98 * at g. 99 */ 100 rb_set_parent_color(tmp, gparent, RB_BLACK); 101 rb_set_parent_color(parent, gparent, RB_BLACK); 102 node = gparent; 103 parent = rb_parent(node); 104 rb_set_parent_color(node, parent, RB_RED); 105 continue; 106 } 107 108 tmp = parent->rb_right; 109 if (node == tmp) { 110 /* 111 * Case 2 - left rotate at parent 112 * 113 * G G 114 * / \ / \ 115 * p U --> n U 116 * \ / 117 * n p 118 * 119 * This still leaves us in violation of 4), the 120 * continuation into Case 3 will fix that. 121 */ 122 parent->rb_right = tmp = node->rb_left; 123 node->rb_left = parent; 124 if (tmp) 125 rb_set_parent_color(tmp, parent, 126 RB_BLACK); 127 rb_set_parent_color(parent, node, RB_RED); 128 augment_rotate(parent, node); 129 parent = node; 130 tmp = node->rb_right; 131 } 132 133 /* 134 * Case 3 - right rotate at gparent 135 * 136 * G P 137 * / \ / \ 138 * p U --> n g 139 * / \ 140 * n U 141 */ 142 gparent->rb_left = tmp; /* == parent->rb_right */ 143 parent->rb_right = gparent; 144 if (tmp) 145 rb_set_parent_color(tmp, gparent, RB_BLACK); 146 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 147 augment_rotate(gparent, parent); 148 break; 149 } else { 150 tmp = gparent->rb_left; 151 if (tmp && rb_is_red(tmp)) { 152 /* Case 1 - color flips */ 153 rb_set_parent_color(tmp, gparent, RB_BLACK); 154 rb_set_parent_color(parent, gparent, RB_BLACK); 155 node = gparent; 156 parent = rb_parent(node); 157 rb_set_parent_color(node, parent, RB_RED); 158 continue; 159 } 160 161 tmp = parent->rb_left; 162 if (node == tmp) { 163 /* Case 2 - right rotate at parent */ 164 parent->rb_left = tmp = node->rb_right; 165 node->rb_right = parent; 166 if (tmp) 167 rb_set_parent_color(tmp, parent, 168 RB_BLACK); 169 rb_set_parent_color(parent, node, RB_RED); 170 augment_rotate(parent, node); 171 parent = node; 172 tmp = node->rb_left; 173 } 174 175 /* Case 3 - left rotate at gparent */ 176 gparent->rb_right = tmp; /* == parent->rb_left */ 177 parent->rb_left = gparent; 178 if (tmp) 179 rb_set_parent_color(tmp, gparent, RB_BLACK); 180 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 181 augment_rotate(gparent, parent); 182 break; 183 } 184 } 185 } 186 187 /* 188 * Inline version for rb_erase() use - we want to be able to inline 189 * and eliminate the dummy_rotate callback there 190 */ 191 static __always_inline void 192 ____rb_erase_color(struct rb_node *parent, struct rb_root *root, 193 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 194 { 195 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; 196 197 while (true) { 198 /* 199 * Loop invariants: 200 * - node is black (or NULL on first iteration) 201 * - node is not the root (parent is not NULL) 202 * - All leaf paths going through parent and node have a 203 * black node count that is 1 lower than other leaf paths. 204 */ 205 sibling = parent->rb_right; 206 if (node != sibling) { /* node == parent->rb_left */ 207 if (rb_is_red(sibling)) { 208 /* 209 * Case 1 - left rotate at parent 210 * 211 * P S 212 * / \ / \ 213 * N s --> p Sr 214 * / \ / \ 215 * Sl Sr N Sl 216 */ 217 parent->rb_right = tmp1 = sibling->rb_left; 218 sibling->rb_left = parent; 219 rb_set_parent_color(tmp1, parent, RB_BLACK); 220 __rb_rotate_set_parents(parent, sibling, root, 221 RB_RED); 222 augment_rotate(parent, sibling); 223 sibling = tmp1; 224 } 225 tmp1 = sibling->rb_right; 226 if (!tmp1 || rb_is_black(tmp1)) { 227 tmp2 = sibling->rb_left; 228 if (!tmp2 || rb_is_black(tmp2)) { 229 /* 230 * Case 2 - sibling color flip 231 * (p could be either color here) 232 * 233 * (p) (p) 234 * / \ / \ 235 * N S --> N s 236 * / \ / \ 237 * Sl Sr Sl Sr 238 * 239 * This leaves us violating 5) which 240 * can be fixed by flipping p to black 241 * if it was red, or by recursing at p. 242 * p is red when coming from Case 1. 243 */ 244 rb_set_parent_color(sibling, parent, 245 RB_RED); 246 if (rb_is_red(parent)) 247 rb_set_black(parent); 248 else { 249 node = parent; 250 parent = rb_parent(node); 251 if (parent) 252 continue; 253 } 254 break; 255 } 256 /* 257 * Case 3 - right rotate at sibling 258 * (p could be either color here) 259 * 260 * (p) (p) 261 * / \ / \ 262 * N S --> N Sl 263 * / \ \ 264 * sl Sr s 265 * \ 266 * Sr 267 */ 268 sibling->rb_left = tmp1 = tmp2->rb_right; 269 tmp2->rb_right = sibling; 270 parent->rb_right = tmp2; 271 if (tmp1) 272 rb_set_parent_color(tmp1, sibling, 273 RB_BLACK); 274 augment_rotate(sibling, tmp2); 275 tmp1 = sibling; 276 sibling = tmp2; 277 } 278 /* 279 * Case 4 - left rotate at parent + color flips 280 * (p and sl could be either color here. 281 * After rotation, p becomes black, s acquires 282 * p's color, and sl keeps its color) 283 * 284 * (p) (s) 285 * / \ / \ 286 * N S --> P Sr 287 * / \ / \ 288 * (sl) sr N (sl) 289 */ 290 parent->rb_right = tmp2 = sibling->rb_left; 291 sibling->rb_left = parent; 292 rb_set_parent_color(tmp1, sibling, RB_BLACK); 293 if (tmp2) 294 rb_set_parent(tmp2, parent); 295 __rb_rotate_set_parents(parent, sibling, root, 296 RB_BLACK); 297 augment_rotate(parent, sibling); 298 break; 299 } else { 300 sibling = parent->rb_left; 301 if (rb_is_red(sibling)) { 302 /* Case 1 - right rotate at parent */ 303 parent->rb_left = tmp1 = sibling->rb_right; 304 sibling->rb_right = parent; 305 rb_set_parent_color(tmp1, parent, RB_BLACK); 306 __rb_rotate_set_parents(parent, sibling, root, 307 RB_RED); 308 augment_rotate(parent, sibling); 309 sibling = tmp1; 310 } 311 tmp1 = sibling->rb_left; 312 if (!tmp1 || rb_is_black(tmp1)) { 313 tmp2 = sibling->rb_right; 314 if (!tmp2 || rb_is_black(tmp2)) { 315 /* Case 2 - sibling color flip */ 316 rb_set_parent_color(sibling, parent, 317 RB_RED); 318 if (rb_is_red(parent)) 319 rb_set_black(parent); 320 else { 321 node = parent; 322 parent = rb_parent(node); 323 if (parent) 324 continue; 325 } 326 break; 327 } 328 /* Case 3 - right rotate at sibling */ 329 sibling->rb_right = tmp1 = tmp2->rb_left; 330 tmp2->rb_left = sibling; 331 parent->rb_left = tmp2; 332 if (tmp1) 333 rb_set_parent_color(tmp1, sibling, 334 RB_BLACK); 335 augment_rotate(sibling, tmp2); 336 tmp1 = sibling; 337 sibling = tmp2; 338 } 339 /* Case 4 - left rotate at parent + color flips */ 340 parent->rb_left = tmp2 = sibling->rb_right; 341 sibling->rb_right = parent; 342 rb_set_parent_color(tmp1, sibling, RB_BLACK); 343 if (tmp2) 344 rb_set_parent(tmp2, parent); 345 __rb_rotate_set_parents(parent, sibling, root, 346 RB_BLACK); 347 augment_rotate(parent, sibling); 348 break; 349 } 350 } 351 } 352 353 /* Non-inline version for rb_erase_augmented() use */ 354 void __rb_erase_color(struct rb_node *parent, struct rb_root *root, 355 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 356 { 357 ____rb_erase_color(parent, root, augment_rotate); 358 } 359 EXPORT_SYMBOL(__rb_erase_color); 360 361 /* 362 * Non-augmented rbtree manipulation functions. 363 * 364 * We use dummy augmented callbacks here, and have the compiler optimize them 365 * out of the rb_insert_color() and rb_erase() function definitions. 366 */ 367 368 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} 369 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} 370 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} 371 372 static const struct rb_augment_callbacks dummy_callbacks = { 373 dummy_propagate, dummy_copy, dummy_rotate 374 }; 375 376 void rb_insert_color(struct rb_node *node, struct rb_root *root) 377 { 378 __rb_insert(node, root, dummy_rotate); 379 } 380 EXPORT_SYMBOL(rb_insert_color); 381 382 void rb_erase(struct rb_node *node, struct rb_root *root) 383 { 384 struct rb_node *rebalance; 385 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); 386 if (rebalance) 387 ____rb_erase_color(rebalance, root, dummy_rotate); 388 } 389 EXPORT_SYMBOL(rb_erase); 390 391 /* 392 * Augmented rbtree manipulation functions. 393 * 394 * This instantiates the same __always_inline functions as in the non-augmented 395 * case, but this time with user-defined callbacks. 396 */ 397 398 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, 399 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 400 { 401 __rb_insert(node, root, augment_rotate); 402 } 403 EXPORT_SYMBOL(__rb_insert_augmented); 404 405 /* 406 * This function returns the first node (in sort order) of the tree. 407 */ 408 struct rb_node *rb_first(const struct rb_root *root) 409 { 410 struct rb_node *n; 411 412 n = root->rb_node; 413 if (!n) 414 return NULL; 415 while (n->rb_left) 416 n = n->rb_left; 417 return n; 418 } 419 EXPORT_SYMBOL(rb_first); 420 421 struct rb_node *rb_last(const struct rb_root *root) 422 { 423 struct rb_node *n; 424 425 n = root->rb_node; 426 if (!n) 427 return NULL; 428 while (n->rb_right) 429 n = n->rb_right; 430 return n; 431 } 432 EXPORT_SYMBOL(rb_last); 433 434 struct rb_node *rb_next(const struct rb_node *node) 435 { 436 struct rb_node *parent; 437 438 if (RB_EMPTY_NODE(node)) 439 return NULL; 440 441 /* 442 * If we have a right-hand child, go down and then left as far 443 * as we can. 444 */ 445 if (node->rb_right) { 446 node = node->rb_right; 447 while (node->rb_left) 448 node=node->rb_left; 449 return (struct rb_node *)node; 450 } 451 452 /* 453 * No right-hand children. Everything down and left is smaller than us, 454 * so any 'next' node must be in the general direction of our parent. 455 * Go up the tree; any time the ancestor is a right-hand child of its 456 * parent, keep going up. First time it's a left-hand child of its 457 * parent, said parent is our 'next' node. 458 */ 459 while ((parent = rb_parent(node)) && node == parent->rb_right) 460 node = parent; 461 462 return parent; 463 } 464 EXPORT_SYMBOL(rb_next); 465 466 struct rb_node *rb_prev(const struct rb_node *node) 467 { 468 struct rb_node *parent; 469 470 if (RB_EMPTY_NODE(node)) 471 return NULL; 472 473 /* 474 * If we have a left-hand child, go down and then right as far 475 * as we can. 476 */ 477 if (node->rb_left) { 478 node = node->rb_left; 479 while (node->rb_right) 480 node=node->rb_right; 481 return (struct rb_node *)node; 482 } 483 484 /* 485 * No left-hand children. Go up till we find an ancestor which 486 * is a right-hand child of its parent. 487 */ 488 while ((parent = rb_parent(node)) && node == parent->rb_left) 489 node = parent; 490 491 return parent; 492 } 493 EXPORT_SYMBOL(rb_prev); 494 495 void rb_replace_node(struct rb_node *victim, struct rb_node *new, 496 struct rb_root *root) 497 { 498 struct rb_node *parent = rb_parent(victim); 499 500 /* Set the surrounding nodes to point to the replacement */ 501 __rb_change_child(victim, new, parent, root); 502 if (victim->rb_left) 503 rb_set_parent(victim->rb_left, new); 504 if (victim->rb_right) 505 rb_set_parent(victim->rb_right, new); 506 507 /* Copy the pointers/colour from the victim to the replacement */ 508 *new = *victim; 509 } 510 EXPORT_SYMBOL(rb_replace_node); 511 512 static struct rb_node *rb_left_deepest_node(const struct rb_node *node) 513 { 514 for (;;) { 515 if (node->rb_left) 516 node = node->rb_left; 517 else if (node->rb_right) 518 node = node->rb_right; 519 else 520 return (struct rb_node *)node; 521 } 522 } 523 524 struct rb_node *rb_next_postorder(const struct rb_node *node) 525 { 526 const struct rb_node *parent; 527 if (!node) 528 return NULL; 529 parent = rb_parent(node); 530 531 /* If we're sitting on node, we've already seen our children */ 532 if (parent && node == parent->rb_left && parent->rb_right) { 533 /* If we are the parent's left node, go to the parent's right 534 * node then all the way down to the left */ 535 return rb_left_deepest_node(parent->rb_right); 536 } else 537 /* Otherwise we are the parent's right node, and the parent 538 * should be next */ 539 return (struct rb_node *)parent; 540 } 541 EXPORT_SYMBOL(rb_next_postorder); 542 543 struct rb_node *rb_first_postorder(const struct rb_root *root) 544 { 545 if (!root->rb_node) 546 return NULL; 547 548 return rb_left_deepest_node(root->rb_node); 549 } 550 EXPORT_SYMBOL(rb_first_postorder); 551
