1/* $NetBSD: tree.h,v 1.21 2024/05/12 10:34:56 rillig Exp $ */
2/* $OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $ */
3/*
4 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
27
28#ifndef _SYS_TREE_H_
29#define _SYS_TREE_H_
30
31/*
32 * This file defines data structures for different types of trees:
33 * splay trees and red-black trees.
34 *
35 * A splay tree is a self-organizing data structure. Every operation
36 * on the tree causes a splay to happen. The splay moves the requested
37 * node to the root of the tree and partly rebalances it.
38 *
39 * This has the benefit that request locality causes faster lookups as
40 * the requested nodes move to the top of the tree. On the other hand,
41 * every lookup causes memory writes.
42 *
43 * The Balance Theorem bounds the total access time for m operations
44 * and n inserts on an initially empty tree as O((m + n)lg n). The
45 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
46 *
47 * A red-black tree is a binary search tree with the node color as an
48 * extra attribute. It fulfills a set of conditions:
49 * - every search path from the root to a leaf consists of the
50 * same number of black nodes,
51 * - each red node (except for the root) has a black parent,
52 * - each leaf node is black.
53 *
54 * Every operation on a red-black tree is bounded as O(lg n).
55 * The maximum height of a red-black tree is 2lg (n+1).
56 */
57
58#define SPLAY_HEAD(name, type) \
59struct name { \
60 struct type *sph_root; /* root of the tree */ \
61}
62
63#define SPLAY_INITIALIZER(root) \
64 { NULL }
65
66#define SPLAY_INIT(root) do { \
67 (root)->sph_root = NULL; \
68} while (0)
69
70#define SPLAY_ENTRY(type) \
71struct { \
72 struct type *spe_left; /* left element */ \
73 struct type *spe_right; /* right element */ \
74}
75
76#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
77#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
78#define SPLAY_ROOT(head) (head)->sph_root
79#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
80
81/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
82#define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
83 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
84 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
85 (head)->sph_root = tmp; \
86} while (0)
87
88#define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
89 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
90 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
91 (head)->sph_root = tmp; \
92} while (0)
93
94#define SPLAY_LINKLEFT(head, tmp, field) do { \
95 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
96 tmp = (head)->sph_root; \
97 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
98} while (0)
99
100#define SPLAY_LINKRIGHT(head, tmp, field) do { \
101 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
102 tmp = (head)->sph_root; \
103 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
104} while (0)
105
106#define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
107 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
108 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
109 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
110 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
111} while (0)
112
113/* Generates prototypes and inline functions */
114
115#define SPLAY_PROTOTYPE(name, type, field, cmp) \
116void name##_SPLAY(struct name *, struct type *); \
117void name##_SPLAY_MINMAX(struct name *, int); \
118struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
119struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
120 \
121/* Finds the node with the same key as elm */ \
122static __inline struct type * \
123name##_SPLAY_FIND(struct name *head, struct type *elm) \
124{ \
125 if (SPLAY_EMPTY(head)) \
126 return(NULL); \
127 name##_SPLAY(head, elm); \
128 if ((cmp)(elm, (head)->sph_root) == 0) \
129 return (head->sph_root); \
130 return (NULL); \
131} \
132 \
133static __inline __unused struct type * \
134name##_SPLAY_NEXT(struct name *head, struct type *elm) \
135{ \
136 name##_SPLAY(head, elm); \
137 if (SPLAY_RIGHT(elm, field) != NULL) { \
138 elm = SPLAY_RIGHT(elm, field); \
139 while (SPLAY_LEFT(elm, field) != NULL) { \
140 elm = SPLAY_LEFT(elm, field); \
141 } \
142 } else \
143 elm = NULL; \
144 return (elm); \
145} \
146 \
147static __unused __inline struct type * \
148name##_SPLAY_MIN_MAX(struct name *head, int val) \
149{ \
150 name##_SPLAY_MINMAX(head, val); \
151 return (SPLAY_ROOT(head)); \
152}
153
154/* Main splay operation.
155 * Moves node close to the key of elm to top
156 */
157#define SPLAY_GENERATE(name, type, field, cmp) \
158struct type * \
159name##_SPLAY_INSERT(struct name *head, struct type *elm) \
160{ \
161 if (SPLAY_EMPTY(head)) { \
162 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
163 } else { \
164 int __comp; \
165 name##_SPLAY(head, elm); \
166 __comp = (cmp)(elm, (head)->sph_root); \
167 if(__comp < 0) { \
168 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
169 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
170 SPLAY_LEFT((head)->sph_root, field) = NULL; \
171 } else if (__comp > 0) { \
172 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
173 SPLAY_LEFT(elm, field) = (head)->sph_root; \
174 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
175 } else \
176 return ((head)->sph_root); \
177 } \
178 (head)->sph_root = (elm); \
179 return (NULL); \
180} \
181 \
182struct type * \
183name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
184{ \
185 struct type *__tmp; \
186 if (SPLAY_EMPTY(head)) \
187 return (NULL); \
188 name##_SPLAY(head, elm); \
189 if ((cmp)(elm, (head)->sph_root) == 0) { \
190 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
191 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
192 } else { \
193 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
194 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
195 name##_SPLAY(head, elm); \
196 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
197 } \
198 return (elm); \
199 } \
200 return (NULL); \
201} \
202 \
203void \
204name##_SPLAY(struct name *head, struct type *elm) \
205{ \
206 struct type __node, *__left, *__right, *__tmp; \
207 int __comp; \
208\
209 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
210 __left = __right = &__node; \
211\
212 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
213 if (__comp < 0) { \
214 __tmp = SPLAY_LEFT((head)->sph_root, field); \
215 if (__tmp == NULL) \
216 break; \
217 if ((cmp)(elm, __tmp) < 0){ \
218 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
219 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
220 break; \
221 } \
222 SPLAY_LINKLEFT(head, __right, field); \
223 } else if (__comp > 0) { \
224 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
225 if (__tmp == NULL) \
226 break; \
227 if ((cmp)(elm, __tmp) > 0){ \
228 SPLAY_ROTATE_LEFT(head, __tmp, field); \
229 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
230 break; \
231 } \
232 SPLAY_LINKRIGHT(head, __left, field); \
233 } \
234 } \
235 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
236} \
237 \
238/* Splay with either the minimum or the maximum element \
239 * Used to find minimum or maximum element in tree. \
240 */ \
241void name##_SPLAY_MINMAX(struct name *head, int __comp) \
242{ \
243 struct type __node, *__left, *__right, *__tmp; \
244\
245 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
246 __left = __right = &__node; \
247\
248 while (1) { \
249 if (__comp < 0) { \
250 __tmp = SPLAY_LEFT((head)->sph_root, field); \
251 if (__tmp == NULL) \
252 break; \
253 if (__comp < 0){ \
254 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
255 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
256 break; \
257 } \
258 SPLAY_LINKLEFT(head, __right, field); \
259 } else if (__comp > 0) { \
260 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
261 if (__tmp == NULL) \
262 break; \
263 if (__comp > 0) { \
264 SPLAY_ROTATE_LEFT(head, __tmp, field); \
265 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
266 break; \
267 } \
268 SPLAY_LINKRIGHT(head, __left, field); \
269 } \
270 } \
271 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
272}
273
274#define SPLAY_NEGINF -1
275#define SPLAY_INF 1
276
277#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
278#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
279#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
280#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
281#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
282 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
283#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
284 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
285
286#define SPLAY_FOREACH(x, name, head) \
287 for ((x) = SPLAY_MIN(name, head); \
288 (x) != NULL; \
289 (x) = SPLAY_NEXT(name, head, x))
290
291/* Macros that define a red-black tree */
292#define RB_HEAD(name, type) \
293struct name { \
294 struct type *rbh_root; /* root of the tree */ \
295}
296
297#define RB_INITIALIZER(root) \
298 { NULL }
299
300#define RB_INIT(root) do { \
301 (root)->rbh_root = NULL; \
302} while (0)
303
304#define RB_BLACK 0
305#define RB_RED 1
306#define RB_ENTRY(type) \
307struct { \
308 struct type *rbe_left; /* left element */ \
309 struct type *rbe_right; /* right element */ \
310 struct type *rbe_parent; /* parent element */ \
311 int rbe_color; /* node color */ \
312}
313
314#define RB_LEFT(elm, field) (elm)->field.rbe_left
315#define RB_RIGHT(elm, field) (elm)->field.rbe_right
316#define RB_PARENT(elm, field) (elm)->field.rbe_parent
317#define RB_COLOR(elm, field) (elm)->field.rbe_color
318#define RB_ROOT(head) (head)->rbh_root
319#define RB_EMPTY(head) (RB_ROOT(head) == NULL)
320
321#define RB_SET(elm, parent, field) do { \
322 RB_PARENT(elm, field) = parent; \
323 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
324 RB_COLOR(elm, field) = RB_RED; \
325} while (0)
326
327#define RB_SET_BLACKRED(black, red, field) do { \
328 RB_COLOR(black, field) = RB_BLACK; \
329 RB_COLOR(red, field) = RB_RED; \
330} while (0)
331
332#ifndef RB_AUGMENT
333#define RB_AUGMENT(x) do {} while (0)
334#endif
335
336#define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
337 (tmp) = RB_RIGHT(elm, field); \
338 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
339 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
340 } \
341 RB_AUGMENT(elm); \
342 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
343 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
344 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
345 else \
346 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
347 } else \
348 (head)->rbh_root = (tmp); \
349 RB_LEFT(tmp, field) = (elm); \
350 RB_PARENT(elm, field) = (tmp); \
351 RB_AUGMENT(tmp); \
352 if ((RB_PARENT(tmp, field))) \
353 RB_AUGMENT(RB_PARENT(tmp, field)); \
354} while (0)
355
356#define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
357 (tmp) = RB_LEFT(elm, field); \
358 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
359 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
360 } \
361 RB_AUGMENT(elm); \
362 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
363 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
364 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
365 else \
366 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
367 } else \
368 (head)->rbh_root = (tmp); \
369 RB_RIGHT(tmp, field) = (elm); \
370 RB_PARENT(elm, field) = (tmp); \
371 RB_AUGMENT(tmp); \
372 if ((RB_PARENT(tmp, field))) \
373 RB_AUGMENT(RB_PARENT(tmp, field)); \
374} while (0)
375
376/* Generates prototypes and inline functions */
377#define RB_PROTOTYPE(name, type, field, cmp) \
378 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
379#define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
380 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
381#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
382attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
383attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
384attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
385attr struct type *name##_RB_INSERT(struct name *, struct type *); \
386attr struct type *name##_RB_FIND(struct name *, struct type *); \
387attr struct type *name##_RB_NFIND(struct name *, struct type *); \
388attr struct type *name##_RB_NEXT(struct type *); \
389attr struct type *name##_RB_PREV(struct type *); \
390attr struct type *name##_RB_MINMAX(struct name *, int); \
391 \
392
393/* Main rb operation.
394 * Moves node close to the key of elm to top
395 */
396#define RB_GENERATE(name, type, field, cmp) \
397 RB_GENERATE_INTERNAL(name, type, field, cmp,)
398#define RB_GENERATE_STATIC(name, type, field, cmp) \
399 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
400#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
401attr void \
402name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
403{ \
404 struct type *parent, *gparent, *tmp; \
405 while ((parent = RB_PARENT(elm, field)) != NULL && \
406 RB_COLOR(parent, field) == RB_RED) { \
407 gparent = RB_PARENT(parent, field); \
408 if (parent == RB_LEFT(gparent, field)) { \
409 tmp = RB_RIGHT(gparent, field); \
410 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
411 RB_COLOR(tmp, field) = RB_BLACK; \
412 RB_SET_BLACKRED(parent, gparent, field);\
413 elm = gparent; \
414 continue; \
415 } \
416 if (RB_RIGHT(parent, field) == elm) { \
417 RB_ROTATE_LEFT(head, parent, tmp, field);\
418 tmp = parent; \
419 parent = elm; \
420 elm = tmp; \
421 } \
422 RB_SET_BLACKRED(parent, gparent, field); \
423 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
424 } else { \
425 tmp = RB_LEFT(gparent, field); \
426 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
427 RB_COLOR(tmp, field) = RB_BLACK; \
428 RB_SET_BLACKRED(parent, gparent, field);\
429 elm = gparent; \
430 continue; \
431 } \
432 if (RB_LEFT(parent, field) == elm) { \
433 RB_ROTATE_RIGHT(head, parent, tmp, field);\
434 tmp = parent; \
435 parent = elm; \
436 elm = tmp; \
437 } \
438 RB_SET_BLACKRED(parent, gparent, field); \
439 RB_ROTATE_LEFT(head, gparent, tmp, field); \
440 } \
441 } \
442 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
443} \
444 \
445attr void \
446name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
447{ \
448 struct type *tmp; \
449 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
450 elm != RB_ROOT(head)) { \
451 if (RB_LEFT(parent, field) == elm) { \
452 tmp = RB_RIGHT(parent, field); \
453 if (RB_COLOR(tmp, field) == RB_RED) { \
454 RB_SET_BLACKRED(tmp, parent, field); \
455 RB_ROTATE_LEFT(head, parent, tmp, field);\
456 tmp = RB_RIGHT(parent, field); \
457 } \
458 if ((RB_LEFT(tmp, field) == NULL || \
459 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
460 (RB_RIGHT(tmp, field) == NULL || \
461 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
462 RB_COLOR(tmp, field) = RB_RED; \
463 elm = parent; \
464 parent = RB_PARENT(elm, field); \
465 } else { \
466 if (RB_RIGHT(tmp, field) == NULL || \
467 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
468 struct type *oleft; \
469 if ((oleft = RB_LEFT(tmp, field)) \
470 != NULL) \
471 RB_COLOR(oleft, field) = RB_BLACK;\
472 RB_COLOR(tmp, field) = RB_RED; \
473 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
474 tmp = RB_RIGHT(parent, field); \
475 } \
476 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
477 RB_COLOR(parent, field) = RB_BLACK; \
478 if (RB_RIGHT(tmp, field)) \
479 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
480 RB_ROTATE_LEFT(head, parent, tmp, field);\
481 elm = RB_ROOT(head); \
482 break; \
483 } \
484 } else { \
485 tmp = RB_LEFT(parent, field); \
486 if (RB_COLOR(tmp, field) == RB_RED) { \
487 RB_SET_BLACKRED(tmp, parent, field); \
488 RB_ROTATE_RIGHT(head, parent, tmp, field);\
489 tmp = RB_LEFT(parent, field); \
490 } \
491 if ((RB_LEFT(tmp, field) == NULL || \
492 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
493 (RB_RIGHT(tmp, field) == NULL || \
494 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
495 RB_COLOR(tmp, field) = RB_RED; \
496 elm = parent; \
497 parent = RB_PARENT(elm, field); \
498 } else { \
499 if (RB_LEFT(tmp, field) == NULL || \
500 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
501 struct type *oright; \
502 if ((oright = RB_RIGHT(tmp, field)) \
503 != NULL) \
504 RB_COLOR(oright, field) = RB_BLACK;\
505 RB_COLOR(tmp, field) = RB_RED; \
506 RB_ROTATE_LEFT(head, tmp, oright, field);\
507 tmp = RB_LEFT(parent, field); \
508 } \
509 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
510 RB_COLOR(parent, field) = RB_BLACK; \
511 if (RB_LEFT(tmp, field)) \
512 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
513 RB_ROTATE_RIGHT(head, parent, tmp, field);\
514 elm = RB_ROOT(head); \
515 break; \
516 } \
517 } \
518 } \
519 if (elm) \
520 RB_COLOR(elm, field) = RB_BLACK; \
521} \
522 \
523attr struct type * \
524name##_RB_REMOVE(struct name *head, struct type *elm) \
525{ \
526 struct type *child, *parent, *old = elm; \
527 int color; \
528 if (RB_LEFT(elm, field) == NULL) \
529 child = RB_RIGHT(elm, field); \
530 else if (RB_RIGHT(elm, field) == NULL) \
531 child = RB_LEFT(elm, field); \
532 else { \
533 struct type *left; \
534 elm = RB_RIGHT(elm, field); \
535 while ((left = RB_LEFT(elm, field)) != NULL) \
536 elm = left; \
537 child = RB_RIGHT(elm, field); \
538 parent = RB_PARENT(elm, field); \
539 color = RB_COLOR(elm, field); \
540 if (child) \
541 RB_PARENT(child, field) = parent; \
542 if (parent) { \
543 if (RB_LEFT(parent, field) == elm) \
544 RB_LEFT(parent, field) = child; \
545 else \
546 RB_RIGHT(parent, field) = child; \
547 RB_AUGMENT(parent); \
548 } else \
549 RB_ROOT(head) = child; \
550 if (RB_PARENT(elm, field) == old) \
551 parent = elm; \
552 (elm)->field = (old)->field; \
553 if (RB_PARENT(old, field)) { \
554 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
555 RB_LEFT(RB_PARENT(old, field), field) = elm;\
556 else \
557 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
558 RB_AUGMENT(RB_PARENT(old, field)); \
559 } else \
560 RB_ROOT(head) = elm; \
561 RB_PARENT(RB_LEFT(old, field), field) = elm; \
562 if (RB_RIGHT(old, field)) \
563 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
564 if (parent) { \
565 left = parent; \
566 do { \
567 RB_AUGMENT(left); \
568 } while ((left = RB_PARENT(left, field)) != NULL); \
569 } \
570 goto color; \
571 } \
572 parent = RB_PARENT(elm, field); \
573 color = RB_COLOR(elm, field); \
574 if (child) \
575 RB_PARENT(child, field) = parent; \
576 if (parent) { \
577 if (RB_LEFT(parent, field) == elm) \
578 RB_LEFT(parent, field) = child; \
579 else \
580 RB_RIGHT(parent, field) = child; \
581 RB_AUGMENT(parent); \
582 } else \
583 RB_ROOT(head) = child; \
584color: \
585 if (color == RB_BLACK) \
586 name##_RB_REMOVE_COLOR(head, parent, child); \
587 return (old); \
588} \
589 \
590/* Inserts a node into the RB tree */ \
591attr struct type * \
592name##_RB_INSERT(struct name *head, struct type *elm) \
593{ \
594 struct type *tmp; \
595 struct type *parent = NULL; \
596 int comp = 0; \
597 tmp = RB_ROOT(head); \
598 while (tmp) { \
599 parent = tmp; \
600 comp = (cmp)(elm, parent); \
601 if (comp < 0) \
602 tmp = RB_LEFT(tmp, field); \
603 else if (comp > 0) \
604 tmp = RB_RIGHT(tmp, field); \
605 else \
606 return (tmp); \
607 } \
608 RB_SET(elm, parent, field); \
609 if (parent != NULL) { \
610 if (comp < 0) \
611 RB_LEFT(parent, field) = elm; \
612 else \
613 RB_RIGHT(parent, field) = elm; \
614 RB_AUGMENT(parent); \
615 } else \
616 RB_ROOT(head) = elm; \
617 name##_RB_INSERT_COLOR(head, elm); \
618 return (NULL); \
619} \
620 \
621/* Finds the node with the same key as elm */ \
622attr struct type * \
623name##_RB_FIND(struct name *head, struct type *elm) \
624{ \
625 struct type *tmp = RB_ROOT(head); \
626 int comp; \
627 while (tmp) { \
628 comp = cmp(elm, tmp); \
629 if (comp < 0) \
630 tmp = RB_LEFT(tmp, field); \
631 else if (comp > 0) \
632 tmp = RB_RIGHT(tmp, field); \
633 else \
634 return (tmp); \
635 } \
636 return (NULL); \
637} \
638 \
639/* Finds the first node greater than or equal to the search key */ \
640attr struct type * \
641name##_RB_NFIND(struct name *head, struct type *elm) \
642{ \
643 struct type *tmp = RB_ROOT(head); \
644 struct type *res = NULL; \
645 int comp; \
646 while (tmp) { \
647 comp = cmp(elm, tmp); \
648 if (comp < 0) { \
649 res = tmp; \
650 tmp = RB_LEFT(tmp, field); \
651 } \
652 else if (comp > 0) \
653 tmp = RB_RIGHT(tmp, field); \
654 else \
655 return (tmp); \
656 } \
657 return (res); \
658} \
659 \
660/* ARGSUSED */ \
661attr struct type * \
662name##_RB_NEXT(struct type *elm) \
663{ \
664 if (RB_RIGHT(elm, field)) { \
665 elm = RB_RIGHT(elm, field); \
666 while (RB_LEFT(elm, field)) \
667 elm = RB_LEFT(elm, field); \
668 } else { \
669 if (RB_PARENT(elm, field) && \
670 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
671 elm = RB_PARENT(elm, field); \
672 else { \
673 while (RB_PARENT(elm, field) && \
674 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
675 elm = RB_PARENT(elm, field); \
676 elm = RB_PARENT(elm, field); \
677 } \
678 } \
679 return (elm); \
680} \
681 \
682/* ARGSUSED */ \
683attr struct type * \
684name##_RB_PREV(struct type *elm) \
685{ \
686 if (RB_LEFT(elm, field)) { \
687 elm = RB_LEFT(elm, field); \
688 while (RB_RIGHT(elm, field)) \
689 elm = RB_RIGHT(elm, field); \
690 } else { \
691 if (RB_PARENT(elm, field) && \
692 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
693 elm = RB_PARENT(elm, field); \
694 else { \
695 while (RB_PARENT(elm, field) && \
696 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
697 elm = RB_PARENT(elm, field); \
698 elm = RB_PARENT(elm, field); \
699 } \
700 } \
701 return (elm); \
702} \
703 \
704attr struct type * \
705name##_RB_MINMAX(struct name *head, int val) \
706{ \
707 struct type *tmp = RB_ROOT(head); \
708 struct type *parent = NULL; \
709 while (tmp) { \
710 parent = tmp; \
711 if (val < 0) \
712 tmp = RB_LEFT(tmp, field); \
713 else \
714 tmp = RB_RIGHT(tmp, field); \
715 } \
716 return (parent); \
717}
718
719#define RB_NEGINF -1
720#define RB_INF 1
721
722#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
723#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
724#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
725#define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
726#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
727#define RB_PREV(name, x, y) name##_RB_PREV(y)
728#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
729#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
730
731#define RB_FOREACH(x, name, head) \
732 for ((x) = RB_MIN(name, head); \
733 (x) != NULL; \
734 (x) = name##_RB_NEXT(x))
735
736#define RB_FOREACH_FROM(x, name, y) \
737 for ((x) = (y); \
738 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
739 (x) = (y))
740
741#define RB_FOREACH_SAFE(x, name, head, y) \
742 for ((x) = RB_MIN(name, head); \
743 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
744 (x) = (y))
745
746#define RB_FOREACH_REVERSE(x, name, head) \
747 for ((x) = RB_MAX(name, head); \
748 (x) != NULL; \
749 (x) = name##_RB_PREV(x))
750
751#define RB_FOREACH_REVERSE_FROM(x, name, y) \
752 for ((x) = (y); \
753 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
754 (x) = (y))
755
756#define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
757 for ((x) = RB_MAX(name, head); \
758 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
759 (x) = (y))
760
761#endif /* _SYS_TREE_H_ */