2 * Written by Josh Dybnis and released to the public domain, as explained at
3 * http://creativecommons.org/licenses/publicdomain
5 * Implementation of the lock-free skiplist data-structure created by Maurice Herlihy, Yossi Lev,
6 * and Nir Shavit. See Herlihy's and Shivit's book "The Art of Multiprocessor Programming".
7 * http://www.amazon.com/Art-Multiprocessor-Programming-Maurice-Herlihy/dp/0123705916/
9 * See also Kir Fraser's dissertation "Practical Lock Freedom".
10 * www.cl.cam.ac.uk/techreports/UCAM-CL-TR-579.pdf
12 * I've generalized the data structure to support update operations like set() and CAS() in addition to
13 * the normal add() and remove() operations.
15 * Warning: This code is written for the x86 memory-model. The algorithim depends on certain stores
16 * and loads being ordered. This code won't work correctly on platforms with weaker memory models if
17 * you don't add memory barriers in the right places.
29 // Setting MAX_LEVEL to 0 essentially makes this data structure the Harris-Michael lock-free list (in list.c).
45 const datatype_t *key_type;
46 int high_water; // max level of any item in the list
49 // Marking the <next> field of a node logically removes it from the list
51 static inline markable_t MARK_NODE(node_t * x) { return TAG_VALUE((markable_t)x, 0x1); }
52 static inline int HAS_MARK(markable_t x) { return (IS_TAGGED(x, 0x1) == 0x1); }
53 static inline node_t * GET_NODE(markable_t x) { assert(!HAS_MARK(x)); return (node_t *)x; }
54 static inline node_t * STRIP_MARK(markable_t x) { return ((node_t *)STRIP_TAG(x, 0x1)); }
56 #define MARK_NODE(x) TAG_VALUE((markable_t)(x), 0x1)
57 #define HAS_MARK(x) (IS_TAGGED((x), 0x1) == 0x1)
58 #define GET_NODE(x) ((node_t *)(x))
59 #define STRIP_MARK(x) ((node_t *)STRIP_TAG((x), 0x1))
62 static int random_level (void) {
63 unsigned r = nbd_rand();
64 int n = __builtin_ctz(r) / 2;
65 if (n > MAX_LEVEL) { n = MAX_LEVEL; }
69 static node_t *node_alloc (int level, map_key_t key, map_val_t val) {
70 assert(level >= 0 && level <= MAX_LEVEL);
71 size_t sz = sizeof(node_t) + level * sizeof(node_t *);
72 node_t *item = (node_t *)nbd_malloc(sz);
76 item->top_level = level;
77 TRACE("s2", "node_alloc: new node %p (%llu levels)", item, level);
81 skiplist_t *sl_alloc (const datatype_t *key_type) {
82 skiplist_t *sl = (skiplist_t *)nbd_malloc(sizeof(skiplist_t));
83 sl->key_type = key_type;
85 sl->head = node_alloc(MAX_LEVEL, 0, 0);
86 memset(sl->head->next, 0, (MAX_LEVEL+1) * sizeof(skiplist_t *));
90 void sl_free (skiplist_t *sl) {
91 node_t *item = GET_NODE(sl->head->next[0]);
93 node_t *next = STRIP_MARK(item->next[0]);
94 if (sl->key_type != NULL) {
95 nbd_free((void *)item->key);
102 size_t sl_count (skiplist_t *sl) {
104 node_t *item = GET_NODE(sl->head->next[0]);
106 if (!HAS_MARK(item->next[0])) {
109 item = STRIP_MARK(item->next[0]);
114 static node_t *find_preds (node_t **preds, node_t **succs, int n, skiplist_t *sl, map_key_t key, int help_remove) {
115 node_t *pred = sl->head;
117 TRACE("s2", "find_preds: searching for key %p in skiplist (head is %p)", key, pred);
119 int start_level = sl->high_water;
120 if (EXPECT_FALSE(start_level < n)) {
124 // Traverse the levels of <sl> from the top level to the bottom
125 for (int level = start_level; level >= 0; --level) {
126 markable_t next = pred->next[level];
127 if (next == DOES_NOT_EXIST && level > n)
129 TRACE("s3", "find_preds: traversing level %p starting at %p", level, pred);
130 if (EXPECT_FALSE(HAS_MARK(next))) {
131 TRACE("s2", "find_preds: pred %p is marked for removal (next %p); retry", pred, next);
132 ASSERT(level == pred->top_level || HAS_MARK(pred->next[level+1]));
133 return find_preds(preds, succs, n, sl, key, help_remove); // retry
135 item = GET_NODE(next);
136 while (item != NULL) {
137 next = item->next[level];
139 // A tag means an item is logically removed but not physically unlinked yet.
140 while (EXPECT_FALSE(HAS_MARK(next))) {
141 TRACE("s3", "find_preds: found marked item %p (next is %p)", item, next);
144 // Skip over logically removed items.
145 item = STRIP_MARK(next);
146 if (EXPECT_FALSE(item == NULL))
148 next = item->next[level];
151 // Unlink logically removed items.
152 markable_t other = SYNC_CAS(&pred->next[level], item, STRIP_MARK(next));
153 if (other == (markable_t)item) {
154 TRACE("s3", "find_preds: unlinked item from pred %p", pred, 0);
155 item = STRIP_MARK(next);
157 TRACE("s3", "find_preds: lost race to unlink item pred %p's link changed to %p", pred, other);
159 return find_preds(preds, succs, n, sl, key, help_remove); // retry
160 item = GET_NODE(other);
162 next = (item != NULL) ? item->next[level] : DOES_NOT_EXIST;
166 if (EXPECT_FALSE(item == NULL)) {
167 TRACE("s3", "find_preds: past the last item in the skiplist", 0, 0);
171 TRACE("s4", "find_preds: visiting item %p (next is %p)", item, next);
172 TRACE("s4", "find_preds: key %p val %p", STRIP_MARK(item->key), item->val);
174 if (EXPECT_TRUE(sl->key_type == NULL)) {
177 d = sl->key_type->cmp((void *)item->key, (void *)key);
184 item = GET_NODE(next);
187 TRACE("s3", "find_preds: found pred %p next %p", pred, item);
189 // The cast to unsigned is for the case when n is -1.
190 if ((unsigned)level <= (unsigned)n) {
200 // fill in empty levels
201 if (n == -1 && item != NULL && preds != NULL) {
202 assert(item->top_level <= MAX_LEVEL);
203 for (int level = start_level + 1; level <= item->top_level; ++level) {
204 preds[level] = sl->head;
209 TRACE("s2", "find_preds: found matching item %p in skiplist, pred is %p", item, pred);
212 TRACE("s2", "find_preds: found proper place for key %p in skiplist, pred is %p. returning null", key, pred);
216 static void sl_unlink (skiplist_t *sl, map_key_t key) {
217 node_t *pred = sl->head;
219 TRACE("s2", "sl_unlink: unlinking marked item with key %p", key, 0);
222 // Traverse the levels of <sl> from the top level to the bottom
223 for (int level = sl->high_water; level >= 0; --level) {
224 markable_t next = pred->next[level];
225 if (next == DOES_NOT_EXIST)
227 TRACE("s3", "sl_unlink: traversing level %p starting at %p", level, pred);
228 if (EXPECT_FALSE(HAS_MARK(next))) {
229 TRACE("s2", "sl_unlink: lost a race; pred %p is marked for removal (next %p); retry", pred, next);
230 ASSERT(level == pred->top_level || HAS_MARK(pred->next[level+1]));
231 return sl_unlink(sl, key); // retry
233 item = GET_NODE(next);
234 while (item != NULL) {
235 next = item->next[level];
237 while (HAS_MARK(next)) {
238 TRACE("s3", "sl_unlink: found marked item %p (next is %p)", item, next);
240 markable_t other = SYNC_CAS(&pred->next[level], item, STRIP_MARK(next));
241 if (other == (markable_t)item) {
242 TRACE("s3", "sl_unlink: unlinked item from pred %p", pred, 0);
243 item = STRIP_MARK(next);
245 TRACE("s3", "sl_unlink: lost race to unlink item, pred %p's link changed to %p", pred, other);
247 return sl_unlink(sl, key); // retry
248 item = GET_NODE(other);
250 next = (item != NULL) ? item->next[level] : DOES_NOT_EXIST;
253 if (EXPECT_FALSE(item == NULL)) {
254 TRACE("s3", "sl_unlink: past the last item in the skiplist", 0, 0);
258 TRACE("s4", "sl_unlink: visiting item %p (next is %p)", item, next);
259 TRACE("s4", "sl_unlink: key %p val %p", STRIP_MARK(item->key), item->val);
261 if (EXPECT_TRUE(sl->key_type == NULL)) {
264 d = sl->key_type->cmp((void *)item->key, (void *)key);
271 item = GET_NODE(next);
274 TRACE("s3", "sl_unlink: at pred %p next %p", pred, item);
278 // Fast find that does not help unlink partially removed nodes and does not return the node's predecessors.
279 map_val_t sl_lookup (skiplist_t *sl, map_key_t key) {
280 TRACE("s1", "sl_lookup: searching for key %p in skiplist %p", key, sl);
281 node_t *item = find_preds(NULL, NULL, 0, sl, key, FALSE);
283 // If we found an <item> matching the <key> return its value.
285 map_val_t val = item->val;
286 if (val != DOES_NOT_EXIST) {
287 TRACE("s1", "sl_lookup: found item %p. val %p. returning item", item, item->val);
292 TRACE("l1", "sl_lookup: no item in the skiplist matched the key", 0, 0);
293 return DOES_NOT_EXIST;
296 map_key_t sl_min_key (skiplist_t *sl) {
297 node_t *item = GET_NODE(sl->head->next[0]);
298 while (item != NULL) {
299 markable_t next = item->next[0];
302 item = STRIP_MARK(next);
304 return DOES_NOT_EXIST;
307 static map_val_t update_item (node_t *item, map_val_t expectation, map_val_t new_val) {
308 map_val_t old_val = item->val;
310 // If the item's value is DOES_NOT_EXIST it means another thread removed the node out from under us.
311 if (EXPECT_FALSE(old_val == DOES_NOT_EXIST)) {
312 TRACE("s2", "update_item: lost a race to another thread removing the item. retry", 0, 0);
313 return DOES_NOT_EXIST; // retry
316 if (EXPECT_FALSE(expectation == CAS_EXPECT_DOES_NOT_EXIST)) {
317 TRACE("s1", "update_item: found an item %p in the skiplist that matched the key. the expectation was "
318 "not met, the skiplist was not changed", item, old_val);
319 return old_val; // failure
322 // Use a CAS and not a SWAP. If the CAS fails it means another thread removed the node or updated its
323 // value. If another thread removed the node but it is not unlinked yet and we used a SWAP, we could
324 // replace DOES_NOT_EXIST with our value. Then another thread that is updating the value could think it
325 // succeeded and return our value even though it should return DOES_NOT_EXIST.
326 if (old_val == SYNC_CAS(&item->val, old_val, new_val)) {
327 TRACE("s1", "update_item: the CAS succeeded. updated the value of the item", 0, 0);
328 return old_val; // success
330 TRACE("s2", "update_item: lost a race. the CAS failed. another thread changed the item's value", 0, 0);
333 return update_item(item, expectation, new_val); // tail call
336 map_val_t sl_cas (skiplist_t *sl, map_key_t key, map_val_t expectation, map_val_t new_val) {
337 TRACE("s1", "sl_cas: key %p skiplist %p", key, sl);
338 TRACE("s1", "sl_cas: expectation %p new value %p", expectation, new_val);
339 ASSERT((int64_t)new_val > 0);
341 node_t *preds[MAX_LEVEL+1];
342 node_t *nexts[MAX_LEVEL+1];
343 node_t *new_item = NULL;
344 int n = random_level();
345 node_t *old_item = find_preds(preds, nexts, n, sl, key, TRUE);
347 // If there is already an item in the skiplist that matches the key just update its value.
348 if (old_item != NULL) {
349 map_val_t ret_val = update_item(old_item, expectation, new_val);
350 if (ret_val != DOES_NOT_EXIST)
353 // If we lose a race with a thread removing the item we tried to update then we have to retry.
354 return sl_cas(sl, key, expectation, new_val); // tail call
357 if (EXPECT_FALSE(expectation != CAS_EXPECT_DOES_NOT_EXIST && expectation != CAS_EXPECT_WHATEVER)) {
358 TRACE("l1", "sl_cas: the expectation was not met, the skiplist was not changed", 0, 0);
359 return DOES_NOT_EXIST; // failure, the caller expected an item for the <key> to already exist
362 // Create a new node and insert it into the skiplist.
363 TRACE("s3", "sl_cas: attempting to insert a new item between %p and %p", preds[0], nexts[0]);
364 map_key_t new_key = sl->key_type == NULL ? key : (map_key_t)sl->key_type->clone((void *)key);
365 if (n > sl->high_water) {
366 n = sl->high_water + 1;
367 int x = SYNC_ADD(&sl->high_water, 1);
369 TRACE("s2", "sl_cas: incremented high water mark to %p", x, 0);
371 new_item = node_alloc(n, new_key, new_val);
373 // Set <new_item>'s next pointers to their proper values
374 markable_t next = new_item->next[0] = (markable_t)nexts[0];
375 for (int level = 1; level <= new_item->top_level; ++level) {
376 new_item->next[level] = (markable_t)nexts[level];
379 // Link <new_item> into <sl> from the bottom level up. After <new_item> is inserted into the bottom level
380 // it is officially part of the skiplist.
381 node_t *pred = preds[0];
382 markable_t other = SYNC_CAS(&pred->next[0], next, new_item);
384 TRACE("s3", "sl_cas: failed to change pred's link: expected %p found %p", next, other);
386 // Lost a race to another thread modifying the skiplist. Free the new item we allocated and retry.
387 if (sl->key_type != NULL) {
388 nbd_free((void *)new_key);
391 return sl_cas(sl, key, expectation, new_val); // tail call
394 TRACE("s3", "sl_cas: successfully inserted a new item %p at the bottom level", new_item, 0);
396 for (int level = 1; level <= new_item->top_level; ++level) {
397 TRACE("s3", "sl_cas: inserting the new item %p at level %p", new_item, level);
399 node_t * pred = preds[level];
400 ASSERT(new_item->next[level]==(markable_t)nexts[level] || new_item->next[level]==MARK_NODE(nexts[level]));
401 TRACE("s3", "sl_cas: attempting to to insert the new item between %p and %p", pred, nexts[level]);
403 markable_t other = SYNC_CAS(&pred->next[level], nexts[level], (markable_t)new_item);
404 if (other == (markable_t)nexts[level])
405 break; // successfully linked <new_item> into the skiplist at the current <level>
406 TRACE("s3", "sl_cas: lost a race. failed to change pred's link. expected %p found %p", nexts[level], other);
408 // Find <new_item>'s new preds and nexts.
409 find_preds(preds, nexts, new_item->top_level, sl, key, TRUE);
411 for (int i = level; i <= new_item->top_level; ++i) {
412 markable_t old_next = new_item->next[i];
413 if ((markable_t)nexts[i] == old_next)
416 // Update <new_item>'s inconsistent next pointer before trying again. Use a CAS so if another thread
417 // is trying to remove the new item concurrently we do not stomp on the mark it places on the item.
418 TRACE("s3", "sl_cas: attempting to update the new item's link from %p to %p", old_next, nexts[i]);
419 other = SYNC_CAS(&new_item->next[i], old_next, nexts[i]);
420 ASSERT(other == old_next || other == MARK_NODE(old_next));
422 // If another thread is removing this item we can stop linking it into to skiplist
423 if (HAS_MARK(other)) {
424 sl_unlink(sl, key); // see comment below
425 return DOES_NOT_EXIST;
431 // In case another thread was in the process of removing the <new_item> while we were added it, we have to
432 // make sure it is completely unlinked before we return. We might have lost a race and inserted the new item
433 // at some level after the other thread thought it was fully removed. That is a problem because once a thread
434 // thinks it completely unlinks a node it queues it to be freed
435 if (HAS_MARK(new_item->next[new_item->top_level])) {
439 return DOES_NOT_EXIST; // success, inserted a new item
442 map_val_t sl_remove (skiplist_t *sl, map_key_t key) {
443 TRACE("s1", "sl_remove: removing item with key %p from skiplist %p", key, sl);
444 node_t *preds[MAX_LEVEL+1];
445 node_t *item = find_preds(preds, NULL, -1, sl, key, TRUE);
447 TRACE("s3", "sl_remove: remove failed, an item with a matching key does not exist in the skiplist", 0, 0);
448 return DOES_NOT_EXIST;
451 // Mark <item> at each level of <sl> from the top down. If multiple threads try to concurrently remove
452 // the same item only one of them should succeed. Marking the bottom level establishes which of them succeeds.
453 markable_t old_next = 0;
454 for (int level = item->top_level; level >= 0; --level) {
456 old_next = item->next[level];
458 TRACE("s3", "sl_remove: marking item at level %p (next %p)", level, old_next);
460 old_next = SYNC_CAS(&item->next[level], next, MARK_NODE((node_t *)next));
461 if (HAS_MARK(old_next)) {
462 TRACE("s2", "sl_remove: %p is already marked for removal by another thread (next %p)", item, old_next);
464 return DOES_NOT_EXIST;
467 } while (next != old_next);
470 // Atomically swap out the item's value in case another thread is updating the item while we are
471 // removing it. This establishes which operation occurs first logically, the update or the remove.
472 map_val_t val = SYNC_SWAP(&item->val, DOES_NOT_EXIST);
473 TRACE("s2", "sl_remove: replaced item %p's value with DOES_NOT_EXIT", item, 0);
479 if (sl->key_type != NULL) {
480 rcu_defer_free((void *)item->key);
482 rcu_defer_free(item);
487 void sl_print (skiplist_t *sl) {
489 printf("high water: %d levels\n", sl->high_water);
490 for (int level = MAX_LEVEL; level >= 0; --level) {
491 node_t *item = sl->head;
492 if (item->next[level] == DOES_NOT_EXIST)
494 printf("(%d) ", level);
497 markable_t next = item->next[level];
498 printf("%s%p ", HAS_MARK(next) ? "*" : "", item);
499 item = STRIP_MARK(next);
508 node_t *item = sl->head;
511 int is_marked = HAS_MARK(item->next[0]);
512 printf("%s%p:0x%llx ", is_marked ? "*" : "", item, (uint64_t)item->key);
513 if (item != sl->head) {
514 printf("[%d]", item->top_level);
518 for (int level = 1; level <= item->top_level; ++level) {
519 node_t *next = STRIP_MARK(item->next[level]);
520 is_marked = HAS_MARK(item->next[0]);
521 printf(" %p%s", next, is_marked ? "*" : "");
522 if (item == sl->head && item->next[level] == DOES_NOT_EXIST)
527 item = STRIP_MARK(item->next[0]);
535 sl_iter_t *sl_iter_begin (skiplist_t *sl, map_key_t key) {
536 sl_iter_t *iter = (sl_iter_t *)nbd_malloc(sizeof(sl_iter_t));
537 if (key != DOES_NOT_EXIST) {
538 find_preds(NULL, &iter->next, 0, sl, key, FALSE);
540 iter->next = GET_NODE(sl->head->next[0]);
545 map_val_t sl_iter_next (sl_iter_t *iter, map_key_t *key_ptr) {
547 node_t *item = iter->next;
548 while (item != NULL && HAS_MARK(item->next[0])) {
549 item = STRIP_MARK(item->next[0]);
553 return DOES_NOT_EXIST;
555 iter->next = STRIP_MARK(item->next[0]);
556 if (key_ptr != NULL) {
557 *key_ptr = item->key;
562 void sl_iter_free (sl_iter_t *iter) {