~ [ source navigation ] ~ [ diff markup ] ~ [ identifier search ] ~

TOMOYO Linux Cross Reference
Linux/Documentation/locking/lockdep-design.rst

Version: ~ [ linux-6.12-rc7 ] ~ [ linux-6.11.7 ] ~ [ linux-6.10.14 ] ~ [ linux-6.9.12 ] ~ [ linux-6.8.12 ] ~ [ linux-6.7.12 ] ~ [ linux-6.6.60 ] ~ [ linux-6.5.13 ] ~ [ linux-6.4.16 ] ~ [ linux-6.3.13 ] ~ [ linux-6.2.16 ] ~ [ linux-6.1.116 ] ~ [ linux-6.0.19 ] ~ [ linux-5.19.17 ] ~ [ linux-5.18.19 ] ~ [ linux-5.17.15 ] ~ [ linux-5.16.20 ] ~ [ linux-5.15.171 ] ~ [ linux-5.14.21 ] ~ [ linux-5.13.19 ] ~ [ linux-5.12.19 ] ~ [ linux-5.11.22 ] ~ [ linux-5.10.229 ] ~ [ linux-5.9.16 ] ~ [ linux-5.8.18 ] ~ [ linux-5.7.19 ] ~ [ linux-5.6.19 ] ~ [ linux-5.5.19 ] ~ [ linux-5.4.285 ] ~ [ linux-5.3.18 ] ~ [ linux-5.2.21 ] ~ [ linux-5.1.21 ] ~ [ linux-5.0.21 ] ~ [ linux-4.20.17 ] ~ [ linux-4.19.323 ] ~ [ linux-4.18.20 ] ~ [ linux-4.17.19 ] ~ [ linux-4.16.18 ] ~ [ linux-4.15.18 ] ~ [ linux-4.14.336 ] ~ [ linux-4.13.16 ] ~ [ linux-4.12.14 ] ~ [ linux-4.11.12 ] ~ [ linux-4.10.17 ] ~ [ linux-4.9.337 ] ~ [ linux-4.4.302 ] ~ [ linux-3.10.108 ] ~ [ linux-2.6.32.71 ] ~ [ linux-2.6.0 ] ~ [ linux-2.4.37.11 ] ~ [ unix-v6-master ] ~ [ ccs-tools-1.8.12 ] ~ [ policy-sample ] ~
Architecture: ~ [ i386 ] ~ [ alpha ] ~ [ m68k ] ~ [ mips ] ~ [ ppc ] ~ [ sparc ] ~ [ sparc64 ] ~

Diff markup

Differences between /Documentation/locking/lockdep-design.rst (Version linux-6.12-rc7) and /Documentation/locking/lockdep-design.rst (Version ccs-tools-1.8.12)


  1 Runtime locking correctness validator             
  2 =====================================             
  3                                                   
  4 started by Ingo Molnar <mingo@redhat.com>          
  5                                                   
  6 additions by Arjan van de Ven <arjan@linux.inte    
  7                                                   
  8 Lock-class                                        
  9 ----------                                        
 10                                                   
 11 The basic object the validator operates upon i    
 12                                                   
 13 A class of locks is a group of locks that are     
 14 respect to locking rules, even if the locks ma    
 15 tens of thousands of) instantiations. For exam    
 16 struct is one class, while each inode has its     
 17 lock class.                                       
 18                                                   
 19 The validator tracks the 'usage state' of lock    
 20 the dependencies between different lock-classe    
 21 how a lock is used with regard to its IRQ cont    
 22 dependency can be understood as lock order, wh    
 23 a task is attempting to acquire L2 while holdi    
 24 perspective, the two locks (L1 and L2) are not    
 25 dependency just means the order ever happened.    
 26 continuing effort to prove lock usages and dep    
 27 the validator will shoot a splat if incorrect.    
 28                                                   
 29 A lock-class's behavior is constructed by its     
 30 when the first instance of a lock-class is use    
 31 gets registered, then all (subsequent) instanc    
 32 class and hence their usages and dependencies     
 33 the class. A lock-class does not go away when     
 34 it can be removed if the memory space of the l    
 35 dynamic) is reclaimed, this happens for exampl    
 36 unloaded or a workqueue is destroyed.             
 37                                                   
 38 State                                             
 39 -----                                             
 40                                                   
 41 The validator tracks lock-class usage history     
 42 (4 usages * n STATEs + 1) categories:             
 43                                                   
 44 where the 4 usages can be:                        
 45                                                   
 46 - 'ever held in STATE context'                    
 47 - 'ever held as readlock in STATE context'        
 48 - 'ever held with STATE enabled'                  
 49 - 'ever held as readlock with STATE enabled'      
 50                                                   
 51 where the n STATEs are coded in kernel/locking    
 52 now they include:                                 
 53                                                   
 54 - hardirq                                         
 55 - softirq                                         
 56                                                   
 57 where the last 1 category is:                     
 58                                                   
 59 - 'ever used'                                     
 60                                                   
 61 When locking rules are violated, these usage b    
 62 locking error messages, inside curlies, with a    
 63 A contrived example::                             
 64                                                   
 65    modprobe/2287 is trying to acquire lock:       
 66     (&sio_locks[i].lock){-.-.}, at: [<c02867fd    
 67                                                   
 68    but task is already holding lock:              
 69     (&sio_locks[i].lock){-.-.}, at: [<c02867fd    
 70                                                   
 71                                                   
 72 For a given lock, the bit positions from left     
 73 of the lock and readlock (if exists), for each    
 74 above respectively, and the character displaye    
 75 indicates:                                        
 76                                                   
 77    ===  ======================================    
 78    '.'  acquired while irqs disabled and not i    
 79    '-'  acquired in irq context                   
 80    '+'  acquired with irqs enabled                
 81    '?'  acquired in irq context with irqs enab    
 82    ===  ======================================    
 83                                                   
 84 The bits are illustrated with an example::        
 85                                                   
 86     (&sio_locks[i].lock){-.-.}, at: [<c02867fd    
 87                          ||||                     
 88                          ||| \-> softirq disab    
 89                          || \--> acquired in s    
 90                          | \---> hardirq disab    
 91                           \----> acquired in h    
 92                                                   
 93                                                   
 94 For a given STATE, whether the lock is ever ac    
 95 context and whether that STATE is enabled yiel    
 96 shown in the table below. The bit character is    
 97 exact case is for the lock as of the reporting    
 98                                                   
 99   +--------------+-------------+--------------    
100   |              | irq enabled | irq disabled     
101   +--------------+-------------+--------------    
102   | ever in irq  |     '?'     |      '-'         
103   +--------------+-------------+--------------    
104   | never in irq |     '+'     |      '.'         
105   +--------------+-------------+--------------    
106                                                   
107 The character '-' suggests irq is disabled bec    
108 character '?' would have been shown instead. S    
109 applied for '+' too.                              
110                                                   
111 Unused locks (e.g., mutexes) cannot be part of    
112                                                   
113                                                   
114 Single-lock state rules:                          
115 ------------------------                          
116                                                   
117 A lock is irq-safe means it was ever used in a    
118 is irq-unsafe means it was ever acquired with     
119                                                   
120 A softirq-unsafe lock-class is automatically h    
121 following states must be exclusive: only one o    
122 for any lock-class based on its usage::           
123                                                   
124  <hardirq-safe> or <hardirq-unsafe>               
125  <softirq-safe> or <softirq-unsafe>               
126                                                   
127 This is because if a lock can be used in irq c    
128 cannot be ever acquired with irq enabled (irq-    
129 deadlock may happen. For example, in the scena    
130 was acquired but before released, if the conte    
131 lock will be attempted to acquire twice, which    
132 referred to as lock recursion deadlock.           
133                                                   
134 The validator detects and reports lock usage t    
135 single-lock state rules.                          
136                                                   
137 Multi-lock dependency rules:                      
138 ----------------------------                      
139                                                   
140 The same lock-class must not be acquired twice    
141 to lock recursion deadlocks.                      
142                                                   
143 Furthermore, two locks can not be taken in inv    
144                                                   
145  <L1> -> <L2>                                     
146  <L2> -> <L1>                                     
147                                                   
148 because this could lead to a deadlock - referr    
149 deadlock - as attempts to acquire the two lock    
150 could lead to the two contexts waiting for eac    
151 validator will find such dependency circle in     
152 i.e., there can be any other locking sequence     
153 operations; the validator will still find whet    
154 acquired in a circular fashion.                   
155                                                   
156 Furthermore, the following usage based lock de    
157 between any two lock-classes::                    
158                                                   
159    <hardirq-safe>   ->  <hardirq-unsafe>          
160    <softirq-safe>   ->  <softirq-unsafe>          
161                                                   
162 The first rule comes from the fact that a hard    
163 taken by a hardirq context, interrupting a har    
164 thus could result in a lock inversion deadlock    
165 lock could be taken by an softirq context, int    
166 lock.                                             
167                                                   
168 The above rules are enforced for any locking s    
169 kernel: when acquiring a new lock, the validat    
170 any rule violation between the new lock and an    
171                                                   
172 When a lock-class changes its state, the follo    
173 dependency rules are enforced:                    
174                                                   
175 - if a new hardirq-safe lock is discovered, we    
176   took any hardirq-unsafe lock in the past.       
177                                                   
178 - if a new softirq-safe lock is discovered, we    
179   any softirq-unsafe lock in the past.            
180                                                   
181 - if a new hardirq-unsafe lock is discovered,     
182   hardirq-safe lock took it in the past.          
183                                                   
184 - if a new softirq-unsafe lock is discovered,     
185   softirq-safe lock took it in the past.          
186                                                   
187 (Again, we do these checks too on the basis th    
188 could interrupt _any_ of the irq-unsafe or har    
189 could lead to a lock inversion deadlock - even    
190 not trigger in practice yet.)                     
191                                                   
192 Exception: Nested data dependencies leading to    
193 ----------------------------------------------    
194                                                   
195 There are a few cases where the Linux kernel a    
196 instance of the same lock-class. Such cases ty    
197 is some sort of hierarchy within objects of th    
198 cases there is an inherent "natural" ordering     
199 (defined by the properties of the hierarchy),     
200 locks in this fixed order on each of the objec    
201                                                   
202 An example of such an object hierarchy that re    
203 is that of a "whole disk" block-dev object and    
204 object; the partition is "part of" the whole d    
205 always takes the whole disk lock as a higher l    
206 lock, the lock ordering is fully correct. The     
207 automatically detect this natural ordering, as    
208 the ordering is not static.                       
209                                                   
210 In order to teach the validator about this cor    
211 versions of the various locking primitives wer    
212 specify a "nesting level". An example call, fo    
213 looks like this::                                 
214                                                   
215   enum bdev_bd_mutex_lock_class                   
216   {                                               
217        BD_MUTEX_NORMAL,                           
218        BD_MUTEX_WHOLE,                            
219        BD_MUTEX_PARTITION                         
220   };                                              
221                                                   
222   mutex_lock_nested(&bdev->bd_contains->bd_mut    
223                                                   
224 In this case the locking is done on a bdev obj    
225 partition.                                        
226                                                   
227 The validator treats a lock that is taken in s    
228 separate (sub)class for the purposes of valida    
229                                                   
230 Note: When changing code to use the _nested()     
231 check really thoroughly that the hierarchy is     
232 you can get false positives or false negatives    
233                                                   
234 Annotations                                       
235 -----------                                       
236                                                   
237 Two constructs can be used to annotate and che    
238 must be held: lockdep_assert_held*(&lock) and     
239                                                   
240 As the name suggests, lockdep_assert_held* fam    
241 particular lock is held at a certain time (and    
242 This annotation is largely used all over the k    
243 core.c::                                          
244                                                   
245   void update_rq_clock(struct rq *rq)             
246   {                                               
247         s64 delta;                                
248                                                   
249         lockdep_assert_held(&rq->lock);           
250         [...]                                     
251   }                                               
252                                                   
253 where holding rq->lock is required to safely u    
254                                                   
255 The other family of macros is lockdep_*pin_loc    
256 used for rq->lock ATM. Despite their limited a    
257 generate a WARN() if the lock of interest is "    
258 out to be especially helpful to debug code wit    
259 layer assumes a lock remains taken, but a lowe    
260 and reacquire the lock ("unwittingly" introduc    
261 returns a 'struct pin_cookie' that is then use    
262 that nobody tampered with the lock, e.g. kerne    
263                                                   
264   static inline void rq_pin_lock(struct rq *rq    
265   {                                               
266         rf->cookie = lockdep_pin_lock(&rq->loc    
267         [...]                                     
268   }                                               
269                                                   
270   static inline void rq_unpin_lock(struct rq *    
271   {                                               
272         [...]                                     
273         lockdep_unpin_lock(&rq->lock, rf->cook    
274   }                                               
275                                                   
276 While comments about locking requirements migh    
277 the runtime checks performed by annotations ar    
278 locking problems and they carry the same level    
279 code.  Always prefer annotations when in doubt    
280                                                   
281 Proof of 100% correctness:                        
282 --------------------------                        
283                                                   
284 The validator achieves perfect, mathematical '    
285 correctness) in the sense that for every simpl    
286 locking sequence that occurred at least once d    
287 kernel, the validator proves it with a 100% ce    
288 combination and timing of these locking sequen    
289 lock related deadlock. [1]_                       
290                                                   
291 I.e. complex multi-CPU and multi-task locking     
292 occur in practice to prove a deadlock: only th    
293 locking chains have to occur at least once (an    
294 task/context) for the validator to be able to     
295 example, complex deadlocks that would normally    
296 a very unlikely constellation of tasks, irq-co    
297 occur, can be detected on a plain, lightly loa    
298 well!)                                            
299                                                   
300 This radically decreases the complexity of loc    
301 kernel: what has to be done during QA is to tr    
302 single-task locking dependencies in the kernel    
303 once, to prove locking correctness - instead o    
304 possible combination of locking interaction be    
305 every possible hardirq and softirq nesting sce    
306 to do in practice).                               
307                                                   
308 .. [1]                                            
309                                                   
310     assuming that the validator itself is 100%    
311     part of the system corrupts the state of t    
312     We also assume that all NMI/SMM paths [whi    
313     even hardirq-disabled codepaths] are corre    
314     with the validator. We also assume that th    
315     value is unique for every lock-chain in th    
316     recursion must not be higher than 20.         
317                                                   
318 Performance:                                      
319 ------------                                      
320                                                   
321 The above rules require **massive** amounts of    
322 that for every lock taken and for every irqs-e    
323 render the system practically unusably slow. T    
324 is O(N^2), so even with just a few hundred loc    
325 tens of thousands of checks for every event.      
326                                                   
327 This problem is solved by checking any given '    
328 sequence of locks taken after each other) only    
329 held locks is maintained, and a lightweight 64    
330 calculated, which hash is unique for every loc    
331 when the chain is validated for the first time    
332 table, which hash-table can be checked in a lo    
333 locking chain occurs again later on, the hash     
334 don't have to validate the chain again.           
335                                                   
336 Troubleshooting:                                  
337 ----------------                                  
338                                                   
339 The validator tracks a maximum of MAX_LOCKDEP_    
340 Exceeding this number will trigger the followi    
341                                                   
342         (DEBUG_LOCKS_WARN_ON(id >= MAX_LOCKDEP    
343                                                   
344 By default, MAX_LOCKDEP_KEYS is currently set     
345 desktop systems have less than 1,000 lock clas    
346 normally results from lock-class leakage or fa    
347 initialize locks.  These two problems are illu    
348                                                   
349 1.      Repeated module loading and unloading     
350         will result in lock-class leakage.  Th    
351         load of the module will create a new s    
352         that module's locks, but module unload    
353         classes (see below discussion of reuse    
354         Therefore, if that module is loaded an    
355         the number of lock classes will eventu    
356                                                   
357 2.      Using structures such as arrays that h    
358         locks that are not explicitly initiali    
359         a hash table with 8192 buckets where e    
360         spinlock_t will consume 8192 lock clas    
361         is explicitly initialized at runtime,     
362         run-time spin_lock_init() as opposed t    
363         such as __SPIN_LOCK_UNLOCKED().  Failu    
364         the per-bucket spinlocks would guarant    
365         In contrast, a loop that called spin_l    
366         would place all 8192 locks into a sing    
367                                                   
368         The moral of this story is that you sh    
369         initialize your locks.                    
370                                                   
371 One might argue that the validator should be m    
372 lock classes to be reused.  However, if you ar    
373 argument, first review the code and think thro    
374 be required, keeping in mind that the lock cla    
375 likely to be linked into the lock-dependency g    
376 be harder to do than to say.                      
377                                                   
378 Of course, if you do run out of lock classes,     
379 to find the offending lock classes.  First, th    
380 you the number of lock classes currently in us    
381                                                   
382         grep "lock-classes" /proc/lockdep_stat    
383                                                   
384 This command produces the following output on     
385                                                   
386         lock-classes:                             
387                                                   
388 If the number allocated (748 above) increases     
389 then there is likely a leak.  The following co    
390 identify the leaking lock classes::               
391                                                   
392         grep "BD" /proc/lockdep                   
393                                                   
394 Run the command and save the output, then comp    
395 a later run of this command to identify the le    
396 can also help you find situations where runtim    
397 been omitted.                                     
398                                                   
399 Recursive read locks:                             
400 ---------------------                             
401 The whole of the rest document tries to prove     
402 to deadlock possibility.                          
403                                                   
404 There are three types of lockers: writers (i.e    
405 spin_lock() or write_lock()), non-recursive re    
406 down_read()) and recursive readers (recursive     
407 And we use the following notations of those lo    
408                                                   
409         W or E: stands for writers (exclusive     
410         r:      stands for non-recursive reade    
411         R:      stands for recursive readers.     
412         S:      stands for all readers (non-re    
413         N:      stands for writers and non-rec    
414                                                   
415 Obviously, N is "r or W" and S is "r or R".       
416                                                   
417 Recursive readers, as their name indicates, ar    
418 even inside the critical section of another re    
419 in other words, allowing nested read-side crit    
420                                                   
421 While non-recursive readers will cause a self     
422 the critical section of another reader of the     
423                                                   
424 The difference between recursive readers and n    
425 recursive readers get blocked only by a write     
426 readers could get blocked by a write lock *wai    
427 example::                                         
428                                                   
429         TASK A:                 TASK B:           
430                                                   
431         read_lock(X);                             
432                                 write_lock(X);    
433         read_lock_2(X);                           
434                                                   
435 Task A gets the reader (no matter whether recu    
436 read_lock() first. And when task B tries to ac    
437 and become a waiter for writer on X. Now if re    
438 task A will make progress, because writer wait    
439 and there is no deadlock. However, if read_loc    
440 it will get blocked by writer waiter B, and ca    
441                                                   
442 Block conditions on readers/writers of the sam    
443 ----------------------------------------------    
444 There are simply four block conditions:           
445                                                   
446 1.      Writers block other writers.              
447 2.      Readers block writers.                    
448 3.      Writers block both recursive readers a    
449 4.      And readers (recursive or not) don't b    
450         may block non-recursive readers (becau    
451         writer waiters)                           
452                                                   
453 Block condition matrix, Y means the row blocks    
454                                                   
455         +---+---+---+---+                         
456         |   | W | r | R |                         
457         +---+---+---+---+                         
458         | W | Y | Y | Y |                         
459         +---+---+---+---+                         
460         | r | Y | Y | N |                         
461         +---+---+---+---+                         
462         | R | Y | Y | N |                         
463         +---+---+---+---+                         
464                                                   
465         (W: writers, r: non-recursive readers,    
466                                                   
467                                                   
468 acquired recursively. Unlike non-recursive rea    
469 only get blocked by current write lock *holder    
470 *waiters*, for example::                          
471                                                   
472         TASK A:                 TASK B:           
473                                                   
474         read_lock(X);                             
475                                                   
476                                 write_lock(X);    
477                                                   
478         read_lock(X);                             
479                                                   
480 is not a deadlock for recursive read locks, as    
481 the lock X, the second read_lock() doesn't nee    
482 read lock. However if the read_lock() is non-r    
483 case is a deadlock, because even if the write_    
484 lock, but it can block the second read_lock()     
485                                                   
486 Note that a lock can be a write lock (exclusiv    
487 lock (non-recursive shared lock) or a recursiv    
488 lock), depending on the lock operations used t    
489 the value of the 'read' parameter for lock_acq    
490 lock instance has three types of acquisition d    
491 functions: exclusive, non-recursive read, and     
492                                                   
493 To be concise, we call that write locks and no    
494 "non-recursive" locks and recursive read locks    
495                                                   
496 Recursive locks don't block each other, while     
497 even true for two non-recursive read locks). A    
498 corresponding recursive lock, and vice versa.     
499                                                   
500 A deadlock case with recursive locks involved     
501                                                   
502         TASK A:                 TASK B:           
503                                                   
504         read_lock(X);                             
505                                 read_lock(Y);     
506         write_lock(Y);                            
507                                 write_lock(X);    
508                                                   
509 Task A is waiting for task B to read_unlock()     
510 A to read_unlock() X.                             
511                                                   
512 Dependency types and strong dependency paths:     
513 ---------------------------------------------     
514 Lock dependencies record the orders of the acq    
515 because there are 3 types for lockers, there a    
516 dependencies, but we can show that 4 types of     
517 deadlock detection.                               
518                                                   
519 For each lock dependency::                        
520                                                   
521         L1 -> L2                                  
522                                                   
523 , which means lockdep has seen L1 held before     
524 And in deadlock detection, we care whether we     
525 IOW, whether there is a locker L3 that L1 bloc    
526 we only care about 1) what L1 blocks and 2) wh    
527 recursive readers and non-recursive readers fo    
528 we can combine writers and non-recursive reade    
529 same types).                                      
530                                                   
531 With the above combination for simplification,    
532 in the lockdep graph:                             
533                                                   
534 1) -(ER)->:                                       
535             exclusive writer to recursive read    
536             X -> Y and X is a writer and Y is     
537                                                   
538 2) -(EN)->:                                       
539             exclusive writer to non-recursive     
540             X -> Y and X is a writer and Y is     
541                                                   
542 3) -(SR)->:                                       
543             shared reader to recursive reader     
544             X -> Y and X is a reader (recursiv    
545                                                   
546 4) -(SN)->:                                       
547             shared reader to non-recursive loc    
548             X -> Y and X is a reader (recursiv    
549             non-recursive reader.                 
550                                                   
551 Note that given two locks, they may have multi    
552 for example::                                     
553                                                   
554         TASK A:                                   
555                                                   
556         read_lock(X);                             
557         write_lock(Y);                            
558         ...                                       
559                                                   
560         TASK B:                                   
561                                                   
562         write_lock(X);                            
563         write_lock(Y);                            
564                                                   
565 , we have both X -(SN)-> Y and X -(EN)-> Y in     
566                                                   
567 We use -(xN)-> to represent edges that are eit    
568 similar for -(Ex)->, -(xR)-> and -(Sx)->          
569                                                   
570 A "path" is a series of conjunct dependency ed    
571 "strong" path, which indicates the strong depe    
572 in the path, as the path that doesn't have two    
573 -(xR)-> and -(Sx)->. In other words, a "strong    
574 walking to another through the lock dependenci    
575 path (where X, Y, Z are locks), and the walk f    
576 -(ER)-> dependency, the walk from Y to Z must     
577 -(SR)-> dependency.                               
578                                                   
579 We will see why the path is called "strong" in    
580                                                   
581 Recursive Read Deadlock Detection:                
582 ----------------------------------                
583                                                   
584 We now prove two things:                          
585                                                   
586 Lemma 1:                                          
587                                                   
588 If there is a closed strong path (i.e. a stron    
589 combination of locking sequences that causes d    
590 sufficient for deadlock detection.                
591                                                   
592 Lemma 2:                                          
593                                                   
594 If there is no closed strong path (i.e. strong    
595 combination of locking sequences that could ca    
596 circles are necessary for deadlock detection.     
597                                                   
598 With these two Lemmas, we can easily say a clo    
599 and necessary for deadlocks, therefore a close    
600 deadlock possibility. As a closed strong path     
601 could cause deadlocks, so we call it "strong",    
602 circles that won't cause deadlocks.               
603                                                   
604 Proof for sufficiency (Lemma 1):                  
605                                                   
606 Let's say we have a strong circle::               
607                                                   
608         L1 -> L2 ... -> Ln -> L1                  
609                                                   
610 , which means we have dependencies::              
611                                                   
612         L1 -> L2                                  
613         L2 -> L3                                  
614         ...                                       
615         Ln-1 -> Ln                                
616         Ln -> L1                                  
617                                                   
618 We now can construct a combination of locking     
619                                                   
620 Firstly let's make one CPU/task get the L1 in     
621 the L2 in L2 -> L3, and so on. After this, all    
622 held by different CPU/tasks.                      
623                                                   
624 And then because we have L1 -> L2, so the hold    
625 in L1 -> L2, however since L2 is already held     
626 L2 and L2 -> L3 are not -(xR)-> and -(Sx)-> (t    
627 means either L2 in L1 -> L2 is a non-recursive    
628 the L2 in L2 -> L3, is writer (blocking anyone    
629 cannot get L2, it has to wait L2's holder to r    
630                                                   
631 Moreover, we can have a similar conclusion for    
632 holder to release, and so on. We now can prove    
633 Lx+1's holder to release, and note that Ln+1 i    
634 waiting scenario and nobody can get progress,     
635                                                   
636 Proof for necessary (Lemma 2):                    
637                                                   
638 Lemma 2 is equivalent to: If there is a deadlo    
639 strong circle in the dependency graph.            
640                                                   
641 According to Wikipedia[1], if there is a deadl    
642 waiting scenario, means there are N CPU/tasks,    
643 a lock held by P2, and P2 is waiting for a loc    
644 for a lock held by P1. Let's name the lock Px     
645 for L1 and holding Ln, so we will have Ln -> L    
646 we have L1 -> L2, L2 -> L3, ..., Ln-1 -> Ln in    
647 have a circle::                                   
648                                                   
649         Ln -> L1 -> L2 -> ... -> Ln               
650                                                   
651 , and now let's prove the circle is strong:       
652                                                   
653 For a lock Lx, Px contributes the dependency L    
654 the dependency Lx -> Lx+1, and since Px is wai    
655 so it's impossible that Lx on Px+1 is a reader    
656 reader, because readers (no matter recursive o    
657 readers, therefore Lx-1 -> Lx and Lx -> Lx+1 c    
658 and this is true for any lock in the circle, t    
659                                                   
660 References:                                       
661 -----------                                       
662 [1]: https://en.wikipedia.org/wiki/Deadlock       
663 [2]: Shibu, K. (2009). Intro To Embedded Syste    
                                                      

~ [ source navigation ] ~ [ diff markup ] ~ [ identifier search ] ~

kernel.org | git.kernel.org | LWN.net | Project Home | SVN repository | Mail admin

Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.

sflogo.php