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1Linux-Kernel Memory Model Litmus Tests
2======================================
3
4This file describes the LKMM litmus-test format by example, describes
5some tricks and traps, and finally outlines LKMM's limitations. Earlier
6versions of this material appeared in a number of LWN articles, including:
7
8https://lwn.net/Articles/720550/
9 A formal kernel memory-ordering model (part 2)
10https://lwn.net/Articles/608550/
11 Axiomatic validation of memory barriers and atomic instructions
12https://lwn.net/Articles/470681/
13 Validating Memory Barriers and Atomic Instructions
14
15This document presents information in decreasing order of applicability,
16so that, where possible, the information that has proven more commonly
17useful is shown near the beginning.
18
19For information on installing LKMM, including the underlying "herd7"
20tool, please see tools/memory-model/README.
21
22
23Copy-Pasta
24==========
25
26As with other software, it is often better (if less macho) to adapt an
27existing litmus test than it is to create one from scratch. A number
28of litmus tests may be found in the kernel source tree:
29
30 tools/memory-model/litmus-tests/
31 Documentation/litmus-tests/
32
33Several thousand more example litmus tests are available on github
34and kernel.org:
35
36 https://github.com/paulmckrcu/litmus
37 https://git.kernel.org/pub/scm/linux/kernel/git/paulmck/perfbook.git/tree/CodeSamples/formal/herd
38 https://git.kernel.org/pub/scm/linux/kernel/git/paulmck/perfbook.git/tree/CodeSamples/formal/litmus
39
40The -l and -L arguments to "git grep" can be quite helpful in identifying
41existing litmus tests that are similar to the one you need. But even if
42you start with an existing litmus test, it is still helpful to have a
43good understanding of the litmus-test format.
44
45
46Examples and Format
47===================
48
49This section describes the overall format of litmus tests, starting
50with a small example of the message-passing pattern and moving on to
51more complex examples that illustrate explicit initialization and LKMM's
52minimalistic set of flow-control statements.
53
54
55Message-Passing Example
56-----------------------
57
58This section gives an overview of the format of a litmus test using an
59example based on the common message-passing use case. This use case
60appears often in the Linux kernel. For example, a flag (modeled by "y"
61below) indicates that a buffer (modeled by "x" below) is now completely
62filled in and ready for use. It would be very bad if the consumer saw the
63flag set, but, due to memory misordering, saw old values in the buffer.
64
65This example asks whether smp_store_release() and smp_load_acquire()
66suffices to avoid this bad outcome:
67
68 1 C MP+pooncerelease+poacquireonce
69 2
70 3 {}
71 4
72 5 P0(int *x, int *y)
73 6 {
74 7 WRITE_ONCE(*x, 1);
75 8 smp_store_release(y, 1);
76 9 }
7710
7811 P1(int *x, int *y)
7912 {
8013 int r0;
8114 int r1;
8215
8316 r0 = smp_load_acquire(y);
8417 r1 = READ_ONCE(*x);
8518 }
8619
8720 exists (1:r0=1 /\ 1:r1=0)
88
89Line 1 starts with "C", which identifies this file as being in the
90LKMM C-language format (which, as we will see, is a small fragment
91of the full C language). The remainder of line 1 is the name of
92the test, which by convention is the filename with the ".litmus"
93suffix stripped. In this case, the actual test may be found in
94tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus
95in the Linux-kernel source tree.
96
97Mechanically generated litmus tests will often have an optional
98double-quoted comment string on the second line. Such strings are ignored
99when running the test. Yes, you can add your own comments to litmus
100tests, but this is a bit involved due to the use of multiple parsers.
101For now, you can use C-language comments in the C code, and these comments
102may be in either the "/* */" or the "//" style. A later section will
103cover the full litmus-test commenting story.
104
105Line 3 is the initialization section. Because the default initialization
106to zero suffices for this test, the "{}" syntax is used, which mean the
107initialization section is empty. Litmus tests requiring non-default
108initialization must have non-empty initialization sections, as in the
109example that will be presented later in this document.
110
111Lines 5-9 show the first process and lines 11-18 the second process. Each
112process corresponds to a Linux-kernel task (or kthread, workqueue, thread,
113and so on; LKMM discussions often use these terms interchangeably).
114The name of the first process is "P0" and that of the second "P1".
115You can name your processes anything you like as long as the names consist
116of a single "P" followed by a number, and as long as the numbers are
117consecutive starting with zero. This can actually be quite helpful,
118for example, a .litmus file matching "^P1(" but not matching "^P2("
119must contain a two-process litmus test.
120
121The argument list for each function are pointers to the global variables
122used by that function. Unlike normal C-language function parameters, the
123names are significant. The fact that both P0() and P1() have a formal
124parameter named "x" means that these two processes are working with the
125same global variable, also named "x". So the "int *x, int *y" on P0()
126and P1() mean that both processes are working with two shared global
127variables, "x" and "y". Global variables are always passed to processes
128by reference, hence "P0(int *x, int *y)", but *never* "P0(int x, int y)".
129
130P0() has no local variables, but P1() has two of them named "r0" and "r1".
131These names may be freely chosen, but for historical reasons stemming from
132other litmus-test formats, it is conventional to use names consisting of
133"r" followed by a number as shown here. A common bug in litmus tests
134is forgetting to add a global variable to a process's parameter list.
135This will sometimes result in an error message, but can also cause the
136intended global to instead be silently treated as an undeclared local
137variable.
138
139Each process's code is similar to Linux-kernel C, as can be seen on lines
1407-8 and 13-17. This code may use many of the Linux kernel's atomic
141operations, some of its exclusive-lock functions, and some of its RCU
142and SRCU functions. An approximate list of the currently supported
143functions may be found in the linux-kernel.def file.
144
145The P0() process does "WRITE_ONCE(*x, 1)" on line 7. Because "x" is a
146pointer in P0()'s parameter list, this does an unordered store to global
147variable "x". Line 8 does "smp_store_release(y, 1)", and because "y"
148is also in P0()'s parameter list, this does a release store to global
149variable "y".
150
151The P1() process declares two local variables on lines 13 and 14.
152Line 16 does "r0 = smp_load_acquire(y)" which does an acquire load
153from global variable "y" into local variable "r0". Line 17 does a
154"r1 = READ_ONCE(*x)", which does an unordered load from "*x" into local
155variable "r1". Both "x" and "y" are in P1()'s parameter list, so both
156reference the same global variables that are used by P0().
157
158Line 20 is the "exists" assertion expression to evaluate the final state.
159This final state is evaluated after the dust has settled: both processes
160have completed and all of their memory references and memory barriers
161have propagated to all parts of the system. The references to the local
162variables "r0" and "r1" in line 24 must be prefixed with "1:" to specify
163which process they are local to.
164
165Note that the assertion expression is written in the litmus-test
166language rather than in C. For example, single "=" is an equality
167operator rather than an assignment. The "/\" character combination means
168"and". Similarly, "\/" stands for "or". Both of these are ASCII-art
169representations of the corresponding mathematical symbols. Finally,
170"~" stands for "logical not", which is "!" in C, and not to be confused
171with the C-language "~" operator which instead stands for "bitwise not".
172Parentheses may be used to override precedence.
173
174The "exists" assertion on line 20 is satisfied if the consumer sees the
175flag ("y") set but the buffer ("x") as not yet filled in, that is, if P1()
176loaded a value from "x" that was equal to 1 but loaded a value from "y"
177that was still equal to zero.
178
179This example can be checked by running the following command, which
180absolutely must be run from the tools/memory-model directory and from
181this directory only:
182
183herd7 -conf linux-kernel.cfg litmus-tests/MP+pooncerelease+poacquireonce.litmus
184
185The output is the result of something similar to a full state-space
186search, and is as follows:
187
188 1 Test MP+pooncerelease+poacquireonce Allowed
189 2 States 3
190 3 1:r0=0; 1:r1=0;
191 4 1:r0=0; 1:r1=1;
192 5 1:r0=1; 1:r1=1;
193 6 No
194 7 Witnesses
195 8 Positive: 0 Negative: 3
196 9 Condition exists (1:r0=1 /\ 1:r1=0)
19710 Observation MP+pooncerelease+poacquireonce Never 0 3
19811 Time MP+pooncerelease+poacquireonce 0.00
19912 Hash=579aaa14d8c35a39429b02e698241d09
200
201The most pertinent line is line 10, which contains "Never 0 3", which
202indicates that the bad result flagged by the "exists" clause never
203happens. This line might instead say "Sometimes" to indicate that the
204bad result happened in some but not all executions, or it might say
205"Always" to indicate that the bad result happened in all executions.
206(The herd7 tool doesn't judge, so it is only an LKMM convention that the
207"exists" clause indicates a bad result. To see this, invert the "exists"
208clause's condition and run the test.) The numbers ("0 3") at the end
209of this line indicate the number of end states satisfying the "exists"
210clause (0) and the number not not satisfying that clause (3).
211
212Another important part of this output is shown in lines 2-5, repeated here:
213
214 2 States 3
215 3 1:r0=0; 1:r1=0;
216 4 1:r0=0; 1:r1=1;
217 5 1:r0=1; 1:r1=1;
218
219Line 2 gives the total number of end states, and each of lines 3-5 list
220one of these states, with the first ("1:r0=0; 1:r1=0;") indicating that
221both of P1()'s loads returned the value "0". As expected, given the
222"Never" on line 10, the state flagged by the "exists" clause is not
223listed. This full list of states can be helpful when debugging a new
224litmus test.
225
226The rest of the output is not normally needed, either due to irrelevance
227or due to being redundant with the lines discussed above. However, the
228following paragraph lists them for the benefit of readers possessed of
229an insatiable curiosity. Other readers should feel free to skip ahead.
230
231Line 1 echos the test name, along with the "Test" and "Allowed". Line 6's
232"No" says that the "exists" clause was not satisfied by any execution,
233and as such it has the same meaning as line 10's "Never". Line 7 is a
234lead-in to line 8's "Positive: 0 Negative: 3", which lists the number
235of end states satisfying and not satisfying the "exists" clause, just
236like the two numbers at the end of line 10. Line 9 repeats the "exists"
237clause so that you don't have to look it up in the litmus-test file.
238The number at the end of line 11 (which begins with "Time") gives the
239time in seconds required to analyze the litmus test. Small tests such
240as this one complete in a few milliseconds, so "0.00" is quite common.
241Line 12 gives a hash of the contents for the litmus-test file, and is used
242by tooling that manages litmus tests and their output. This tooling is
243used by people modifying LKMM itself, and among other things lets such
244people know which of the several thousand relevant litmus tests were
245affected by a given change to LKMM.
246
247
248Initialization
249--------------
250
251The previous example relied on the default zero initialization for
252"x" and "y", but a similar litmus test could instead initialize them
253to some other value:
254
255 1 C MP+pooncerelease+poacquireonce
256 2
257 3 {
258 4 x=42;
259 5 y=42;
260 6 }
261 7
262 8 P0(int *x, int *y)
263 9 {
26410 WRITE_ONCE(*x, 1);
26511 smp_store_release(y, 1);
26612 }
26713
26814 P1(int *x, int *y)
26915 {
27016 int r0;
27117 int r1;
27218
27319 r0 = smp_load_acquire(y);
27420 r1 = READ_ONCE(*x);
27521 }
27622
27723 exists (1:r0=1 /\ 1:r1=42)
278
279Lines 3-6 now initialize both "x" and "y" to the value 42. This also
280means that the "exists" clause on line 23 must change "1:r1=0" to
281"1:r1=42".
282
283Running the test gives the same overall result as before, but with the
284value 42 appearing in place of the value zero:
285
286 1 Test MP+pooncerelease+poacquireonce Allowed
287 2 States 3
288 3 1:r0=1; 1:r1=1;
289 4 1:r0=42; 1:r1=1;
290 5 1:r0=42; 1:r1=42;
291 6 No
292 7 Witnesses
293 8 Positive: 0 Negative: 3
294 9 Condition exists (1:r0=1 /\ 1:r1=42)
29510 Observation MP+pooncerelease+poacquireonce Never 0 3
29611 Time MP+pooncerelease+poacquireonce 0.02
29712 Hash=ab9a9b7940a75a792266be279a980156
298
299It is tempting to avoid the open-coded repetitions of the value "42"
300by defining another global variable "initval=42" and replacing all
301occurrences of "42" with "initval". This will not, repeat *not*,
302initialize "x" and "y" to 42, but instead to the address of "initval"
303(try it!). See the section below on linked lists to learn more about
304why this approach to initialization can be useful.
305
306
307Control Structures
308------------------
309
310LKMM supports the C-language "if" statement, which allows modeling of
311conditional branches. In LKMM, conditional branches can affect ordering,
312but only if you are *very* careful (compilers are surprisingly able
313to optimize away conditional branches). The following example shows
314the "load buffering" (LB) use case that is used in the Linux kernel to
315synchronize between ring-buffer producers and consumers. In the example
316below, P0() is one side checking to see if an operation may proceed and
317P1() is the other side completing its update.
318
319 1 C LB+fencembonceonce+ctrlonceonce
320 2
321 3 {}
322 4
323 5 P0(int *x, int *y)
324 6 {
325 7 int r0;
326 8
327 9 r0 = READ_ONCE(*x);
32810 if (r0)
32911 WRITE_ONCE(*y, 1);
33012 }
33113
33214 P1(int *x, int *y)
33315 {
33416 int r0;
33517
33618 r0 = READ_ONCE(*y);
33719 smp_mb();
33820 WRITE_ONCE(*x, 1);
33921 }
34022
34123 exists (0:r0=1 /\ 1:r0=1)
342
343P1()'s "if" statement on line 10 works as expected, so that line 11 is
344executed only if line 9 loads a non-zero value from "x". Because P1()'s
345write of "1" to "x" happens only after P1()'s read from "y", one would
346hope that the "exists" clause cannot be satisfied. LKMM agrees:
347
348 1 Test LB+fencembonceonce+ctrlonceonce Allowed
349 2 States 2
350 3 0:r0=0; 1:r0=0;
351 4 0:r0=1; 1:r0=0;
352 5 No
353 6 Witnesses
354 7 Positive: 0 Negative: 2
355 8 Condition exists (0:r0=1 /\ 1:r0=1)
356 9 Observation LB+fencembonceonce+ctrlonceonce Never 0 2
35710 Time LB+fencembonceonce+ctrlonceonce 0.00
35811 Hash=e5260556f6de495fd39b556d1b831c3b
359
360However, there is no "while" statement due to the fact that full
361state-space search has some difficulty with iteration. However, there
362are tricks that may be used to handle some special cases, which are
363discussed below. In addition, loop-unrolling tricks may be applied,
364albeit sparingly.
365
366
367Tricks and Traps
368================
369
370This section covers extracting debug output from herd7, emulating
371spin loops, handling trivial linked lists, adding comments to litmus tests,
372emulating call_rcu(), and finally tricks to improve herd7 performance
373in order to better handle large litmus tests.
374
375
376Debug Output
377------------
378
379By default, the herd7 state output includes all variables mentioned
380in the "exists" clause. But sometimes debugging efforts are greatly
381aided by the values of other variables. Consider this litmus test
382(tools/memory-order/litmus-tests/SB+rfionceonce-poonceonces.litmus but
383slightly modified), which probes an obscure corner of hardware memory
384ordering:
385
386 1 C SB+rfionceonce-poonceonces
387 2
388 3 {}
389 4
390 5 P0(int *x, int *y)
391 6 {
392 7 int r1;
393 8 int r2;
394 9
39510 WRITE_ONCE(*x, 1);
39611 r1 = READ_ONCE(*x);
39712 r2 = READ_ONCE(*y);
39813 }
39914
40015 P1(int *x, int *y)
40116 {
40217 int r3;
40318 int r4;
40419
40520 WRITE_ONCE(*y, 1);
40621 r3 = READ_ONCE(*y);
40722 r4 = READ_ONCE(*x);
40823 }
40924
41025 exists (0:r2=0 /\ 1:r4=0)
411
412The herd7 output is as follows:
413
414 1 Test SB+rfionceonce-poonceonces Allowed
415 2 States 4
416 3 0:r2=0; 1:r4=0;
417 4 0:r2=0; 1:r4=1;
418 5 0:r2=1; 1:r4=0;
419 6 0:r2=1; 1:r4=1;
420 7 Ok
421 8 Witnesses
422 9 Positive: 1 Negative: 3
42310 Condition exists (0:r2=0 /\ 1:r4=0)
42411 Observation SB+rfionceonce-poonceonces Sometimes 1 3
42512 Time SB+rfionceonce-poonceonces 0.01
42613 Hash=c7f30fe0faebb7d565405d55b7318ada
427
428(This output indicates that CPUs are permitted to "snoop their own
429store buffers", which all of Linux's CPU families other than s390 will
430happily do. Such snooping results in disagreement among CPUs on the
431order of stores from different CPUs, which is rarely an issue.)
432
433But the herd7 output shows only the two variables mentioned in the
434"exists" clause. Someone modifying this test might wish to know the
435values of "x", "y", "0:r1", and "0:r3" as well. The "locations"
436statement on line 25 shows how to cause herd7 to display additional
437variables:
438
439 1 C SB+rfionceonce-poonceonces
440 2
441 3 {}
442 4
443 5 P0(int *x, int *y)
444 6 {
445 7 int r1;
446 8 int r2;
447 9
44810 WRITE_ONCE(*x, 1);
44911 r1 = READ_ONCE(*x);
45012 r2 = READ_ONCE(*y);
45113 }
45214
45315 P1(int *x, int *y)
45416 {
45517 int r3;
45618 int r4;
45719
45820 WRITE_ONCE(*y, 1);
45921 r3 = READ_ONCE(*y);
46022 r4 = READ_ONCE(*x);
46123 }
46224
46325 locations [0:r1; 1:r3; x; y]
46426 exists (0:r2=0 /\ 1:r4=0)
465
466The herd7 output then displays the values of all the variables:
467
468 1 Test SB+rfionceonce-poonceonces Allowed
469 2 States 4
470 3 0:r1=1; 0:r2=0; 1:r3=1; 1:r4=0; x=1; y=1;
471 4 0:r1=1; 0:r2=0; 1:r3=1; 1:r4=1; x=1; y=1;
472 5 0:r1=1; 0:r2=1; 1:r3=1; 1:r4=0; x=1; y=1;
473 6 0:r1=1; 0:r2=1; 1:r3=1; 1:r4=1; x=1; y=1;
474 7 Ok
475 8 Witnesses
476 9 Positive: 1 Negative: 3
47710 Condition exists (0:r2=0 /\ 1:r4=0)
47811 Observation SB+rfionceonce-poonceonces Sometimes 1 3
47912 Time SB+rfionceonce-poonceonces 0.01
48013 Hash=40de8418c4b395388f6501cafd1ed38d
481
482What if you would like to know the value of a particular global variable
483at some particular point in a given process's execution? One approach
484is to use a READ_ONCE() to load that global variable into a new local
485variable, then add that local variable to the "locations" clause.
486But be careful: In some litmus tests, adding a READ_ONCE() will change
487the outcome! For one example, please see the C-READ_ONCE.litmus and
488C-READ_ONCE-omitted.litmus tests located here:
489
490 https://github.com/paulmckrcu/litmus/blob/master/manual/kernel/
491
492
493Spin Loops
494----------
495
496The analysis carried out by herd7 explores full state space, which is
497at best of exponential time complexity. Adding processes and increasing
498the amount of code in a give process can greatly increase execution time.
499Potentially infinite loops, such as those used to wait for locks to
500become available, are clearly problematic.
501
502Fortunately, it is possible to avoid state-space explosion by specially
503modeling such loops. For example, the following litmus tests emulates
504locking using xchg_acquire(), but instead of enclosing xchg_acquire()
505in a spin loop, it instead excludes executions that fail to acquire the
506lock using a herd7 "filter" clause. Note that for exclusive locking, you
507are better off using the spin_lock() and spin_unlock() that LKMM directly
508models, if for no other reason that these are much faster. However, the
509techniques illustrated in this section can be used for other purposes,
510such as emulating reader-writer locking, which LKMM does not yet model.
511
512 1 C C-SB+l-o-o-u+l-o-o-u-X
513 2
514 3 {
515 4 }
516 5
517 6 P0(int *sl, int *x0, int *x1)
518 7 {
519 8 int r2;
520 9 int r1;
52110
52211 r2 = xchg_acquire(sl, 1);
52312 WRITE_ONCE(*x0, 1);
52413 r1 = READ_ONCE(*x1);
52514 smp_store_release(sl, 0);
52615 }
52716
52817 P1(int *sl, int *x0, int *x1)
52918 {
53019 int r2;
53120 int r1;
53221
53322 r2 = xchg_acquire(sl, 1);
53423 WRITE_ONCE(*x1, 1);
53524 r1 = READ_ONCE(*x0);
53625 smp_store_release(sl, 0);
53726 }
53827
53928 filter (0:r2=0 /\ 1:r2=0)
54029 exists (0:r1=0 /\ 1:r1=0)
541
542This litmus test may be found here:
543
544https://git.kernel.org/pub/scm/linux/kernel/git/paulmck/perfbook.git/tree/CodeSamples/formal/herd/C-SB+l-o-o-u+l-o-o-u-X.litmus
545
546This test uses two global variables, "x1" and "x2", and also emulates a
547single global spinlock named "sl". This spinlock is held by whichever
548process changes the value of "sl" from "0" to "1", and is released when
549that process sets "sl" back to "0". P0()'s lock acquisition is emulated
550on line 11 using xchg_acquire(), which unconditionally stores the value
551"1" to "sl" and stores either "0" or "1" to "r2", depending on whether
552the lock acquisition was successful or unsuccessful (due to "sl" already
553having the value "1"), respectively. P1() operates in a similar manner.
554
555Rather unconventionally, execution appears to proceed to the critical
556section on lines 12 and 13 in either case. Line 14 then uses an
557smp_store_release() to store zero to "sl", thus emulating lock release.
558
559The case where xchg_acquire() fails to acquire the lock is handled by
560the "filter" clause on line 28, which tells herd7 to keep only those
561executions in which both "0:r2" and "1:r2" are zero, that is to pay
562attention only to those executions in which both locks are actually
563acquired. Thus, the bogus executions that would execute the critical
564sections are discarded and any effects that they might have had are
565ignored. Note well that the "filter" clause keeps those executions
566for which its expression is satisfied, that is, for which the expression
567evaluates to true. In other words, the "filter" clause says what to
568keep, not what to discard.
569
570The result of running this test is as follows:
571
572 1 Test C-SB+l-o-o-u+l-o-o-u-X Allowed
573 2 States 2
574 3 0:r1=0; 1:r1=1;
575 4 0:r1=1; 1:r1=0;
576 5 No
577 6 Witnesses
578 7 Positive: 0 Negative: 2
579 8 Condition exists (0:r1=0 /\ 1:r1=0)
580 9 Observation C-SB+l-o-o-u+l-o-o-u-X Never 0 2
58110 Time C-SB+l-o-o-u+l-o-o-u-X 0.03
582
583The "Never" on line 9 indicates that this use of xchg_acquire() and
584smp_store_release() really does correctly emulate locking.
585
586Why doesn't the litmus test take the simpler approach of using a spin loop
587to handle failed spinlock acquisitions, like the kernel does? The key
588insight behind this litmus test is that spin loops have no effect on the
589possible "exists"-clause outcomes of program execution in the absence
590of deadlock. In other words, given a high-quality lock-acquisition
591primitive in a deadlock-free program running on high-quality hardware,
592each lock acquisition will eventually succeed. Because herd7 already
593explores the full state space, the length of time required to actually
594acquire the lock does not matter. After all, herd7 already models all
595possible durations of the xchg_acquire() statements.
596
597Why not just add the "filter" clause to the "exists" clause, thus
598avoiding the "filter" clause entirely? This does work, but is slower.
599The reason that the "filter" clause is faster is that (in the common case)
600herd7 knows to abandon an execution as soon as the "filter" expression
601fails to be satisfied. In contrast, the "exists" clause is evaluated
602only at the end of time, thus requiring herd7 to waste time on bogus
603executions in which both critical sections proceed concurrently. In
604addition, some LKMM users like the separation of concerns provided by
605using the both the "filter" and "exists" clauses.
606
607Readers lacking a pathological interest in odd corner cases should feel
608free to skip the remainder of this section.
609
610But what if the litmus test were to temporarily set "0:r2" to a non-zero
611value? Wouldn't that cause herd7 to abandon the execution prematurely
612due to an early mismatch of the "filter" clause?
613
614Why not just try it? Line 4 of the following modified litmus test
615introduces a new global variable "x2" that is initialized to "1". Line 23
616of P1() reads that variable into "1:r2" to force an early mismatch with
617the "filter" clause. Line 24 does a known-true "if" condition to avoid
618and static analysis that herd7 might do. Finally the "exists" clause
619on line 32 is updated to a condition that is alway satisfied at the end
620of the test.
621
622 1 C C-SB+l-o-o-u+l-o-o-u-X
623 2
624 3 {
625 4 x2=1;
626 5 }
627 6
628 7 P0(int *sl, int *x0, int *x1)
629 8 {
630 9 int r2;
63110 int r1;
63211
63312 r2 = xchg_acquire(sl, 1);
63413 WRITE_ONCE(*x0, 1);
63514 r1 = READ_ONCE(*x1);
63615 smp_store_release(sl, 0);
63716 }
63817
63918 P1(int *sl, int *x0, int *x1, int *x2)
64019 {
64120 int r2;
64221 int r1;
64322
64423 r2 = READ_ONCE(*x2);
64524 if (r2)
64625 r2 = xchg_acquire(sl, 1);
64726 WRITE_ONCE(*x1, 1);
64827 r1 = READ_ONCE(*x0);
64928 smp_store_release(sl, 0);
65029 }
65130
65231 filter (0:r2=0 /\ 1:r2=0)
65332 exists (x1=1)
654
655If the "filter" clause were to check each variable at each point in the
656execution, running this litmus test would display no executions because
657all executions would be filtered out at line 23. However, the output
658is instead as follows:
659
660 1 Test C-SB+l-o-o-u+l-o-o-u-X Allowed
661 2 States 1
662 3 x1=1;
663 4 Ok
664 5 Witnesses
665 6 Positive: 2 Negative: 0
666 7 Condition exists (x1=1)
667 8 Observation C-SB+l-o-o-u+l-o-o-u-X Always 2 0
668 9 Time C-SB+l-o-o-u+l-o-o-u-X 0.04
66910 Hash=080bc508da7f291e122c6de76c0088e3
670
671Line 3 shows that there is one execution that did not get filtered out,
672so the "filter" clause is evaluated only on the last assignment to
673the variables that it checks. In this case, the "filter" clause is a
674disjunction, so it might be evaluated twice, once at the final (and only)
675assignment to "0:r2" and once at the final assignment to "1:r2".
676
677
678Linked Lists
679------------
680
681LKMM can handle linked lists, but only linked lists in which each node
682contains nothing except a pointer to the next node in the list. This is
683of course quite restrictive, but there is nevertheless quite a bit that
684can be done within these confines, as can be seen in the litmus test
685at tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus:
686
687 1 C MP+onceassign+derefonce
688 2
689 3 {
690 4 y=z;
691 5 z=0;
692 6 }
693 7
694 8 P0(int *x, int **y)
695 9 {
69610 WRITE_ONCE(*x, 1);
69711 rcu_assign_pointer(*y, x);
69812 }
69913
70014 P1(int *x, int **y)
70115 {
70216 int *r0;
70317 int r1;
70418
70519 rcu_read_lock();
70620 r0 = rcu_dereference(*y);
70721 r1 = READ_ONCE(*r0);
70822 rcu_read_unlock();
70923 }
71024
71125 exists (1:r0=x /\ 1:r1=0)
712
713Line 4's "y=z" may seem odd, given that "z" has not yet been initialized.
714But "y=z" does not set the value of "y" to that of "z", but instead
715sets the value of "y" to the *address* of "z". Lines 4 and 5 therefore
716create a simple linked list, with "y" pointing to "z" and "z" having a
717NULL pointer. A much longer linked list could be created if desired,
718and circular singly linked lists can also be created and manipulated.
719
720The "exists" clause works the same way, with the "1:r0=x" comparing P1()'s
721"r0" not to the value of "x", but again to its address. This term of the
722"exists" clause therefore tests whether line 20's load from "y" saw the
723value stored by line 11, which is in fact what is required in this case.
724
725P0()'s line 10 initializes "x" to the value 1 then line 11 links to "x"
726from "y", replacing "z".
727
728P1()'s line 20 loads a pointer from "y", and line 21 dereferences that
729pointer. The RCU read-side critical section spanning lines 19-22 is just
730for show in this example. Note that the address used for line 21's load
731depends on (in this case, "is exactly the same as") the value loaded by
732line 20. This is an example of what is called an "address dependency".
733This particular address dependency extends from the load on line 20 to the
734load on line 21. Address dependencies provide a weak form of ordering.
735
736Running this test results in the following:
737
738 1 Test MP+onceassign+derefonce Allowed
739 2 States 2
740 3 1:r0=x; 1:r1=1;
741 4 1:r0=z; 1:r1=0;
742 5 No
743 6 Witnesses
744 7 Positive: 0 Negative: 2
745 8 Condition exists (1:r0=x /\ 1:r1=0)
746 9 Observation MP+onceassign+derefonce Never 0 2
74710 Time MP+onceassign+derefonce 0.00
74811 Hash=49ef7a741563570102448a256a0c8568
749
750The only possible outcomes feature P1() loading a pointer to "z"
751(which contains zero) on the one hand and P1() loading a pointer to "x"
752(which contains the value one) on the other. This should be reassuring
753because it says that RCU readers cannot see the old preinitialization
754values when accessing a newly inserted list node. This undesirable
755scenario is flagged by the "exists" clause, and would occur if P1()
756loaded a pointer to "x", but obtained the pre-initialization value of
757zero after dereferencing that pointer.
758
759
760Comments
761--------
762
763Different portions of a litmus test are processed by different parsers,
764which has the charming effect of requiring different comment syntax in
765different portions of the litmus test. The C-syntax portions use
766C-language comments (either "/* */" or "//"), while the other portions
767use Ocaml comments "(* *)".
768
769The following litmus test illustrates the comment style corresponding
770to each syntactic unit of the test:
771
772 1 C MP+onceassign+derefonce (* A *)
773 2
774 3 (* B *)
775 4
776 5 {
777 6 y=z; (* C *)
778 7 z=0;
779 8 } // D
780 9
78110 // E
78211
78312 P0(int *x, int **y) // F
78413 {
78514 WRITE_ONCE(*x, 1); // G
78615 rcu_assign_pointer(*y, x);
78716 }
78817
78918 // H
79019
79120 P1(int *x, int **y)
79221 {
79322 int *r0;
79423 int r1;
79524
79625 rcu_read_lock();
79726 r0 = rcu_dereference(*y);
79827 r1 = READ_ONCE(*r0);
79928 rcu_read_unlock();
80029 }
80130
80231 // I
80332
80433 exists (* J *) (1:r0=x /\ (* K *) 1:r1=0) (* L *)
805
806In short, use C-language comments in the C code and Ocaml comments in
807the rest of the litmus test.
808
809On the other hand, if you prefer C-style comments everywhere, the
810C preprocessor is your friend.
811
812
813Asynchronous RCU Grace Periods
814------------------------------
815
816The following litmus test is derived from the example show in
817Documentation/litmus-tests/rcu/RCU+sync+free.litmus, but converted to
818emulate call_rcu():
819
820 1 C RCU+sync+free
821 2
822 3 {
823 4 int x = 1;
824 5 int *y = &x;
825 6 int z = 1;
826 7 }
827 8
828 9 P0(int *x, int *z, int **y)
82910 {
83011 int *r0;
83112 int r1;
83213
83314 rcu_read_lock();
83415 r0 = rcu_dereference(*y);
83516 r1 = READ_ONCE(*r0);
83617 rcu_read_unlock();
83718 }
83819
83920 P1(int *z, int **y, int *c)
84021 {
84122 rcu_assign_pointer(*y, z);
84223 smp_store_release(*c, 1); // Emulate call_rcu().
84324 }
84425
84526 P2(int *x, int *z, int **y, int *c)
84627 {
84728 int r0;
84829
84930 r0 = smp_load_acquire(*c); // Note call_rcu() request.
85031 synchronize_rcu(); // Wait one grace period.
85132 WRITE_ONCE(*x, 0); // Emulate the RCU callback.
85233 }
85334
85435 filter (2:r0=1) (* Reject too-early starts. *)
85536 exists (0:r0=x /\ 0:r1=0)
856
857Lines 4-6 initialize a linked list headed by "y" that initially contains
858"x". In addition, "z" is pre-initialized to prepare for P1(), which
859will replace "x" with "z" in this list.
860
861P0() on lines 9-18 enters an RCU read-side critical section, loads the
862list header "y" and dereferences it, leaving the node in "0:r0" and
863the node's value in "0:r1".
864
865P1() on lines 20-24 updates the list header to instead reference "z",
866then emulates call_rcu() by doing a release store into "c".
867
868P2() on lines 27-33 emulates the behind-the-scenes effect of doing a
869call_rcu(). Line 30 first does an acquire load from "c", then line 31
870waits for an RCU grace period to elapse, and finally line 32 emulates
871the RCU callback, which in turn emulates a call to kfree().
872
873Of course, it is possible for P2() to start too soon, so that the
874value of "2:r0" is zero rather than the required value of "1".
875The "filter" clause on line 35 handles this possibility, rejecting
876all executions in which "2:r0" is not equal to the value "1".
877
878
879Performance
880-----------
881
882LKMM's exploration of the full state-space can be extremely helpful,
883but it does not come for free. The price is exponential computational
884complexity in terms of the number of processes, the average number
885of statements in each process, and the total number of stores in the
886litmus test.
887
888So it is best to start small and then work up. Where possible, break
889your code down into small pieces each representing a core concurrency
890requirement.
891
892That said, herd7 is quite fast. On an unprepossessing x86 laptop, it
893was able to analyze the following 10-process RCU litmus test in about
894six seconds.
895
896https://github.com/paulmckrcu/litmus/blob/master/auto/C-RW-R+RW-R+RW-G+RW-G+RW-G+RW-G+RW-R+RW-R+RW-R+RW-R.litmus
897
898One way to make herd7 run faster is to use the "-speedcheck true" option.
899This option prevents herd7 from generating all possible end states,
900instead causing it to focus solely on whether or not the "exists"
901clause can be satisfied. With this option, herd7 evaluates the above
902litmus test in about 300 milliseconds, for more than an order of magnitude
903improvement in performance.
904
905Larger 16-process litmus tests that would normally consume 15 minutes
906of time complete in about 40 seconds with this option. To be fair,
907you do get an extra 65,535 states when you leave off the "-speedcheck
908true" option.
909
910https://github.com/paulmckrcu/litmus/blob/master/auto/C-RW-R+RW-R+RW-G+RW-G+RW-G+RW-G+RW-R+RW-R+RW-R+RW-R+RW-G+RW-G+RW-G+RW-G+RW-R+RW-R.litmus
911
912Nevertheless, litmus-test analysis really is of exponential complexity,
913whether with or without "-speedcheck true". Increasing by just three
914processes to a 19-process litmus test requires 2 hours and 40 minutes
915without, and about 8 minutes with "-speedcheck true". Each of these
916results represent roughly an order of magnitude slowdown compared to the
91716-process litmus test. Again, to be fair, the multi-hour run explores
918no fewer than 524,287 additional states compared to the shorter one.
919
920https://github.com/paulmckrcu/litmus/blob/master/auto/C-RW-R+RW-R+RW-G+RW-G+RW-G+RW-G+RW-R+RW-R+RW-R+RW-R+RW-R+RW-R+RW-G+RW-G+RW-G+RW-G+RW-R+RW-R+RW-R.litmus
921
922If you don't like command-line arguments, you can obtain a similar speedup
923by adding a "filter" clause with exactly the same expression as your
924"exists" clause.
925
926However, please note that seeing the full set of states can be extremely
927helpful when developing and debugging litmus tests.
928
929
930LIMITATIONS
931===========
932
933Limitations of the Linux-kernel memory model (LKMM) include:
934
9351. Compiler optimizations are not accurately modeled. Of course,
936 the use of READ_ONCE() and WRITE_ONCE() limits the compiler's
937 ability to optimize, but under some circumstances it is possible
938 for the compiler to undermine the memory model. For more
939 information, see Documentation/explanation.txt (in particular,
940 the "THE PROGRAM ORDER RELATION: po AND po-loc" and "A WARNING"
941 sections).
942
943 Note that this limitation in turn limits LKMM's ability to
944 accurately model address, control, and data dependencies.
945 For example, if the compiler can deduce the value of some variable
946 carrying a dependency, then the compiler can break that dependency
947 by substituting a constant of that value.
948
949 Conversely, LKMM will sometimes overestimate the amount of
950 reordering compilers and CPUs can carry out, leading it to miss
951 some pretty obvious cases of ordering. A simple example is:
952
953 r1 = READ_ONCE(x);
954 if (r1 == 0)
955 smp_mb();
956 WRITE_ONCE(y, 1);
957
958 The WRITE_ONCE() does not depend on the READ_ONCE(), and as a
959 result, LKMM does not claim ordering. However, even though no
960 dependency is present, the WRITE_ONCE() will not be executed before
961 the READ_ONCE(). There are two reasons for this:
962
963 The presence of the smp_mb() in one of the branches
964 prevents the compiler from moving the WRITE_ONCE()
965 up before the "if" statement, since the compiler has
966 to assume that r1 will sometimes be 0 (but see the
967 comment below);
968
969 CPUs do not execute stores before po-earlier conditional
970 branches, even in cases where the store occurs after the
971 two arms of the branch have recombined.
972
973 It is clear that it is not dangerous in the slightest for LKMM to
974 make weaker guarantees than architectures. In fact, it is
975 desirable, as it gives compilers room for making optimizations.
976 For instance, suppose that a 0 value in r1 would trigger undefined
977 behavior elsewhere. Then a clever compiler might deduce that r1
978 can never be 0 in the if condition. As a result, said clever
979 compiler might deem it safe to optimize away the smp_mb(),
980 eliminating the branch and any ordering an architecture would
981 guarantee otherwise.
982
9832. Multiple access sizes for a single variable are not supported,
984 and neither are misaligned or partially overlapping accesses.
985
9863. Exceptions and interrupts are not modeled. In some cases,
987 this limitation can be overcome by modeling the interrupt or
988 exception with an additional process.
989
9904. I/O such as MMIO or DMA is not supported.
991
9925. Self-modifying code (such as that found in the kernel's
993 alternatives mechanism, function tracer, Berkeley Packet Filter
994 JIT compiler, and module loader) is not supported.
995
9966. Complete modeling of all variants of atomic read-modify-write
997 operations, locking primitives, and RCU is not provided.
998 For example, call_rcu() and rcu_barrier() are not supported.
999 However, a substantial amount of support is provided for these
1000 operations, as shown in the linux-kernel.def file.
1001
1002 Here are specific limitations:
1003
1004 a. When rcu_assign_pointer() is passed NULL, the Linux
1005 kernel provides no ordering, but LKMM models this
1006 case as a store release.
1007
1008 b. The "unless" RMW operations are not currently modeled:
1009 atomic_long_add_unless(), atomic_inc_unless_negative(),
1010 and atomic_dec_unless_positive(). These can be emulated
1011 in litmus tests, for example, by using atomic_cmpxchg().
1012
1013 One exception of this limitation is atomic_add_unless(),
1014 which is provided directly by herd7 (so no corresponding
1015 definition in linux-kernel.def). atomic_add_unless() is
1016 modeled by herd7 therefore it can be used in litmus tests.
1017
1018 c. The call_rcu() function is not modeled. As was shown above,
1019 it can be emulated in litmus tests by adding another
1020 process that invokes synchronize_rcu() and the body of the
1021 callback function, with (for example) a release-acquire
1022 from the site of the emulated call_rcu() to the beginning
1023 of the additional process.
1024
1025 d. The rcu_barrier() function is not modeled. It can be
1026 emulated in litmus tests emulating call_rcu() via
1027 (for example) a release-acquire from the end of each
1028 additional call_rcu() process to the site of the
1029 emulated rcu-barrier().
1030
1031 e. Reader-writer locking is not modeled. It can be
1032 emulated in litmus tests using atomic read-modify-write
1033 operations.
1034
1035The fragment of the C language supported by these litmus tests is quite
1036limited and in some ways non-standard:
1037
10381. There is no automatic C-preprocessor pass. You can of course
1039 run it manually, if you choose.
1040
10412. There is no way to create functions other than the Pn() functions
1042 that model the concurrent processes.
1043
10443. The Pn() functions' formal parameters must be pointers to the
1045 global shared variables. Nothing can be passed by value into
1046 these functions.
1047
10484. The only functions that can be invoked are those built directly
1049 into herd7 or that are defined in the linux-kernel.def file.
1050
10515. The "switch", "do", "for", "while", and "goto" C statements are
1052 not supported. The "switch" statement can be emulated by the
1053 "if" statement. The "do", "for", and "while" statements can
1054 often be emulated by manually unrolling the loop, or perhaps by
1055 enlisting the aid of the C preprocessor to minimize the resulting
1056 code duplication. Some uses of "goto" can be emulated by "if",
1057 and some others by unrolling.
1058
10596. Although you can use a wide variety of types in litmus-test
1060 variable declarations, and especially in global-variable
1061 declarations, the "herd7" tool understands only int and
1062 pointer types. There is no support for floating-point types,
1063 enumerations, characters, strings, arrays, or structures.
1064
10657. Parsing of variable declarations is very loose, with almost no
1066 type checking.
1067
10688. Initializers differ from their C-language counterparts.
1069 For example, when an initializer contains the name of a shared
1070 variable, that name denotes a pointer to that variable, not
1071 the current value of that variable. For example, "int x = y"
1072 is interpreted the way "int x = &y" would be in C.
1073
10749. Dynamic memory allocation is not supported, although this can
1075 be worked around in some cases by supplying multiple statically
1076 allocated variables.
1077
1078Some of these limitations may be overcome in the future, but others are
1079more likely to be addressed by incorporating the Linux-kernel memory model
1080into other tools.
1081
1082Finally, please note that LKMM is subject to change as hardware, use cases,
1083and compilers evolve.