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Linux-Kernel Memory Model Litmus Tests
This file describes the LKMM litmus-test format by example, describes
some tricks and traps, and finally outlines LKMM's limitations. Earlier
versions of this material appeared in a number of LWN articles, including:
A formal kernel memory-ordering model (part 2)
Axiomatic validation of memory barriers and atomic instructions
Validating Memory Barriers and Atomic Instructions
This document presents information in decreasing order of applicability,
so that, where possible, the information that has proven more commonly
useful is shown near the beginning.
For information on installing LKMM, including the underlying "herd7"
tool, please see tools/memory-model/README.
As with other software, it is often better (if less macho) to adapt an
existing litmus test than it is to create one from scratch. A number
of litmus tests may be found in the kernel source tree:
Several thousand more example litmus tests are available on github
The -l and -L arguments to "git grep" can be quite helpful in identifying
existing litmus tests that are similar to the one you need. But even if
you start with an existing litmus test, it is still helpful to have a
good understanding of the litmus-test format.
Examples and Format
This section describes the overall format of litmus tests, starting
with a small example of the message-passing pattern and moving on to
more complex examples that illustrate explicit initialization and LKMM's
minimalistic set of flow-control statements.
Message-Passing Example
This section gives an overview of the format of a litmus test using an
example based on the common message-passing use case. This use case
appears often in the Linux kernel. For example, a flag (modeled by "y"
below) indicates that a buffer (modeled by "x" below) is now completely
filled in and ready for use. It would be very bad if the consumer saw the
flag set, but, due to memory misordering, saw old values in the buffer.
This example asks whether smp_store_release() and smp_load_acquire()
suffices to avoid this bad outcome:
1 C MP+pooncerelease+poacquireonce
3 {}
5 P0(int *x, int *y)
6 {
7 WRITE_ONCE(*x, 1);
8 smp_store_release(y, 1);
9 }
11 P1(int *x, int *y)
12 {
13 int r0;
14 int r1;
16 r0 = smp_load_acquire(y);
17 r1 = READ_ONCE(*x);
18 }
20 exists (1:r0=1 /\ 1:r1=0)
Line 1 starts with "C", which identifies this file as being in the
LKMM C-language format (which, as we will see, is a small fragment
of the full C language). The remainder of line 1 is the name of
the test, which by convention is the filename with the ".litmus"
suffix stripped. In this case, the actual test may be found in
in the Linux-kernel source tree.
Mechanically generated litmus tests will often have an optional
double-quoted comment string on the second line. Such strings are ignored
when running the test. Yes, you can add your own comments to litmus
tests, but this is a bit involved due to the use of multiple parsers.
For now, you can use C-language comments in the C code, and these comments
may be in either the "/* */" or the "//" style. A later section will
cover the full litmus-test commenting story.
Line 3 is the initialization section. Because the default initialization
to zero suffices for this test, the "{}" syntax is used, which mean the
initialization section is empty. Litmus tests requiring non-default
initialization must have non-empty initialization sections, as in the
example that will be presented later in this document.
Lines 5-9 show the first process and lines 11-18 the second process. Each
process corresponds to a Linux-kernel task (or kthread, workqueue, thread,
and so on; LKMM discussions often use these terms interchangeably).
The name of the first process is "P0" and that of the second "P1".
You can name your processes anything you like as long as the names consist
of a single "P" followed by a number, and as long as the numbers are
consecutive starting with zero. This can actually be quite helpful,
for example, a .litmus file matching "^P1(" but not matching "^P2("
must contain a two-process litmus test.
The argument list for each function are pointers to the global variables
used by that function. Unlike normal C-language function parameters, the
names are significant. The fact that both P0() and P1() have a formal
parameter named "x" means that these two processes are working with the
same global variable, also named "x". So the "int *x, int *y" on P0()
and P1() mean that both processes are working with two shared global
variables, "x" and "y". Global variables are always passed to processes
by reference, hence "P0(int *x, int *y)", but *never* "P0(int x, int y)".
P0() has no local variables, but P1() has two of them named "r0" and "r1".
These names may be freely chosen, but for historical reasons stemming from
other litmus-test formats, it is conventional to use names consisting of
"r" followed by a number as shown here. A common bug in litmus tests
is forgetting to add a global variable to a process's parameter list.
This will sometimes result in an error message, but can also cause the
intended global to instead be silently treated as an undeclared local
Each process's code is similar to Linux-kernel C, as can be seen on lines
7-8 and 13-17. This code may use many of the Linux kernel's atomic
operations, some of its exclusive-lock functions, and some of its RCU
and SRCU functions. An approximate list of the currently supported
functions may be found in the linux-kernel.def file.
The P0() process does "WRITE_ONCE(*x, 1)" on line 7. Because "x" is a
pointer in P0()'s parameter list, this does an unordered store to global
variable "x". Line 8 does "smp_store_release(y, 1)", and because "y"
is also in P0()'s parameter list, this does a release store to global
variable "y".
The P1() process declares two local variables on lines 13 and 14.
Line 16 does "r0 = smp_load_acquire(y)" which does an acquire load
from global variable "y" into local variable "r0". Line 17 does a
"r1 = READ_ONCE(*x)", which does an unordered load from "*x" into local
variable "r1". Both "x" and "y" are in P1()'s parameter list, so both
reference the same global variables that are used by P0().
Line 20 is the "exists" assertion expression to evaluate the final state.
This final state is evaluated after the dust has settled: both processes
have completed and all of their memory references and memory barriers
have propagated to all parts of the system. The references to the local
variables "r0" and "r1" in line 24 must be prefixed with "1:" to specify
which process they are local to.
Note that the assertion expression is written in the litmus-test
language rather than in C. For example, single "=" is an equality
operator rather than an assignment. The "/\" character combination means
"and". Similarly, "\/" stands for "or". Both of these are ASCII-art
representations of the corresponding mathematical symbols. Finally,
"~" stands for "logical not", which is "!" in C, and not to be confused
with the C-language "~" operator which instead stands for "bitwise not".
Parentheses may be used to override precedence.
The "exists" assertion on line 20 is satisfied if the consumer sees the
flag ("y") set but the buffer ("x") as not yet filled in, that is, if P1()
loaded a value from "x" that was equal to 1 but loaded a value from "y"
that was still equal to zero.
This example can be checked by running the following command, which
absolutely must be run from the tools/memory-model directory and from
this directory only:
herd7 -conf linux-kernel.cfg litmus-tests/MP+pooncerelease+poacquireonce.litmus
The output is the result of something similar to a full state-space
search, and is as follows:
1 Test MP+pooncerelease+poacquireonce Allowed
2 States 3
3 1:r0=0; 1:r1=0;
4 1:r0=0; 1:r1=1;
5 1:r0=1; 1:r1=1;
6 No
7 Witnesses
8 Positive: 0 Negative: 3
9 Condition exists (1:r0=1 /\ 1:r1=0)
10 Observation MP+pooncerelease+poacquireonce Never 0 3
11 Time MP+pooncerelease+poacquireonce 0.00
12 Hash=579aaa14d8c35a39429b02e698241d09
The most pertinent line is line 10, which contains "Never 0 3", which
indicates that the bad result flagged by the "exists" clause never
happens. This line might instead say "Sometimes" to indicate that the
bad result happened in some but not all executions, or it might say
"Always" to indicate that the bad result happened in all executions.
(The herd7 tool doesn't judge, so it is only an LKMM convention that the
"exists" clause indicates a bad result. To see this, invert the "exists"
clause's condition and run the test.) The numbers ("0 3") at the end
of this line indicate the number of end states satisfying the "exists"
clause (0) and the number not not satisfying that clause (3).
Another important part of this output is shown in lines 2-5, repeated here:
2 States 3
3 1:r0=0; 1:r1=0;
4 1:r0=0; 1:r1=1;
5 1:r0=1; 1:r1=1;
Line 2 gives the total number of end states, and each of lines 3-5 list
one of these states, with the first ("1:r0=0; 1:r1=0;") indicating that
both of P1()'s loads returned the value "0". As expected, given the
"Never" on line 10, the state flagged by the "exists" clause is not
listed. This full list of states can be helpful when debugging a new
litmus test.
The rest of the output is not normally needed, either due to irrelevance
or due to being redundant with the lines discussed above. However, the
following paragraph lists them for the benefit of readers possessed of
an insatiable curiosity. Other readers should feel free to skip ahead.
Line 1 echos the test name, along with the "Test" and "Allowed". Line 6's
"No" says that the "exists" clause was not satisfied by any execution,
and as such it has the same meaning as line 10's "Never". Line 7 is a
lead-in to line 8's "Positive: 0 Negative: 3", which lists the number
of end states satisfying and not satisfying the "exists" clause, just
like the two numbers at the end of line 10. Line 9 repeats the "exists"
clause so that you don't have to look it up in the litmus-test file.
The number at the end of line 11 (which begins with "Time") gives the
time in seconds required to analyze the litmus test. Small tests such
as this one complete in a few milliseconds, so "0.00" is quite common.
Line 12 gives a hash of the contents for the litmus-test file, and is used
by tooling that manages litmus tests and their output. This tooling is
used by people modifying LKMM itself, and among other things lets such
people know which of the several thousand relevant litmus tests were
affected by a given change to LKMM.
The previous example relied on the default zero initialization for
"x" and "y", but a similar litmus test could instead initialize them
to some other value:
1 C MP+pooncerelease+poacquireonce
3 {
4 x=42;
5 y=42;
6 }
8 P0(int *x, int *y)
9 {
10 WRITE_ONCE(*x, 1);
11 smp_store_release(y, 1);
12 }
14 P1(int *x, int *y)
15 {
16 int r0;
17 int r1;
19 r0 = smp_load_acquire(y);
20 r1 = READ_ONCE(*x);
21 }
23 exists (1:r0=1 /\ 1:r1=42)
Lines 3-6 now initialize both "x" and "y" to the value 42. This also
means that the "exists" clause on line 23 must change "1:r1=0" to
Running the test gives the same overall result as before, but with the
value 42 appearing in place of the value zero:
1 Test MP+pooncerelease+poacquireonce Allowed
2 States 3
3 1:r0=1; 1:r1=1;
4 1:r0=42; 1:r1=1;
5 1:r0=42; 1:r1=42;
6 No
7 Witnesses
8 Positive: 0 Negative: 3
9 Condition exists (1:r0=1 /\ 1:r1=42)
10 Observation MP+pooncerelease+poacquireonce Never 0 3
11 Time MP+pooncerelease+poacquireonce 0.02
12 Hash=ab9a9b7940a75a792266be279a980156
It is tempting to avoid the open-coded repetitions of the value "42"
by defining another global variable "initval=42" and replacing all
occurrences of "42" with "initval". This will not, repeat *not*,
initialize "x" and "y" to 42, but instead to the address of "initval"
(try it!). See the section below on linked lists to learn more about
why this approach to initialization can be useful.
Control Structures
LKMM supports the C-language "if" statement, which allows modeling of
conditional branches. In LKMM, conditional branches can affect ordering,
but only if you are *very* careful (compilers are surprisingly able
to optimize away conditional branches). The following example shows
the "load buffering" (LB) use case that is used in the Linux kernel to
synchronize between ring-buffer producers and consumers. In the example
below, P0() is one side checking to see if an operation may proceed and
P1() is the other side completing its update.
1 C LB+fencembonceonce+ctrlonceonce
3 {}
5 P0(int *x, int *y)
6 {
7 int r0;
9 r0 = READ_ONCE(*x);
10 if (r0)
11 WRITE_ONCE(*y, 1);
12 }
14 P1(int *x, int *y)
15 {
16 int r0;
18 r0 = READ_ONCE(*y);
19 smp_mb();
20 WRITE_ONCE(*x, 1);
21 }
23 exists (0:r0=1 /\ 1:r0=1)
P1()'s "if" statement on line 10 works as expected, so that line 11 is
executed only if line 9 loads a non-zero value from "x". Because P1()'s
write of "1" to "x" happens only after P1()'s read from "y", one would
hope that the "exists" clause cannot be satisfied. LKMM agrees:
1 Test LB+fencembonceonce+ctrlonceonce Allowed
2 States 2
3 0:r0=0; 1:r0=0;
4 0:r0=1; 1:r0=0;
5 No
6 Witnesses
7 Positive: 0 Negative: 2
8 Condition exists (0:r0=1 /\ 1:r0=1)
9 Observation LB+fencembonceonce+ctrlonceonce Never 0 2
10 Time LB+fencembonceonce+ctrlonceonce 0.00
11 Hash=e5260556f6de495fd39b556d1b831c3b
However, there is no "while" statement due to the fact that full
state-space search has some difficulty with iteration. However, there
are tricks that may be used to handle some special cases, which are
discussed below. In addition, loop-unrolling tricks may be applied,
albeit sparingly.
Tricks and Traps
This section covers extracting debug output from herd7, emulating
spin loops, handling trivial linked lists, adding comments to litmus tests,
emulating call_rcu(), and finally tricks to improve herd7 performance
in order to better handle large litmus tests.
Debug Output
By default, the herd7 state output includes all variables mentioned
in the "exists" clause. But sometimes debugging efforts are greatly
aided by the values of other variables. Consider this litmus test
(tools/memory-order/litmus-tests/SB+rfionceonce-poonceonces.litmus but
slightly modified), which probes an obscure corner of hardware memory
1 C SB+rfionceonce-poonceonces
3 {}
5 P0(int *x, int *y)
6 {
7 int r1;
8 int r2;
10 WRITE_ONCE(*x, 1);
11 r1 = READ_ONCE(*x);
12 r2 = READ_ONCE(*y);
13 }
15 P1(int *x, int *y)
16 {
17 int r3;
18 int r4;
20 WRITE_ONCE(*y, 1);
21 r3 = READ_ONCE(*y);
22 r4 = READ_ONCE(*x);
23 }
25 exists (0:r2=0 /\ 1:r4=0)
The herd7 output is as follows:
1 Test SB+rfionceonce-poonceonces Allowed
2 States 4
3 0:r2=0; 1:r4=0;
4 0:r2=0; 1:r4=1;
5 0:r2=1; 1:r4=0;
6 0:r2=1; 1:r4=1;
7 Ok
8 Witnesses
9 Positive: 1 Negative: 3
10 Condition exists (0:r2=0 /\ 1:r4=0)
11 Observation SB+rfionceonce-poonceonces Sometimes 1 3
12 Time SB+rfionceonce-poonceonces 0.01
13 Hash=c7f30fe0faebb7d565405d55b7318ada
(This output indicates that CPUs are permitted to "snoop their own
store buffers", which all of Linux's CPU families other than s390 will
happily do. Such snooping results in disagreement among CPUs on the
order of stores from different CPUs, which is rarely an issue.)
But the herd7 output shows only the two variables mentioned in the
"exists" clause. Someone modifying this test might wish to know the
values of "x", "y", "0:r1", and "0:r3" as well. The "locations"
statement on line 25 shows how to cause herd7 to display additional
1 C SB+rfionceonce-poonceonces
3 {}
5 P0(int *x, int *y)
6 {
7 int r1;
8 int r2;
10 WRITE_ONCE(*x, 1);
11 r1 = READ_ONCE(*x);
12 r2 = READ_ONCE(*y);
13 }
15 P1(int *x, int *y)
16 {
17 int r3;
18 int r4;
20 WRITE_ONCE(*y, 1);
21 r3 = READ_ONCE(*y);
22 r4 = READ_ONCE(*x);
23 }
25 locations [0:r1; 1:r3; x; y]
26 exists (0:r2=0 /\ 1:r4=0)
The herd7 output then displays the values of all the variables:
1 Test SB+rfionceonce-poonceonces Allowed
2 States 4
3 0:r1=1; 0:r2=0; 1:r3=1; 1:r4=0; x=1; y=1;
4 0:r1=1; 0:r2=0; 1:r3=1; 1:r4=1; x=1; y=1;
5 0:r1=1; 0:r2=1; 1:r3=1; 1:r4=0; x=1; y=1;
6 0:r1=1; 0:r2=1; 1:r3=1; 1:r4=1; x=1; y=1;
7 Ok
8 Witnesses
9 Positive: 1 Negative: 3
10 Condition exists (0:r2=0 /\ 1:r4=0)
11 Observation SB+rfionceonce-poonceonces Sometimes 1 3
12 Time SB+rfionceonce-poonceonces 0.01
13 Hash=40de8418c4b395388f6501cafd1ed38d
What if you would like to know the value of a particular global variable
at some particular point in a given process's execution? One approach
is to use a READ_ONCE() to load that global variable into a new local
variable, then add that local variable to the "locations" clause.
But be careful: In some litmus tests, adding a READ_ONCE() will change
the outcome! For one example, please see the C-READ_ONCE.litmus and
C-READ_ONCE-omitted.litmus tests located here:
Spin Loops
The analysis carried out by herd7 explores full state space, which is
at best of exponential time complexity. Adding processes and increasing
the amount of code in a give process can greatly increase execution time.
Potentially infinite loops, such as those used to wait for locks to
become available, are clearly problematic.
Fortunately, it is possible to avoid state-space explosion by specially
modeling such loops. For example, the following litmus tests emulates
locking using xchg_acquire(), but instead of enclosing xchg_acquire()
in a spin loop, it instead excludes executions that fail to acquire the
lock using a herd7 "filter" clause. Note that for exclusive locking, you
are better off using the spin_lock() and spin_unlock() that LKMM directly
models, if for no other reason that these are much faster. However, the
techniques illustrated in this section can be used for other purposes,
such as emulating reader-writer locking, which LKMM does not yet model.
1 C C-SB+l-o-o-u+l-o-o-u-X
3 {
4 }
6 P0(int *sl, int *x0, int *x1)
7 {
8 int r2;
9 int r1;
11 r2 = xchg_acquire(sl, 1);
12 WRITE_ONCE(*x0, 1);
13 r1 = READ_ONCE(*x1);
14 smp_store_release(sl, 0);
15 }
17 P1(int *sl, int *x0, int *x1)
18 {
19 int r2;
20 int r1;
22 r2 = xchg_acquire(sl, 1);
23 WRITE_ONCE(*x1, 1);
24 r1 = READ_ONCE(*x0);
25 smp_store_release(sl, 0);
26 }
28 filter (0:r2=0 /\ 1:r2=0)
29 exists (0:r1=0 /\ 1:r1=0)
This litmus test may be found here:
This test uses two global variables, "x1" and "x2", and also emulates a
single global spinlock named "sl". This spinlock is held by whichever
process changes the value of "sl" from "0" to "1", and is released when
that process sets "sl" back to "0". P0()'s lock acquisition is emulated
on line 11 using xchg_acquire(), which unconditionally stores the value
"1" to "sl" and stores either "0" or "1" to "r2", depending on whether
the lock acquisition was successful or unsuccessful (due to "sl" already
having the value "1"), respectively. P1() operates in a similar manner.
Rather unconventionally, execution appears to proceed to the critical
section on lines 12 and 13 in either case. Line 14 then uses an
smp_store_release() to store zero to "sl", thus emulating lock release.
The case where xchg_acquire() fails to acquire the lock is handled by
the "filter" clause on line 28, which tells herd7 to keep only those
executions in which both "0:r2" and "1:r2" are zero, that is to pay
attention only to those executions in which both locks are actually
acquired. Thus, the bogus executions that would execute the critical
sections are discarded and any effects that they might have had are
ignored. Note well that the "filter" clause keeps those executions
for which its expression is satisfied, that is, for which the expression
evaluates to true. In other words, the "filter" clause says what to
keep, not what to discard.
The result of running this test is as follows:
1 Test C-SB+l-o-o-u+l-o-o-u-X Allowed
2 States 2
3 0:r1=0; 1:r1=1;
4 0:r1=1; 1:r1=0;
5 No
6 Witnesses
7 Positive: 0 Negative: 2
8 Condition exists (0:r1=0 /\ 1:r1=0)
9 Observation C-SB+l-o-o-u+l-o-o-u-X Never 0 2
10 Time C-SB+l-o-o-u+l-o-o-u-X 0.03
The "Never" on line 9 indicates that this use of xchg_acquire() and
smp_store_release() really does correctly emulate locking.
Why doesn't the litmus test take the simpler approach of using a spin loop
to handle failed spinlock acquisitions, like the kernel does? The key
insight behind this litmus test is that spin loops have no effect on the
possible "exists"-clause outcomes of program execution in the absence
of deadlock. In other words, given a high-quality lock-acquisition
primitive in a deadlock-free program running on high-quality hardware,
each lock acquisition will eventually succeed. Because herd7 already
explores the full state space, the length of time required to actually
acquire the lock does not matter. After all, herd7 already models all
possible durations of the xchg_acquire() statements.
Why not just add the "filter" clause to the "exists" clause, thus
avoiding the "filter" clause entirely? This does work, but is slower.
The reason that the "filter" clause is faster is that (in the common case)
herd7 knows to abandon an execution as soon as the "filter" expression
fails to be satisfied. In contrast, the "exists" clause is evaluated
only at the end of time, thus requiring herd7 to waste time on bogus
executions in which both critical sections proceed concurrently. In
addition, some LKMM users like the separation of concerns provided by
using the both the "filter" and "exists" clauses.
Readers lacking a pathological interest in odd corner cases should feel
free to skip the remainder of this section.
But what if the litmus test were to temporarily set "0:r2" to a non-zero
value? Wouldn't that cause herd7 to abandon the execution prematurely
due to an early mismatch of the "filter" clause?
Why not just try it? Line 4 of the following modified litmus test
introduces a new global variable "x2" that is initialized to "1". Line 23
of P1() reads that variable into "1:r2" to force an early mismatch with
the "filter" clause. Line 24 does a known-true "if" condition to avoid
and static analysis that herd7 might do. Finally the "exists" clause
on line 32 is updated to a condition that is alway satisfied at the end
of the test.
1 C C-SB+l-o-o-u+l-o-o-u-X
3 {
4 x2=1;
5 }
7 P0(int *sl, int *x0, int *x1)
8 {
9 int r2;
10 int r1;
12 r2 = xchg_acquire(sl, 1);
13 WRITE_ONCE(*x0, 1);
14 r1 = READ_ONCE(*x1);
15 smp_store_release(sl, 0);
16 }
18 P1(int *sl, int *x0, int *x1, int *x2)
19 {
20 int r2;
21 int r1;
23 r2 = READ_ONCE(*x2);
24 if (r2)
25 r2 = xchg_acquire(sl, 1);
26 WRITE_ONCE(*x1, 1);
27 r1 = READ_ONCE(*x0);
28 smp_store_release(sl, 0);
29 }
31 filter (0:r2=0 /\ 1:r2=0)
32 exists (x1=1)
If the "filter" clause were to check each variable at each point in the
execution, running this litmus test would display no executions because
all executions would be filtered out at line 23. However, the output
is instead as follows:
1 Test C-SB+l-o-o-u+l-o-o-u-X Allowed
2 States 1
3 x1=1;
4 Ok
5 Witnesses
6 Positive: 2 Negative: 0
7 Condition exists (x1=1)
8 Observation C-SB+l-o-o-u+l-o-o-u-X Always 2 0
9 Time C-SB+l-o-o-u+l-o-o-u-X 0.04
10 Hash=080bc508da7f291e122c6de76c0088e3
Line 3 shows that there is one execution that did not get filtered out,
so the "filter" clause is evaluated only on the last assignment to
the variables that it checks. In this case, the "filter" clause is a
disjunction, so it might be evaluated twice, once at the final (and only)
assignment to "0:r2" and once at the final assignment to "1:r2".
Linked Lists
LKMM can handle linked lists, but only linked lists in which each node
contains nothing except a pointer to the next node in the list. This is
of course quite restrictive, but there is nevertheless quite a bit that
can be done within these confines, as can be seen in the litmus test
at tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus:
1 C MP+onceassign+derefonce
3 {
4 y=z;
5 z=0;
6 }
8 P0(int *x, int **y)
9 {
10 WRITE_ONCE(*x, 1);
11 rcu_assign_pointer(*y, x);
12 }
14 P1(int *x, int **y)
15 {
16 int *r0;
17 int r1;
19 rcu_read_lock();
20 r0 = rcu_dereference(*y);
21 r1 = READ_ONCE(*r0);
22 rcu_read_unlock();
23 }
25 exists (1:r0=x /\ 1:r1=0)
Line 4's "y=z" may seem odd, given that "z" has not yet been initialized.
But "y=z" does not set the value of "y" to that of "z", but instead
sets the value of "y" to the *address* of "z". Lines 4 and 5 therefore
create a simple linked list, with "y" pointing to "z" and "z" having a
NULL pointer. A much longer linked list could be created if desired,
and circular singly linked lists can also be created and manipulated.
The "exists" clause works the same way, with the "1:r0=x" comparing P1()'s
"r0" not to the value of "x", but again to its address. This term of the
"exists" clause therefore tests whether line 20's load from "y" saw the
value stored by line 11, which is in fact what is required in this case.
P0()'s line 10 initializes "x" to the value 1 then line 11 links to "x"
from "y", replacing "z".
P1()'s line 20 loads a pointer from "y", and line 21 dereferences that
pointer. The RCU read-side critical section spanning lines 19-22 is just
for show in this example. Note that the address used for line 21's load
depends on (in this case, "is exactly the same as") the value loaded by
line 20. This is an example of what is called an "address dependency".
This particular address dependency extends from the load on line 20 to the
load on line 21. Address dependencies provide a weak form of ordering.
Running this test results in the following:
1 Test MP+onceassign+derefonce Allowed
2 States 2
3 1:r0=x; 1:r1=1;
4 1:r0=z; 1:r1=0;
5 No
6 Witnesses
7 Positive: 0 Negative: 2
8 Condition exists (1:r0=x /\ 1:r1=0)
9 Observation MP+onceassign+derefonce Never 0 2
10 Time MP+onceassign+derefonce 0.00
11 Hash=49ef7a741563570102448a256a0c8568
The only possible outcomes feature P1() loading a pointer to "z"
(which contains zero) on the one hand and P1() loading a pointer to "x"
(which contains the value one) on the other. This should be reassuring
because it says that RCU readers cannot see the old preinitialization
values when accessing a newly inserted list node. This undesirable
scenario is flagged by the "exists" clause, and would occur if P1()
loaded a pointer to "x", but obtained the pre-initialization value of
zero after dereferencing that pointer.
Different portions of a litmus test are processed by different parsers,
which has the charming effect of requiring different comment syntax in
different portions of the litmus test. The C-syntax portions use
C-language comments (either "/* */" or "//"), while the other portions
use Ocaml comments "(* *)".
The following litmus test illustrates the comment style corresponding
to each syntactic unit of the test:
1 C MP+onceassign+derefonce (* A *)
3 (* B *)
5 {
6 y=z; (* C *)
7 z=0;
8 } // D
10 // E
12 P0(int *x, int **y) // F
13 {
14 WRITE_ONCE(*x, 1); // G
15 rcu_assign_pointer(*y, x);
16 }
18 // H
20 P1(int *x, int **y)
21 {
22 int *r0;
23 int r1;
25 rcu_read_lock();
26 r0 = rcu_dereference(*y);
27 r1 = READ_ONCE(*r0);
28 rcu_read_unlock();
29 }
31 // I
33 exists (* J *) (1:r0=x /\ (* K *) 1:r1=0) (* L *)
In short, use C-language comments in the C code and Ocaml comments in
the rest of the litmus test.
On the other hand, if you prefer C-style comments everywhere, the
C preprocessor is your friend.
Asynchronous RCU Grace Periods
The following litmus test is derived from the example show in
Documentation/litmus-tests/rcu/RCU+sync+free.litmus, but converted to
emulate call_rcu():
1 C RCU+sync+free
3 {
4 int x = 1;
5 int *y = &x;
6 int z = 1;
7 }
9 P0(int *x, int *z, int **y)
10 {
11 int *r0;
12 int r1;
14 rcu_read_lock();
15 r0 = rcu_dereference(*y);
16 r1 = READ_ONCE(*r0);
17 rcu_read_unlock();
18 }
20 P1(int *z, int **y, int *c)
21 {
22 rcu_assign_pointer(*y, z);
23 smp_store_release(*c, 1); // Emulate call_rcu().
24 }
26 P2(int *x, int *z, int **y, int *c)
27 {
28 int r0;
30 r0 = smp_load_acquire(*c); // Note call_rcu() request.
31 synchronize_rcu(); // Wait one grace period.
32 WRITE_ONCE(*x, 0); // Emulate the RCU callback.
33 }
35 filter (2:r0=1) (* Reject too-early starts. *)
36 exists (0:r0=x /\ 0:r1=0)
Lines 4-6 initialize a linked list headed by "y" that initially contains
"x". In addition, "z" is pre-initialized to prepare for P1(), which
will replace "x" with "z" in this list.
P0() on lines 9-18 enters an RCU read-side critical section, loads the
list header "y" and dereferences it, leaving the node in "0:r0" and
the node's value in "0:r1".
P1() on lines 20-24 updates the list header to instead reference "z",
then emulates call_rcu() by doing a release store into "c".
P2() on lines 27-33 emulates the behind-the-scenes effect of doing a
call_rcu(). Line 30 first does an acquire load from "c", then line 31
waits for an RCU grace period to elapse, and finally line 32 emulates
the RCU callback, which in turn emulates a call to kfree().
Of course, it is possible for P2() to start too soon, so that the
value of "2:r0" is zero rather than the required value of "1".
The "filter" clause on line 35 handles this possibility, rejecting
all executions in which "2:r0" is not equal to the value "1".
LKMM's exploration of the full state-space can be extremely helpful,
but it does not come for free. The price is exponential computational
complexity in terms of the number of processes, the average number
of statements in each process, and the total number of stores in the
litmus test.
So it is best to start small and then work up. Where possible, break
your code down into small pieces each representing a core concurrency
That said, herd7 is quite fast. On an unprepossessing x86 laptop, it
was able to analyze the following 10-process RCU litmus test in about
six seconds.
One way to make herd7 run faster is to use the "-speedcheck true" option.
This option prevents herd7 from generating all possible end states,
instead causing it to focus solely on whether or not the "exists"
clause can be satisfied. With this option, herd7 evaluates the above
litmus test in about 300 milliseconds, for more than an order of magnitude
improvement in performance.
Larger 16-process litmus tests that would normally consume 15 minutes
of time complete in about 40 seconds with this option. To be fair,
you do get an extra 65,535 states when you leave off the "-speedcheck
true" option.
Nevertheless, litmus-test analysis really is of exponential complexity,
whether with or without "-speedcheck true". Increasing by just three
processes to a 19-process litmus test requires 2 hours and 40 minutes
without, and about 8 minutes with "-speedcheck true". Each of these
results represent roughly an order of magnitude slowdown compared to the
16-process litmus test. Again, to be fair, the multi-hour run explores
no fewer than 524,287 additional states compared to the shorter one.
If you don't like command-line arguments, you can obtain a similar speedup
by adding a "filter" clause with exactly the same expression as your
"exists" clause.
However, please note that seeing the full set of states can be extremely
helpful when developing and debugging litmus tests.
Limitations of the Linux-kernel memory model (LKMM) include:
1. Compiler optimizations are not accurately modeled. Of course,
the use of READ_ONCE() and WRITE_ONCE() limits the compiler's
ability to optimize, but under some circumstances it is possible
for the compiler to undermine the memory model. For more
information, see Documentation/explanation.txt (in particular,
Note that this limitation in turn limits LKMM's ability to
accurately model address, control, and data dependencies.
For example, if the compiler can deduce the value of some variable
carrying a dependency, then the compiler can break that dependency
by substituting a constant of that value.
Conversely, LKMM sometimes doesn't recognize that a particular
optimization is not allowed, and as a result, thinks that a
dependency is not present (because the optimization would break it).
The memory model misses some pretty obvious control dependencies
because of this limitation. A simple example is:
r1 = READ_ONCE(x);
if (r1 == 0)
There is a control dependency from the READ_ONCE to the WRITE_ONCE,
even when r1 is nonzero, but LKMM doesn't realize this and thinks
that the write may execute before the read if r1 != 0. (Yes, that
doesn't make sense if you think about it, but the memory model's
intelligence is limited.)
2. Multiple access sizes for a single variable are not supported,
and neither are misaligned or partially overlapping accesses.
3. Exceptions and interrupts are not modeled. In some cases,
this limitation can be overcome by modeling the interrupt or
exception with an additional process.
4. I/O such as MMIO or DMA is not supported.
5. Self-modifying code (such as that found in the kernel's
alternatives mechanism, function tracer, Berkeley Packet Filter
JIT compiler, and module loader) is not supported.
6. Complete modeling of all variants of atomic read-modify-write
operations, locking primitives, and RCU is not provided.
For example, call_rcu() and rcu_barrier() are not supported.
However, a substantial amount of support is provided for these
operations, as shown in the linux-kernel.def file.
Here are specific limitations:
a. When rcu_assign_pointer() is passed NULL, the Linux
kernel provides no ordering, but LKMM models this
case as a store release.
b. The "unless" RMW operations are not currently modeled:
atomic_long_add_unless(), atomic_inc_unless_negative(),
and atomic_dec_unless_positive(). These can be emulated
in litmus tests, for example, by using atomic_cmpxchg().
One exception of this limitation is atomic_add_unless(),
which is provided directly by herd7 (so no corresponding
definition in linux-kernel.def). atomic_add_unless() is
modeled by herd7 therefore it can be used in litmus tests.
c. The call_rcu() function is not modeled. As was shown above,
it can be emulated in litmus tests by adding another
process that invokes synchronize_rcu() and the body of the
callback function, with (for example) a release-acquire
from the site of the emulated call_rcu() to the beginning
of the additional process.
d. The rcu_barrier() function is not modeled. It can be
emulated in litmus tests emulating call_rcu() via
(for example) a release-acquire from the end of each
additional call_rcu() process to the site of the
emulated rcu-barrier().
e. Although sleepable RCU (SRCU) is now modeled, there
are some subtle differences between its semantics and
those in the Linux kernel. For example, the kernel
might interpret the following sequence as two partially
overlapping SRCU read-side critical sections:
1 r1 = srcu_read_lock(&my_srcu);
2 do_something_1();
3 r2 = srcu_read_lock(&my_srcu);
4 do_something_2();
5 srcu_read_unlock(&my_srcu, r1);
6 do_something_3();
7 srcu_read_unlock(&my_srcu, r2);
In contrast, LKMM will interpret this as a nested pair of
SRCU read-side critical sections, with the outer critical
section spanning lines 1-7 and the inner critical section
spanning lines 3-5.
This difference would be more of a concern had anyone
identified a reasonable use case for partially overlapping
SRCU read-side critical sections. For more information
on the trickiness of such overlapping, please see:
f. Reader-writer locking is not modeled. It can be
emulated in litmus tests using atomic read-modify-write
The fragment of the C language supported by these litmus tests is quite
limited and in some ways non-standard:
1. There is no automatic C-preprocessor pass. You can of course
run it manually, if you choose.
2. There is no way to create functions other than the Pn() functions
that model the concurrent processes.
3. The Pn() functions' formal parameters must be pointers to the
global shared variables. Nothing can be passed by value into
these functions.
4. The only functions that can be invoked are those built directly
into herd7 or that are defined in the linux-kernel.def file.
5. The "switch", "do", "for", "while", and "goto" C statements are
not supported. The "switch" statement can be emulated by the
"if" statement. The "do", "for", and "while" statements can
often be emulated by manually unrolling the loop, or perhaps by
enlisting the aid of the C preprocessor to minimize the resulting
code duplication. Some uses of "goto" can be emulated by "if",
and some others by unrolling.
6. Although you can use a wide variety of types in litmus-test
variable declarations, and especially in global-variable
declarations, the "herd7" tool understands only int and
pointer types. There is no support for floating-point types,
enumerations, characters, strings, arrays, or structures.
7. Parsing of variable declarations is very loose, with almost no
type checking.
8. Initializers differ from their C-language counterparts.
For example, when an initializer contains the name of a shared
variable, that name denotes a pointer to that variable, not
the current value of that variable. For example, "int x = y"
is interpreted the way "int x = &y" would be in C.
9. Dynamic memory allocation is not supported, although this can
be worked around in some cases by supplying multiple statically
allocated variables.
Some of these limitations may be overcome in the future, but others are
more likely to be addressed by incorporating the Linux-kernel memory model
into other tools.
Finally, please note that LKMM is subject to change as hardware, use cases,
and compilers evolve.