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Automate memory-barriers.txt; provide Linux-kernel memory model

Browse Source 
There is some reason to believe that Documentation/memory-barriers.txt
could use some help, and a major purpose of this patch is to provide
that help in the form of a design-time tool that can produce all valid
executions of a small fragment of concurrent Linux-kernel code, which is
called a "litmus test".  This tool's functionality is roughly similar to
a full state-space search.  Please note that this is a design-time tool,
not useful for regression testing.  However, we hope that the underlying
Linux-kernel memory model will be incorporated into other tools capable
of analyzing large bodies of code for regression-testing purposes.

The main tool is herd7, together with the linux-kernel.bell,
linux-kernel.cat, linux-kernel.cfg, linux-kernel.def, and lock.cat files
added by this patch.  The herd7 executable takes the other files as input,
and all of these files collectively define the Linux-kernel memory memory
model.  A brief description of each of these other files is provided
in the README file.  Although this tool does have its limitations,
which are documented in the README file, it does improve on the version
reported on in the LWN series (https://lwn.net/Articles/718628/ and
https://lwn.net/Articles/720550/) by supporting locking and arithmetic,
including a much wider variety of read-modify-write atomic operations.
Please note that herd7 is not part of this submission, but is freely
available from http://diy.inria.fr/sources/index.html (and via "git"
at https://github.com/herd/herdtools7).

A second tool is klitmus7, which converts litmus tests to loadable
kernel modules for direct testing.  As with herd7, the klitmus7
code is freely available from http://diy.inria.fr/sources/index.html
(and via "git" at https://github.com/herd/herdtools7).

Of course, litmus tests are not always the best way to fully understand a
memory model, so this patch also includes Documentation/explanation.txt,
which describes the memory model in detail.  In addition,
Documentation/recipes.txt provides example known-good and known-bad use
cases for those who prefer working by example.

This patch also includes a few sample litmus tests, and a great many
more litmus tests are available at https://github.com/paulmckrcu/litmus.

This patch was the result of a most excellent collaboration founded
by Jade Alglave and also including Alan Stern, Andrea Parri, and Luc
Maranget.  For more details on the history of this collaboration, please
refer to the Linux-kernel memory model presentations at 2016 LinuxCon EU,
2016 Kernel Summit, 2016 Linux Plumbers Conference, 2017 linux.conf.au,
or 2017 Linux Plumbers Conference microconference.  However, one aspect
of the history does bear repeating due to weak copyright tracking earlier
in this project, which extends back to early 2015.  This weakness came
to light in late 2017 after an LKMM presentation by Paul in which an
audience member noted the similarity of some LKMM code to code in early
published papers.  This prompted a copyright review.

From Alan Stern:

	To say that the model was mine is not entirely accurate.
	Pieces of it (especially the Scpv and Atomic axioms) were taken
	directly from Jade's models.  And of course the Happens-before
	and Propagation relations and axioms were heavily based on
	Jade and Luc's work, even though they weren't identical to the
	earlier versions.  Only the RCU portion was completely original.

	. . .

	One can make a much better case that I wrote the bulk of lock.cat.
	However, it was inspired by Luc's earlier version (and still
	shares some elements in common), and of course it benefited from
	feedback and testing from all members of our group.

The model prior to Alan's was Luc Maranget's.  From Luc:

	 I totally agree on Alan Stern's account of the linux kernel model
	 genesis.  I thank him for his acknowledgments of my participation
	 to previous model drafts.  I'd like to complete Alan Stern's
	 statement: any bell cat code I have written has its roots in
	 discussions with Jade Alglave and Paul McKenney. Moreover I
	 have borrowed cat and bell code written by Jade Alglave freely.

This copyright review therefore resulted in late adds to the copyright
statements of several files.

Discussion of v1 has raised several issues, which we do not believe should
block acceptance given that this level of change will be ongoing, just
as it has been with memory-barriers.txt:

o	Under what conditions should ordering provided by pure locking
	be seen by CPUs not holding the relevant lock(s)?  In particular,
	should the message-passing pattern be forbidden?

o	Should examples involving C11 release sequences be forbidden?
	Note that this C11 is still a moving target for this issue:
	http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0735r0.html

o	Some details of the handling of internal dependencies for atomic
	read-modify-write atomic operations are still subject to debate.

o	Changes recently accepted into mainline greatly reduce the need
	to handle DEC Alpha as a special case.  These changes add an
	smp_read_barrier_depends() to READ_ONCE(), thus causing Alpha
	to respect ordering of dependent reads.  If these changes stick,
	the memory model can be simplified accordingly.

o	Will changes be required to accommodate RISC-V?

Differences from v1:
	(http://lkml.kernel.org/r/20171113184031.GA26302@linux.vnet.ibm.com)

o	Add SPDX notations to .bell and .cat files, replacing
	textual license statements.

o	Add reference to upcoming ASPLOS paper to .bell and .cat files.

o	Updated identifier names in .bell and .cat files to match those
	used in the ASPLOS paper.

o	Updates to READMEs and other documentation based on review
	feedback.

o	Added a memory-ordering cheatsheet.

o	Update sigs to new Co-Developed-by and add acks and
	reviewed-bys.

o	Simplify rules detecting nested RCU read-side critical sections.

o	Update copyright statements as noted above.

Co-Developed-by: Alan Stern <stern@rowland.harvard.edu>
Co-Developed-by: Andrea Parri <parri.andrea@gmail.com>
Co-Developed-by: Jade Alglave <j.alglave@ucl.ac.uk>
Co-Developed-by: Luc Maranget <luc.maranget@inria.fr>
Co-Developed-by: "Paul E. McKenney" <paulmck@linux.vnet.ibm.com>
Signed-off-by: Alan Stern <stern@rowland.harvard.edu>
Signed-off-by: Andrea Parri <parri.andrea@gmail.com>
Signed-off-by: Jade Alglave <j.alglave@ucl.ac.uk>
Signed-off-by: Luc Maranget <luc.maranget@inria.fr>
Signed-off-by: "Paul E. McKenney" <paulmck@linux.vnet.ibm.com>
Reviewed-by: Boqun Feng <boqun.feng@gmail.com>
Acked-by: Will Deacon <will.deacon@arm.com>
Acked-by: Peter Zijlstra <peterz@infradead.org>
Acked-by: Nicholas Piggin <npiggin@gmail.com>
Acked-by: David Howells <dhowells@redhat.com>
Acked-by: "Reshetova, Elena" <elena.reshetova@intel.com>
Acked-by: Michal Hocko <mhocko@suse.com>
Acked-by: Akira Yokosawa <akiyks@gmail.com>
Cc: <linux-arch@vger.kernel.org>
This commit is contained in:
Paul E. McKenney 2018-01-18 19:58:55 -08:00
parent 0c5b9b5d9a
commit 1c27b644c0
40 changed files with 3973 additions and 0 deletions
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Prior Operation Subsequent Operation
--------------- ---------------------------
C Self R W RWM Self R W DR DW RMW SV
__ ---- - - --- ---- - - -- -- --- --
Store, e.g., WRITE_ONCE() Y Y
Load, e.g., READ_ONCE() Y Y Y
Unsuccessful RMW operation Y Y Y
smp_read_barrier_depends() Y Y Y
*_dereference() Y Y Y Y
Successful *_acquire() R Y Y Y Y Y Y
Successful *_release() C Y Y Y W Y
smp_rmb() Y R Y Y R
smp_wmb() Y W Y Y W
smp_mb() & synchronize_rcu() CP Y Y Y Y Y Y Y Y
Successful full non-void RMW CP Y Y Y Y Y Y Y Y Y Y Y
smp_mb__before_atomic() CP Y Y Y a a a a Y
smp_mb__after_atomic() CP a a Y Y Y Y Y
Key: C: Ordering is cumulative
P: Ordering propagates
R: Read, for example, READ_ONCE(), or read portion of RMW
W: Write, for example, WRITE_ONCE(), or write portion of RMW
Y: Provides ordering
a: Provides ordering given intervening RMW atomic operation
DR: Dependent read (address dependency)
DW: Dependent write (address, data, or control dependency)
RMW: Atomic read-modify-write operation
SV Same-variable access

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This document provides "recipes", that is, litmus tests for commonly
occurring situations, as well as a few that illustrate subtly broken but
attractive nuisances. Many of these recipes include example code from
v4.13 of the Linux kernel.
The first section covers simple special cases, the second section
takes off the training wheels to cover more involved examples,
and the third section provides a few rules of thumb.
Simple special cases
====================
This section presents two simple special cases, the first being where
there is only one CPU or only one memory location is accessed, and the
second being use of that old concurrency workhorse, locking.
Single CPU or single memory location
------------------------------------
If there is only one CPU on the one hand or only one variable
on the other, the code will execute in order. There are (as
usual) some things to be careful of:
1. Some aspects of the C language are unordered. For example,
in the expression "f(x) + g(y)", the order in which f and g are
called is not defined; the object code is allowed to use either
order or even to interleave the computations.
2. Compilers are permitted to use the "as-if" rule. That is, a
compiler can emit whatever code it likes for normal accesses,
as long as the results of a single-threaded execution appear
just as if the compiler had followed all the relevant rules.
To see this, compile with a high level of optimization and run
the debugger on the resulting binary.
3. If there is only one variable but multiple CPUs, that variable
must be properly aligned and all accesses to that variable must
be full sized. Variables that straddle cachelines or pages void
your full-ordering warranty, as do undersized accesses that load
from or store to only part of the variable.
4. If there are multiple CPUs, accesses to shared variables should
use READ_ONCE() and WRITE_ONCE() or stronger to prevent load/store
tearing, load/store fusing, and invented loads and stores.
There are exceptions to this rule, including:
i. When there is no possibility of a given shared variable
being updated by some other CPU, for example, while
holding the update-side lock, reads from that variable
need not use READ_ONCE().
ii. When there is no possibility of a given shared variable
being either read or updated by other CPUs, for example,
when running during early boot, reads from that variable
need not use READ_ONCE() and writes to that variable
need not use WRITE_ONCE().
Locking
-------
Locking is well-known and straightforward, at least if you don't think
about it too hard. And the basic rule is indeed quite simple: Any CPU that
has acquired a given lock sees any changes previously seen or made by any
CPU before it released that same lock. Note that this statement is a bit
stronger than "Any CPU holding a given lock sees all changes made by any
CPU during the time that CPU was holding this same lock". For example,
consider the following pair of code fragments:
/* See MP+polocks.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
spin_lock(&mylock);
WRITE_ONCE(y, 1);
spin_unlock(&mylock);
}
void CPU1(void)
{
spin_lock(&mylock);
r0 = READ_ONCE(y);
spin_unlock(&mylock);
r1 = READ_ONCE(x);
}
The basic rule guarantees that if CPU0() acquires mylock before CPU1(),
then both r0 and r1 must be set to the value 1. This also has the
consequence that if the final value of r0 is equal to 1, then the final
value of r1 must also be equal to 1. In contrast, the weaker rule would
say nothing about the final value of r1.
The converse to the basic rule also holds, as illustrated by the
following litmus test:
/* See MP+porevlocks.litmus. */
void CPU0(void)
{
r0 = READ_ONCE(y);
spin_lock(&mylock);
r1 = READ_ONCE(x);
spin_unlock(&mylock);
}
void CPU1(void)
{
spin_lock(&mylock);
WRITE_ONCE(x, 1);
spin_unlock(&mylock);
WRITE_ONCE(y, 1);
}
This converse to the basic rule guarantees that if CPU0() acquires
mylock before CPU1(), then both r0 and r1 must be set to the value 0.
This also has the consequence that if the final value of r1 is equal
to 0, then the final value of r0 must also be equal to 0. In contrast,
the weaker rule would say nothing about the final value of r0.
These examples show only a single pair of CPUs, but the effects of the
locking basic rule extend across multiple acquisitions of a given lock
across multiple CPUs.
However, it is not necessarily the case that accesses ordered by
locking will be seen as ordered by CPUs not holding that lock.
Consider this example:
/* See Z6.0+pooncelock+pooncelock+pombonce.litmus. */
void CPU0(void)
{
spin_lock(&mylock);
WRITE_ONCE(x, 1);
WRITE_ONCE(y, 1);
spin_unlock(&mylock);
}
void CPU1(void)
{
spin_lock(&mylock);
r0 = READ_ONCE(y);
WRITE_ONCE(z, 1);
spin_unlock(&mylock);
}
void CPU2(void)
{
WRITE_ONCE(z, 2);
smp_mb();
r1 = READ_ONCE(x);
}
Counter-intuitive though it might be, it is quite possible to have
the final value of r0 be 1, the final value of z be 2, and the final
value of r1 be 0. The reason for this surprising outcome is that
CPU2() never acquired the lock, and thus did not benefit from the
lock's ordering properties.
Ordering can be extended to CPUs not holding the lock by careful use
of smp_mb__after_spinlock():
/* See Z6.0+pooncelock+poonceLock+pombonce.litmus. */
void CPU0(void)
{
spin_lock(&mylock);
WRITE_ONCE(x, 1);
WRITE_ONCE(y, 1);
spin_unlock(&mylock);
}
void CPU1(void)
{
spin_lock(&mylock);
smp_mb__after_spinlock();
r0 = READ_ONCE(y);
WRITE_ONCE(z, 1);
spin_unlock(&mylock);
}
void CPU2(void)
{
WRITE_ONCE(z, 2);
smp_mb();
r1 = READ_ONCE(x);
}
This addition of smp_mb__after_spinlock() strengthens the lock acquisition
sufficiently to rule out the counter-intuitive outcome.
Taking off the training wheels
==============================
This section looks at more complex examples, including message passing,
load buffering, release-acquire chains, store buffering.
Many classes of litmus tests have abbreviated names, which may be found
here: https://www.cl.cam.ac.uk/~pes20/ppc-supplemental/test6.pdf
Message passing (MP)
--------------------
The MP pattern has one CPU execute a pair of stores to a pair of variables
and another CPU execute a pair of loads from this same pair of variables,
but in the opposite order. The goal is to avoid the counter-intuitive
outcome in which the first load sees the value written by the second store
but the second load does not see the value written by the first store.
In the absence of any ordering, this goal may not be met, as can be seen
in the MP+poonceonces.litmus litmus test. This section therefore looks at
a number of ways of meeting this goal.
Release and acquire
~~~~~~~~~~~~~~~~~~~
Use of smp_store_release() and smp_load_acquire() is one way to force
the desired MP ordering. The general approach is shown below:
/* See MP+pooncerelease+poacquireonce.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
smp_store_release(&y, 1);
}
void CPU1(void)
{
r0 = smp_load_acquire(&y);
r1 = READ_ONCE(x);
}
The smp_store_release() macro orders any prior accesses against the
store, while the smp_load_acquire macro orders the load against any
subsequent accesses. Therefore, if the final value of r0 is the value 1,
the final value of r1 must also be the value 1.
The init_stack_slab() function in lib/stackdepot.c uses release-acquire
in this way to safely initialize of a slab of the stack. Working out
the mutual-exclusion design is left as an exercise for the reader.
Assign and dereference
~~~~~~~~~~~~~~~~~~~~~~
Use of rcu_assign_pointer() and rcu_dereference() is quite similar to the
use of smp_store_release() and smp_load_acquire(), except that both
rcu_assign_pointer() and rcu_dereference() operate on RCU-protected
pointers. The general approach is shown below:
/* See MP+onceassign+derefonce.litmus. */
int z;
int *y = &z;
int x;
void CPU0(void)
{
WRITE_ONCE(x, 1);
rcu_assign_pointer(y, &x);
}
void CPU1(void)
{
rcu_read_lock();
r0 = rcu_dereference(y);
r1 = READ_ONCE(*r0);
rcu_read_unlock();
}
In this example, if the final value of r0 is &x then the final value of
r1 must be 1.
The rcu_assign_pointer() macro has the same ordering properties as does
smp_store_release(), but the rcu_dereference() macro orders the load only
against later accesses that depend on the value loaded. A dependency
is present if the value loaded determines the address of a later access
(address dependency, as shown above), the value written by a later store
(data dependency), or whether or not a later store is executed in the
first place (control dependency). Note that the term "data dependency"
is sometimes casually used to cover both address and data dependencies.
In lib/prime_numbers.c, the expand_to_next_prime() function invokes
rcu_assign_pointer(), and the next_prime_number() function invokes
rcu_dereference(). This combination mediates access to a bit vector
that is expanded as additional primes are needed.
Write and read memory barriers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
It is usually better to use smp_store_release() instead of smp_wmb()
and to use smp_load_acquire() instead of smp_rmb(). However, the older
smp_wmb() and smp_rmb() APIs are still heavily used, so it is important
to understand their use cases. The general approach is shown below:
/* See MP+wmbonceonce+rmbonceonce.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
smp_wmb();
WRITE_ONCE(y, 1);
}
void CPU1(void)
{
r0 = READ_ONCE(y);
smp_rmb();
r1 = READ_ONCE(x);
}
The smp_wmb() macro orders prior stores against later stores, and the
smp_rmb() macro orders prior loads against later loads. Therefore, if
the final value of r0 is 1, the final value of r1 must also be 1.
The the xlog_state_switch_iclogs() function in fs/xfs/xfs_log.c contains
the following write-side code fragment:
log->l_curr_block -= log->l_logBBsize;
ASSERT(log->l_curr_block >= 0);
smp_wmb();
log->l_curr_cycle++;
And the xlog_valid_lsn() function in fs/xfs/xfs_log_priv.h contains
the corresponding read-side code fragment:
cur_cycle = ACCESS_ONCE(log->l_curr_cycle);
smp_rmb();
cur_block = ACCESS_ONCE(log->l_curr_block);
Alternatively, consider the following comment in function
perf_output_put_handle() in kernel/events/ring_buffer.c:
* kernel user
*
* if (LOAD ->data_tail) { LOAD ->data_head
* (A) smp_rmb() (C)
* STORE $data LOAD $data
* smp_wmb() (B) smp_mb() (D)
* STORE ->data_head STORE ->data_tail
* }
The B/C pairing is an example of the MP pattern using smp_wmb() on the
write side and smp_rmb() on the read side.
Of course, given that smp_mb() is strictly stronger than either smp_wmb()
or smp_rmb(), any code fragment that would work with smp_rmb() and
smp_wmb() would also work with smp_mb() replacing either or both of the
weaker barriers.
Load buffering (LB)
-------------------
The LB pattern has one CPU load from one variable and then store to a
second, while another CPU loads from the second variable and then stores
to the first. The goal is to avoid the counter-intuitive situation where
each load reads the value written by the other CPU's store. In the
absence of any ordering it is quite possible that this may happen, as
can be seen in the LB+poonceonces.litmus litmus test.
One way of avoiding the counter-intuitive outcome is through the use of a
control dependency paired with a full memory barrier:
/* See LB+ctrlonceonce+mbonceonce.litmus. */
void CPU0(void)
{
r0 = READ_ONCE(x);
if (r0)
WRITE_ONCE(y, 1);
}
void CPU1(void)
{
r1 = READ_ONCE(y);
smp_mb();
WRITE_ONCE(x, 1);
}
This pairing of a control dependency in CPU0() with a full memory
barrier in CPU1() prevents r0 and r1 from both ending up equal to 1.
The A/D pairing from the ring-buffer use case shown earlier also
illustrates LB. Here is a repeat of the comment in
perf_output_put_handle() in kernel/events/ring_buffer.c, showing a
control dependency on the kernel side and a full memory barrier on
the user side:
* kernel user
*
* if (LOAD ->data_tail) { LOAD ->data_head
* (A) smp_rmb() (C)
* STORE $data LOAD $data
* smp_wmb() (B) smp_mb() (D)
* STORE ->data_head STORE ->data_tail
* }
*
* Where A pairs with D, and B pairs with C.
The kernel's control dependency between the load from ->data_tail
and the store to data combined with the user's full memory barrier
between the load from data and the store to ->data_tail prevents
the counter-intuitive outcome where the kernel overwrites the data
before the user gets done loading it.
Release-acquire chains
----------------------
Release-acquire chains are a low-overhead, flexible, and easy-to-use
method of maintaining order. However, they do have some limitations that
need to be fully understood. Here is an example that maintains order:
/* See ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
smp_store_release(&y, 1);
}
void CPU1(void)
{
r0 = smp_load_acquire(y);
smp_store_release(&z, 1);
}
void CPU2(void)
{
r1 = smp_load_acquire(z);
r2 = READ_ONCE(x);
}
In this case, if r0 and r1 both have final values of 1, then r2 must
also have a final value of 1.
The ordering in this example is stronger than it needs to be. For
example, ordering would still be preserved if CPU1()'s smp_load_acquire()
invocation was replaced with READ_ONCE().
It is tempting to assume that CPU0()'s store to x is globally ordered
before CPU1()'s store to z, but this is not the case:
/* See Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
smp_store_release(&y, 1);
}
void CPU1(void)
{
r0 = smp_load_acquire(y);
smp_store_release(&z, 1);
}
void CPU2(void)
{
WRITE_ONCE(z, 2);
smp_mb();
r1 = READ_ONCE(x);
}
One might hope that if the final value of r0 is 1 and the final value
of z is 2, then the final value of r1 must also be 1, but it really is
possible for r1 to have the final value of 0. The reason, of course,
is that in this version, CPU2() is not part of the release-acquire chain.
This situation is accounted for in the rules of thumb below.
Despite this limitation, release-acquire chains are low-overhead as
well as simple and powerful, at least as memory-ordering mechanisms go.
Store buffering
---------------
Store buffering can be thought of as upside-down load buffering, so
that one CPU first stores to one variable and then loads from a second,
while another CPU stores to the second variable and then loads from the
first. Preserving order requires nothing less than full barriers:
/* See SB+mbonceonces.litmus. */
void CPU0(void)
{
WRITE_ONCE(x, 1);
smp_mb();
r0 = READ_ONCE(y);
}
void CPU1(void)
{
WRITE_ONCE(y, 1);
smp_mb();
r1 = READ_ONCE(x);
}
Omitting either smp_mb() will allow both r0 and r1 to have final
values of 0, but providing both full barriers as shown above prevents
this counter-intuitive outcome.
This pattern most famously appears as part of Dekker's locking
algorithm, but it has a much more practical use within the Linux kernel
of ordering wakeups. The following comment taken from waitqueue_active()
in include/linux/wait.h shows the canonical pattern:
* CPU0 - waker CPU1 - waiter
*
* for (;;) {
* @cond = true; prepare_to_wait(&wq_head, &wait, state);
* smp_mb(); // smp_mb() from set_current_state()
* if (waitqueue_active(wq_head)) if (@cond)
* wake_up(wq_head); break;
* schedule();
* }
* finish_wait(&wq_head, &wait);
On CPU0, the store is to @cond and the load is in waitqueue_active().
On CPU1, prepare_to_wait() contains both a store to wq_head and a call
to set_current_state(), which contains an smp_mb() barrier; the load is
"if (@cond)". The full barriers prevent the undesirable outcome where
CPU1 puts the waiting task to sleep and CPU0 fails to wake it up.
Note that use of locking can greatly simplify this pattern.
Rules of thumb
==============
There might seem to be no pattern governing what ordering primitives are
needed in which situations, but this is not the case. There is a pattern
based on the relation between the accesses linking successive CPUs in a
given litmus test. There are three types of linkage:
1. Write-to-read, where the next CPU reads the value that the
previous CPU wrote. The LB litmus-test patterns contain only
this type of relation. In formal memory-modeling texts, this
relation is called "reads-from" and is usually abbreviated "rf".
2. Read-to-write, where the next CPU overwrites the value that the
previous CPU read. The SB litmus test contains only this type
of relation. In formal memory-modeling texts, this relation is
often called "from-reads" and is sometimes abbreviated "fr".
3. Write-to-write, where the next CPU overwrites the value written
by the previous CPU. The Z6.0 litmus test pattern contains a
write-to-write relation between the last access of CPU1() and
the first access of CPU2(). In formal memory-modeling texts,
this relation is often called "coherence order" and is sometimes
abbreviated "co". In the C++ standard, it is instead called
"modification order" and often abbreviated "mo".
The strength of memory ordering required for a given litmus test to
avoid a counter-intuitive outcome depends on the types of relations
linking the memory accesses for the outcome in question:
o If all links are write-to-read links, then the weakest
possible ordering within each CPU suffices. For example, in
the LB litmus test, a control dependency was enough to do the
job.
o If all but one of the links are write-to-read links, then a
release-acquire chain suffices. Both the MP and the ISA2
litmus tests illustrate this case.
o If more than one of the links are something other than
write-to-read links, then a full memory barrier is required
between each successive pair of non-write-to-read links. This
case is illustrated by the Z6.0 litmus tests, both in the
locking and in the release-acquire sections.
However, if you find yourself having to stretch these rules of thumb
to fit your situation, you should consider creating a litmus test and
running it on the model.

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This document provides background reading for memory models and related
tools. These documents are aimed at kernel hackers who are interested
in memory models.
Hardware manuals and models
===========================
o SPARC International Inc. (Ed.). 1994. "The SPARC Architecture
Reference Manual Version 9". SPARC International Inc.
o Compaq Computer Corporation (Ed.). 2002. "Alpha Architecture
Reference Manual". Compaq Computer Corporation.
o Intel Corporation (Ed.). 2002. "A Formal Specification of Intel
Itanium Processor Family Memory Ordering". Intel Corporation.
o Intel Corporation (Ed.). 2002. "Intel 64 and IA-32 Architectures
Software Developer’s Manual". Intel Corporation.
o Peter Sewell, Susmit Sarkar, Scott Owens, Francesco Zappa Nardelli,
and Magnus O. Myreen. 2010. "x86-TSO: A Rigorous and Usable
Programmer's Model for x86 Multiprocessors". Commun. ACM 53, 7
(July, 2010), 89-97. http://doi.acm.org/10.1145/1785414.1785443
o IBM Corporation (Ed.). 2009. "Power ISA Version 2.06". IBM
Corporation.
o ARM Ltd. (Ed.). 2009. "ARM Barrier Litmus Tests and Cookbook".
ARM Ltd.
o Susmit Sarkar, Peter Sewell, Jade Alglave, Luc Maranget, and
Derek Williams. 2011. "Understanding POWER Multiprocessors". In
Proceedings of the 32Nd ACM SIGPLAN Conference on Programming
Language Design and Implementation (PLDI ’11). ACM, New York,
NY, USA, 175–186.
o Susmit Sarkar, Kayvan Memarian, Scott Owens, Mark Batty,
Peter Sewell, Luc Maranget, Jade Alglave, and Derek Williams.
2012. "Synchronising C/C++ and POWER". In Proceedings of the 33rd
ACM SIGPLAN Conference on Programming Language Design and
Implementation (PLDI '12). ACM, New York, NY, USA, 311-322.
o ARM Ltd. (Ed.). 2014. "ARM Architecture Reference Manual (ARMv8,
for ARMv8-A architecture profile)". ARM Ltd.
o Imagination Technologies, LTD. 2015. "MIPS(R) Architecture
For Programmers, Volume II-A: The MIPS64(R) Instruction,
Set Reference Manual". Imagination Technologies,
LTD. https://imgtec.com/?do-download=4302.
o Shaked Flur, Kathryn E. Gray, Christopher Pulte, Susmit
Sarkar, Ali Sezgin, Luc Maranget, Will Deacon, and Peter
Sewell. 2016. "Modelling the ARMv8 Architecture, Operationally:
Concurrency and ISA". In Proceedings of the 43rd Annual ACM
SIGPLAN-SIGACT Symposium on Principles of Programming Languages
(POPL ’16). ACM, New York, NY, USA, 608–621.
o Shaked Flur, Susmit Sarkar, Christopher Pulte, Kyndylan Nienhuis,
Luc Maranget, Kathryn E. Gray, Ali Sezgin, Mark Batty, and Peter
Sewell. 2017. "Mixed-size Concurrency: ARM, POWER, C/C++11,
and SC". In Proceedings of the 44th ACM SIGPLAN Symposium on
Principles of Programming Languages (POPL 2017). ACM, New York,
NY, USA, 429–442.
Linux-kernel memory model
=========================
o Andrea Parri, Alan Stern, Luc Maranget, Paul E. McKenney,
and Jade Alglave. 2017. "A formal model of
Linux-kernel memory ordering - companion webpage".
http://moscova.inria.fr/∼maranget/cats7/linux/. (2017). [Online;
accessed 30-January-2017].
o Jade Alglave, Luc Maranget, Paul E. McKenney, Andrea Parri, and
Alan Stern. 2017. "A formal kernel memory-ordering model (part 1)"
Linux Weekly News. https://lwn.net/Articles/718628/
o Jade Alglave, Luc Maranget, Paul E. McKenney, Andrea Parri, and
Alan Stern. 2017. "A formal kernel memory-ordering model (part 2)"
Linux Weekly News. https://lwn.net/Articles/720550/
Memory-model tooling
====================
o Daniel Jackson. 2002. "Alloy: A Lightweight Object Modelling
Notation". ACM Trans. Softw. Eng. Methodol. 11, 2 (April 2002),
256–290. http://doi.acm.org/10.1145/505145.505149
o Jade Alglave, Luc Maranget, and Michael Tautschnig. 2014. "Herding
Cats: Modelling, Simulation, Testing, and Data Mining for Weak
Memory". ACM Trans. Program. Lang. Syst. 36, 2, Article 7 (July
2014), 7:1–7:74 pages.
o Jade Alglave, Patrick Cousot, and Luc Maranget. 2016. "Syntax and
semantics of the weak consistency model specification language
cat". CoRR abs/1608.07531 (2016). http://arxiv.org/abs/1608.07531
Memory-model comparisons
========================
o Paul E. McKenney, Ulrich Weigand, Andrea Parri, and Boqun
Feng. 2016. "Linux-Kernel Memory Model". (6 June 2016).
http://open-std.org/JTC1/SC22/WG21/docs/papers/2016/p0124r2.html.

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LINUX KERNEL MEMORY MODEL
M: Alan Stern <stern@rowland.harvard.edu>
M: Andrea Parri <parri.andrea@gmail.com>
M: Will Deacon <will.deacon@arm.com>
M: Peter Zijlstra <peterz@infradead.org>
M: Boqun Feng <boqun.feng@gmail.com>
M: Nicholas Piggin <npiggin@gmail.com>
M: David Howells <dhowells@redhat.com>
M: Jade Alglave <j.alglave@ucl.ac.uk>
M: Luc Maranget <luc.maranget@inria.fr>
M: "Paul E. McKenney" <paulmck@linux.vnet.ibm.com>
L: linux-kernel@vger.kernel.org
S: Supported
T: git git://git.kernel.org/pub/scm/linux/kernel/git/paulmck/linux-rcu.git
F: tools/memory-model/

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=========================
LINUX KERNEL MEMORY MODEL
=========================
============
INTRODUCTION
============
This directory contains the memory model of the Linux kernel, written
in the "cat" language and executable by the (externally provided)
"herd7" simulator, which exhaustively explores the state space of
small litmus tests.
In addition, the "klitmus7" tool (also externally provided) may be used
to convert a litmus test to a Linux kernel module, which in turn allows
that litmus test to be exercised within the Linux kernel.
============
REQUIREMENTS
============
The "herd7" and "klitmus7" tools must be downloaded separately:
https://github.com/herd/herdtools7
See "herdtools7/INSTALL.md" for installation instructions.
Alternatively, Abhishek Bhardwaj has kindly provided a Docker image
of these tools at "abhishek40/memory-model". Abhishek suggests the
following commands to install and use this image:
- Users should install Docker for their distribution.
- docker run -itd abhishek40/memory-model
- docker attach <id-emitted-from-the-previous-command>
Gentoo users might wish to make use of Patrick McLean's package:
https://gitweb.gentoo.org/repo/gentoo.git/tree/dev-util/herdtools7
These packages may not be up-to-date with respect to the GitHub
repository.
==================
BASIC USAGE: HERD7
==================
The memory model is used, in conjunction with "herd7", to exhaustively
explore the state space of small litmus tests.
For example, to run SB+mbonceonces.litmus against the memory model:
$ herd7 -conf linux-kernel.cfg litmus-tests/SB+mbonceonces.litmus
Here is the corresponding output:
Test SB+mbonceonces Allowed
States 3
0:r0=0; 1:r0=1;
0:r0=1; 1:r0=0;
0:r0=1; 1:r0=1;
No
Witnesses
Positive: 0 Negative: 3
Condition exists (0:r0=0 /\ 1:r0=0)
Observation SB+mbonceonces Never 0 3
Time SB+mbonceonces 0.01
Hash=d66d99523e2cac6b06e66f4c995ebb48
The "Positive: 0 Negative: 3" and the "Never 0 3" each indicate that
this litmus test's "exists" clause can not be satisfied.
See "herd7 -help" or "herdtools7/doc/" for more information.
=====================
BASIC USAGE: KLITMUS7
=====================
The "klitmus7" tool converts a litmus test into a Linux kernel module,
which may then be loaded and run.
For example, to run SB+mbonceonces.litmus against hardware:
$ mkdir mymodules
$ klitmus7 -o mymodules litmus-tests/SB+mbonceonces.litmus
$ cd mymodules ; make
$ sudo sh run.sh
The corresponding output includes:
Test SB+mbonceonces Allowed
Histogram (3 states)
644580 :>0:r0=1; 1:r0=0;
644328 :>0:r0=0; 1:r0=1;
711092 :>0:r0=1; 1:r0=1;
No
Witnesses
Positive: 0, Negative: 2000000
Condition exists (0:r0=0 /\ 1:r0=0) is NOT validated
Hash=d66d99523e2cac6b06e66f4c995ebb48
Observation SB+mbonceonces Never 0 2000000
Time SB+mbonceonces 0.16
The "Positive: 0 Negative: 2000000" and the "Never 0 2000000" indicate
that during two million trials, the state specified in this litmus
test's "exists" clause was not reached.
And, as with "herd7", please see "klitmus7 -help" or "herdtools7/doc/"
for more information.
====================
DESCRIPTION OF FILES
====================
Documentation/cheatsheet.txt
Quick-reference guide to the Linux-kernel memory model.
Documentation/explanation.txt
Describes the memory model in detail.
Documentation/recipes.txt
Lists common memory-ordering patterns.
Documentation/references.txt
Provides background reading.
linux-kernel.bell
Categorizes the relevant instructions, including memory
references, memory barriers, atomic read-modify-write operations,
lock acquisition/release, and RCU operations.
More formally, this file (1) lists the subtypes of the various
event types used by the memory model and (2) performs RCU
read-side critical section nesting analysis.
linux-kernel.cat
Specifies what reorderings are forbidden by memory references,
memory barriers, atomic read-modify-write operations, and RCU.
More formally, this file specifies what executions are forbidden
by the memory model. Allowed executions are those which
satisfy the model's "coherence", "atomic", "happens-before",
"propagation", and "rcu" axioms, which are defined in the file.
linux-kernel.cfg
Convenience file that gathers the common-case herd7 command-line
arguments.
linux-kernel.def
Maps from C-like syntax to herd7's internal litmus-test
instruction-set architecture.
litmus-tests
Directory containing a few representative litmus tests, which
are listed in litmus-tests/README. A great deal more litmus
tests are available at https://github.com/paulmckrcu/litmus.
lock.cat
Provides a front-end analysis of lock acquisition and release,
for example, associating a lock acquisition with the preceding
and following releases and checking for self-deadlock.
More formally, this file defines a performance-enhanced scheme
for generation of the possible reads-from and coherence order
relations on the locking primitives.
README
This file.
===========
LIMITATIONS
===========
The Linux-kernel memory model has the following limitations:
1. Compiler optimizations are not modeled. Of course, the use
of READ_ONCE() and WRITE_ONCE() limits the compiler's ability
to optimize, but there is Linux-kernel code that uses bare C
memory accesses. Handling this code is on the to-do list.
For more information, see Documentation/explanation.txt (in
particular, the "THE PROGRAM ORDER RELATION: po AND po-loc"
and "A WARNING" sections).
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.
The "herd7" tool has some additional limitations of its own, apart from
the memory model:
1. Non-trivial data structures such as arrays or structures are
not supported. However, pointers are supported, allowing trivial
linked lists to be constructed.
2. 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.

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// SPDX-License-Identifier: GPL-2.0+
(*
* Copyright (C) 2015 Jade Alglave <j.alglave@ucl.ac.uk>,
* Copyright (C) 2016 Luc Maranget <luc.maranget@inria.fr> for Inria
* Copyright (C) 2017 Alan Stern <stern@rowland.harvard.edu>,
* Andrea Parri <parri.andrea@gmail.com>
*
* An earlier version of this file appears in the companion webpage for
* "Frightening small children and disconcerting grown-ups: Concurrency
* in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
* which is to appear in ASPLOS 2018.
*)
"Linux kernel memory model"
enum Accesses = 'once (*READ_ONCE,WRITE_ONCE,ACCESS_ONCE*) ||
'release (*smp_store_release*) ||
'acquire (*smp_load_acquire*) ||
'noreturn (* R of non-return RMW *)
instructions R[{'once,'acquire,'noreturn}]
instructions W[{'once,'release}]
instructions RMW[{'once,'acquire,'release}]
enum Barriers = 'wmb (*smp_wmb*) ||
'rmb (*smp_rmb*) ||
'mb (*smp_mb*) ||
'rb_dep (*smp_read_barrier_depends*) ||
'rcu-lock (*rcu_read_lock*) ||
'rcu-unlock (*rcu_read_unlock*) ||
'sync-rcu (*synchronize_rcu*) ||
'before_atomic (*smp_mb__before_atomic*) ||
'after_atomic (*smp_mb__after_atomic*) ||
'after_spinlock (*smp_mb__after_spinlock*)
instructions F[Barriers]
(* Compute matching pairs of nested Rcu-lock and Rcu-unlock *)
let matched = let rec
unmatched-locks = Rcu-lock \ domain(matched)
and unmatched-unlocks = Rcu-unlock \ range(matched)
and unmatched = unmatched-locks | unmatched-unlocks
and unmatched-po = [unmatched] ; po ; [unmatched]
and unmatched-locks-to-unlocks =
[unmatched-locks] ; po ; [unmatched-unlocks]
and matched = matched | (unmatched-locks-to-unlocks \
(unmatched-po ; unmatched-po))
in matched
(* Validate nesting *)
flag ~empty Rcu-lock \ domain(matched) as unbalanced-rcu-locking
flag ~empty Rcu-unlock \ range(matched) as unbalanced-rcu-locking
(* Outermost level of nesting only *)
let crit = matched \ (po^-1 ; matched ; po^-1)

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// SPDX-License-Identifier: GPL-2.0+
(*
* Copyright (C) 2015 Jade Alglave <j.alglave@ucl.ac.uk>,
* Copyright (C) 2016 Luc Maranget <luc.maranget@inria.fr> for Inria
* Copyright (C) 2017 Alan Stern <stern@rowland.harvard.edu>,
* Andrea Parri <parri.andrea@gmail.com>
*
* An earlier version of this file appears in the companion webpage for
* "Frightening small children and disconcerting grown-ups: Concurrency
* in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
* which is to appear in ASPLOS 2018.
*)
"Linux kernel memory model"
(*
* File "lock.cat" handles locks and is experimental.
* It can be replaced by include "cos.cat" for tests that do not use locks.
*)
include "lock.cat"
(*******************)
(* Basic relations *)
(*******************)
(* Fences *)
let rb-dep = [R] ; fencerel(Rb_dep) ; [R]
let rmb = [R \ Noreturn] ; fencerel(Rmb) ; [R \ Noreturn]
let wmb = [W] ; fencerel(Wmb) ; [W]
let mb = ([M] ; fencerel(Mb) ; [M]) |
([M] ; fencerel(Before_atomic) ; [RMW] ; po? ; [M]) |
([M] ; po? ; [RMW] ; fencerel(After_atomic) ; [M]) |
([M] ; po? ; [LKW] ; fencerel(After_spinlock) ; [M])
let gp = po ; [Sync-rcu] ; po?
let strong-fence = mb | gp
(* Release Acquire *)
let acq-po = [Acquire] ; po ; [M]
let po-rel = [M] ; po ; [Release]
let rfi-rel-acq = [Release] ; rfi ; [Acquire]
(**********************************)
(* Fundamental coherence ordering *)
(**********************************)
(* Sequential Consistency Per Variable *)
let com = rf | co | fr
acyclic po-loc | com as coherence
(* Atomic Read-Modify-Write *)
empty rmw & (fre ; coe) as atomic
(**********************************)
(* Instruction execution ordering *)
(**********************************)
(* Preserved Program Order *)
let dep = addr | data
let rwdep = (dep | ctrl) ; [W]
let overwrite = co | fr
let to-w = rwdep | (overwrite & int)
let rrdep = addr | (dep ; rfi)
let strong-rrdep = rrdep+ & rb-dep
let to-r = strong-rrdep | rfi-rel-acq
let fence = strong-fence | wmb | po-rel | rmb | acq-po
let ppo = rrdep* ; (to-r | to-w | fence)
(* Propagation: Ordering from release operations and strong fences. *)
let A-cumul(r) = rfe? ; r
let cumul-fence = A-cumul(strong-fence | po-rel) | wmb
let prop = (overwrite & ext)? ; cumul-fence* ; rfe?
(*
* Happens Before: Ordering from the passage of time.
* No fences needed here for prop because relation confined to one process.
*)
let hb = ppo | rfe | ((prop \ id) & int)
acyclic hb as happens-before
(****************************************)
(* Write and fence propagation ordering *)
(****************************************)
(* Propagation: Each non-rf link needs a strong fence. *)
let pb = prop ; strong-fence ; hb*
acyclic pb as propagation
(*******)
(* RCU *)
(*******)
(*
* Effect of read-side critical section proceeds from the rcu_read_lock()
* onward on the one hand and from the rcu_read_unlock() backwards on the
* other hand.
*)
let rscs = po ; crit^-1 ; po?
(*
* The synchronize_rcu() strong fence is special in that it can order not
* one but two non-rf relations, but only in conjunction with an RCU
* read-side critical section.
*)
let link = hb* ; pb* ; prop
(* Chains that affect the RCU grace-period guarantee *)
let gp-link = gp ; link
let rscs-link = rscs ; link
(*
* A cycle containing at least as many grace periods as RCU read-side
* critical sections is forbidden.
*)
let rec rcu-path =
gp-link |
(gp-link ; rscs-link) |
(rscs-link ; gp-link) |
(rcu-path ; rcu-path) |
(gp-link ; rcu-path ; rscs-link) |
(rscs-link ; rcu-path ; gp-link)
irreflexive rcu-path as rcu

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macros linux-kernel.def
bell linux-kernel.bell
model linux-kernel.cat
graph columns
squished true
showevents noregs
movelabel true
fontsize 8
xscale 2.0
yscale 1.5
arrowsize 0.8
showinitrf false
showfinalrf false
showinitwrites false
splines spline
pad 0.1
edgeattr hb,color,indigo
edgeattr co,color,blue
edgeattr mb,color,darkgreen
edgeattr wmb,color,darkgreen
edgeattr rmb,color,darkgreen

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// SPDX-License-Identifier: GPL-2.0+
//
// An earlier version of this file appears in the companion webpage for
// "Frightening small children and disconcerting grown-ups: Concurrency
// in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
// which is to appear in ASPLOS 2018.
// ONCE
READ_ONCE(X) __load{once}(X)
WRITE_ONCE(X,V) { __store{once}(X,V); }
// Release Acquire and friends
smp_store_release(X,V) { __store{release}(*X,V); }
smp_load_acquire(X) __load{acquire}(*X)
rcu_assign_pointer(X,V) { __store{release}(X,V); }
lockless_dereference(X) __load{lderef}(X)
rcu_dereference(X) __load{deref}(X)
// Fences
smp_mb() { __fence{mb} ; }
smp_rmb() { __fence{rmb} ; }
smp_wmb() { __fence{wmb} ; }
smp_read_barrier_depends() { __fence{rb_dep}; }
smp_mb__before_atomic() { __fence{before_atomic} ; }
smp_mb__after_atomic() { __fence{after_atomic} ; }
smp_mb__after_spinlock() { __fence{after_spinlock} ; }
// Exchange
xchg(X,V) __xchg{mb}(X,V)
xchg_relaxed(X,V) __xchg{once}(X,V)
xchg_release(X,V) __xchg{release}(X,V)
xchg_acquire(X,V) __xchg{acquire}(X,V)
cmpxchg(X,V,W) __cmpxchg{mb}(X,V,W)
cmpxchg_relaxed(X,V,W) __cmpxchg{once}(X,V,W)
cmpxchg_acquire(X,V,W) __cmpxchg{acquire}(X,V,W)
cmpxchg_release(X,V,W) __cmpxchg{release}(X,V,W)
// Spinlocks
spin_lock(X) { __lock(X) ; }
spin_unlock(X) { __unlock(X) ; }
spin_trylock(X) __trylock(X)
// RCU
rcu_read_lock() { __fence{rcu-lock}; }
rcu_read_unlock() { __fence{rcu-unlock};}
synchronize_rcu() { __fence{sync-rcu}; }
synchronize_rcu_expedited() { __fence{sync-rcu}; }
// Atomic
atomic_read(X) READ_ONCE(*X)
atomic_set(X,V) { WRITE_ONCE(*X,V) ; }
atomic_read_acquire(X) smp_load_acquire(X)
atomic_set_release(X,V) { smp_store_release(X,V); }
atomic_add(V,X) { __atomic_op(X,+,V) ; }
atomic_sub(V,X) { __atomic_op(X,-,V) ; }
atomic_inc(X) { __atomic_op(X,+,1) ; }
atomic_dec(X) { __atomic_op(X,-,1) ; }
atomic_add_return(V,X) __atomic_op_return{mb}(X,+,V)
atomic_add_return_relaxed(V,X) __atomic_op_return{once}(X,+,V)
atomic_add_return_acquire(V,X) __atomic_op_return{acquire}(X,+,V)
atomic_add_return_release(V,X) __atomic_op_return{release}(X,+,V)
atomic_fetch_add(V,X) __atomic_fetch_op{mb}(X,+,V)
atomic_fetch_add_relaxed(V,X) __atomic_fetch_op{once}(X,+,V)
atomic_fetch_add_acquire(V,X) __atomic_fetch_op{acquire}(X,+,V)
atomic_fetch_add_release(V,X) __atomic_fetch_op{release}(X,+,V)
atomic_inc_return(X) __atomic_op_return{mb}(X,+,1)
atomic_inc_return_relaxed(X) __atomic_op_return{once}(X,+,1)
atomic_inc_return_acquire(X) __atomic_op_return{acquire}(X,+,1)
atomic_inc_return_release(X) __atomic_op_return{release}(X,+,1)
atomic_fetch_inc(X) __atomic_fetch_op{mb}(X,+,1)
atomic_fetch_inc_relaxed(X) __atomic_fetch_op{once}(X,+,1)
atomic_fetch_inc_acquire(X) __atomic_fetch_op{acquire}(X,+,1)
atomic_fetch_inc_release(X) __atomic_fetch_op{release}(X,+,1)
atomic_sub_return(V,X) __atomic_op_return{mb}(X,-,V)
atomic_sub_return_relaxed(V,X) __atomic_op_return{once}(X,-,V)
atomic_sub_return_acquire(V,X) __atomic_op_return{acquire}(X,-,V)
atomic_sub_return_release(V,X) __atomic_op_return{release}(X,-,V)
atomic_fetch_sub(V,X) __atomic_fetch_op{mb}(X,-,V)
atomic_fetch_sub_relaxed(V,X) __atomic_fetch_op{once}(X,-,V)
atomic_fetch_sub_acquire(V,X) __atomic_fetch_op{acquire}(X,-,V)
atomic_fetch_sub_release(V,X) __atomic_fetch_op{release}(X,-,V)
atomic_dec_return(X) __atomic_op_return{mb}(X,-,1)
atomic_dec_return_relaxed(X) __atomic_op_return{once}(X,-,1)
atomic_dec_return_acquire(X) __atomic_op_return{acquire}(X,-,1)
atomic_dec_return_release(X) __atomic_op_return{release}(X,-,1)
atomic_fetch_dec(X) __atomic_fetch_op{mb}(X,-,1)
atomic_fetch_dec_relaxed(X) __atomic_fetch_op{once}(X,-,1)
atomic_fetch_dec_acquire(X) __atomic_fetch_op{acquire}(X,-,1)
atomic_fetch_dec_release(X) __atomic_fetch_op{release}(X,-,1)
atomic_xchg(X,V) __xchg{mb}(X,V)
atomic_xchg_relaxed(X,V) __xchg{once}(X,V)
atomic_xchg_release(X,V) __xchg{release}(X,V)
atomic_xchg_acquire(X,V) __xchg{acquire}(X,V)
atomic_cmpxchg(X,V,W) __cmpxchg{mb}(X,V,W)
atomic_cmpxchg_relaxed(X,V,W) __cmpxchg{once}(X,V,W)
atomic_cmpxchg_acquire(X,V,W) __cmpxchg{acquire}(X,V,W)
atomic_cmpxchg_release(X,V,W) __cmpxchg{release}(X,V,W)
atomic_sub_and_test(V,X) __atomic_op_return{mb}(X,-,V) == 0
atomic_dec_and_test(X) __atomic_op_return{mb}(X,-,1) == 0
atomic_inc_and_test(X) __atomic_op_return{mb}(X,+,1) == 0
atomic_add_negative(V,X) __atomic_op_return{mb}(X,+,V) < 0

19
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C CoRR+poonceonce+Once
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
}
P1(int *x)
{
int r0;
int r1;
r0 = READ_ONCE(*x);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0)

18
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C CoRW+poonceonce+Once
{}
P0(int *x)
{
int r0;
r0 = READ_ONCE(*x);
WRITE_ONCE(*x, 1);
}
P1(int *x)
{
WRITE_ONCE(*x, 2);
}
exists (x=2 /\ 0:r0=2)

18
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C CoWR+poonceonce+Once
{}
P0(int *x)
{
int r0;
WRITE_ONCE(*x, 1);
r0 = READ_ONCE(*x);
}
P1(int *x)
{
WRITE_ONCE(*x, 2);
}
exists (x=1 /\ 0:r0=2)

11
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C CoWW+poonceonce
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
WRITE_ONCE(*x, 2);
}
exists (x=1)

35
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C IRIW+mbonceonces+OnceOnce
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
}
P1(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*x);
smp_mb();
r1 = READ_ONCE(*y);
}
P2(int *y)
{
WRITE_ONCE(*y, 1);
}
P3(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
smp_mb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0 /\ 3:r0=1 /\ 3:r1=0)

33
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C IRIW+poonceonces+OnceOnce
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
}
P1(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*x);
r1 = READ_ONCE(*y);
}
P2(int *y)
{
WRITE_ONCE(*y, 1);
}
P3(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0 /\ 3:r0=1 /\ 3:r1=0)

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C ISA2+poonceonces
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
WRITE_ONCE(*y, 1);
}
P1(int *y, int *z)
{
int r0;
r0 = READ_ONCE(*y);
WRITE_ONCE(*z, 1);
}
P2(int *x, int *z)
{
int r0;
int r1;
r0 = READ_ONCE(*z);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

28
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C ISA2+pooncerelease+poacquirerelease+poacquireonce
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
smp_store_release(y, 1);
}
P1(int *y, int *z)
{
int r0;
r0 = smp_load_acquire(y);
smp_store_release(z, 1);
}
P2(int *x, int *z)
{
int r0;
int r1;
r0 = smp_load_acquire(z);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

23
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C LB+ctrlonceonce+mbonceonce
{}
P0(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*x);
if (r0)
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*y);
smp_mb();
WRITE_ONCE(*x, 1);
}
exists (0:r0=1 /\ 1:r0=1)

21
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C LB+poacquireonce+pooncerelease
{}
P0(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*x);
smp_store_release(y, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = smp_load_acquire(y);
WRITE_ONCE(*x, 1);
}
exists (0:r0=1 /\ 1:r0=1)

21
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C LB+poonceonces
{}
P0(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*x);
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*y);
WRITE_ONCE(*x, 1);
}
exists (0:r0=1 /\ 1:r0=1)

25
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C MP+onceassign+derefonce.litmus
{
y=z;
z=0;
}
P0(int *x, int **y)
{
WRITE_ONCE(*x, 1);
rcu_assign_pointer(*y, x);
}
P1(int *x, int **y)
{
int *r0;
int r1;
rcu_read_lock();
r0 = rcu_dereference(*y);
r1 = READ_ONCE(*r0);
rcu_read_unlock();
}
exists (1:r0=x /\ 1:r1=0)

24
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C MP+polocks
{}
P0(int *x, int *y, spinlock_t *mylock)
{
WRITE_ONCE(*x, 1);
spin_lock(mylock);
WRITE_ONCE(*y, 1);
spin_unlock(mylock);
}
P1(int *x, int *y, spinlock_t *mylock)
{
int r0;
int r1;
spin_lock(mylock);
r0 = READ_ONCE(*y);
spin_unlock(mylock);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0)

20
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C MP+poonceonces
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0)

20
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C MP+pooncerelease+poacquireonce
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
smp_store_release(y, 1);
}
P1(int *x, int *y)
{
int r0;
int r1;
r0 = smp_load_acquire(y);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0)

24
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C MP+porevlocks
{}
P0(int *x, int *y, spinlock_t *mylock)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
spin_lock(mylock);
r1 = READ_ONCE(*x);
spin_unlock(mylock);
}
P1(int *x, int *y, spinlock_t *mylock)
{
spin_lock(mylock);
WRITE_ONCE(*x, 1);
spin_unlock(mylock);
WRITE_ONCE(*y, 1);
}
exists (0:r0=1 /\ 0:r1=0)

22
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C MP+wmbonceonce+rmbonceonce
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
smp_wmb();
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
smp_rmb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 1:r1=0)

21
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C R+mbonceonces
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
smp_mb();
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
WRITE_ONCE(*y, 2);
smp_mb();
r0 = READ_ONCE(*x);
}
exists (y=2 /\ 1:r0=0)

19
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C R+poonceonces
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
WRITE_ONCE(*y, 2);
r0 = READ_ONCE(*x);
}
exists (y=2 /\ 1:r0=0)

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This directory contains the following litmus tests:
CoRR+poonceonce+Once.litmus
Test of read-read coherence, that is, whether or not two
successive reads from the same variable are ordered.
CoRW+poonceonce+Once.litmus
Test of read-write coherence, that is, whether or not a read
from a given variable followed by a write to that same variable
are ordered.
CoWR+poonceonce+Once.litmus
Test of write-read coherence, that is, whether or not a write
to a given variable followed by a read from that same variable
are ordered.
CoWW+poonceonce.litmus
Test of write-write coherence, that is, whether or not two
successive writes to the same variable are ordered.
IRIW+mbonceonces+OnceOnce.litmus
Test of independent reads from independent writes with smp_mb()
between each pairs of reads. In other words, is smp_mb()
sufficient to cause two different reading processes to agree on
the order of a pair of writes, where each write is to a different
variable by a different process.
IRIW+poonceonces+OnceOnce.litmus
Test of independent reads from independent writes with nothing
between each pairs of reads. In other words, is anything at all
needed to cause two different reading processes to agree on the
order of a pair of writes, where each write is to a different
variable by a different process.
ISA2+poonceonces.litmus
As below, but with store-release replaced with WRITE_ONCE()
and load-acquire replaced with READ_ONCE().
ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus
Can a release-acquire chain order a prior store against
a later load?
LB+ctrlonceonce+mbonceonce.litmus
Does a control dependency and an smp_mb() suffice for the
load-buffering litmus test, where each process reads from one
of two variables then writes to the other?
LB+poacquireonce+pooncerelease.litmus
Does a release-acquire pair suffice for the load-buffering
litmus test, where each process reads from one of two variables then
writes to the other?
LB+poonceonces.litmus
As above, but with store-release replaced with WRITE_ONCE()
and load-acquire replaced with READ_ONCE().
MP+onceassign+derefonce.litmus
As below, but with rcu_assign_pointer() and an rcu_dereference().
MP+polocks.litmus
As below, but with the second access of the writer process
and the first access of reader process protected by a lock.
MP+poonceonces.litmus
As below, but without the smp_rmb() and smp_wmb().
MP+pooncerelease+poacquireonce.litmus
As below, but with a release-acquire chain.
MP+porevlocks.litmus
As below, but with the first access of the writer process
and the second access of reader process protected by a lock.
MP+wmbonceonce+rmbonceonce.litmus
Does a smp_wmb() (between the stores) and an smp_rmb() (between
the loads) suffice for the message-passing litmus test, where one
process writes data and then a flag, and the other process reads
the flag and then the data. (This is similar to the ISA2 tests,
but with two processes instead of three.)
R+mbonceonces.litmus
This is the fully ordered (via smp_mb()) version of one of
the classic counterintuitive litmus tests that illustrates the
effects of store propagation delays.
R+poonceonces.litmus
As above, but without the smp_mb() invocations.
SB+mbonceonces.litmus
This is the fully ordered (again, via smp_mb() version of store
buffering, which forms the core of Dekker's mutual-exclusion
algorithm.
SB+poonceonces.litmus
As above, but without the smp_mb() invocations.
S+poonceonces.litmus
As below, but without the smp_wmb() and acquire load.
S+wmbonceonce+poacquireonce.litmus
Can a smp_wmb(), instead of a release, and an acquire order
a prior store against a subsequent store?
WRC+poonceonces+Once.litmus
WRC+pooncerelease+rmbonceonce+Once.litmus
These two are members of an extension of the MP litmus-test class
in which the first write is moved to a separate process.
Z6.0+pooncelock+pooncelock+pombonce.litmus
Is the ordering provided by a spin_unlock() and a subsequent
spin_lock() sufficient to make ordering apparent to accesses
by a process not holding the lock?
Z6.0+pooncelock+poonceLock+pombonce.litmus
As above, but with smp_mb__after_spinlock() immediately
following the spin_lock().
Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus
Is the ordering provided by a release-acquire chain sufficient
to make ordering apparent to accesses by a process that does
not participate in that release-acquire chain?
A great many more litmus tests are available here:
https://github.com/paulmckrcu/litmus

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C S+poonceonces
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 2);
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*y);
WRITE_ONCE(*x, 1);
}
exists (x=2 /\ 1:r0=1)

20
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C S+wmbonceonce+poacquireonce
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 2);
smp_wmb();
WRITE_ONCE(*y, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = smp_load_acquire(y);
WRITE_ONCE(*x, 1);
}
exists (x=2 /\ 1:r0=1)

23
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C SB+mbonceonces
{}
P0(int *x, int *y)
{
int r0;
WRITE_ONCE(*x, 1);
smp_mb();
r0 = READ_ONCE(*y);
}
P1(int *x, int *y)
{
int r0;
WRITE_ONCE(*y, 1);
smp_mb();
r0 = READ_ONCE(*x);
}
exists (0:r0=0 /\ 1:r0=0)

21
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C SB+poonceonces
{}
P0(int *x, int *y)
{
int r0;
WRITE_ONCE(*x, 1);
r0 = READ_ONCE(*y);
}
P1(int *x, int *y)
{
int r0;
WRITE_ONCE(*y, 1);
r0 = READ_ONCE(*x);
}
exists (0:r0=0 /\ 1:r0=0)

27
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C WRC+poonceonces+Once
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*x);
WRITE_ONCE(*y, 1);
}
P2(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

28
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C WRC+pooncerelease+rmbonceonce+Once
{}
P0(int *x)
{
WRITE_ONCE(*x, 1);
}
P1(int *x, int *y)
{
int r0;
r0 = READ_ONCE(*x);
smp_store_release(y, 1);
}
P2(int *x, int *y)
{
int r0;
int r1;
r0 = READ_ONCE(*y);
smp_rmb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ 2:r0=1 /\ 2:r1=0)

33
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C Z6.0+pooncelock+poonceLock+pombonce
{}
P0(int *x, int *y, spinlock_t *mylock)
{
spin_lock(mylock);
WRITE_ONCE(*x, 1);
WRITE_ONCE(*y, 1);
spin_unlock(mylock);
}
P1(int *y, int *z, spinlock_t *mylock)
{
int r0;
spin_lock(mylock);
smp_mb__after_spinlock();
r0 = READ_ONCE(*y);
WRITE_ONCE(*z, 1);
spin_unlock(mylock);
}
P2(int *x, int *z)
{
int r1;
WRITE_ONCE(*z, 2);
smp_mb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ z=2 /\ 2:r1=0)

32
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C Z6.0+pooncelock+pooncelock+pombonce
{}
P0(int *x, int *y, spinlock_t *mylock)
{
spin_lock(mylock);
WRITE_ONCE(*x, 1);
WRITE_ONCE(*y, 1);
spin_unlock(mylock);
}
P1(int *y, int *z, spinlock_t *mylock)
{
int r0;
spin_lock(mylock);
r0 = READ_ONCE(*y);
WRITE_ONCE(*z, 1);
spin_unlock(mylock);
}
P2(int *x, int *z)
{
int r1;
WRITE_ONCE(*z, 2);
smp_mb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ z=2 /\ 2:r1=0)

28
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C Z6.0+pooncerelease+poacquirerelease+mbonceonce
{}
P0(int *x, int *y)
{
WRITE_ONCE(*x, 1);
smp_store_release(y, 1);
}
P1(int *y, int *z)
{
int r0;
r0 = smp_load_acquire(y);
smp_store_release(z, 1);
}
P2(int *x, int *z)
{
int r1;
WRITE_ONCE(*z, 2);
smp_mb();
r1 = READ_ONCE(*x);
}
exists (1:r0=1 /\ z=2 /\ 2:r1=0)

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// SPDX-License-Identifier: GPL-2.0+
(*
* Copyright (C) 2016 Luc Maranget <luc.maranget@inria.fr> for Inria
* Copyright (C) 2017 Alan Stern <stern@rowland.harvard.edu>
*)
(* Generate coherence orders and handle lock operations *)
include "cross.cat"
(* From lock reads to their partner lock writes *)
let lk-rmw = ([LKR] ; po-loc ; [LKW]) \ (po ; po)
let rmw = rmw | lk-rmw
(*
* A paired LKR must always see an unlocked value; spin_lock() calls nested
* inside a critical section (for the same lock) always deadlock.
*)
empty ([LKW] ; po-loc ; [domain(lk-rmw)]) \ (po-loc ; [UL] ; po-loc)
as lock-nest
(* The litmus test is invalid if an LKW event is not part of an RMW pair *)
flag ~empty LKW \ range(lk-rmw) as unpaired-LKW
(* This will be allowed if we implement spin_is_locked() *)
flag ~empty LKR \ domain(lk-rmw) as unpaired-LKR
(* There should be no R or W accesses to spinlocks *)
let ALL-LOCKS = LKR | LKW | UL | LF
flag ~empty [M \ IW] ; loc ; [ALL-LOCKS] as mixed-lock-accesses
(* The final value of a spinlock should not be tested *)
flag ~empty [FW] ; loc ; [ALL-LOCKS] as lock-final
(*
* Put lock operations in their appropriate classes, but leave UL out of W
* until after the co relation has been generated.
*)
let R = R | LKR | LF
let W = W | LKW
let Release = Release | UL
let Acquire = Acquire | LKR
(* Match LKW events to their corresponding UL events *)
let critical = ([LKW] ; po-loc ; [UL]) \ (po-loc ; [LKW | UL] ; po-loc)
flag ~empty UL \ range(critical) as unmatched-unlock
(* Allow up to one unmatched LKW per location; more must deadlock *)
let UNMATCHED-LKW = LKW \ domain(critical)
empty ([UNMATCHED-LKW] ; loc ; [UNMATCHED-LKW]) \ id as unmatched-locks
(* rfi for LF events: link each LKW to the LF events in its critical section *)
let rfi-lf = ([LKW] ; po-loc ; [LF]) \ ([LKW] ; po-loc ; [UL] ; po-loc)
(* rfe for LF events *)
let all-possible-rfe-lf =
(*
* Given an LF event r, compute the possible rfe edges for that event
* (all those starting from LKW events in other threads),
* and then convert that relation to a set of single-edge relations.
*)
let possible-rfe-lf r =
let pair-to-relation p = p ++ 0
in map pair-to-relation ((LKW * {r}) & loc & ext)
(* Do this for each LF event r that isn't in rfi-lf *)
in map possible-rfe-lf (LF \ range(rfi-lf))
(* Generate all rf relations for LF events *)
with rfe-lf from cross(all-possible-rfe-lf)
let rf = rf | rfi-lf | rfe-lf
(* Generate all co relations, including LKW events but not UL *)
let co0 = co0 | ([IW] ; loc ; [LKW]) |
(([LKW] ; loc ; [UNMATCHED-LKW]) \ [UNMATCHED-LKW])
include "cos-opt.cat"
let W = W | UL
let M = R | W
(* Merge UL events into co *)
let co = (co | critical | (critical^-1 ; co))+
let coe = co & ext
let coi = co & int
(* Merge LKR events into rf *)
let rf = rf | ([IW | UL] ; singlestep(co) ; lk-rmw^-1)
let rfe = rf & ext
let rfi = rf & int
let fr = rf^-1 ; co
let fre = fr & ext
let fri = fr & int
show co,rf,fr