The Java Memory Model is a predicate on execution traces1 of multi-threaded Java programs. It gives meaning to programs using Java’s concurrency facilities, and (hence) constraints transformations that may be performed on the program by the program’s execution environment. The execution environment (a non-standard term I just made up) typically includes javac and the JVM the generated bytecodes execute on, but in theory could involve other tools depending on the toolchain. For example, if you post-process the generated .class files using some bytecode level tool, that tool needs to understand and respect the JMM if it wants to make semantic preserving transformations.

My interest in the Java Memory Model stems from working on JIT compilers for a JVM2. JIT compilers too are a part of the execution environment as defined above, and can optimize programs only in ways allowed by the JMM specification. People much smarter than me have come up with ways to safely (but conservatively) compile standard Java concurrency primitives3, but it is a nice exercise to try to prove legality (or illegality, in case of this post) of certain transforms from scratch. This blog post tries to show how some re-orderings (that may be done in as part of optimizing a Java program for performance) that intuitively seem illegal are, in fact, illegal, by deriving that illegality from directly the JMM spec. I’ve assumed passing familiarity with the Java Memory Model, but I’ve also tried to give references to the actual memory model specification wherever appropriate.

# A Correctly Synchronized Example

Assume we’ve declared a class Tuple

Now consider the following snippet in Java (we’ll call this the pre-transform snippet):

Can the above be transformed to the following (that we will call the post-transform snippet)?

Giving a precise answer involves examining the complete Java program – depending on the context in which this snippet executes, the transformed snippet may or may not be equivalent to the original. For example, if there are no writes to volatileF (and so regV is always 0 and so is regNV) in the Java program then the transform is trivially safe. However, it is more interesting to be able to make local judgments when JIT compiling a single method. Specifically, we’d like to know if a certain transformation is legal (or not) in all contexts because if it is, we can make the transformation without probing the rest of the environment at all4. It follows that we can prove a transform illegal (in this restricted sense of illegal) by giving a context that acts as a counterexample – the existence of one context in which the pre-transform Java snippet and the post-transform Java snippet behave in incompatible ways is enough to make the transform unsafe to do locally, without global analysis.

If you’re familiar with the Java Memory Model, you’d probably guess that the transform above is not legal. We’ll show this by choosing a global context in which the pre-transform snippet guarantees something that the post-transform snippet doesn’t.

Let’s say that there is some other thread running writer, making the full program:

reader and writer are being called on the same Tuple object that was allocated at program startup.

It is easy to show that all sequentially consistent execution traces of this program are race free, and hence the program as such is correctly synchronized (all these terms have very specific meanings, see 17.4.5 5). Correctly synchronized programs behave as if they were executing on a sequentially consistent runtime6, so every execution of this program will look like an interleaving of actions performed by each of the individual threads (including non-volatile reads and writes). Given that, we can show that regV == 1 implies regNV == 5.

Now let us put the post-transform Java snippet in the same context.

Note that this is no longer correctly synchronized and hence the above reasoning doesn’t follow directly. To show that the assertion “regV == 1 implies regNV == 5” no longer holds, we will demonstrate a legal execution that results in regV == 1 and regNV == 0:

Let $E$ be an execution (see 17.4.65) with obvious $P$, $A$, $po$, $V$; $so$ = $so'$ $\cup$ $($ tuple.volatileF = 1, int regV = tuple.volatileF $)$ for some $so'$ 7; $W$ such that regV is 1 and cache is 0; and computed $sw$ and $hb$ (their values are functions of the other parameters of the execution). Something to note about $sw$: “(17.4.45) The write of the default value (zero, false, or null) to each variable synchronizes-with the first action in every thread.”

We now need a set of committing actions (17.4.85) culminating in the execution $E$. Fortunately this is simpler than it sounds, let:

• $C_0$ is $\emptyset$ (by definition)

• $C_1$ includes everything up to the point the two threads started. I’m hand-waving here – in general you won’t be able to compress the entire sequence of actions leading up to the thread launch state into one commit. But I don’t think that restriction affects this proof.

• $C_2$ is $C_1$ $\cup$ $\{$ tuple.nonVolatileF = 5, tuple.volatileF = 1 $\}$

• $C_3$ is $C_2$ $\cup$ $\{$ int cache = tuple.nonVolatileF, int regV = tuple.volatileF $\}$

• $C_4$ is $C_3$ $\cup$ all thread finalization logic (the conditional assignment to the local variable regNV, calls to join(), the exit sequence deployed by main etc.). $C_4$ too is hand-wavy, and in the same sense as $C_1$.

From this we create $E_i$ with $E = E_4$ such that $A_i = C_i$. We now need to show that the reads in $C_3$ can see the write $W$ thinks they should. The specification allows “freshly committed reads” (i.e. reads in $A_i$ that aren’t in $C_{i - 1}$) to see writes in the execution they’re introduced in ($E_i$) that are different from what they see in the final execution but we won’t need to exploit that allowance here8.

From JMM section 17.4.85: “All reads in $E_i$ that are not in $C_{i-1}$ must see writes that happen-before them. Each read $r$ in $C_{i} - C_{i-1}$ must see writes in $C_{i-1}$ in both $E_i$ and $E$, but may see a different write in $E_i$ from the one it sees in $E$.” and section 17.4.55: “The default initialization of any object happens-before any other actions (other than default-writes) of a program.” give us that it is legal for int cache = tuple.nonVolatileF to see the initial write to nonVolatileF of its default value (0) that happens-before it (and everything else), and int regV = tuple.volatileF to see the write tuple.volatileF = 1 that also happens-before it (since tuple.volatileF = 1 is before int regV = tuple.volatileF in the synchronization order, and hence they have a happens-before relationship via the synchronizes with relationship). Since none of these judgments break happens-before consistency, we’ve thus justified $E$, and hence proved that regV == 1 and regNV == 0 is a legal result.

## Exercise

Find a series of committing actions that end with regV as 1 and cache as 5 in this second example.

# A Racy Example

The first example had an interesting property – the pre-transform program was correctly synchronized while the post-transform program wasn’t. Let’s try an example where the pre-transform program isn’t correctly synchronized either. Is it legal to transform

to the following?

Like in the previous case, the real, precise answer depends on the global context in which the snippets are being evaluated for equivalence. But we can still try to answer the question in terms of the stronger notion of “equivalent in every context”.

We build a set-up similar to what we used last time, and also use the same guarantee (or invariant) – that regV == 1 implies regNV == 5 to differentiate the pre-transform and the post-transform programs:

Observe that there is a race here9 so the earlier logic that exploited “as-if” sequentially consistency semantics will not directly work. However, happens-before consistency is enough to give us what we need.

“(17.4.55) A set of actions $A$ is happens-before consistent if for all reads $r$ in $A$, where $W(r)$ is the write action seen by $r$, it is not the case that either $hb(r, W(r))$ or that there exists a write $w$ in $A$ such that $w.v = r.v$ and $hb(W(r), w)$ and $hb(w, r)$.”

In plain English, this says the following two things:

1. A read cannot see a write that it happened before
2. A write overrides other writes to the same memory location that happened before it (in terms of the happens before relation) – a read cannot observe a write that happened before a write that happened before it (i.e. is two or more steps away on the happens before relation).

We can use (2) to prove the required guarantee – given that regV is 1, we know (since volatile loads and stores have a total order) that tuple.volatileF = 1 happens before int regV = tuple.volatileF. This means (by program order and transitivity) tuple.nonVolatileF = 5 happens before int regNV = tuple.nonVolatileF. The only other write to nonVolatileF in the system, the write of the default value10 (0 in this case), happens before tuple.nonVolatileF = 5 so by (2) above, int regNV = tuple.nonVolatileF cannot see it. In the language of the JMM, we have int regNV = tuple.nonVolatileF as $r$, the initial write of 0 to tuple.nonVolatileF as $W(r)$ and tuple.nonVolatileF = 5 as $w$. By 17.4.55, $r$ cannot observe $W(r)$.

The post-transform snippet in the same context looks like

We’ll again try to show the legality of an execution that results in regNV == 0 with regV == 1. Reasoning about this is very similar to reasoning about the previous case, and we can use the same commit sequence (modulo changing $C_4$ in obvious ways, since we don’t have a local variable involved here) to show legality of an execution that ends with regNV == 0 and regV == 1.

## Exercise

Using similar techniques, show that you cannot optimize (the proof will have the same structure as the second example):

to

.

# Conclusion and Future Posts

There are several aspects of the Java Memory Model specification that I’m confused about:

• What does the JSR-133 Cookbook do to prevent values from appearing of “thin-air”? Does the cookbook by itself prevent problematic causality loops?

• There are several interesting and well-known categories of optimizations that are allegedly prevented by the memory model. What are those optimizations, what is the impact of this restriction? Is there a clean subset of compiler optimizations that are allowed? This is more of a reading project – several papers have been published on this topic.

It will be interesting to see how my understanding of the JMM evolves over time. I think I’ve sort of started to see the big picture, but there is still a long way to go.

1. An execution trace is a tuple consisting of sets and relations on those sets. See section 17.4.6 in the “Java Language Specification” for a precise definition.

2. Unfortunately, unlike Java the programming language, Java bytecodes don’t have a defined memory model. In practice this isn’t a problem since the bytecodes closely follow constructs present in the Java programming language, and hence have a default “inherited” memory model.

3. See the The JSR-133 Cookbook for Compiler Writers by Doug Lea et. al.

4. In general it isn’t even possible to make global statements about a program that stay correct throughout the program lifetime because Java bytecodes are allowed to load arbitrary Java classes at run-time. So even if some forms of such global analysis may be feasible from a computational perspective, predicates computed by such global analyses will not stay correct throughout the lifetime of the program. There is a standard solution for such issues though: you register dependencies on bits of compiled code that records the falsifiable assumptions made during the compilation and when any of these assumptions are violated, the associated blobs of code are thrown away. Of course, the more aggressive you are in making falsifiable assumptions the more frequently you’ll have to throw away compiled code, so there is a natural trade-off here.

5. See “The Java Language Specification”  2 3 4 5 6 7 8

6. Interestingly, this isn’t an axiom (even though we state as such). Any Java runtime providing happens before consistency and well-ordered executions automatically provides the “if correctly synchronized then sequentially consistent” invariant. For a proof see “The Java Memory Model”, POPL ‘05

7. This notation is just a fancy way of saying tuple.volatileF = 1 is before int regV = tuple.volatileF in $so$ and I don’t care about the remaining part of the relation. Also, there is something worth noting here – volatile reads and writes have a total order to them, and given that regV is 1, there can be only one way tuple.volatileF = 1 relates to int regV = tuple.volatileF in $so$

8. For an example that actually uses that clause, see section 6 in “The Java Memory Model”, POPL ‘05

9. If you pick a sequentially consistent execution where int regV = tuple.volatileF is before tuple.volatileF = 1 in the synchronization order, then the pair of conflicting access (17.4.55) tuple.nonVolatileF = 5 and int regNV = tuple.nonVolatileF are not ordered in happens-before

10. Also mentioned earlier, “(17.4.45) The write of the default value (zero, false, or null) to each variable synchronizes-with the first action in every thread.”