Breaking and entering: lose the lock while embracing concurrency, Part II

September 10, 2015

This is the second half of a two-part series on applied lock-free techniques.

In part one of this series, we discussed the problem of subscription matching for messaging systems and how it can be modeled using a trie. We also explored linearizability, which is a correctness condition for concurrent data structures.

Let's revisit our subscription trie from earlier. Our naive approach to making it linearizable was to protect it with a lock. This proved easy, but as we observed, severely limited throughput. For a message broker, access to this trie is a critical path, and we usually have multiple threads performing inserts, removals, and lookups on it concurrently. Intuition tells us we can implement these operations without coarse-grained locking by relying on a CAS to perform mutations on the trie.

Lock-free applied

If we recall, read-modify-write is typically applied by copying a shared variable to a local variable, performing some speculative work on it, and attempting to publish the changes with a CAS. When inserting into the trie, our speculative work is creating an updated copy of a node. We commit the new node by updating the parent's reference with a CAS. For example, if we want to add a subscriber to a node, we would copy the node, add the new subscriber, and CAS the pointer to it in the parent.

This approach is broken, however. To see why, imagine if a thread inserts a subscription on a node while another thread concurrently inserts a subscription as a child of that node. The second insert could be lost due to the sequencing of the reference updates. The diagram below illustrates this problem. Dotted lines represent a reference updated with a CAS.

The orphaned nodes containing "x" and "z" mean the subscription to "foo.bar" was lost. The trie is in an inconsistent state.

We looked to existing research in the field of non-blocking data structures to help illuminate a path. "Concurrent Tries with Efficient Non-Blocking Snapshots" by Prokopec et al. introduces the Ctrie, a non-blocking, concurrent hash trie based on shared-memory, single-word CAS instructions.

A hash array mapped trie (HAMT) is an implementation of an associative array which, unlike a hashmap, is dynamically allocated. Memory consumption is always proportional to the number of keys in the trie. A HAMT works by hashing keys and using the resulting bits in the hash code to determine which branches to follow down the trie. Each node contains a table with a fixed number of branch slots. Typically, the number of branch slots is 32. On a 64-bit machine, this would mean it takes 256 bytes (32 branches x 8-byte pointers) to store the branch table of a node.

The size of L1-L3 cache lines is 64 bytes on most modern processors. We can't fit the branch table in a CPU cache line, let alone the entire node. Instead of allocating space for all branches, we use a bitmap to indicate the presence of a branch at a particular slot. This reduces the size of an empty node from roughly 264 bytes to 12 bytes. We can safely fit a node with up to six branches in a single cache line.

The Ctrie is a concurrent, lock-free version of the HAMT which ensures progress and linearizability. It solves the CAS problem described above by introducing indirection nodes, or I-nodes, which remain present in the trie even as nodes above and below change. This invariant ensures correctness on inserts by applying the CAS operation on the I-node instead of the internal node array.

An I-node may point to a Ctrie node, or C-node, which is an internal node containing a bitmap and array of references to branches. A branch is either an I-node or a singleton node (S-node) containing a key-value pair. The S-node is a leaf in the Ctrie. A newly initialized Ctrie starts with a root pointer to an I-node which points to an empty C-node. The diagram below illustrates a sequence of inserts on a Ctrie.

An insert starts by atomically reading the I-node's reference. Next, we copy the C-node and add the new key, recursively insert on an I-node, or extend the Ctrie with a new I-node. The new C-node is then published by performing a CAS on the parent I-node. A failed CAS indicates another thread has mutated the I-node. We re-linearize by atomically reading the I-node's reference again, which gives us the current state of the Ctrie according to its linearizable history. We then retry the operation until the CAS succeeds. In this case, the linearization point is a successful CAS. The following figure shows why the presence of I-nodes ensures consistency.

In the above diagram, (k4,v4) is inserted into a Ctrie containing (k1,v1), (k2,v2), and (k3,v3). The new key-value pair is added to node C1 by creating a copy, C1', with the new entry. A CAS is then performed on the pointer at I1, indicated by the dotted line. Since C1' continues pointing to I2, any concurrent updates which occur below it will remain present in the trie. C1 is then garbage collected once no more threads are accessing it. Because of this, Ctries are much easier to implement in a garbage-collected language. It turns out that this deferred reclamation also solves the ABA problem described earlier by ensuring memory addresses are recycled only when it's safe to do so.

The I-node invariant is enough to guarantee correctness for inserts and lookups, but removals require some additional invariants in order to avoid update loss. Insertions extend the Ctrie with additional levels, while removals eliminate the need for some of these levels. This is because we want to keep the Ctrie as compact as possible while still remaining correct. For example, a remove operation could result in a C-node with a single S-node below it. This state is valid, but the Ctrie could be made more compact and lookups on the lone S-node more efficient if it were moved up into the C-node above. This would allow the I-node and C-node to be removed.

The problem with this approach is it will cause insertions to be lost. If we move the S-node up and replace the dangling I-node reference with it, another thread could perform a concurrent insert on that I-node just before the compression occurs. The insert would be lost because the pointer to the I-node would be removed.

This issue is solved by introducing a new type of node called the tomb node (T-node) and an associated invariant. The T-node is used to ensure proper ordering during removals. The invariant is as follows: if an I-node points to a T-node at some time t0, then for all times greater than t0, the I-node points to the same T-node. More concisely, a T-node is the last value assigned to an I-node. This ensures that no insertions occur at an I-node if it is being compressed. We call such an I-node a tombed I-node.

If a removal results in a non-root-level C-node with a single S-node below it, the C-node is replaced with a T-node wrapping the S-node. This guarantees that every I-node except the root points to a C-node with at least one branch. This diagram depicts the result of removing (k2,v2) from a Ctrie:

Removing (k2,v2) results in a C-node with a single branch, so it's subsequently replaced with a T-node. The T-node provides a sequencing mechanism by effectively acting as a marker. While it solves the problem of lost updates, it doesn't give us a compacted trie. If two keys have long matching hash code prefixes, removing one of the keys would result in a long chain of C-nodes followed by a single T-node at the end.

An invariant was introduced which says once an I-node points to a T-node, it will always point to that T-node. This means we can't change a tombed I-node's pointer, so instead we replace the I-node with its resurrection. The resurrection of a tombed I-node is the S-node wrapped in its T-node. When a T-node is produced during a removal, we ensure that it's still reachable, and if it is, resurrect its tombed I-node in the C-node above. If it's not reachable, another thread has already performed the compression. To ensure lock-freedom, all operations which read a T-node must help compress it instead of waiting for the removing thread to complete. Compression on the Ctrie from the previous diagram is illustrated below.

The resurrection of the tombed I-node ensures the Ctrie is optimally compressed for arbitrarily long chains while maintaining integrity.

With a 32-bit hash code space, collisions are rare but still nontrivial. To deal with this, we introduce one final node, the list node (L-node). An L-node is essentially a persistent linked list. If there is a collision between the hash codes of two different keys, they are placed in an L-node. This is analogous to a hash table using separate chaining to resolve collisions.

One interesting property of the Ctrie is support for lock-free, linearizable, constant-time snapshots. Most concurrent data structures do not support snapshots, instead opting for locks or requiring a quiescent state. This allows Ctries to have O(1) iterator creation, clear, and size retrieval (amortized).

Constant-time snapshots are implemented by writing the Ctrie as a persistent data structure and assigning a generation count to each I-node. A persistent hash trie is updated by rewriting the path from the root of the trie down to the leaf the key belongs to while leaving the rest of the trie intact. The generation demarcates Ctrie snapshots. To create a new snapshot, we copy the root I-node and assign it a new generation. When an operation detects that an I-node's generation is older than the root's generation, it copies the I-node to the new generation and updates the parent. The path from the root to some node is only updated the first time it's accessed, making the snapshot a O(1) operation.

The final piece needed for snapshots is a special type of CAS operation. There is a race condition between the thread creating a snapshot and the threads which have already read the root I-node with the previous generation. The linearization point for an insert is a successful CAS on an I-node, but we need to ensure that both the I-node has not been modified and its generation matches that of the root. This could be accomplished with a double compare-and-swap, but most architectures do not support such an operation.

The alternative is to use a RDCSS double-compare-single-swap originally described by Harris et al. We implement an operation with similar semantics to RDCSS called GCAS, or generation compare-and-swap. The GCAS allows us to atomically compare both the I-node pointer and its generation to the expected values before committing an update.

After researching the Ctrie, we wrote a go implementation in order to gain a deeper understanding of the applied techniques. These same ideas would hopefully be adaptable to our problem domain.

Generalizing the Ctrie

The subscription trie shares some similarities to the hash array mapped trie but there are some key differences. First, values are not strictly stored at the leaves but can be on internal nodes as well. Second, the decomposed topic is used to determine how the trie is descended rather than a hash code. Wildcards complicate lookups further by requiring backtracking. Lastly, the number of branches on a node is not a fixed size. Applying the Ctrie techniques to the subscription trie, we end up with something like this:

Much of the same logic applies. The main distinctions are the branch traversal based on topic words and rules around wildcards. Each branch is associated with a word and set of subscribers and may or may not point to an I-node. The I-nodes still ensure correctness on inserts. The behavior of T-nodes changes slightly. With the Ctrie, a T-node is created from a C-node with a single branch and then compressed. With the subscription trie, we don't introduce a T-node until all branches are removed. A branch is pruned if it has no subscribers and points to nowhere or it has no subscribers and points to a tombed I-node. The GCAS and snapshotting remain unchanged.

We implemented this Ctrie derivative in order to build our concurrent pattern-matching engine, matchbox. This library provides an exceptionally simple API which allows a client to subscribe to a topic, unsubscribe from a topic, and lookup a topic's subscribers. Snapshotting is also leveraged to retrieve the global subscription tree and the topics to which clients are currently subscribed. These are useful to see who _currently has subscriptions and for _what.

In practice

Matchbox has been pretty extensively benchmarked, but to see how it behaves, it's critical to observe its performance under contention. Many messaging systems opt for a mutex which tends to result in a lot of lock contention. It's important to know what the access patterns look like in practice, but for our purposes, it's heavily parallel. We don't want to waste CPU cycles if we can help it.

To see how matchbox compares to lock-based subscription structures, I benchmarked it against gnatsd, a popular high-performance messaging system also written in Go. Gnatsd uses a tree-like structure protected by a mutex to manage subscriptions and offers similar wildcard semantics.

The benchmarks consist of one or more insertion goroutines and one or more lookup goroutines. Each insertion goroutine inserts 1000 subscriptions, and each lookup goroutine looks up 1000 subscriptions. We scale these goroutines up to see how the systems behave under contention.

The first benchmark is a 1:1 concurrent insert-to-lookup workload. A lookup corresponds to a message being published and matched to interested subscribers, while an insert occurs when a client subscribes to a topic. In practice, lookups are much more frequent than inserts, so the second benchmark is a 1:3 concurrent insert-to-lookup workload to help simulate this. The timings correspond to the complete insert and lookup workload. GOMAXPROCS was set to 8, which controls the number of operating system threads that can execute simultaneously. The benchmarks were run on a machine with a 2.6 GHz Intel Core i7 processor.

It's quite clear that the lock-free approach scales a lot better under contention. This follows our intuition because lock-freedom allows system-wide progress even when a thread is blocked. If one goroutine is blocked on an insert or lookup operation, other operations may proceed. With a mutex, this isn't possible.

Matchbox performs well, particularly in multithreaded environments, but there are still more optimizations to be made. This includes improvements both in memory consumption and runtime performance. Applying the Ctrie techniques to this type of trie results in a fairly non-compact structure. There may be ways to roll up branches—either eagerly or after removals—and expand them lazily as necessary. Other optimizations might include placing a cache or Bloom filter in front of the trie to avoid descending it. The main difficulty with these will be managing support for wildcards.

Conclusion

To summarize, we've seen why subscription matching is often a major concern for message-oriented middleware and why it's frequently a bottleneck. Concurrency is crucial for high-performance systems, and we've looked at how we can achieve concurrency without relying on locks while framing it within the context of linearizability. Compare-and-swap is a fundamental tool used to implement lock-free data structures, but it's important to be conscious of the pitfalls. We introduce invariants to protect data consistency. The Ctrie is a great example of how to do this and was foundational in our lock-free subscription-matching implementation. Finally, we validated our work by showing that lock-free data structures scale dramatically better with multithreaded workloads under contention.

My thanks to Steven Osborne and Dustin Hiatt for reviewing this series.

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