The New Scalable ETS ordered_set

August 19, 2020 · by Kjell Winblad

The scalability of ETS tables of type ordered_set with the write_concurrency option is substantially better in Erlang/OTP 22 than earlier releases. In some extreme cases, you can expect more than 100 times better throughput in Erlang/OTP 22 compared to Erlang/OTP 21. The cause of this improvement is a new data structure called the contention adapting search tree (CA tree for short). This blog post will give you insights into how the CA tree works and show you benchmark results comparing the performance of ETS ordered_set tables in OTP 21 and OTP 22.

Try it Out! #

[This escript]/blog/code/insert_disjoint_ranges.erl) makes it convenient for you to try the new ordered_set implementation on your own machine with Erlang/OTP 22+ installed.

The escript measures the time it takes for P Erlang processes to insert N integers into an ordered_set ETS table, where P and N are parameters to the escript. The CA tree is only utilized when the ETS table options ordered_set and {write_concurrency, true} are active. One can, therefore, easily compare the new data structure’s performance with the old one (an AVL tree protected by a single readers-writer lock). The write_concurrency option had no effect on ordered_set tables before the release of Erlang/OTP 22.

We get the following results when running the escript on a developer laptop with two cores (Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz):

$ escript insert_disjoint_ranges.erl old 1 10000000
Time: 3.352332 seconds
$ escript insert_disjoint_ranges.erl old 2 10000000
Time: 3.961732 seconds
$ escript insert_disjoint_ranges.erl old 4 10000000
Time: 6.382199 seconds
$ escript insert_disjoint_ranges.erl new 1 10000000
Time: 3.832119 seconds
$ escript insert_disjoint_ranges.erl new 2 10000000
Time: 2.109476 seconds
$ escript insert_disjoint_ranges.erl new 4 10000000
Time: 1.66509 seconds

We see that in this particular benchmark, the CA tree has superior scalability to the old data structure. The benchmark ran about twice as fast with the new data structure and four processes as with the old data structure and one process (the machine only has two cores). We will look at the performance and scalability of the new CA tree-based implementation in greater detail later after describing how the CA tree works.

The Contention Adapting Search Tree in a Nutshell #

The key feature that distinguishes the CA tree from other concurrent data structures is that the CA tree dynamically changes its synchronization granularity based on how much contention is detected inside the data structure. This way, the CA tree can avoid the performance and memory overheads that come from using many unnecessary locks without sacrificing performance when many operations happen in parallel. For example, let us imagine a scenario where the CA tree is initially populated from many threads in parallel, and then it is only used from a single thread. In this scenario, the CA tree will adapt to use fine-grained synchronization in the population phase (when fine-grained synchronization reduces contention). The CA tree will then change to use coarse-grained synchronization in the single-threaded phase (when coarse-grained synchronization reduces the locking and memory overheads).

The structure of a CA tree is illustrated in the following picture:

![alt text]/blog/images/ca_tree/ca_tree_9.png “Contention Adapting Search Tree Structure”)

The actual items stored in the CA tree are located in sequential data structures in the bottom layer. These sequential data structures are protected by the locks in the base nodes in the middle layer. The base node locks have counters associated with them. The counter of a base node lock is increased when contention is detected in the base node lock and decreased when no such contention is detected. The value of this base node lock counter decides if a split or a join should happen after an operation has been performed in a base node. The routing nodes at the top of the picture above form a binary search tree that directs the search for a particular item. A routing node also contains a lock and a flag. These are used when joining base nodes. The details of how splitting and joining work will not be described in this article, but the interested reader can find a detailed description in this CA tree paper (preprint PDF). We will now illustrate how the CA tree changes its synchronization granularity by going through an example:

  1. Initially, a CA tree only consists of a single base node with a sequential data structure as is depicted in the picture below:

    ![alt text]/blog/images/ca_tree/ca_tree_1.png “Initial Contention Adapting Search Tree”)

  2. If parallel threads access the CA tree, the value of a base node’s counter may eventually reach the threshold that indicates that the base node should be split. A base node split divides the items in a base node between two new base nodes and replaces the original base node with a routing node where the two new base nodes are rooted. The following picture shows the CA tree after the base node pointed to by the tree’s root has been split:

    ![alt text]/blog/images/ca_tree/ca_tree_2.png “First Split Contention Adapting Search Tree”)

  3. The process of base node splitting will continue as long as there is enough contention in base node locks or until the max depth of the routing layer is reached. The following picture shows how the CA tree looks like after another split:

    ![alt text]/blog/images/ca_tree/ca_tree_3.png “Second Split Contention Adapting Search Tree”)

  4. The synchronization granularity may differ in different parts of a CA tree if, for example, a particular part of a CA tree is accessed more frequently in parallel than the rest. The following picture shows the CA tree after yet another split:

    ![alt text]/blog/images/ca_tree/ca_tree_4.png “Third Split Contention Adapting Search Tree”)

  5. The following picture shows the CA tree after the fourth split:

    ![alt text]/blog/images/ca_tree/ca_tree_5.png “Fourth Split Contention Adapting Search Tree”)

  6. The following picture shows the CA tree after the fifth split:

    ![alt text]/blog/images/ca_tree/ca_tree_6.png “Fifth Split Contention Adapting Search Tree”)

  7. Two base nodes holding adjacent ranges of items can be joined. Such a join will be triggered after an operation sees that a base node counter’s value is below a certain threshold. Remember that a base node’s counter is decreased if a thread does not experience contention when acquiring the base node’s lock.

    ![alt text]/blog/images/ca_tree/ca_tree_7.png “Join of two base nodes in a Contention Adapting Search Tree”)

  8. As you might have noticed from the illustrations above, splitting and joining results in that old base nodes and routing nodes gets spliced-out from the tree. The memory that these nodes occupy needs to be reclaimed, but this can not happen directly after they have got spliced-out as some threads might still be reading them. The Erlang run-time system has a mechanism called thread progress, which the ETS CA tree implementation uses to reclaim these nodes safely.

    ![alt text]/blog/images/ca_tree/ca_tree_8.png “Spliced-out base nodes and routing nodes have been reclaimed.”)

[Click here]/blog/images/ca_tree/ca_tree_ani.gif) to see an animation of the example.

Benchmark #

The performance of the new CA tree-based ETS ordered_set implementation has been evaluated in a benchmark that measures the throughput (operations per second) in many scenarios. The benchmark lets a configurable number of Erlang processes perform a configurable distribution of operations on a single ETS table. The curious reader can find the source code of the benchmark in the test suite for ETS.

The following figures show results from this benchmark on a machine with two Intel(R) Xeon(R) CPU E5-2673 v4 @ 2.30GHz (32 cores in total with hyper-threading). The average set size in all scenarios was about 500K. More details about the benchmark machine and configuration can be found on this page.

alt text

alt text

alt text

alt text

alt text

alt text

alt text

alt text

We see that the throughput of the CA tree-based ordered_set (OTP-22) improves when we add cores all the way up to 64 cores, while the old implementation’s (OTP-21) throughput often gets worse when more processes are added. The old implementation’s write operations are serialized as the data structure is protected by a single readers-writer lock. The slowdown of the old version when adding more cores is mainly caused by increased communication overhead when more cores try to acquire the same lock and by the fact that the competing cores frequently invalidate each other’s cache lines.

The graph for the 100% lookups scenario (the last graph in the list of graphs above) looks a bit strange at first sight. Why does the CA tree scale so much better than the old implementation in this scenario? The answer is almost impossible to guess without knowing the implementation details of the ordered_set table type. First of all, the CA tree uses the same readers-writer lock implementation for its base node locks as the old implementation uses to protect the whole table. The difference is thus not due to any lock differences. The default ordered_set implementation (the one that is active when write_concurrency is off) has an optimization that mainly improves usage scenarios where a single process iterates over items of the table, for example, with a sequence of calls to the ets:next/2 function. This optimization keeps a static stack per table. Some operations use this stack to reduce the number of tree nodes that need to be traversed. For example, the ets:next/2 operation does not need to recreate the stack, if the top of the stack contains the same key as the one passed to the operation (see here). As there is only one static stack per table and potentially many readers (due to the readers-writer lock), the static stack has to be reserved by the thread that is currently using it. Unfortunately, the static stack handling is a scalability bottleneck in scenarios like the one with 100% lookups above. The CA tree implementation does not have this type of optimization, so it does not suffer from this scalability bottleneck. However, this also means that the old implementation may perform better than the new one when the table is mainly sequentially accessed. One example of when the old implementation (that still can be used by setting the write_concurrency option to false) performs better is the single process case of the 10% insert, 10% delete, 40% lookup and 40% nextseq1000 (a sequence of 1000 ets:next/2 calls) scenario (the second last graph in the list of graphs above).

Therefore, we can conclude that that turning on write_concurrency for an ordered_set table is probably a good idea if the table is accessed from multiple processes in parallel. Still, turning off write_concurrency might be better if you mainly access the table sequentially.

A Note on Decentralized Counters #

The CA tree implementation was not the only optimization introduced in Erlang/OTP 22, affecting the scalability of ordered_set with write_concurrency. An optimization that decentralized counters in ordered_set tables with write_concurrency turned on was also introduced in Erlang/OTP 22 (see here). An option to enable the same optimization in all table types was introduced in Erlang/OTP 23 (see here). You can find benchmark results comparing the scalability of the tables with and without decentralized counters here.

Further Reading #

The following paper describes the CA tree and some optimizations (of which some have not been applied to the ETS CA tree yet) in much more detail than this blog post. The paper also includes an experimental comparison with related data structures.

There is also a lock-free variant of the CA tree that is described in the following paper. The lock-free CA tree uses immutable data structures in its base nodes to substantially reduce the amount of time range queries, and similar operations can conflict with other operations.

The following paper, which discusses and evaluates a prototypical CA tree implementation for ETS, was the first CA tree-related paper.

You can look directly at the ETS CA tree source code if you are interested in specific implementation details. Finally, it might also be interesting to look at the author’s Ph.D. thesis if you want to get more links to related work or want to know more about the motivation for concurrent data structures that adapt to contention.

Conclusion #

The Erlang/OTP 22 release introduced a new ETS ordered_set implementation that is active when the write_concurrency option is turned on. This data structure (a contention adapting search tree) has superior scalability to the old data structure in many different scenarios and a design that gives it excellent performance in a variety of scenarios that benefit from different synchronization granularities.