Introduction

Reference counting (RC) has rather been a minor party to the other garbage collection (GC) algorithms in functional programming in the last decades as, for example, OCaml and Haskell use non-RC GC. However, several recent papers, such as Counting Immutable Beans: Reference Counting Optimized for Purely Functional Programming and Perceus: Garbage Free Reference Counting with Reuse, showed the efficiency of highly optimized RC GC in functional languages with sacrifice or restriction of some language features like circular references. The latter paper introduced an efficient RC GC algorithm called Perceus which is basically all-in-one RC.

In this post, I describe my experience and some caveats about implementing and gaining benefits from the Perceus RC. I've been developing a programming language called Pen and implemented a large part of the Perceus RC there. I hope this post helps someone who is implementing the algorithm or even deciding if it's worth implementing it in their own languages.

Overview of Perceus

The Perceus reference counting algorithm is a thread-safe ownership-based reference counting algorithm with several optimizations:

• Heap reuse on data structure construction and deconstruction (pattern matching)
• Heap reuse specialization (in-place updates of data structures)
• Non-atomic operations or atomic operations with relaxed memory ordering for heap blocks not shared by multiple threads
• Borrow inference to reduce reference count operations

By implementing all of those optimizations in the Koka programming language, they achieved GC overhead much less and execution time faster than the other languages including OCaml, Haskell, and even C++ in several algorithms and data structures that frequently keep common sub-structures of them, such as red-black trees. For more information, see the latest version of the paper.

Implementing the algorithm

What I've implemented so far in Pen are two core functionalities of the Perceus algorithm:

• In-place updates of records on heap
  • This corresponds to heap reuse specialization described above.
• Relaxed atomic operations on references not shared by multiple threads

Due to some differences in language features between Koka and Pen, I needed to make some modifications to the algorithm. First, Pen doesn't need any complex algorithm for in-place record updates with heap reuse specialization because it has syntax for record updates, and its lowered directly into its mid-level intermediate representation (MIR) where the RC algorithm is applied.

Secondly, although I've also implemented generic reuse of heap blocks that matches their frees and allocations in functions initially, I've reverted it for now since I realized that it won't improve performance much in Pen because of the lack of pattern matching syntax with deconstruction and another optimization of small record unboxing planned to be implemented later. In addition, the implementation doesn't include borrow inference yet as it had the least contribution to the performance reported in a previous paper.

The main part of the algorithm is implemented in the source files of a compiler itself and an FFI library in Rust listed below:

• https://github.com/pen-lang/pen/blob/d44df6d9cdcbe97fcdd5ac14c4de30f4897664ff/lib/mir-fmm/src/reference_count/pointer.rs
• https://github.com/pen-lang/pen/blob/d44df6d9cdcbe97fcdd5ac14c4de30f4897664ff/lib/ffi/src/arc/arc_block.rs

Counting back synchronized references to 0

In this section, I use the term "synchronized" to mean "marked as shared by multiple threads." In Koka and Lean 4, they use the term "shared" to mean the same thing but I rephrased it to reduce confusion.

In the Perceus reference counting GC, memory blocks have mainly two un-synchronized and synchronized states represented by positive and negative counts respectively. Heap blocks are synchronized before they get shared with other threads and are never reverted back to un-synchronized states once they get synchronized. But you may wonder if this is necessary or not. If we have a memory block with a reference count of 1, that also means it's not shared with any other threads anymore. So isn't it possible to use a common count value of 0 to represent unique references and reduce the overhead of some atomic operations potentially?

The answer is no because in that case, we need to synchronize memory operations on those references un-synchronized back with drops of those references by the other threads with release memory ordering. For example, let's consider a situation where a thread shares a reference with the other thread:

1. Thread A shares a reference with thread B.
2. Some computation goes on...
3. Thread B drops the reference.
4. Thread A drops the reference and frees its inner memory block.
   • Or, thread A reuses the memory block for heap reuse optimization mentioned in the earlier section.

So if references can be un-synchronized back, we always need to use atomic operations with acquire memory ordering at the point (4) above to make all side effects performed by thread B at the point (3) visible for thread A. Otherwise, thread A might free or rewrite memory locations thread B is trying to read! So as a result, we are rather increasing the overhead of atomic operations for references never synchronized before.

Benefitting from the algorithm

In general, to get the most out of heap reuse in the Perceus algorithm, we need to write codes so that data structures filled with old data are updated with a small portion of new data. Pen's compiler previously had a performance bug where a relatively old data structure was merged into a new one of the same type. As a result, the code to merge two pieces of data was taking almost double in time although the logic was semantically correct.

Recursive data types

When your language has record types and syntax for record field access, things might be a little complex. Let's think about the following pseudo code where we want to update a recursive data structure of type A in place (The code is written in Elm but assume that we implemented it with Perceus.):

type alias A =
  { x : Maybe A
  , y : Int
  }

f : A -> A

-- From here, assume that we are in a function scope rather than a module scope.
foo : A
foo = { x = Nothing, y = 42 }

bar : A
bar =
  -- Here, we want to reuse a memory block of `foo`...
  { foo |
    x = case foo.x of
      Nothing -> Nothing
      -- There are two references to `x` on evaluation of `f x` here!
      Just x -> f x
  }

At the line of Just x -> f x, the program applies a function f to a field value x which originates from foo. However, at this point of the function application, we are still keeping the record value foo itself and the value of x has two references! Therefore, heap reuse specialization (i.e. in-place record update) cannot be applied there. In order to update the value of x in place instead, we need to rather deconstruct foo into its inner values first as follows.

bar =
  let { x, y } = foo
  in
    { x =
      case x of
        Nothing -> Nothing
        Just x -> f x
    , y = y
    }

Note that, even if languages do not support record deconstruction, for self-recursive types, dropping fields containing the types themselves is possible in most cases in practice because otherwise such types' values cannot exist at runtime unless they are dynamically generated in functions or thunks in those fields.

When I look at the Koka's documentation, it seems to support record types but I couldn't find out how it handles this specific case yet. It's also an option to expose the compiler's details and allow annotations to enforce in-place updates for end-users while it might not be the best option in a long term.

Benchmarking

Here, I'm excited to show some benchmark results and their improvements. Details of their configurations are in a section later. Note that Pen still lacks some basic optimizations to reduce heap allocations (e.g. lambda lifting, unboxing small values on heap.) So the eventual performance improvements by Perceus would be lower than those results.

Since I've never implemented the other GC methods like mark-and-sweep for Pen before, this is not a comparison of RC GC vs non-RC GC but rather a proof of how performant traditional thread-safe RC can be adopting Perceus on functional programming languages.

Configuration

Conway's game of life

The implementation uses lists to represent a field and lives so that it causes many allocations and deallocations of memory blocks on heap.

• Field size: 20 x 40
• Iterations: 100
• Implementation

Hash map insertion/update

The map update benchmark includes the time taken by insertion for map initialization as well.

• A number of entries: 100,000
• Key type: 64-bit floating point number
• Data structure: Hash-Array Mapped Trie (HAMT)
• Implementation
  • Insertion
  • Update

Conclusion

In my experience so far, implementing the Perceus algorithm appears to be fairly straightforward compared with the other non-RC GC algorithms while there are a few stumbling blocks especially if you are not familiar with low-level concurrency and atomic instructions.

I'm pretty happy having the algorithm implemented in my language and seeing it performing well despite its simple implementation. The Perceus RC can be a game changer in functional programming as it outperforms traditional GC on several common patterns in functional programming. However, it's definitely not for everyone and most likely affects language design.

Finally, thanks for reading! I would appreciate your feedback on this post and the Pen programming language. The language's new release has been blocked by LLVM 14 adoption in Homebrew but the ticket had some progress in the last few weeks. So I can probably release v0.4 of it soon...

Also, special thanks to the developers of Koka for answering my questions on the algorithm! That was really helpful!

Appendix

Raw benchmark results

Environment:

> uname -a
Linux xenon 5.13.0-1033-gcp #40~20.04.1-Ubuntu SMP Tue Jun 14 00:44:12 UTC 2022 x86_64 x86_64 x86_64 GNU/Linux

> lscpu
Architecture:            x86_64
  CPU op-mode(s):        32-bit, 64-bit
  Address sizes:         46 bits physical, 48 bits virtual
CPU(s):                  4
  On-line CPU(s) list:   0-3
Vendor ID:               GenuineIntel
  Model name:            Intel(R) Xeon(R) CPU @ 2.20GHz
Virtualization features:
  Hypervisor vendor:     KVM
Caches (sum of all):
  L1d:                   64 KiB (2 instances)
  L1i:                   64 KiB (2 instances)
  L2:                    512 KiB (2 instances)
  L3:                    55 MiB (1 instance)

> lsmem
Memory block size:       128M
Total online memory:       4G

Conway's game of life

> hyperfine -w 3 ./life-old ./life-new
Benchmark 1: ./life-old
  Time (mean ± σ):      2.136 s ±  0.033 s    [User: 1.699 s, System: 0.392 s]
  Range (min … max):    2.097 s …  2.206 s    10 runs

Benchmark 2: ./life-new
  Time (mean ± σ):      1.142 s ±  0.035 s    [User: 1.087 s, System: 0.009 s]
  Range (min … max):    1.102 s …  1.203 s    10 runs

Summary
  './life-new' ran
    1.87 ± 0.06 times faster than './life-old'

Hash map insertion

> hyperfine -w 3 ./insert-old ./insert-new
Benchmark 1: ./insert-old
  Time (mean ± σ):     909.0 ms ±  14.2 ms    [User: 605.7 ms, System: 250.6 ms]
  Range (min … max):   890.7 ms … 932.8 ms    10 runs

Benchmark 2: ./insert-new
  Time (mean ± σ):     254.8 ms ±   5.1 ms    [User: 189.1 ms, System: 15.0 ms]
  Range (min … max):   247.0 ms … 263.4 ms    12 runs

Summary
  './insert-new' ran
    3.57 ± 0.09 times faster than './insert-old'

Hash map update

> hyperfine -w 3 ./update-old ./update-new
Benchmark 1: ./update-old
  Time (mean ± σ):      1.935 s ±  0.032 s    [User: 1.405 s, System: 0.476 s]
  Range (min … max):    1.879 s …  1.976 s    10 runs

Benchmark 2: ./update-new
  Time (mean ± σ):     448.6 ms ±  14.4 ms    [User: 381.5 ms, System: 15.1 ms]
  Range (min … max):   430.9 ms … 484.3 ms    10 runs

Summary
  './update-new' ran
    4.31 ± 0.16 times faster than './update-old'