Parallel Programming in Multicore OCaml

This tutorial will help you get started with writing parallel programs in Multicore OCaml. All the code examples along with their corresponding dune file are available in the

code/

• Introduction
  • Installation
  • Compatibility with existing code
• Domains
• Domainslib
  • Task pool
  • Parallel for
  • Async-Await
  • Fibonacci numbers in parallel
• Channels
  • Bounded Channels
  • Task Distribution using Channels
• Profiling your code
  • Perf
  • Eventlog

Introduction

Multicore OCaml is an extension of OCaml with native support for Shared-Memory Parallelism (SMP) through

Domains

Algebraic Effects

Concurrency is how we partition multiple computations such that they can run in overlapping time periods rather than strictly sequentially. Parallelism is the act of running multiple computations simultaneously, primarily by using multiple cores on a multicore machine. The Multicore Wiki has comprehensive notes on the design decisions and current status of Concurrency and Parallelism in Multicore OCaml.

The Multicore OCaml compiler ships with a concurrent major and a stop-the-world minor garbage collector (GC). The parallel minor GC doesn't require any changes to the C API, thereby not breaking any associated code with C API. The Multicore bits of the compiler are actively being integrated with the mainstream OCaml compiler with some PRs already merged into its trunk. OCaml 5.0 is expected to land with support for Shared-Memory Parallelism and Algebraic Effects in later releases. A historical variant of the Multicore minor garbage collector is the concurrent minor collector. Benchmarking experiments showed better results in terms of throughput and latency on the stop-the-world parallel minor collector, hence that's chosen to be the default minor collector on Multicore OCaml, and the concurrent minor collector is not actively developed. For the intrigued, details on the design and evaluation of the Multicore GC and compiler are in our academic publications.

The Multicore ecosystem also has the following libraries to complement the compiler:

• Domainslib: data and control structures for parallel programming
• Lockfree: lock-free data structures (list, hash, bag and queue)
• Reagents: composable lock-free concurrency library for expressing fine grained parallel programs on Multicore OCaml
• Kcas: multi-word compare and swap library

Find ways to profitably write parallel programs in Multicore OCaml. The reader is assumed to be familiar with OCaml. If not, they are encouraged to read Real World OCaml. The effect handlers' story is not covered here. For anyone interested, please check out this tutorial and some examples.

Installation

The latest Multicore compiler version (4.12) can be obtained from multicore-opam. Installation instructions for the Multicore compiler and parallel programming library

domainslib

It will also be useful to install

utop

opam install utop

Compiler Variants and Compatibility

4.12.0+domains

ppx

4.12.0+domains+effects

Domains

Domains are the basic unit of Parallelism in Multicore OCaml.

let square n = n * n

let x = 5
let y = 10
let _ =
  let d = Domain.spawn (fun _ -> square x) in
  let sy = square y in
  let sx = Domain.join d in
  Printf.printf "x = %d, y = %d\n" sx sy

Domain.spawn

Domain.join d

d

Domain.join d

Note that the square of x is computed in a new domain and that of y in the parent domain.

To create its corresponding dune file, run this code:

(executable
  (name square_domain)
  (modules square_domain))

Make sure to use a Multicore switch to build this and all other subsequent examples in this tutorial.

To execute the code:

$ dune build square_domain.exe
$ ./_build/default/square_domain.exe
x = 25, y = 100

As expected, the squares of x and y are 25 and 100.

Common Error Message

Some common errors while compiling Multicore code are:

Error: Unbound module Domain

Error: Unbound module Atomic

Error: Library "domainslib" not found.

These errors usually mean that the compiler switch used is not a Multicore switch. Using a Multicore compiler variant should resolve them.

Domainslib

Domainslib

• Task: Work stealing task pool with async/await Parallelism and

  parallel_{for, scan}

• Channels: Multiple Producer Multiple Consumer channels which come in two flavours—bounded and unbounded

Domainslib

Task.pool

In the Domains section, we saw how to run programs on multiple cores by spawning new domains. We often find ourselves spawning and joining new domains numerous times in the same program, if we were to use that approach for executing code in parallel. Creating new domains is an expensive operation, so we should attempt to limit those when possible.

Task.pool

Note: If you are running this on

utop,

#require "domainslib"

# open Domainslib

let pool = Task.setup_pool ~num_additional_domains:3
val pool : Task.pool = 

We have created a new task pool with three new domains. The parent domain is also part of this pool, thus making it a pool of four domains. After the pool is setup, we can use it to execute all tasks we want to run in parallel. The

setup_pool

num_additional_domains

Although not strictly necessary, we highly recommended closing the task pool after execution of all tasks. This can be done as follows:

# Task.teardown_pool pool

This deactivates the pool, so it's no longer usable. Make sure to do this only after all tasks are done.

Parallel_for

In the Task API, a powerful primitive called

parallel_for

for

Consider the example of matrix multiplication.

First, write the sequential version of a function which performs matrix multiplication of two matrices and returns the result:

let matrix_multiply a b =
  let i_n = Array.length a in
  let j_n = Array.length b.(0) in
  let k_n = Array.length b in
  let res = Array.make_matrix i_n j_n 0 in
  for i = 0 to i_n - 1 do
    for j = 0 to j_n - 1 do
      for k = 0 to k_n - 1 do
        res.(i).(j) 
To make this function run in parallel, one might be inclined to spawn a new
domain for every iteration in the loop, which would look like:
  let domains = Array.init i_n (fun i ->
    Domain.spawn(fun _ ->
      for j = 0 to j_n - 1 do
        for k = 0 to k_n - 1 do
          res.(i).(j) 
This will be disastrous in terms of performance, mostly because 
spawning a new domain is an expensive operation. Alternatively, a task pool offers 
a finite set of available domains that can be used to run your
computations in parallel.

Arrays are usually more efficient compared with lists in Multicore OCaml. 
Although they are not generally favoured in functional
programming, using arrays for the sake of efficiency is a reasonable trade-off.

A better way to parallelise matrix multiplication is with the help of a
parallel_for
.
let parallel_matrix_multiply pool a b =
  let i_n = Array.length a in
  let j_n = Array.length b.(0) in
  let k_n = Array.length b in
  let res = Array.make_matrix i_n j_n 0 in

  Task.parallel_for pool ~start:0 ~finish:(i_n - 1) ~body:(fun i ->
    for j = 0 to j_n - 1 do
      for k = 0 to k_n - 1 do
        res.(i).(j) 
Observe quite a few differences between the parallel and sequential
versions: The parallel version takes an additional parameter 
pool
 because 
the 
parallel_for
 executes the 
for
 loop on the domains present in
that task pool. While it is possible to initialise a task pool inside the
function itself, it's always better to have a single task pool used across the
entire program. As mentioned earlier, this is to minimise the cost involved in
spawning a new domain. It's also possible to create a global task pool to use 
across, but for the sake of reasoning better about your code, it's recommended 
to use it as a function parameter.

Let's examine the parameters of 
parallel_for
. It takes in 
- 
pool
, as discussed earlier 
- 
start
 and 
finish
, as the names suggest, are the starting
and ending values of the loop iterations
- 
body
 contains the actual loop body to be executed

parallel_for
 also has an optional parameter: 
chunk_size
, which determines the
granularity of tasks when executing on multiple domains. If no parameter
is given for 
chunk size
, the program determines a default chunk size that performs
well in most cases. Only if the default chunk size doesn't work well is it
recommended to experiment with different chunk sizes. The ideal 
chunk_size
depends on a combination of factors:

• Nature of the Loop: There are two things to consider pertaining to the loop when deciding on a

  chunk_size

  —the number of iterations in the loop and the amount of time each iteration takes. If the amount of time is roughly equal, then the

  chunk_size

  could be the number of iterations divided by the number of cores. On the other hand, if the amount of time taken is different for every iteration, the chunks should be smaller. If the total number of iterations is a sizeable number, a

  chunk_size

  like 32 or 16 is safe to use, whearas if the number of iterations is low, like 10, a

  chunk_size

  of 1 would perform best.

• Machine: Optimal chunk size varies across machines, so it's recommended to experiment with a range of values to find out what works best on yours.

Speedup

Let's find how the parallel matrix multiplication scales on multiple cores.

Speedup

The speedup vs. core is enumerated below for input matrices of size 1024x1024:

| Cores | Time (s) | Speedup | |-------|----------|-------------| | 1 | 9.172 | 1 | | 2 | 4.692 | 1.954816709 | | 4 | 2.293 | 4 | | 8 | 1.196 | 7.668896321 | | 12 | 0.854 | 10.74004684 | | 16 | 0.76 | 12.06842105 | | 20 | 0.66 | 13.8969697 | | 24 | 0.587 | 15.62521295 |

We've achieved a speedup of 16 with the help of a

parallel_for

Note that parallel code performance heavily depends on the machine. Some machine settings specific to Linux systems for obtaining optimal results are described here.

Properties and Caveats of

parallel_for

Implicit Barrier

The

parallel_for

parallel_for

parallel_for

parallel_for

m1

m2

m3

(m1*m2) * m3

*

let parallel_matrix_multiply_3 pool m1 m2 m3 =
  let size = Array.length m1 in
  let t = Array.make_matrix size size 0 in (* stores m1*m2 *)
  let res = Array.make_matrix size size 0 in

  Task.parallel_for pool ~start:0 ~finish:(size - 1) ~body:(fun i ->
    for j = 0 to size - 1 do
      for k = 0 to size - 1 do
        t.(i).(j) 
    for j = 0 to size - 1 do
      for k = 0 to size - 1 do
        res.(i).(j) 
In a hypothetical situation where 
parallel_for
 didn't have an implicit
barrier, as in the example above, it's very likely that the computation of 
res
wouldn't be correct. Since we already have an implicit barrier, it will perform 
the right computation.

Order of Execution
for i = start to finish do

done

A sequential 
for
 loop, like the one above, runs its iterations in the exact
same order, from 
start
 to 
finish
. However, 
parallel_for
 makes the order of
execution arbitrary and varies it between two runs of the exact same code. If
the iteration order is important for your code, it's
advisable to use 
parallel_for
 with some caution.

Dependencies Within the Loop

If there are any dependencies within the loop, such as a current iteration
depending on the result of a previous iteration, odds are very high that the
correctness of the code no longer holds if 
parallel_for
 is used. Task API has
a primitive 
parallel_scan
 which might come in handy in scenarios like this.

Async-Await

A 
parallel_for
 loop easily parallelises iterative tasks. Async-Await offers more
flexibility to execute parallel tasks, which is especially useful in
recursive functions. Earlier we saw how to setup and tear down a task
pool. The Task API also has the facility to run specific tasks on a task pool.

Fibonacci Numbers in Parallel

To calculate a Fibonacci Sequence in parallel, first write a sequential function to calculate Fibonacci numbers. 
The following is a naive Fibonacci function without tail-recursion:
let rec fib n =
if n < 2 then 1
else fib (n - 1) + fib (n - 2)

Observe that the two operations in recursive case 
fib (n - 1)
 and 
fib (n -2)
 
do not have any mutual dependencies, which makes it convenient to
compute them in parallel. Essentially, we can calculate 
fib (n - 1)
 and 
fib (n - 2)
 
in parallel and then add the results to get the answer.

Do this by spawning a new domain for performing the calculation and joining
it to obtain the result. Be careful to not spawn more domains
than number of cores available.
let rec fib_par n d =
  if d <= 1 then fib n
  else
    let a = fib_par (n-1) (d-1) in
    let b = Domain.spawn (fun _ -> fib_par (n-2) (d-1)) in
    a + Domain.join b

We can also use task pools to execute tasks asynchronously, which is less tedious and scales better.
let rec fib_par pool n =
  if n <= 40 then fib n
  else
    let a = Task.async pool (fun _ -> fib_par pool (n-1)) in
    let b = Task.async pool (fun _ -> fib_par pool (n-2)) in
    Task.await pool a + Task.await pool b

Note some differences from the sequential version of Fibonacci:

• pool

  —> an additional parameter for the same reasons in

  parallel_for

• if n <= 40 then fib n

  -> when the input is less than 40, run the sequential

  fib

  function. When the input number is small enough, it's better to perform the calculations sequentially. We've taken

  40

  as the threshold (above). Some experimentation would help find an acceptible threshold, below which the computation can be performed sequentially.

• Task.async

  and

  Task.await

  -> used to run the tasks in parallel
  • Task.async executes the task in the pool asynchronously and returns a promise, a computation that is not yet complete. After the execution finishes, it result will be stored in the promise.
  • Task.await waits for the promise to complete its execution. Once it's done, it returns the result of the task. In case the task raises an uncaught exception,

    await

    also raises the same exception.

Channels

Bounded Channels

Channels act as a medium to communicate data between domains and can be shared between multiple sending and receiving domains. Channels in Multicore OCaml come in two flavours:

• Bounded: buffered channels with a fixed size. A channel with the buffer size 0 corresponds to a synchronised channel, and buffer size 1 gives the

  MVar

  structure. Bounded channels can be created with any buffer size.

• Unbounded: unbounded channels have no limit on the number of objects they can hold, so they are only constrained by memory availability.

open Domainslib

let c = Chan.make_bounded 0
let _ =
  let send = Domain.spawn(fun _ -> Chan.send c "hello") in
  let msg =  Chan.recv c in
  Domain.join send;
  Printf.printf "Message: %s\n" msg

In the above example, we have a bounded channel

c

send

recv

recv

open Domainslib

let c = Chan.make_bounded 0
let _ =
  let send = Domain.spawn(fun _ -> Chan.send c "hello") in
  Domain.join send;

The above example would block indefinitely because the

send

recv

open Domainslib

let c = Chan.make_bounded 1
let _ =
  let send = Domain.spawn(fun _ -> Chan.send c "hello") in
  Domain.join send;

Now the send will not block anymore.

If you don't want to block in

send

recv

send_poll

recv_poll

true

false

open Domainslib

let c = Chan.make_bounded 0
let _ =
  let send = Domain.spawn(fun _ ->
          let b = Chan.send_poll c "hello" in
          Printf.printf "%B\n" b) in
  Domain.join send;

Here the buffer size is 0 and the channel cannot hold any object, so this program prints a false.

The same channel may be shared by multiple sending and receiving domains.

open Domainslib

let num_domains = try int_of_string Sys.argv.(1) with _ -> 4
let c = Chan.make_bounded num_domains
let send c =
  Printf.printf "Sending from: %d\n" (Domain.self () :> int);
  Chan.send c "howdy!"
let recv c =
  Printf.printf "Receiving at: %d\n" (Domain.self () :> int);
  Chan.recv c |> ignore
let _ =
  let senders = Array.init num_domains
                  (fun _ -> Domain.spawn(fun _ -> send c )) in
  let receivers = Array.init num_domains
                  (fun _ -> Domain.spawn(fun _ -> recv c)) in
  Array.iter Domain.join senders;
  Array.iter Domain.join receivers

(Domain.self () :> int)

Task Distribution Using Channels

Now that we have some idea about how channels work, let's consider a more realistic example by writing a generic task distributor that executes tasks on multiple domains:

module C = Domainslib.Chan
let num_domains = try int_of_string Sys.argv.(1) with _ -> 4
let n = try int_of_string Sys.argv.(2) with _ -> 100

type 'a message = Task of 'a | Quit
let c = C.make_unbounded ()
let create_work tasks =
  Array.iter (fun t -> C.send c (Task t)) tasks;
  for _ = 1 to num_domains do
    C.send c Quit
  done
let rec worker f () =
  match C.recv c with
  | Task a ->
      f a;
      worker f ()
  | Quit -> ()
let _ =
  let tasks = Array.init n (fun i -> i) in
  create_work tasks ;
  let factorial n =
    let rec aux n acc =
        if (n > 0) then aux (n-1) (acc*n)
        else acc in
    aux n 1
  in
  let results = Array.make n 0 in
  let update r i = r.(i)  Domain.spawn(worker (update results))) in
  worker (update results) ();
  Array.iter Domain.join domains;
  Array.iter (Printf.printf "%d ") results

We have created an unbounded channel

c

create_work

worker

create_work

c

worker

f

Quit

worker

Use this template to run any task on multiple cores by running the

worker

worker

worker

Profiling Your Code

While writing parallel programs in Multicore OCaml, it's quite common to encounter overheads that might deteriorate the code's performance. This section describes ways to discover and fix those overheads. Within the Multicore runtime, Linux commands

perf

eventlog

Perf

The Linux

perf

Profiling Serial Code

Profiling serial code can help identify parts of code that can potentially benefit from parallelising. Let's do it for the sequential version of matrix multiplication:

perf record --call-graph dwarf ./matrix_multiplication.exe 1024

This results in a profile showing how much time is spent in the

matrix_multiply

Profiling serial code can help reveal the hotspots where we might want to introduce parallelism.

Samples: 51K of event 'cycles:u', Event count (approx.): 28590830181
  Children      Self  Command     Shared Object     Symbol
+   99.84%     0.00%  matmul.exe  matmul.exe        [.] caml_start_program
+   99.84%     0.00%  matmul.exe  matmul.exe        [.] caml_program
+   99.84%     0.00%  matmul.exe  matmul.exe        [.] camlDune__exe__Matmul__entry
+   99.32%    99.31%  matmul.exe  matmul.exe        [.] camlDune__exe__Matmul__matrix_multiply_211
+    0.57%     0.04%  matmul.exe  matmul.exe        [.] camlStdlib__array__init_104
     0.47%     0.37%  matmul.exe  matmul.exe        [.] camlStdlib__random__intaux_278

Overheads in Parallel Code

Linux

perf

Parallel Initialisation of a Float Array with Random Numbers

Array initialisation using the standard library's

Array.init

For float arrays, we have

Array.create_float

Naive Implementation

Below is a naive implementation that will initialise all array elements with a Random number:

open Domainslib

let num_domains = try int_of_string Sys.argv.(1) with _ -> 4
let n = try int_of_string Sys.argv.(2) with _ -> 100000
let a = Array.create_float n
let _ =
  let pool = Task.setup_pool ~num_additional_domains:(num_domains - 1) in
  Task.parallel_for pool ~start:0
  ~finish:(n - 1) ~body:(fun i -> Array.set a i (Random.float 1000.));
  Task.teardown_pool pool

Measure how it scales:

| #Cores | Time(s) | |--------|---------| | 1 | 3.136 | | 2 | 10.19 | | 4 | 11.815 |

Although we expected to see speedup executing in multiple cores, the code actually slows down as the number of cores increase. There's something unnoticably wrong with the code.

Let's profile the performance with the Linux

perf

$ perf record ./_build/default/float_init_par.exe 4 100_000_000
$ perf report

The

perf

The overhead at Random bits is a whopping 87.99%! Typically there's no single cause that we can attribute to such overheads, since they are very specific to the program. It might need a little careful inspection to find out what is causing them. In this case, the Random module shares the same state amongst all domains, which causes contention when multiple domains are trying to access it simultaneously.

To overcome that, use a different state for every domain so there isn't any contention from a shared state.

module T = Domainslib.Task
let n = try int_of_string Sys.argv.(2) with _ -> 1000
let num_domains = try int_of_string Sys.argv.(1) with _ -> 4

let arr = Array.create_float n
let _ =
  let domains = T.setup_pool ~num_additional_domains:(num_domains - 1) in
  let states = Array.init num_domains (fun _ -> Random.State.make_self_init()) in
  T.parallel_for domains ~start:0 ~finish:(n-1)
  ~body:(fun i ->
    let d = (Domain.self() :> int) mod num_domains in
    Array.unsafe_set arr i (Random.State.float states.(d) 100. ))

We have created

num_domains

Let's run this on multiple cores:

| #Cores | Time(s) | |--------|---------| | 1 | 3.828 | | 2 | 3.641 | | 4 | 3.119 |

Examining the times, though it is not as bad as the previous case, it isn't close to what we expected. Here's the

perf

The overheads at Random bits is less than the previous case, but it's still quite high at 59.73%. We've used a separate Random State for every domain, so the overheads aren't caused by any shared state; however, if we look closely, the Random States are all allocated by the same domain in an array with a small number of elements, possibly located close to each other in physical memory. When multiple domains try to access them, they might be sharing cache lines, or

false sharing

perf c2c

$ perf c2c record _build/default/float_init_par2.exe 4 100_000_000
$ perf c2c report

Shared Data Cache Line Table     (2 entries, sorted on Total HITMs)
       ----------- Cacheline ----------    Total      Tot  ----- LLC Load Hitm -----  ---- Store Reference ----  --- Loa
Index             Address  Node  PA cnt  records     Hitm    Total      Lcl      Rmt    Total    L1Hit   L1Miss       Lc
    0      0x7f2bf49d7dc0     0   11473    13008   94.23%     1306     1306        0     1560      595      965        ◆
    1      0x7f2bf49a7b80     0     271      368    5.48%       76       76        0      123       76       47

As evident from the report, there's quite a considerable amount of false sharing happening in the code. To eliminate false sharing, allocate the Random State in the domain that is going to use it, so the states will be allocated with memory locations far from each other.

module T = Domainslib.Task
let n = try int_of_string Sys.argv.(2) with _ -> 1000
let num_domains = try int_of_string Sys.argv.(1) with _ -> 4

let arr = Array.create_float n
let init_part s e arr =
    let my_state = Random.State.make_self_init () in
    for i = s to e do
      Array.unsafe_set arr i (Random.State.float my_state 100.)
    done
let _ =
  let domains = T.setup_pool ~num_additional_domains:(num_domains - 1) in
  T.parallel_for domains ~chunk_size:1 ~start:0 ~finish:(num_domains - 1)
  ~body:(fun i -> init_part (i * n / num_domains) ((i+1) * n / num_domains - 1) arr);
  T.teardown_pool domains

Now the results are:

| Cores | Time | Speedup | |-------|-------|-------------| | 1 | 3.055 | 1 | | 2 | 1.552 | 1.968427835 | | 4 | 0.799 | 3.823529412 | | 8 | 0.422 | 7.239336493 | | 12 | 0.302 | 10.11589404 | | 16 | 0.242 | 12.62396694 | | 20 | 0.208 | 14.6875 | | 24 | 0.186 | 16.42473118 |

In this process, we have essentially identified bottlenecks for scaling and eliminated them to achieve better speedups. For more details on profiling with

perf

Eventlog

The Multicore runtime supports OCaml instrumented runtime. The instrumented runtime enables capturing metrics about various GC activities. Eventlog-tools is a library that provides tools to parse the instrumentation logs generated by the runtime. Some handy tools are described in the README.

Eventlog tools can be useful for optimizing Multicore programs.

Identify Large Pausetimes

Identifying and fixing events that cause maximun latency can improve the overall throughput of the program.

ocaml-eventlog-pausetimes

$ ocaml-eventlog-pausetimes caml-10599-0.eventlog caml-10599-2.eventlog caml-10599-4.eventlog caml-10599-6.eventlog
{
  "name": "caml-10599-6.eventlog",
  "mean_latency": 78328,
  "max_latency": 5292643,
  "distr_latency": [85,89,104,231,303,9923,117639,145118,179488,692880,2728990]
}

Diagnose Imbalance in Task Distribution

Eventlog can be useful to find imbalance in task distribution in a parallel program. Imbalance in task distribution essentially means that not all domains are provided with equal amount of computation to perform, so some domains take longer than others to finish their computations, while the idle domains keep waiting. This can occur when a sub- optimal

chunk_size

parallel_for

Time periods show when an idle domain is recorded as

domain/idle_wait

eventlog

eventlog

If we zoom in further, we see many

domain/idle_wait

So far we've only found an imbalance in task distribution in the code, so we'll need to change our code accordingly to make the task distribution more balanced, which could increase the speedup.

Performace debugging can be quite tricky at times, so if you could use some help in debugging your Multicore OCaml code, feel free to create an Issue in the Multicore OCaml issue tracker along with a minimal code example.