What is a concurrent algorithm without order?

I've heard Leslie Lamport mention on multiple occasions: "An algorithm is not a program!"
and I fully agree with him and would like to add that "A concurrent or durable algorithm without ordering is not an algorithm!"

What Leslie says makes sense because code is just a particular implementation or expression of an algorithm in a specific language. Code is bounded by the constructs that form the language in which that code is written.
An algorithm has no such constraints and is the mathematical expression of an idea.

An algorithm is precise, yet, universal.
A program works only for a particular language.

When an algorithm is incorrect, a program that uses such an algorithm will be incorrect as well.
When an algorithm is correct, a program that uses such an algorithm may be incorrect because it implemented the algorithm incorrectly, but the correctness of the underlying algorithm in unaffected.

An algorithm has mathematical beauty.
A well made program can have craftsmanship and be appreciated as beautiful, but rarely (if ever) on the mathematical sense.


So what do I mean by "An algorithm without ordering is not an algorithm"?
In the context of concurrent and/or durable algorithms order is vital for correctness. In concurrency papers, most people assume sequential consistency of the (atomic) steps that the algorithm performs and indeed, the default memory model in C11 and C++11 is memory_order_seq_cst exactly for that reason. In practice, if you were to implement a concurrent algorithm in such a way, it would likely be slow because each store (and load on non-TSO CPUs) would require a fence to guarantee ordering.
Researchers writing papers assume this strong ordering because they focus on "the algorithm" as being a series of steps and leave the dependencies of those steps (ordering) as an implementation detail.
If performance (throughput/scalability/latency) was not an issue, then we would still be using single-core CPUs and single-threaded applications and would not have to deal with all the complexity that concurrent algorithms entail! The amount of fences are (not always, but) usually what dictates the throughput of a concurrent algorithm. This means that the placement and number of fences (ordering constraints) are vital to the algorithm, not just for correctness but also for performance reasons.

The same logic applies to durable algorithms, where the ordering constraints are typically the main performance indicator. A durable algorithm without ordering does not guarantee durability and therefore, it becomes useless. However, not all steps impose a strong ordering among each other. It becomes important when we describe the algorithm to explicitly mention this dependency of steps.

Most of us don't realize the importance of "order" because for the majority of algorithms this order is implicit. For example, consider a sequential algorithm for inserting a new node in the middle of a linked-list:
Step 1) Create a new node;
Step 2) Make the "next" pointer in the node point to the successor node in the list;
Step 3) Make The "next" pointer in the predecessor node of the list point to the new node;
This is trivially simple, but if you try use this algorithm in a system where ordering is not guaranteed, these steps may become re-ordered (from the point of view of another process/thread) and the algorithm becomes incorrect. And this is one of the main issues of concurrent algorithms and even distributed systems.

Going back to Leslie, he was the first to show that to have mutual exclusion on a concurrent system we need to have at least a store-load fence. In other words, there is a minimum amount of ordering that is needed to make an algorithm that is mutually exclusive.
A similar result exists for durable algorithms: atomic durability requires at least two constraints, one for ordering and one for synchronization (round-trip), see this post for more info.
The similarity is such that Paxos, an algorithm discovered by Leslie Lamport and used in distributed systems, can be used not just to provide failure-resilience in concurrent/distributed systems but also to provide failure-resilience for durability. And the reason behind it is somewhat related to ordering.

Unfortunately, there is no easy way or commonly accepted way of expressing ordering constraints in an algorithm and because of that, most people think that orderings constraints are "an implementation detail". Likely this happens because our human brains are so used to thinking in sequential order that we expect the steps (code) that we write in a certain order to be executed in that exact order, because that's how the physical world around us typically behaves.
The problem is, concurrent algorithms don't follow these rules and because of that, ordering must be part of a concurrent algorithm.

IMO, a concurrent algorithm without a specification of the order is an incomplete algorithm. Same thing for durable algorithms. This also implies that an optimal algorithm is one that has the least amount of ordering, or in other words, a good concurrent/durable algorithm is an algorithm with a small number of fences.

Can't protect a pointer without a store-load fence

This post is about memory reclamation algorithms in shared memory concurrency. That's things like Hazard Pointers, Drop the Anchor, epoch-based reclamation (User-space RCUs) and of course, Hazard Eras. There's an insight about memory reclamation, I had a long time ago, that I want to share. This insight probably isn't new, but it was to me when I thought about it  ;)


Let's start from the beginning:

Many years ago, Leslie Lamport made a short paper where he showed that to have mutual exclusion on shared memory system, you need at least one store-load fence. Not sure this is the right reference but it's close enough to this topic:
https://www.microsoft.com/en-us/research/publication/make-multiprocessor-computer-correctly-executes-multiprocess-programs/
In other words, for two threads to have mutually exclusive access to a certain data, this data must be protected with an algorithm (a lock) and to implement this algorithm you will need at least one store and one load, whose visibility must not be re-ordered to the other thread.
It's probably easier to think about this in the context of Peterson's algorithm, or Dekker's, or one of our 10 algorithms which do the same kind of thing:
https://en.wikipedia.org/wiki/Dekker%27s_algorithm
https://en.wikipedia.org/wiki/Peterson%27s_algorithm
https://github.com/pramalhe/ConcurrencyFreaks/blob/master/papers/cr2t-2016.pdf

If you get in the context of these algorithms, you can think about the store as being a way of signaling the intent to acquire the lock, and the load as a check that the other thread doesn't already have the lock. If the effects or visibility of these two operations could be changed (by the compiler or CPU or cache-coherence system) then the algorithm would no longer be correct.
Placing a store-load fence between the store and the load prevents re-ordering from happening, making the algorithm correct, at the cost of adding synchronization.

Another analogy, is to think about a store as a mechanism to send a message to a certain centralized location, and the load as a mechanism to read the message at that centralized location. This is easier for us humans to reason about.
In the end it's all physics, transmitting information takes time, and it involves waiting which by definition is blocking or at least involves some kind of synchronization, in this case, the store-load fence.

As an aside, there are no explicit store-load fences on the C11/C++ memory model, therefore we must use a seq-cst store followed by a seq-cst load, or a relaxed store and relaxed load but with an atomic_thread_fence(memory_order_seq_cst) in the middle.


Waaaaiiit, you said you were going to talk about memory reclamation, but you're talking about mutual exclusion?!? You tricked us!!!

Not exactly, you see, the two-thread mutual exclusion problem and the memory reclamation problem have a lot in common.
A lock algorithm allows two threads to access an object, one a time. Each thread has the guarantee that when it is accessing the object, the other thread is not accessing the object.
A memory reclamation algorithm allows two threads (the reader and the reclaimer) to access an object, with the reclaimer having the guarantee that at a certain point in time the reader will never access the object again.
Notice the difference?

For mutual exclusion a thread needs to know if the other thread is not currently accessing the object, while for memory reclamation, a thread (the reclaimer) needs to know if the other thread (the reader) is not currently accessing the object nor will it ever try to access it again.

In summary, memory reclamation can be seen as mutual exclusion with a stronger requirement.
Which means, that if to do mutual exclusion we need a store-load fence, then we also need (at least) a store-load fence for doing memory reclamation.
To be more precise, a reader needs one store-load fence to signal its intent to protect an object to the reclaimer.

Now, I never proved this formally, this is just a sequence of logical deductions. So let me substantiate this bold statement with some examples.

Start by looking at figure 3 of our Hazard Eras paper:
https://github.com/pramalhe/ConcurrencyFreaks/blob/master/papers/hazarderas-2017.pdf



Looking at the left side, to protect a pointer in Hazard Eras we do a seq-cst store of this pointer on a shared array, and then we check that the pointer is still valid. There is an implicit store-load fence placed in by the compiler when we use seq-cst atomic store followed by a load.
In Hazard Pointers, at least one store-load fence is needed for every object needing protection.

Looking at the right side, to protect a pointer with URCU or Epoch-based reclamation, we do a seq-cst store of an epoch and then load whatever pointer we want to use. Again here there is an implicit store-load fence so that the store of the epoch will not be re-ordered with any of the loads of the object that will be used in the read-side critical section.
In Epoch-based reclamation, a single store-load fence is needed to protect all objects, now and until the read-side critical section ends.

Looking at the middle code, to protect a pointer with Hazard Eras, we do a seq-cst store of an era, load whatever pointers we need, and then check that the era has not changed. Again here, there is an implicit store-load fence between the store of the era and the subsequent loads. In fact, there is also a constraint that the load of the pointer(s) and the following load of the era can not be re-ordered, but that's another story.


Do you see the "pattern" now?
All three classes of algorithms require one store-load fence.
The difference between the three is that:
- Hazard Pointers does one fence to protect one object;
- Epoch-based does one fence to protect all objects (until the end of the read-side critical section);
- Hazard Eras does one fence to protect all currently live objects;
and of course, Epoch-based reclamation is blocking, while Hazard Pointers and Hazard Eras are lock-free.


Having said this, there are some apparent exceptions to this, but I would argue that the synchronization of the store-load fence is always there, it just might be hidden from sight.
For example, we can use hardware transactional memory to do memory reclamation, and no explicit store-load fence is needed... because the hardware does the corresponding synchronization internally.
http://www.cs.technion.ac.il/~erez/Papers/teleportation.pdf
It's also possible to use optimistic memory reclamation, but then we're relaxing the premises of the memory reclamation problem I stated above and that may not always be possible.
http://www.cs.technion.ac.il/~erez/Papers/oa-spaa-15.pdf
There are also other approaches that make use of services provided by the Operating System, just like there are mutual exclusion locks that are OS provided. Ultimately, they will need synchronization or a store-load fence, maybe it's the kernel that's doing it instead of the user code explicitly, but the synchronization is there somewhere, hidden behind all the OS/Kernel layers.

The final insight is the following: If it does correct and safe memory reclamation in a shared memory concurrency system, it needs at least one store-load fence, or an equivalent form of synchronization!

Dawn of the Universal Constructs

Historical Introduction

Some time ago I saw this nice presentation by Andrei Alexandrescu about Generic Locking.
https://www.youtube.com/watch?v=ozOgzlxIsdg
He starts the talk by giving an introduction to how the "Concurrency Problem" has been attacked.

And what is the "Concurrency Problem" you might ask?
Well, remember this little issue about Moore's Law (on CPU clock speed) having stopped back in 2004 and that nowadays to get more performance you need to use multiple cores, which means using some form of concurrency? Yeah, that's the "Concurrency Problem"!
Sure, if you can write your application or algorithms in a map-reduce form, then you can parallelize it, but not all algorithms are inherently parallel to profit from this approach, and those are the ones we need to worry about.

As Andrei says in his presentation, in the beginning there were mutual exclusion locks, and those were pretty much the only way to deal with concurrency.
Then came reader-writer locks, lock-free and wait-free data structures, CSP, Actor Models, Software Transactional Memory, Hardware Transactional Memory and many others.
For a while, lock-free and wait-free data structures seemed to be the thing, but the fact that there wasn't a memory model to program them in, and that it was very hard to verify their correctness, and very hard to do efficient lock-free memory reclamation (wait-free is even harder), it caused people to try the other approaches. Nowadays, there is no clear winner, and maybe there never will be. Actor models have been gaining a lot of followers, with the whole Rx/Reactive movement based on it... I'm not sure they all realize that at the base of the actor model is the message-passing queue between the actors which is itself based on a lock-free queue.

Anyways, fast-forwarding to 2017, one of the upcoming CppCon talks which will definitly be worth watching, is the one by Paul McKennney, Maged Michael and Michael Wong:
https://cppcon2017.sched.com/event/Bgtm/the-landscape-of-parallel-programming-models-is-it-still-hard-or-just-ok-part-1-of-2?iframe=no&w=100%&sidebar=no&bg=no
As they mention in the abstract, there was a time when writing a simple loop seemed as perilous then as writing a lock-free data structure seems now.
I don't know what their talk will be about, but I do agree that most of the dangers in concurrent programming can be avoided by using better programming tools, and on that note, I would dare go so far as to say that we're entering "The Dawn of the Universal Constructs"!

What is a Universal Construct

Universal Constructs aren't a new thing. The first Wait-Free Universal Construct (WFUC) was invented by Maurice Herlihy back in 1993:
http://www.cs.utexas.edu/~lorenzo/corsi/cs380d/papers/p745-herlihy.pdf
WFUCs are a construction that encapsulate an object (or data structure) which was written for single-threaded usage, and provide a way to call its methods with wait-free progress.
It's kind of like wrapping all the methods in an object with a call to lock()/unlock() of a mutual exclusion lock, except that a lock is blocking while WFUC are, well, wait-free!



In summary, a Wait-Free Universal Construct lets you write your favorite data structure as if it was "single-threaded code" and then wraps its methods to provide wait-free progress.
If you saw Andrei's presentation at the beginning of the post, you'll know that he has a cool way (in C++) of automatically exporting the methods of an object/data-structure wrapped with a read-lock or a write-lock depending on whether the methods are mutative or read-only. The same kind of approach can be done with WFUCs, which means that they are truly generic.

How come I never heard of this before?

Well, you kind of have heard about this (if you read this blog).
Left-Right for example, is a Universal Construct that provides wait-free progress for readers and blocking (starvation-free) progress for writers:
http://concurrencyfreaks.blogspot.nl/2013/12/left-right-concurrency-control.html
It's fast, it reclaims memory, it's "universal", but it's not completely wait-free, i.e. it's not wait-free for mutations.

There are truly WFUCs in the literature and we've even added (wait-free) memory reclamation to a few of them. The most famous being P-Sim by Panagiota Fatourou and Nikolaos Kallimanis:
http://thalis.cs.uoi.gr/tech_reports/publications/TR2011-01.pdf

But even the best of them still works on the COW principle, in the sense that it requires a full copy of the data structure for every mutation.
Yes, that's right, if we have a map with 1M keys/values, and we want to insert a new key (or remove an existing one), we have to make a full copy of the 1M nodes of the data structure.

Waaaaiiiit wwwhhhaaat? Did you just say that this thingy has to copy 1 million nodes every time I want to insert a new key/value in my hashmap?

Yes, I'm afraid that's how it works. It's not as bad as it looks if the data structure is small, but as soon as you start going to anything bigger than a few thousand nodes in the data structure, throughput is going to go down the drain. And cache locality is a big issue with COW.

What's on the horizon

I happen to have insider knowledge that it is possible to make a wait-free universal construct that is fast enough to be used in production, because it doesn't have to copy the entire data structure (except on very rare occasions). This new way of doing WFUCs is fast enough to be used in real-life applications, in fact, it's capable of beating hand-written lock-free and wait-free data structures.
Yes, it's that good. We call it CX and the paper is almost ready.
... did I say it does wait-free memory reclamation as well?  ;)

As soon as other researchers see what CX is capable of, I'm sure they will have their own ideas and improve upon it, thus bringing about a new age of production-capable WFUCs.

Going back to the Concurrency Problem, how does this change the way we program multi-threaded applications?

Based on my experience as a developer, software engineers rarely use an off-the-shelf data structure as is. We always add a little twist to it.
I don't know whether this happens due to us having big egos and wanting to give our little personal touch to everything we do (I'm generalizing here), or if it's simply because we're tinkerers and we like to see what's under the hood and tweak it to our own desire. the truth is, if we could use it as is then there wouldn't be a need to write all the software people write, there would be just one search engine, just one banking software, just one customer management software, etc.

Whatever the reason may be, the consequence is, that we always make changes to the data structures, and the problem with that, is that lock-free and wait-free data structures will fall apart if they're touched. They have sequences of instructions that have to be done in a particular way, they have optimizations for relaxed memory orderings and subtle details, and memory reclamation, etc, etc. The temptation to touch and tinker a lock-free data structure is just too much, and we end up getting burned and then we say that "lock-free data structures suck", which is not true.
The algorithms behind these data structures are very subtle, and our human nature is to tinker with it, which is incompatible.

This is where Wait-Free Universal Constructs come in.
With an efficient WFUC, any software engineer without any knowledge of lock-free data structures (or atomics or the memory model) can just take a "single-threaded data structure", modify it to satisfy its needs (or ego) and then wrap it with WFUC and BOOOOM, out comes a fast and scalable implementation of its customized data structure, with wait-free progress.
Even more, another software engineer working on the code can later fix bugs or add new features to the data structure without breaking its correct functionality. Try doing that with a lock-free data structure, it's hard enough to get it right the first time, to add new functionality later is just too nuts.
As a software engineer, what more could I ask for?

No wonder that WFUCs are seen by researchers as the Holy Grail of concurrency, it's because they make it so easy to solve the Concurrency Problem in production.
Yes, I'm a fan boy of Universal Constructs, but the hype is called for and needed. This stuff doesn't solve all the concurrency problems, but it solves a a lot of them, enough to become a standard way of dealing with multi-threaded code, or at least for writing multi-threaded data structures.

Whatever happens, Universal Constructs are here to stay as one of the easiest tools to use when writing multi-threaded applications, and we all know that when it comes to multi-threaded programs, any help we can get is not enough  ;)