Some opinions about “algorithms startups”, from a sample size of approximately 1

Something a little different today. For my regular readers, I promise to try to keep the number of “opinion/rant” posts to a minimum and we’ll be back on our regular technical content in a few days. It’s pretty easy to just whack the keys and issue Epic Pronouncements on things, but the effect is limited:

In any case, I have had this post kicking around in my brain in some form for years.

Preliminary Comments, Background, Disclaimers

I’m going to talk about “algorithms startups”: this is a vague term to mean a startup that is oriented around building and selling (in some form) an algorithm – as opposed to building a complete solution and trying to make money directly from customers. I don’t mean a “pure” IP play where you invent something, patent the hell out of it, and try to extract money from world+dog. I’m assuming we’re talking about inventing something that didn’t exist before, writing the code yourselves, and trying to make money more or less directly from the code.

My experience (short version): I joined a startup (Sensory Networks, founded in 2003) while it was quite large in 2006, watched it lose traction until the end of 2008, and formed part of a small team (5 people, at the start of 2009) which took a small chunk of additional funding and took the business to a decent exit (I claim ‘decent’, in terms of the scale and funding of the startup since 2009) in 2013.

We built a software-based regular expression matcher called Hyperscan which we sold as a closed-source commercial library. Hyperscan was later (2015) open-sourced at Intel. I don’t know how to make money directly off open source so if you’re hoping for insights there I don’t have any experience.

Sensory Networks wasn’t planned to be an pure ‘algorithms startup’ – we just wound up there by default; focusing on the core of the task was the only viable way forward from 2009 onward.

I should note that many – most, even – of the interesting things that happened at Sensory Networks and subsequently at Intel are commercial-in-confidence. So, boringly, I am not going to be reeling forth exciting details of evaluations and commercial deals made with brand name companies That You’ve Probably Heard Of. There will be no exciting insider revelations, just affirmation of principles you’ve probably heard 50 times before for the most part. I will also not discuss acquisition mechanics.

I draw my experience both from Sensory Networks and my continued experiences with the Hyperscan product but also from watching closely a lot of other startups in the area. While we did some things right, we got a lot of stuff wrong, too. Unfortunately, a bunch of the things we didn’t do right are tied up with things that I can’t talk about or they are speculative (it’s easy to speculate about things you should have done but hard to tell whether pursuing alternate strategies would have worked better).

I’m assuming that most readers have already heard about the idea of continuous integration, fixing bugs first, etc. so we can take that stuff as read.

Many of the principles here were applied by much better software engineers than I am; I may talk a great line about testability and API design and fuzzing and so on, but most of the real work in this area was done by the core Sensory Networks team of developers from the restart in 2009 through to the Intel acquisition and beyond: Matt Barr, Alex Coyte, and Justin Viiret.

It’s also clear that the continued good qualities of Hyperscan and the freedom to pursue the strategy of open-sourcing the product are due to many good people at Intel. I don’t want to make it sound like the story of the product is over. What we learned is captured in the existing Hyperscan product and the processes around it. This post doesn’t focus on the post-acquisition side of things; the privilege of being able to give away your software is while working in a large company is a very different story than the process of getting to that point. It’s also a story that you’re not usually allowed to tell! 🙂

Opinions are my own and not that of any other person, past employer, etc.

So, in no particular order, some opinions about ‘algorithms startups’.

Doing an algorithms startup is a lot of fun

First of all, while there were parts of the process that were awful, if you like computer science, this kind of startup can yield an enjoyable experience. This may vary for different team members and at different times, of course. If you want to work on interesting algorithms and have picked a market where that’s actually rewarded, you might enjoy your work.

Doing an algorithms startup won’t necessarily make you tons of money

Obviously, no startup is guaranteed to make tons of money. But algorithms startups have some extra downsides.

  1. You are attempting to make money from other businesses. You’re going to paid a pittance relative to what they are getting, for good reason. They are building the user interfaces, supporting thousands of customers, building all the boring code you aren’t interested in or couldn’t possibly write yourself.

    It’s also very likely that you’ll get paid very slowly. Try not to die in the interim!

    The lifesaver for you is that once you get your system accepted by other businesses, they will keep paying for it and you can go and sell the same code to lots of other companies (“Doctrine of Multiple Use”).

  2. You are competing with Free and Open Source if you are closed-source, or you are trying to make money off a product that people can get for free and dissect if not.

    I have no experience trying to make money off FOSS software so I can’t speculate about how hard that is.

    Competing with FOSS (while still asking for money for closed-source software) is difficult, and you need an enormous advantage. There were a number of FOSS regular expression matchers around when Hyperscan was closed-source, but none of them were close to providing what our customers wanted (large scale pattern matching and ‘streaming’ matching).

I think a startup of this kind can make a fair bit of money, but I would be surprised to hear that it’s in the ‘hyper-growth’ category.

Speculative: What should an algorithms startup do after capturing most of the Total Addressable Market for that algorithm? When are you ready to do that?

This gets into unexplored territory: our answer turned out to be “get acquired”. I would hazard a guess that it’s at least possible for a algorithms startup with a good structure to move into adjacent markets and continue growing. Maybe if you’re good enough at this you could make something big…

Equally speculative would be answers to questions like “when is your core algorithmic product essentially ‘done'”? We continued to tune Hyperscan, always aware of gaps in performance, excessive costs of various kinds (bytecode size, stream size, compile time) and gaps in functionality that might be expected from a regular expression matcher (unsupported constructs).

So we never answered either of these questions – at least not directly – but that answer would be pretty important for a similar startup in a similar place several years in.

Don’t drift into being a consulting business

Stick to the Doctrine of Multiple Use; don’t build special-purpose builds of your software if you can help it, and definitely don’t just wander into consulting if you didn’t intend to have a consulting business.

We had some extra help with this – the Australian government had a nice R&D scheme (now the “Research and Development Tax Incentive”). This mandated a doctrine of “multiple sales” – we couldn’t get a generous credit for work done for just one company. This ‘restraint’ helped us in the long term (not just the money, but the discipline).

We did add a few features in the pre-Hyperscan 4.0-era (before the open source release) that were each ultimately needed by just one customer in the end. These features were always theoretically interesting more broadly and we didn’t do special-purpose builds for single customers; these single-customer features were made available to all. However, they never really got wide adoption.

Ultimately these features were dead-ends – adding a big testing load (adding weird new modes or API functions often increased the test load geometrically) while never getting much use. On the flip side, some of these features were needed to stay alive commercially.

Iterate, and release a Minimum Viable Product (MVP) early, but make the MVP actually Viable

You have to offer something much better than the alternative. A critical functionality improvement or 5-10x on some metric will get you noticed – and unless you’re a drop-in replacement for something else, you’ll probably need that big improvement.

The idea that you build a Minimal Viable Product is now a cliché. It’s harder than it sounds, even when you plan to do it. For an algorithmic startup, there’s a fine line between “unintentionally trivial” and “minimal”.

When we built Hyperscan, the first iteration of what became the successful product (Hyperscan 2.0 – 1.0 was built on different lines and very little aside from the parser was retained) was pretty awful in many respects. Tons of different regular expression constructs would be either slow or not supported (“Pattern too large error”). An extremely early evaluation version even occasionally printed curse words on the console, a behaviour not normally desired in software libraries.

However, we did have some killer features:

  1. Supporting lots of regular expressions at a time (alternatives like libpcre or Java regex only supported 1 at a time),
  2. Streaming (the ability to suspend and resume a regex match, as you would need to if matching a regex across a stream of packets), and
  3. High performance (we were typically quite a bit faster than alternatives – 5-10x was typical).

People were willing to live with a lot of quirks and edge cases if we could deliver on those three items. Over time most of the more obvious quirks and edge cases went away (especially compared to the competition).

We weren’t a drop-in replacement for any other regular expression matcher, so a modest increase in performance was always offset against developer effort at our customers. Evaluations where we couldn’t deliver a big speedup or some substantial new functionality almost always failed. They even failed later, when we were an open source product and were giving Hyperscan away for free.

If your key selling point is performance, but you’re only offering 20% better, you’re in trouble – especially if you’re not a straightforward drop-in replacement for someone else’s product.

Your product will have gaps, but the earlier your customers discover them, the better

Aside from the elevator pitch (hardly the time to tell people how much Hyperscan sucks), we were careful to set expectations early. For us, there was a hierarchy of when the bad news gets found out:

  1. During early discussions (“Your product isn’t a white-box IPS system? Oh.”)
  2. During a technical deep dive (“Your product doesn’t support back-references? No, thank you!”)
  3. During the evaluation when your customer tried to integrate your code (‘doesn’t compile’, ‘API wasn’t actually what we expected’)
  4. When the customer tried to load signatures into our regex engine (“fail at compile time”)
  5. When the customer ran our engine during evaluations (“performance or overheads not good at run-time”)
  6. After the customer has signed a contract and shipped something with our product in it to their customers.

There are a number of terrible strategies that many startups use that pushes the ‘bad news discovery’ downward in this hierarchy. Some of these terrible strategies are technical, some are marketing related.

It’s better to eat the pain early; most developers understand the principle that you’re better off getting a nasty message from the compiler than a crash at run-time. This principle of “bad news early” is good practice beyond that. You won’t screw your customers; you’ll pleasantly surprise them in the evaluations and you’ll get a well-deserved reputation for honesty. You also won’t waste time in meetings or evaluations that can’t end well.

Maybe if you don’t waste their time now, they’ll be more interested in you when your offering is better aligned with what they want.


Work clean and test everything

It’s tempting to cut corners when you’re a struggling startup. However, you’re actually less set up to get away with cutting corners than a big corporation. If you mess things up, that becomes your reputation – you can’t send a VP out with a few more talking points for his or her weekly golf game with his good buddies who are all VPs at the customer whose product you just stuffed up. If you mess up, you’re dead.

Don’t mess up.

We did this once – we disabled a test (unusually large inputs) after we made a few changes with the intent of turning it back on shortly after (this only affected evaluation versions of our code, not commercially shipping versions of our code). As per Murphy’s Law, naturally this bug was found, not by us, but by an evaluation team at one of the biggest networking companies in the world, on the second day of their first evaluation of our product. The evaluation continued, but with an air of forced smiles and gritted teeth, and didn’t go much further.

Assume anything you don’t test is broken.

You will need to test your code relentlessly, and designing your code for “testablity” is critical. We rejected some features strictly because we didn’t know how to quickly and programmatically find a ‘ground truth’ for how they should behave (needed for our fuzz testing). Other features had their design influenced or dictated by testing requirements.

For example, our ‘streaming’ feature has always been guaranteed to behave identically, in terms of matches generated, to the matches generated by block mode writes. This was very hard – many other regular expression implementations either don’t do streaming at all, or sort of ‘fake’ it (i.e. you can get matches as long as they aren’t spread out too far in the buffer, or too spread out over multiple packets, or on some regular expressions you get them accurately but not all, etc).

By sticking to a strong principle (streaming always works the same as block mode) we could test our stream mode programmatically without having a poorly defined notion of when we were and weren’t expecting to be correct.

The ability to ‘fuzz’ a complex system is a lifesaver, but it comes with a trap

Fuzzing is great. I met a couple Microsoft employees at RSA in 2009 and they asked me: “do you fuzz-test your system”? I admitted “no, we don’t, but I’ll try that when I get back”. We found a lot of stuff – before our real customers did.

We invested a lot of effort into the idea of figuring out how to most effectively test regular expressions – they have a complex structure in themselves, and then you’ve got to figure out what sort of inputs will make interesting things happen inside the bytecodes that we built in Hyperscan. There’s no point testing regular expressions with random data – all those nice optimizations that allow you to skip the hard stuff whenever a required “literal factor” isn’t there will “protect” you from finding your bug. Great for performance, bad for fuzzing. Thus, we put a lot of work into building positive and near-miss negative regular expression test cases. We build systems that were every bit as complex and (arguably) interesting as the regex optimizations itself.

Get interested in innovative ways to test your product. This is not a second-class activity for the “lesser developers” (many other firms have discovered this).

The trap: having a good fuzzer gives you a sense of safety, allowing you to build a more complex system than you might have dared to otherwise. Possibly this is dangerous; I’m still thinking about this point. It’s said that people who think their cars are safer are more likely to drive like maniacs…

Assume every metric that isn’t measured is Bad News for you.

In the same way that everything that isn’t tested is broken, any performance metric you don’t regularly measure (and regularly look at the measurements) is ugly news, showing that your system is bad and getting worse.

Assume everything you don’t measure is probably bad

Long after we supposedly knew what we were doing, we managed to regress our main public benchmark case for open source Hyperscan without noticing. It was differently structured than our normal performance runs, so we didn’t put it in our regular performance matrix – so out of the 21,000 numbers generated per night by our Continuous Performance Monitoring infrastructure, we managed to mess up our ‘brag numbers’. It wasn’t hard to fix, and the performance change resulted from a restructure that likely made sense (most performance numbers improved, and these numbers went back on track long-term), but it was a fresh illustration of a principle that we should have grasped already.

Team Issues

Watch out for Individual Contributor “Tourists”

We all know them. These folks are heading for management by the shortest route possible. They don’t like coding or grunt-work and the minute they can stop, they will be telling people what to do. Computer scientists should be skilled professionals, but many people enter the field with the goal of doing as little as possible of that and to get up into management as soon as they can.

I would be stunned to hear that an architect with 3-4 years professional experience (or a structural engineer, or a doctor, etc.) would deem themselves ready to go lead a team of professionals (often with more experience than they have), but a lot of people coming through computing degrees are expressly on that path.


These people are dangerous in startups because there are few reasonable outlets for their ambition. There’s just not that much of a hierarchy to climb; don’t let them make one to suit themselves.


Conversely, reward your Individual Contributors and don’t dead-end them on compensation.

The converse of this comes from the motivation of many of the “tourists” to get out of these individual contributor jobs: the pay sucks. A mediocre manager is usually paid far better than a really great individual contributor. A well-rewarded ‘technical leadership’ track is a good ideal – rather than dead-ending your technical people or hoping that they’ll magically turn into good person-managers.

Of course, this is a nice trick, given as a startup you probably won’t have any money for a while. But it would be good to think about it, especially before you thoughtlessly splash out a salary $20K per year higher to a random VP of Something-or-Other or a Director of Important Sounding Stuff than you pay your absolute best developer.


A good team is not comprised of 100% ‘A’ players on some “Most Awesome Geek” standard.

It’s actually OK to hire people who are ‘B’ or even ‘C’ players in some areas. The right analogy is closer to one of those team sports with relatively specialized players – being an Australian the natural analogies are cricket or Rugby Union, but our American readers might think NFL. A team full of the ‘best all-rounders you can find’ would be mediocre in most sports; and team full of the ‘best quarterbacks/fast bowlers/etc. you can find’ would be terrible.

Even a small startup needs a diversity of skills. If you put everyone through an algorithms-on-the-whiteboard exam and take the top performers, you might wind up with 5 algorithms / compiler / systems nerds and no-one who knows how to talk to customers, write documentation, test your system or do releases and builds.

In the Computer Science world, there’s an snootiness about certain skills trumping all the others. You need to hire people who are excellent at something you need and willing to learn some new things.


API Design

Build only what you need

It’s a lot easier to hear complaints from customers that your API doesn’t do enough, and fix that, than it will be to wean them off stupid things you put in your API back when you didn’t know what you were doing.

We saw a number of preposterously complex APIs for regular expression matching go by over the years. A minimalist API was popular with customers and easier to test.

We made some decisions that meant our API was not necessarily tiny – having streaming, multiple regular expression support, and having to completely avoid dynamic memory allocation meant that Hyperscan’s API is quite a bit more complex than, say, RE2, but we converged pretty quickly to a small API that we were broadly happy with.

Don’t throw extra features in there if you aren’t sure customers really want them. If you have to do it, mark them experimental and kill them off if you don’t hear much about them.

Listen to your customers but don’t let them design your API for you

We had a lot of really valuable feedback over the years from customers. Getting information about their use case was hugely valuable. However, an exercise that never went well was trying to co-design API features with them. It didn’t seem to work. They don’t know enough about how your system operates to make good suggestions.

Capture significant use cases, even when you don’t have a brilliant solution for the use case.

One thing that worked well was to identify important use cases and capture them in an API even if our implementation wasn’t great. For example, a lot of users wanted to be able to identify matches that occurred in a range of the output – e.g. “This regex /<R>/ matches only if the end of the match is between the 100th and 200th byte”. The user could have been told “hey, we don’t have any particularly good way of handling this – why don’t you do that check yourself, as our solution for this will be pretty much equivalent”. However, over time, implementing optimizations for this case is something we did – which we would not have been able to do if we told our users to go away and bake the solution for the problem into their code, which we wouldn’t see.

So if the API requested creates information you can use, it may make sense to capture the requirement even before you have a good solution.

An example of where we didn’t get this right (initially) was regular expression ordering. Due to the way we initially implemented things, we didn’t return regular expression matches in order by ending offset, nor we guarantee that the user would not get the occasional duplicate match (pretty bad, but it turned out that these things were OK in a MVP). One problem, though, was that users who picked up Hyperscan 2.0 (2.1 added ordering and duplicate suppression) built layers of code that dealt with our inadequacies – these layers of code get baked-in and often sprout other functionality, so even after we guaranteed ordering, those layers of code were there, sucking up performance for a task that was mostly no longer even needed.

This isn’t a license to just build castles in the sky – the requirements that you’re capturing should be important. This principle contradicts minimalism, so be careful.

Miscellaneous Issues

Don’t Bog Down on Trivial Stuff Immediately (or at all)

Image result for bikeshedding

There are a lot of decisions to be made early in a startup. One pretentious thing you can do is decide that, because your startup is going to grow to take over the world and be really awesome right from the start, you should definitely spend a nice constructive period of weeks arguing over things like coding standards (and maybe some company values and a mission statement). You will find that Parkinson’s Law of Triviality takes over – everyone has an opinion on this kind of stuff and you’ll get a tedious all-in brawl for weeks, resulting in some standards that everyone will go ahead and ignore.

This didn’t apply to programming languages for us (this was more or less dictated by the level of complexity of the compiler, dictating C++, and the harsh environment of the run-time, dictating C, and the huge variety of platforms and tool-chains we needed to support – ruling out pretty much everything else). But I imagine that a nice knock-down-drag-out pissing contest (not a nice combination of mental images, is it?) about programming languages would be another great way to waste the first 2-4 weeks (months?) of your investors money.

Be aware of the risks of ‘bikeshedding’ at all times, not just starting out. However, it seems particularly unpleasant to get stuck in this phase early – the temptation will be strong when the startup isn’t really working yet.



Work Clean – Legals

batch, books, document

Another area where it’s imperative to work clean, as a small startup, is legally. I am not qualified to provide legal advice, but it is of enormous benefit to think about this from Day 1. Do you own your code? Can you prove that? Have you dragged in random fragments of code that you don’t know the licenses for? Have you hired corner-cutters whose code will be revealed to be 50% copypasta from Stack Overflow and 40% fragments of unacknowledged GPL code?

I’m not specifically recommending you use a service for automated detection of this (Black Duck seems to do well, but I don’t know whether a small startup would want to spend their money on this); just don’t hire people who do that sort of thing, and remind junior developers that it’s not OK.

Similarly, a lot of startups join consortia and relentlessly announce partnerships that amount to little more than a press release and a exchange of banners on your website. These agreements may not bring you much more, but bear in mind, every bit of paper you accumulate will be something that you’ll be hearing about again during due diligence.

Every bit of paper you sign is a potential millstone. Don’t do a whole pile of important-sounding ‘businessing’ stuff that doesn’t get you anything and involves you signing tons of legals.

Think really carefully before you splash out small shareholdings to random people. You’ll need to go back to these people during an acquisition.

Dance like no-one’s watching; enter into agreements like every single thing you have ever done will be meticulously examined by one or more teams of lawyers working on behalf of a Fortune 500 company, as well as your own team of lawyers, who will be billing you for the time.

Work clean – Static and dynamic analysis

In our experience, running every static and dynamic analysis tool you can lay your hands on is worth trying. Both customers and acquirers down the track will thank you. Some tools are garbage, but as a rule, being clean on things like valgrind and clang static analysis and running with all warnings switched on and set to stop compilation was worth the trouble.

This is a day-to-day hit; you will occasionally have to do Weird Things to satisfy these tools. That’s a steady dull pain, but it’s better than the sharp pain you’ll experience if one of these tools could have caught something and didn’t.

Build in an niche appropriate to your scale; don’t take your tricycle out on the expressway

One of the keys to our success is that hardly anyone attempted to muscle in on our territory. While it seems that good quarter of the world’s serious computer scientists have a pet regular expression project, very few of these projects are ever built out as a commercial product. There were a number of regular expression libraries that had quite decent performance on some of our key use cases, but none of these libraries had the work done to make them robust and high-performing across the use cases we handled.

What competition did exist, fortunately, thought hardware-accelerated regular expressions were a great idea. Perhaps this is a stroke of luck that happens only once in a career.

Our job was doable with a small team over a number of years because ‘high-speed software regular expressions’ was a niche: profitable enough, but not too crowded. I’m glad we hadn’t decided that “video compression” or “neural networks” or “machine translation” was actually our niche.

Expect to fail evaluations and keep trying

We had evaluations at big name companies that failed 4 or 5 times before finally getting a win. Sometimes the teams wander away, sometimes your product is just not good enough, sometimes they were just kicking the tires with no intent of ever doing business.

If you go single-threaded with the intent of landing that amazing nameplate customer, it might well kill your company. They might say ‘no’. Worse still, they might say ‘yes’, but you have invested so much time in them, and waited so long for revenue, that you’ll wish you failed the evaluation.

Persist and chase many opportunities; also try to find out what went wrong (in case there’s a next time, or in case the mistakes you made will effect you elsewhere). The latter is surprisingly difficult; in fact, it’s often hard to elicit feedback of any kind – even from a successful evaluation. After bad – or even good – results, you may be like these two gentlemen from the Coen Brothers’ “Burn After Reading” (caution: strong language)

Build a huge database of benchmarks and actually look at them

One of the big advantages that we built over the years at Sensory Networks was a huge database of regular expression patterns that customers had shared with us. We treated this with great care and didn’t leak information from it – but we used it relentlessly to try to improve performance, even on cases where customers had wandered away.

Subsequent dealings with other companies often left us amazed at how little data our competitors had on the complex workload we were all supposedly trying to make go faster/better.

This took a fair bit of pleading with customers to get this information. One of the main selling points was that “if you share your use case with us in enough detail – or something that looks enough like it – we will measure performance on your case and if we mess up our code base relative to your usage we will discover it in 12 hours, not 4 months after we make the mistake and 2 weeks after we send you the release”.

This worked well, but not perfectly. Some of our best customers never, ever showed us their workloads.

As mentioned above, while it’s nice to have all these benchmarks, it helps to look at the results of running them, too. If there are 24,000 metrics on your dashboard you’re probably not looking at them any more.

Expect to be evaluated by the person whose code will be replaced by yours if the evaluation succeeds

If you are an algorithms library, the person who evaluates you will probably be the person who previously wrote the library to do whatever your product does – good luck! They are the domain expert, and if you’re unlucky, they Hate You Already.

There are a surprising number of honest and self-critical computer scientists out there working at big companies who will give respect where it’s due, even when this means admitting that someone else wrote better code (and sometimes, people were glad to give up the role and move on). Sadly, this isn’t universal. Expect to have the goal-posts moved frequently: you will often be competing with someone else’s system that’s being ‘generously benchmarked’ while your system is being ‘adversarially benchmarked’. This means that you really can’t afford to have glaring weaknesses in secondary metrics.

Our primary metric was essentially raw performance. However, there were a host of secondary metrics (size of pattern matching byte code, size of stream state, pattern compile time, etc.) and it was impossible to tell in advance who cared about what. Even worse, in an adversarial benchmark situation, you can expect whoever is doing the evaluation to suddenly ‘care’ about whichever metric makes your code look the worst.

Bonus anti-pattern to look out for: finding out that for months you have been talking to one evaluator who has 100% control of process and is hiding their results away from the rest of their company; you will go back through the email chain and notice that no other email address has ever appeared. Who is their boss? Who is their coworker? If this happens to you, stay not on the order of your going but Go At Once!

Evaluations seem to go a lot better if they are bottom-up and engineer-driven rather than top-down and manager-driven

We had a number of very successful evaluations at companies where the engineers were on our side and they persuaded their management that spending money on us was a good idea. Later on we had a number of evaluations where management of a company descended on their engineers and told them “use Hyperscan”. These evaluations were typically disasters, even though we had a better product and on paper the opportunities were promising. When it comes down to it, engineers don’t like being told what to do.

Expect to not be able to announce successes

For the entire history of Sensory Networks, we were almost never allowed to announce “design wins”. Most vendors who used Hyperscan were adamant that this not be mentioned publicly. I expect this would be similar for most algorithmic startups – too many announcements of this kind is presumably a free invitation to the competitors of those vendors to duplicate their functionality (we use signatures from X, a pattern match engine from Y, hardware from Z, and …).

So, expect your ‘News’ section on your website to be a bit more threadbare than you hoped.

Contract negotiations: don’t lose your nerve

Expect people to try stuff on. Many – most, in fact – of our customers dealt fairly with us as a small company. A few people, at a few companies, tried outrageous last-minute surprises in contracts. Keep your nerve; if that company make-or-break deal gets a horrifying provision added at the last minute, tell them to go away and do better.

Trying to impose exclusivity or various other limits on our freedom of action to sell Hyperscan as we pleased was a popular pastime, but no-one really insisted.

Some things that didn’t seem to be missed

  • A nice looking website.
  • Help from people who have nebulous jobs “helping out startups” (I don’t mean lawyers or accountants, I mean the Picks and Shovels crew that seem to know the real way to make money in a gold rush).
  • Having a roadmap that stretched more than about 2-3 releases and 6-9 months into the future; we almost never achieved any of the ‘long term’ items on our roadmap.
  • Finishing off emulating all the weird bits of libpcre, which was our ‘reference’ library for regular expression semantics (and generally an excellent base for semantics), or supporting a host of other syntaxes and semantics
  • Joining important-sounding consortia that just amount to having a banner on someone else’s website in exchange for having your banner on their website. Does anyone care? The same goes double for being awarded ridiculous startup or small business prizes (“East Sydney’s Most Agile Startup 3 Quarters Running!”), exchanging physical plaques (!), sponsoring random things. etc.
  • Getting all sorts of mysterious certifications about how great our development methodology was, which often seemed to amount to telling some organization “our development methodology is pretty great”, writing a cheque, and getting the certification, without anyone ever actually looking at our code. Odd.

Conclusions, Sort Of

So, that was a bit of a stream-of-consciousness series of opinionated “hints and tips”. I don’t think there’s a really solid conclusion here – we got some things right-ish and some things wrong-ish and didn’t do too badly.

I’d be lying if I said that I thought that doing this type of startup was a route to enormous startup wealth. I’d be surprised to hear that a company can become a 1000X type Silicon Valley success story from algorithms alone; I’m pretty sure that you have to capture a lot more of the value than can be captured if you ship a nifty library and go home. I do think that this kind of startup can yield a reasonable outcome and someone sufficiently interested in their work can have a pretty nice time and learn a lot, while getting paid reasonably for it.

I’d be interested to hear comments or criticisms or links to other similar startup stories. I’d be particularly interested to hear stories of what it’s like on the open source side of the fence; the path taken by Sensory Networks now seems somewhat of a closed-source anachronism.


Performance notes on SMH: measuring throughput vs latency of short C++ sequences

A quick update on last week’s post SMH: The Swiss Army Chainsaw of shuffle-based matching sequences on performance measurement.

During that post, I provided throughput numbers for these sequences but didn’t show latency. This is a critical distinction, and it doesn’t pay to be confused about the the two. I would rather avoid the rather cringeworthy formulation from the Mythical Man Month (where women are “assigned” to the task of bearing children!) and stick to the metaphor of boiling eggs: a suitably large pot of boiling water could boil eggs at a throughput of an egg every 10 seconds, but cannot provide you with a 3-minute-boiled egg in less than 3 minutes.

It is important not to confuse the ability to do something in, say, 10 cycles vs the ability to do 1,000 somethings in 10,000 cycles. The former is always at least as hard and usually much harder. This distinction holds all the way down to the single operation level: for example, a modern x86 processor can launch a multiply operation every cycle, but requires 3 cycles to know the result of a given multiply.

Modern computer architecture conspires against us when we wish to measure latency. Attempting to measure the latency of a single short code sequence is quite error-prone due to the overhead of the various performance counter or clock measurement calls.

Throughput is easy to measure on a larger scale, as we can measure thousands of iterations and establish an average cost per iteration. However, well-written code will usually attempt to minimize dependencies from one iteration to the next. When we attempt to measure, say, the branch-free code of SMH, there is little to prevent a modern, out-of-order processor from getting on with the next iteration or two while the previous iteration is handled.

I tried two approaches both attempting to measure the latency of the various SMH sequences. The first was to insert an LFENCE instruction between each SMH sequence but otherwise keep the code the same. Note that LFENCE in this case can be switched on and off by a macro.

The second approach was to make the location that was read by an SMH sequence depend on the result of the previous SMH sequence. Since I didn’t want to introduce a spurious ‘jumping around memory’ component to the benchmark (which would always be absent from the equivalent throughput metric), I made sure that the previous SMH sequence always happened to return zero (no match): we know this, but the architecture and the compiler don’t.

Creating long chains of dependent operations is also how Agner Fog (and others) measure latency; those who have not yet seen Agner’s Software optimization resources are in for a treat.

The code to measure SMH latency is below (note that LFENCE is switched off by the preprocessor as needed and was not used in the latency-test version of this code at all):

Observe the “tmp” variable in the gist above; it is always zero, but we cannot safely start our matching operation until the architecture has the result of the previous match operation in hand (Intel Architecture has many fascinating optimizations, but generalized value prediction is not one of them).

This gives us somewhat of a hybrid creature: “steady-state” latency. The compiler and architecture are still free to load things into registers that don’t depend on the actual computation – so this latency number is perhaps unrepresentative of a ‘cold start’. However, it is a reasonable measurement of the latency of a single operation in a well-optimized code base.

SMH Variant normal no unroll LFENCE
SMH32-loose Throughput (ns) 0.89 0.98 10.62
Latency (ns) 7.03 6.92 10.65
SMH32 Throughput (ns) 1.12 1.15 11.02
Latency (ns) 7.25 7.30 10.89
SMH64-loose Throughput (ns) 1.35 1.44 11.03
Latency (ns) 7.63 7.61 11.36
SMH64 Throughput (ns) 1.62 1.66 11.67
Latency (ns) 7.95 8.00 11.61
SMH128-loose Throughput (ns) 2.80 2.67 12.39
Latency (ns) 8.97 8.14 12.91
SMH128 Throughput (ns) 3.32 3.08 12.82
Latency (ns) 9.78 8.55 12.91

The above numbers seem reasonable based on a walkthough of the code. I also measured the effect of turning off my manual 8-way unroll. I had focused on smaller models and the metric of throughput as I tuned SMH; it’s marginally interesting to note that latency is generally better without an unroll in the measurement loop if not decisive.

The LFENCE results are hard to interpret – they seem to generally track the latency of the normal case plus around 3.5ns. More work is needed to confirm this; it would be nice to have a way of getting a latency number out of the system that doesn’t rely on an ability to introduce contrived data dependencies from one iteration to the next.

I feel reasonably confident that SMH can be said to do its work in 7-9 cycles; note that the overlap of iterations required to hit the full throughput (looking at the above table) must have to be as many as 8 iterations for the cheapest cases. As always, this implies that being stuck in the ‘latency world’ is miserable – try to phrase your computations to stay in the ‘throughput world’ whenever you can.

Updated code is here

Thoughts on how to measure latency are welcome.

SMH: The Swiss Army Chainsaw of shuffle-based matching sequences

Today I’m going to share with you one of my favorite instruction sequences.


OK, got it? That’s the post. Have a nice day.

Perhaps a little more explanation is in order, especially if you weren’t next to my cubicle for what were no doubt 11 very long years during the creation of Hyperscan. The above sequence, which I have dubbed SMH (an acronym which stands for “I am Not Going to Explain”), appears in various forms in Hyperscan, and has a few expansions and variants which I’ll discuss. I think a full expansion of all the fun of SMH, and a codebase to match, will have to wait.

This sequence looks fairly banal – but it can accomplish a huge range of matching tasks, not all of which are traditional pattern matching tasks. Let’s walk through a basic application and we’ll get to more elaborate ones in later posts.

Keep in mind that the basic unit here is asking questions composed of a bunch of byte-level predicates comparing our input to queries we prepared earlier.

The code for this is up at Github at: Shuffle-based predicate matcher and all-round branch free swiss army chainsaw

Baseline Application: Prefix Matching

Everyone likes a good Prefix Matcher – Prefix or Suffix matchers crop up all over the place in pattern matching as a basic building block. There are plenty of traditional implementations of this (generally involving DFAs or hashing/Bloom Filters).

I’m going to focus on a case that allows SMH to be displayed without too much extra complexity: small-set Prefix matching of literal strings no greater than 16 characters.

Suppose we want to match a few animal names and map those to some sort of id: we have {“cat”, “dog”, “mouse”, “moose”, …}. Here’s a straightforward approach to doing this, assuming we have no more than 32 characters overall in total and a machine handy with AVX2 (if you don’t, buy yourself a better computer and give Grandpa back his Ivy Bridge, or translate everything I’m saying into Neon – there’s nothing here that’s all that Intel specific, but I don’t have a fast ARM workstation so y’all can suck it up and read AVX code):

  1. Load 16 bytes of our input from memory and broadcast it to high and low lanes of an AVX2 register
  2. Shuffle the input with a pre-prepared shuffle mask, so that we can consecutively compare the first 3 bytes against cat at bytes 0..2 of our register, the first 3 bytes again against ‘dog’ in bytes 3..5 of our register, etc.
  3. Compare the input against another pre-prepared mask, this one containing our strings: so the register would pack in ‘catdogmousemoose’.
  4. Use VPMOVMSKB to turn the compare results (which will be 0x00 or 0xff) into single bits in a general purpose register (now, you can put your SIMD units away).

    These steps are illustrated below:

  5. Take the Most Significant Bit of each string in the mask – if we are packing our strings from left to right (it doesn’t really matter which way we do the comparisons) we would have the comparison of ‘cat’ so that ‘c’ is in bit 0, ‘a’ is in bit 1, ‘t’ is in bit 2, and we would declare the bit 2 part of our Most Significant or “high” end, so bit 2, 5, etc. would be our high mask. We’re going to make a temporary mask which is the result of our VPMOVMSKB with the ‘high’ mask zeroed out.
    I refer to this as ‘digging a hole’. We’ll need that ‘hole’ later.
  6. Now take the corresponding ‘low’ mask (the LSB end of each string) and simply add it to our temporary.
    The effect of this will be that if, and only if, all our other bits in the mask are on, there will be an arithmetic carry into that ‘hole’ I mentioned (and you can see why we needed it – we certainly don’t want to carry beyond that point).
  7. Now AND the original mask (not the high mask, but the original mask we got from PMOVMSKB back in). Now the high bits are on if and only if every comparison bit associated with the string is on.
  8. We then AND by our high mask again to turn off everything but our high bits.
  9. We can use LZCNT (leading zero count) to find our first high bit that’s set. We pack our strings in order of priority, so the ‘winning bit’ (in case two bits are on – possible if our strings or later patterns overlap). We don’t have to do it this way – we might want to report all matches. For now, we’ll report a highest priority match.
  10. This LZCNT is then used to read from a table that has ID entries only for the bits that have high bits set (the other entries in the table are never read – this wastes some space but means we don’t need to compress down our table).

    Steps 5-10 are illustrated here:

So – that’s the basic algorithm.

This gist shows the edited highlights (no debugging guff – I have some code that prints out the process in greater detail if that’s what you’re into) of steps 1-9: there’s really not that much run-time code.

There are obvious extensions to handle more than 32 ‘predicates’. We can build a 64-wide version of the above by simply gluing two copies of steps 1-4 together with a shift-by-32 and an OR at the end. A 128-wide version is four copies of steps 1-4 and two separate copies of steps 5-9 with a little bit of logic (a conditional move and an add) to put together our two LZCNT results to turn the result of doing 2 64-bit LZCNTs into a single 128-bit LZCNT.

The above sequence is fast, and reliably so: it doesn’t have any branches and it doesn’t make complex use of memory, so its performance is pretty much constant regardless of input.

It can be made faster if we take a few shortcuts – suppose we have plenty of room in our model, whether it be 32, 64 or 128 bits. We might have, say, 4 strings with 5 characters each, so we’re consuming only 20 slots in a 32-bit model. In this case, why ‘dig holes’? Instead, we can reserve a slot (“gutters” instead of “holes”?) at the high end of the string with a guaranteed zero compare – this means that all we need to do is add our low mask and filter out the carries from the high end, so the ANDN/ADD/AND/AND sequence loses 2 instructions. We refer to this as the “loose fit” model as opposed to the “tight fit” model.

Here are the performance numbers in nanoseconds on a 4.0 Ghz SKL workstation:

Fit Predicate Count ns per sequence (throughput)
Loose 32 0.888
Loose 64 1.38
Loose 128 2.82
Tight 32 1.14
Tight 64 1.65
Tight 128 3.37

I describe these as throughput numbers, because you won’t get a single SMH lookup done at anything like these speeds – the latency of these sequences is much higher than the throughput you can get if you have lots of these sequences to do.

A future blog post will look into generalized ways to measure this latency specifically (I had a unconvincing experiment with LFENCE). In the meantime, be sure to think carefully about experiments where you “do something in N cycles” where you actually mean “doing 10,000 somethings is N*10,000 cycles” I recommend the following three step program. 1) Cook 18 eggs in a pot for 3 minutes. 2) Convince yourself that throughput == latency. 3) Throw away your original eggs, cook another egg for 10 seconds and bon appétit!

Here’s a debug output showing a couple iterations of one of our models (SMH32-loose, the simplest model). I use underscore instead of zero as it’s easier to read:

The curious can go to Github and poke the system with a stick. I cannot guarantee that it won’t fall over; this project is very preliminary.

SMH: Full Sequence

(I will not illustrate this with a movie reference)

At this point, you might be excused for wondering why I called SMH the “Swiss Army Chainsaw”. The instantiation above is pretty simplistic and seems to be covering literals only. The codebase as it stands really only allows this; there’s no compiler to do anything but literal prefixes.


1. Shuffle allows discontinuous things to be compared

Because we are using shuffle, we don’t have to select contiguous parts of a string. Better yet, we don’t have to pay for bits of the string we don’t select to compare on. Using regex notation, the very same sequence could just as easily match /a…b/s as /ab/ and both take the same number of predicate slots.

This means we can range over data structures (subject to our limit of 16 bytes; more on that later); we don’t just have to compare strings in buffers.

2. The full sequence allows masking, ranged comparison and negation

The full sequence adds a couple extra SIMD instructions to the front-end, and changes the nature of the comparison from ‘equal’ to ‘greater-than’.

Inserting an AND into our sequence allows us to carry out a ‘masked’ comparison. This allows us to do some fairly simple things – e.g. make caseless comparisons of alphabetic ASCII characters, check individual bits, or look for a range of values like 0x0-0x3 (but not an arbitrary range).

But even more fun – leave the AND into the sequence and subsequently carry out a subtract and change the comparison to ‘greater-than’ comparison (PAND, PSUBB, PCMPGTB).

This gives us all the old power we had before (if we want to target a given value for ‘equal-to’, we simply use PSUBB to ensure that it’s now at the maximum possible value (+127, as the AVX2 comparison is on signed byte) and compare-greater-than with the value +126. However, we can now also detect ranges, and we can even negate single characters and ranges – it’s just a matter of picking out the right subtract (really, PADDB works just as well) and compare values.

I admit I have not really thought through whether there is interesting power granted by the combination of PAND and the PSUBB/PCMPGTB together; I have really only thought about these in a one-at-a-time fashion. It might be better to follow the PSUBB with the PAND. Insights welcome.

3. The bit arithmetic at the end of the sequence can model more than just ADD

The sequence – whether ‘loose model’ (ANDN, ADD, AND, AND) or the ‘tight model’  (ADD, AND) – carried out over the general purpose registers is used to calculate a series of ANDs of variable length bitfields and produce exactly one result per bitfield.

It has more possibilities:

  1. With a bit of work, it’s possible to handle overlap within the predicates. Suppose we have two strings “dogcow” and “dog”. We can overlap these as long as we either are (a) using the loose model (so we have a safe spot after ‘dogcow’ already) or (b) we separate our ‘dig our holes’ masks and our ‘extract the final comparison masks’. After all, if we overlap “dogcow” and “dog” we don’t want to ‘dig a hole’ at ‘g’, or else we don’t get a carry all the way to the ‘w’. So in a tight model we will still ‘dig a hole’ at “w” but we will have to treat seeing a ‘1’ after than process is done differently – in fact, we will find a match for all of the bolded characters in “dogcow“.

    Note we also need to make sure that the index for successfully seeing “dog” is copied not just to the slot corresponding to “g”, but also “c” and “o”, as if we see “dogco” that’s a match for “dog” but not “dogcow”.

  2. Bizarrely, we can handle OR over some predicates, in some order, and even nest at least one AND-term within that OR (but not two).

    So, suppose we wanted to match (in regex notation) /ab[cx]/ – “a, followed by b, followed by c or x”. We could use 4 slots, comparing the first 2 characters in the typical way, then using 2 byte-predicates against the third. We would then, instead of adding the equivalent of binary 0b0001 (the way we would for, say /abcx/), we add binary 0b0011 – so either the ‘c’ matching or the ‘x’ matching will cause a carry out of our last 2 places. The only difference that results is what’s left behind in bits we don’t care about anyway.

    Even more odd: suppose we wanted to match /ab(cd|x)/. We can still do this – by ordering our predicates to match a, b, x, c and d in appropriate places. We then add 0b00101 to the mask, which gets the carry we need iff we have “cd” or “x”.

    It is not possible to do this trick for an arbitrary combination and something as simple as /ab(cd|xy)/ cannot be done. Only a boolean function where some ordering of the variables allows us to arrange all possible ‘true’ values above or below all possible ‘false’ values can be handled in this way.

    In anyone has any theoretical insight into how to express which functions can and can’t be modeled, please let me know!

Future thingies

Needless to say, this can all be made far more powerful (in case it wasn’t powerful enough) with better instructions. While my long-standing love affair with PSHUFB has already been demonstrated and will be demonstrated again, the limitation of 16-character range is irritating. VBMI and VBMI2 in particular introduce more powerful capabilities, and ARM Neon machines already have the means to do generalized byte shuffles over 1-4 registers. There are also possibilities for using larger data items for both shuffles and for the compares (this yields a different set of functionality).

If anyone wants to send me a Cannonlake machine, or a ARM Neon workstation, I’ll give it a shot, without fear or favor.

A pre-shuffle using the existing AVX2 or AVX512 permutes could extend the range of the finer-grain PSHUFB shuffles, although the functionality provided is a bit complex and hard to characterize.

All this will be explored in due course, but not until the basic SMH models have been fleshed out and grown a slightly usable API.

Summary: The Case for the Swiss Army Chainsaw

Armed with the above features, it seems possible to handle an extraordinary number of possibilities. Note that range checks on larger data types than simple bytes, can be (somewhat laboriously) composed with these features, and obviously the whole range of mask checks (as per many network operations) are easily available.

These comparisons could also be used to combine quantitative checks (e.g. is TTL field > some value) with checks of strings or portions of strings in fixed locations.

The fact that we have a logical combination of predicates could allow checking of a type field to be combined with checks that are specific only to the structure associated with that type field – so a data structure which leads with a type field and has several different interpretations for what follows could be checked for properties branchlessly.

Needless to say, actually doing this is hard. The run-time is easy (add 2-3 more instructions!); the compiler and a good API to express all this – not so easy. I’ve illustrated a simple application in this post, and can see more, but have to admit I don’t really quite understand the full possibilities and limitations of this sequence.

Postscript: A Notes on Comparisons To Trent Nelson’s Prefix Matcher

This work has some similarities to the recent Is Prefix Of String In Table work by Trent Nelson. I’d point out a few issues:

  1. This work is measured in a tighter measurement loop than Trent allows himself, so these numbers are probably artificially better. I’m allowing myself to inline the matching sequence into my measurement code as the SMH sequence here is in a header-only library. I don’t think Trent is doing the same thing so he may be paying some function prologue/epilogue costs. If I get rid of my unrolls and inlines I lose a  couple cycles.
  2. The SMH work presented here isn’t really intended for a larger-scale standalone: it would be more typical to embed it as a second-stage after a first-stage lookup.
  3. Despite this, out of curiosity, I tried putting Trent’s testing strings into my matcher – one of the strings is too long (I can’t handle >16 length strings) but after that is trimmed to length 16, the matcher can fit those strings in the 128-predicate ‘loose’ model or about 11.3 cycles throughput.
  4. If one were to select on (say) the first 11 bits or so of the buffer and look up a SMH data structure after 1 layer of indirection (SMH is too big to really make it fun to have 2048*sizeof(SMH) bytes, so indirection is needed) – a simple load, AND, load sequence, it seems obvious that the “loose 32” model could cover the case (3.6 cycles throughput plus added costs from the loads and AND, as well as whatever costs happen from having to go back and forth between multiple SMH sequences rather than using a statically determined set of sequences continuously). As a bonus, this arrangement could strip the first character out of the workload, allowing us to cover 17 characters.
  5. The SMH code is branch-free and won’t be affected by branch prediction. Trent’s performance analysis doesn’t really cover the effects of branch prediction as it involves benchmarking with the same string over and over again – it is, of course, very hard to come up with realistic benchmarks as there’s no real ‘natural population’ of input to draw from.
  6. I don’t yet bother to deal with length of the strings, which is naughty. Trent is more responsible. However, the more full SMH model is capable of including length information in its predicate calculations, and an alternative strategy of ‘poisoning’ our input (loading ‘out of range’ characters with values that cannot occur at that position in any valid string – not hard when you only have 16 different strings and no wildcards) is also available.



“Say Hello To My Little Friend”: Sheng, a small but fast Deterministic Finite Automaton

Deterministic Finite Automata (DFA, subsequently) are a fundamental structure. Most state machines that programmers build are some variant on a DFA, whether they are built by jumping around inside a switch statement or moving from state to state in a table structure.

They have uses all over the place; they are used heavily in regular expression implementation, and can be used in various validation schemes such as UTF-8 validation. I’m going to show a curious little DFA of my own invention* that we used in Hyperscan**. The presentation here will be an independent re-implementation as the version in Hyperscan is buried in some pretty complex code.

Sheng has some pretty tight limitations, especially in the version I’m presenting here:

  1. It cannot have more than 16 states.
  2. This version of Sheng is ‘quiet’ – it calculates states but doesn’t have an ‘accept state’ that is actively raised. So you can’t detect a regular expression and get a callback or a index as to where it matched.
  3. This version of Sheng is also a bare DFA without a compiler. You need to put the transitions of the state machine in manually.
  4. This version of Sheng depends on x86 instructions, but the principles could allow the extension of Sheng to any system with a similar permute instruction, such as ARM NEON.

Most important: Sheng uses my favorite instruction, PSHUFB!

The Problem in Plain DFA implementations: Memory Latency

A typical problem for DFA implementation is that, at best, each DFA state transition typically involves a single memory access. More compact implementations may use several. Worse still, each of these state transitions depends on the previous state transition, so a simple DFA cannot run faster than the latency of the lowest level of cache (often plus a cycle, if there are things that need to be done to the loaded value from the transition table to make it suitable for another state transition).

This is the critical path of the DFA: the state-to-state transition. Other activities, such as remapping characters to a smaller character set to save space, or checking for accept states, are not on the critical path and are almost ‘free’ in a typical implementation – after all, we’re waiting for the state transition to finish. That’s a lot of free execute slots!

Here’s a not very interesting DFA implementation:

This isn’t a perfect “simple” DFA implementation; we waste at least 1 cycle of latency in our state-to-state transition on index arithmetic to look up that big array (better, but more obscure, would be to track our state as a location within the transition table).

Note the implementation in full unrolls the loop, too.

However, even given a wasted cycle or two of latency, this implementation is close to the limit of memory latency. The DFA is small (4K) so we will be getting it from L1 cache in the steady state, but that means a state-to-state transition at around 4-5 cycles minimum.

Enter My Little Friend: Sheng

Sheng is a different approach. Sheng uses the PSHUFB instruction to implement the state transitions taken by looking up a shuffle mask for each input character. Note that the lookup operation is not on the critical path, as we know our input characters well in advance.

As such, the critical path for Sheng is just 1 cycle on modern architectures; both recent Intel and AMD processors implement PSHUFB with a single cycle of latency.

The variant of Sheng presented is ‘silent’ – it allows us to calculate which state we’re in at a given point but it has no facility to detect whether a match has occurred. We’ll cover the feature of a non-silent Sheng later; sadly, the number of instructions required to check our state means that we will have to add a lot of extra work – too much work to manage 1 cycle per byte (not a critical path issue – it’s just that it’s hard to do that many operations in a cycle).

So this one is a little weird: we heavily depend on my favorite instruction, PSHUFB, included on most x86 processors since its introduction with SSSE3 (the catchily named “Supplemental Streaming SIMD Extensions 3”).

PSHUFB (_mm_shuffle_epi8 in this code) is a bytewise shuffle, using the low 4 bits of each byte from a control mask register to indicate which byte to copy from the source register to the destination. It can be used to permute data, but it can also be used to effectively look up a 16-wide table.

In this usage, PSHUFB masks are found on a per-character basis. We look up a character from our input and use this mask to look up what our next state should be. For example, in the 5th unrolled iteration, our current state is used to index into this mask (“transitions[c5]”) and by permuting that mask, and this yields our new state.

We keep our canonical state in the bottom lane of the 128-bit register.

As a side note, we could actually be processing 16 DFAs at once, with an almost useless set of limitations:

  1. The DFAs all have to have the same structure and character transitions.
  2. The DFAs all have to be acting on the same data.

So really, all we can do is start the DFAs off in different states and then crank those states and see what happens. There is an interesting usage of this (picture what happens when we initialize a register with [0,1,2,3,…, 15] and process a block of data – we now have a function that can be applied as another shufle mask! Details can wait for another followup blog post.

So, what do we get from all this? The main advantage of doing this is speed – here’s the basic comparison of speed between the two systems (measured on a 4Ghz Skylake client machine):

(there’s also a basic-level of traces through states included here so that I could verify that the two state machines are basically sane and doing the same thing; see the code)

So we’re processing 3.92 bytes per nanosecond (pretty close to 1 cycle/byte) as opposed to around 0.6 bytes per nanosecond with a basic DFA implementation (which could probably go about 10-20% faster with a more sophisticated table lookup, but not that much more). Sounds good –  as long as we can live with the long list of limitations of Sheng.

Sheng has a lot of interesting properties, which I’ll follow up in later posts:

  • There are several strategies for having a “noisy” Sheng – that is, one that can stop, raise a callback, or write to a buffer whenever it encounters some “interesting” state (e.g. an accept state).
  • There are also a number of ways Sheng can be adapted to handle a larger portion of the pattern matching task.
  • These is nothing inherently x86-centric about Sheng. The TBL instructions on Neon could be used to build up the same facility on ARM, and the multiple register variants of these instructions could be used to build 32, 48 or 64-state DFAs.
  • An AVX2 machine can run two independent 16-state DFAs at once for the same cost, although there is no cost-free way for them to interact. AVX 512 adaptation of the same techniques allows 4 such independent 16-state DFAs.
  • AVX512 also allows other exotic structures, including larger DFAs using the 16-bit permute operations, including the 2-source permutes.
  • AVX512 VBMI adds VPERMB and 2-source byte permutes, allowing this technique to be extended to 64 or even 128 states! However, the added latency of these permutes means that a simplistic implementation will be much slower.
  • Since PSHUFB is a permute, it’s possible to compute blocks of this operation out-of-order. This can be exploited to improve throughput where latency of an operation is not equal to throughput – this is not true of PSHUFB or VPSHUFB but is true of some of the more recent shuffle instructions (for example, many of the AVX512 16-bit shuffles are latency=7 throughput=2) and will likely be true of the next generation of shuffle instructions.
    • Note that a 2-source permute is not straightforwardly handled by this, as in order to turn permutes over a block on input into a function, we must calculate all possible outcomes on all states. This becomes prohibitively expensive with already large operations.
    • This out-of-order computation is not particularly suitable where a “noisy” Sheng is required

Until then, I hope you enjoyed Sheng, and you can find the code on Github.

[ please note: it is essentially a ‘sketch’, lacking many features and there is approximately zero software engineering applied to it. The Sheng and BasicDFA structures should related through static or dynamic polymorphism so that they can share test drivers, but I didn’t want to start designing a more generalized interface until I have built out more of the Sheng variants, so I used cut-n-paste-polymorphism 🙂 ]

[ also note: yes, there are many ways to make DFAs run faster, including acceleration, gluing the characters together and various other tricks. There are also a bunch of ways to make DFAs run slower; typically by implementing them on specialized hardware add-in cards, then waiting geological ages to get the data to the cards and the matches back. ]

* I independently invented this technique along with some researchers at Microsoft Research; if anyone can recall the paper where this technique is documented, please let me know and I’ll put in a link and appropriate credit.

Update: Anuj Kalia, in comments, identified a Microsoft Research paper that’s possibly what I saw as Data-Parallel Finite-State Machines – Microsoft Research – for the 16-state case, I believe this approach converges to be functionally equivalent to Sheng. We discovered this work only when we went looking to establish originality of Sheng…

** Anatoly Burakov wrote the first implementation of Sheng within Hyperscan. Alex Coyte later extended Sheng to work as part of a much larger DFA, a subsystem which he felt moved to dub “Shengy McShengface”, for reasons he may not be able to adequately explain.

Bits to indexes in BMI2 and AVX-512

[ Please bear with the terrible formatting of the table in this post; I was pretty startled at how limited my options were from a vanilla formatter. Opinions on a better method are welcome. ]

Daniel Lemire, in his post Iterating over set bits quickly (SIMD edition) discusses several techniques to iterate over set bits quickly – or more precisely, to turn a collection of bits into a variable-length buffer full of integers indicating which bits were set.

So, if your code gets given an array with the following 16-bit bitfields (assuming little-endian order):

0x1001, 0x0003, 0xffff

you would want the answer:

indexes = 0, 12, 16, 17, 32, 33, 34, ... , 46, 47

This is an important operation. While it’s a lot of fun to do clever things with SIMD, sooner or later you may need to do something specific with the bits you found in your SIMD registers. For example, we used a number of SIMD techniques in Hyperscan to search for strings, but eventually you would have to report that you’d found something to the rest of the system.

After reading Daniel’s post, and more importantly, taking some time to hack on an AVX-512 system that he generously shared access with me, I think I have invented a new, branch-free way of solving this problem for 64-bit integers. There is the small catch that you will have to have an AVX-512 capable system handy.

(I say I think I invented this as it’s quite possible that (a) I’ve absorbed this technique from somewhere and forgot, or (b) someone else has already independently invented this)

Here’s the technique.

Let’s rig up a bunch of masks with alternating blocks of one and zero bits:

uint64_t msk_1 = 0xffffffff00000000ULL;
uint64_t msk_2 = 0xffff0000ffff0000ULL;
uint64_t msk_3 = 0xff00ff00ff00ff00ULL;
uint64_t msk_4 = 0xf0f0f0f0f0f0f0f0ULL;
uint64_t msk_5 = 0xccccccccccccccccULL;
uint64_t msk_6 = 0xaaaaaaaaaaaaaaaaULL;

Now, suppose I have a bitvector in v that I’d like to turn into a bunch of indexes. I can get a start by doing this:

uint64_t v1 = _pext_u64(msk_1, v);
uint64_t v2 = _pext_u64(msk_2, v);
uint64_t v3 = _pext_u64(msk_3, v);
uint64_t v4 = _pext_u64(msk_4, v);
uint64_t v5 = _pext_u64(msk_5, v);
uint64_t v6 = _pext_u64(msk_6, v);

What did this achieve? Well, suppose I have the 11th bit set in v and nothing else. Looking into my masks, I can see that my PEXT operation (a fast bitwise extract) got me a 1-bit from msk_6, a 1-bit from msk_5, a 0-bit from msk_4, a 1-bit from msk_3 and 0-bits otherwise. These bits will all be deposited into the least significant bits of the v1 through 6 temporaries.

In other works, for each set bit, I’m extracting the bit pattern of its index from the masks and depositing that bit pattern at the lowest-significant bytes on my v1 through v6 temporary values.

So, in the unlikely event that you were hoping to get the right answers, annoyingly bit-smeared across 6 different uint64_t variables, you’re done. But that’s probably not very satisfying. We’ll get to that.

So how do we interleave these 6 values together? This looks pretty ugly – we’re looking at 384 total bits in the worst case of answers. So this doesn’t seem like something we can do fast in the General Purpose Registers. Let’s go to SIMD.

The principle we will apply is that we will use AVX-512’s facility to use 64-bit mask to control a SIMD computation. We will take our 6 values and use them to control the progressive adding of 32, 16, 8, 4, 2 and 1 into a result.

__m512i vec;
vec = _mm512_maskz_add_epi8(v1, v32_bit, _mm512_set1_epi8(0));
vec = _mm512_mask_add_epi8(vec, v2, v16_bit, vec);
vec = _mm512_mask_add_epi8(vec, v3, v8_bit, vec);
vec = _mm512_mask_add_epi8(vec, v4, v4_bit, vec);
vec = _mm512_mask_add_epi8(vec, v5, v2_bit, vec);
vec = _mm512_mask_add_epi8(vec, v6, v1_bit, vec);

Now vec holds the answer we wanted, if we just wanted a bunch of bytes on our output, ranging from 0..63. Unfortunately, we need to write some not very interesting code if we’re doing this over a large range, where we imagine that our offsets might be much larger than a byte. If we’re working continuously over inputs >64K, we would expect to need 4 byte answers. In order to write out up to 64 uint32_t offsets, we’re going to have to spread out our results over 4 registers (spreading the bytes over u32 units), add in a value ‘k’ representing the base offset of our 64-bit value to begin with, and write all 4 of these big registers out.

__m512i base = _mm512_set1_epi32(k*64);
__m512i r1 = _mm512_cvtepi8_epi32(_mm512_extracti32x4_epi32(vec,0));
__m512i r2 = _mm512_cvtepi8_epi32(_mm512_extracti32x4_epi32(vec,1));
__m512i r3 = _mm512_cvtepi8_epi32(_mm512_extracti32x4_epi32(vec,2));
__m512i r4 = _mm512_cvtepi8_epi32(_mm512_extracti32x4_epi32(vec,3));

r1 = _mm512_add_epi32(r1, base);
r2 = _mm512_add_epi32(r2, base);
r3 = _mm512_add_epi32(r3, base);
r4 = _mm512_add_epi32(r4, base);
_mm512_storeu_si512((__m512i *)out, r1);
_mm512_storeu_si512((__m512i *)(out + 16), r2);
_mm512_storeu_si512((__m512i *)(out + 32), r3);
_mm512_storeu_si512((__m512i *)(out + 48), r4);

(note that ‘out’ is a uint32_t so we are actually getting +64, +128, +192 bytes with those last three offsets).

Alert readers will note that this code is writing a lot of stuff out. What happens if we only had 1 bit set? Or 0? Well, this blog isn’t called “Branch Free” for nothing.

More seriously, the point is that it’s usually cheaper to do the same thing every time rather than run the risk of a branch mispredict. Looking back at the code above – sure, it looks like a giant bolus of code. But a branch miss on a modern architecture is around 14 cycles. That’s a lot of missed opportunity to do work.

Even if you accept my above philosophy of doing tons of potentially redundant work over risking a branch miss, there’s one more question – we need to know where our next write should be:

uint8_t advance = __builtin_popcountll(v);
out += advance

That just moves us up (remember ‘out’ is a uint32_t for pointer math purposes) to the last value that actually had something set. And we’re done!

Is it fast?

Here’s a rough spreadsheet of the results measured against several of the other methods described in Daniel’s article. It’s faster than most of the other methods, falling down only for very low ‘bitmap densities’. For these lower densities, taking a conditional branch with the prospect that the expected number of bits set in a word is very low is a winning proposition.

Bitmap density Method Cycles per index
0.03 bitmap_decode_ctz 3.852
bitmap_decode_avx2 10.116
bitmap_decode_avx2_turbo 14.363
bitmap_decode_avx2_turbo_thin 15.736
bitmap_decode_avx2_turbo_nopopcnt 12.624
bitmap_decode_bmi2_avx512 12.9
0.12 bitmap_decode_ctz 4.97
bitmap_decode_avx2 3.003
bitmap_decode_avx2_turbo 4.205
bitmap_decode_avx2_turbo_thin 4.547
bitmap_decode_avx2_turbo_nopopcnt 3.732
bitmap_decode_bmi2_avx512 2.481
0.25 bitmap_decode_ctz 4.251
bitmap_decode_avx2 1.52
bitmap_decode_avx2_turbo 2.09
bitmap_decode_avx2_turbo_thin 2.265
bitmap_decode_avx2_turbo_nopopcnt 1.861
bitmap_decode_bmi2_avx512 1.25
0.5 bitmap_decode_ctz 3.446
bitmap_decode_avx2 0.796
bitmap_decode_avx2_turbo 1.042
bitmap_decode_avx2_turbo_thin 1.131
bitmap_decode_avx2_turbo_nopopcnt 0.92
bitmap_decode_bmi2_avx512 0.616
0.9 bitmap_decode_ctz 3.037
bitmap_decode_avx2 0.444
bitmap_decode_avx2_turbo 0.574
bitmap_decode_avx2_turbo_thin 0.628
bitmap_decode_avx2_turbo_nopopcnt 0.509
bitmap_decode_bmi2_avx512 0.366

Is this a great idea? I don’t know.

There are no doubt other methods to use AVX512 to transform bit vectors in this fashion, and for a relatively low ‘population’ there are a number of ways the bitmap_decode_ctz code can be made to run faster (possibly the topic of another article).

I still think it’s an interesting ‘trick’ and it’s nice to take my second-favorite instruction (PEXT) out for a spin.

Let me know if you’ve seen this trick somewhere before and I’ll be happy to credit where credit is due. As I said, I think I invented it…

The code is available at Daniel Lemire’s Github with an error (my fault, apparently I thought 8+2 = 9) which will be corrected in due course.

ps. In the ‘dynamiting the trout stream’ category, I give you VPCOMPRESSB from Intel® Architecture Instruction Set Extensions Programming Reference (PDF) which will greatly simplify all the above trickery, once we have AVX512_VBMI2 capable machines (Ice Lake time-frame).

pps. There is also a branch-free means where VPCOMPRESSD can be used four times on 16-bit words to solve a similar problem on machines that are publicly available now. This can be left as an exercise for the reader. It might be faster than the BMI2 stuff, but it lacks style points.

Introduction and welcome

Hello, world.

This is my blog where I will talk about things that interest me (and a no doubt small collection of others). Topics that I’m interested in include:

  • Low-level and performance-oriented programming
  • Computer architecture (especially as it related to performance-oriented code)
  • Programming languages
  • Regular expression implementation and automata theory
  • … and of course, implementing things without branches! Thus the name.

I was the designer of the Hyperscan project. I built this system at Sensory Networks, which was acquired by Intel Corporation in 2013, and worked on Hyperscan at Intel for over 4 years.

I hope that I can show you some interesting things. I have a few things in the pipeline that I will show shortly, including some string matching work, fast Random Forest implementation and a lot of my favorite low-level coding tips and tricks.

I request that my readers can bear with me and forgive the (hopefully temporary) amateurish nature of the site; I am not an expert blogger or user of WordPress.