state of js implementations, 2014 edition

9 December 2014 10:29 AM (javascript | v8 | jsc | spidermonkey | igalia | webengineshackfest)

I gave a short talk about the state of JavaScript implementations this year at the Web Engines Hackfest.

29 minutes, vorbis or mp3; slides (PDF)

The talk goes over a bit of the history of JS implementations, with a focus on performance and architecture. It then moves on to talk about what happened in 2014 and some ideas about where 2015 might be going. Have a look if that's a thing you are in to. Thanks to Adobe, Collabora, and Igalia for sponsoring the event.

there are no good constant-time data structures

2 December 2014 10:01 PM (programming | algorithms | security | timing attacks | guile)

Imagine you have a web site that people can access via a password. No user name, just a password. There are a number of valid passwords for your service. Determining whether a password is in that set is security-sensitive: if a user has a valid password then they get access to some secret information; otherwise the site emits a 404. How do you determine whether a password is valid?

The go-to solution for this kind of problem for most programmers is a hash table. A hash table is a set of key-value associations, and its nice property is that looking up a value for a key is quick, because it doesn't have to check against each mapping in the set.

Hash tables are commonly implemented as an array of buckets, where each bucket holds a chain. If the bucket array is 32 elements long, for example, then keys whose hash is H are looked for in bucket H mod 32. The chain contains the key-value pairs in a linked list. Looking up a key traverses the list to find the first pair whose key equals the given key; if no pair matches, then the lookup fails.

Unfortunately, storing passwords in a normal hash table is not a great idea. The problem isn't so much in the hash function (the hash in H = hash(K)) as in the equality function; usually the equality function doesn't run in constant time. Attackers can detect differences in response times according to when the "not-equal" decision is made, and use that to break your passwords.

Edit: Some people are getting confused by my use of the term "password". Really I meant something more like "secret token", for example a session identifier in a cookie. I thought using the word "password" would be a useful simplification but it also adds historical baggage of password quality, key derivation functions, value of passwords as an attack target for reuse on other sites, etc. Mea culpa.

So let's say you ensure that your hash table uses a constant-time string comparator, to protect against the hackers. You're safe! Or not! Because not all chains have the same length, "interested parties" can use lookup timings to distinguish chain lookups that take 2 comparisons compared to 1, for example. In general they will be able to determine the percentage of buckets for each chain length, and given the granularity will probably be able to determine the number of buckets as well (if that's not a secret).

Well, as we all know, small timing differences still leak sensitive information and can lead to complete compromise. So we look for a data structure that takes the same number of algorithmic steps to look up a value. For example, bisection over a sorted array of size SIZE will take ceil(log2(SIZE)) steps to get find the value, independent of what the key is and also independent of what is in the set. At each step, we compare the key and a "mid-point" value to see which is bigger, and recurse on one of the halves.

One problem is, I don't know of a nice constant-time comparison algorithm for (say) 160-bit values. (The "passwords" I am thinking of are randomly generated by the server, and can be as long as I want them to be.) I would appreciate any pointers to such a constant-time less-than algorithm. However a bigger problem is that the time it takes to access memory is not constant; accessing element 0 of the sorted array might take more or less time than accessing element 10. In algorithms we typically model access on a more abstract level, but in hardware there's a complicated parallel and concurrent protocol of low-level memory that takes a non-deterministic time for any given access. "Hot" (more recently accessed) memory is faster to read than "cold" memory.

Non-deterministic memory access leaks timing information, and in the case of binary search the result is disaster: the attacker can literally bisect the actual values of all of the passwords in your set, by observing timing differences. The worst!

You could get around this by ordering "passwords" not by their actual values but by their cryptographic hashes (e.g. by their SHA256 values). This would force the attacker to bisect not over the space of password values but of the space of hash values, which would protect actual password values from the attacker. You still leak some timing information about which paths are "hot" and which are "cold", but you don't expose actual passwords.

It turns out that, as far as I am aware, it is impossible to design a key-value map on common hardware that runs in constant time and is sublinear in the number of entries in the map. As Zooko put it, running in constant time means that the best case and the worst case run in the same amount of time. Of course this is false for bucket-and-chain hash tables, but it's false for binary search as well, as "hot" memory access is faster than "cold" access. The only plausible constant-time operation on a data structure would visit each element of the set in the same order each time. All constant-time operations on data structures are linear in the size of the data structure. Thems the breaks! All you can do is account for the leak in your models, as we did above when ordering values by their hash and not their normal sort order.

Once you have resigned yourself to leaking some bits of the password via timing, you would be fine using normal hash tables as well -- just use a cryptographic hashing function and a constant-time equality function and you're good. No constant-time less-than operator need be invented. You leak something on the order of log2(COUNT) bits via timing, where COUNT is the number of passwords, but since that's behind a hash you can't use it to bisect on actual key values. Of course, you have to ensure that the hash table isn't storing values in sorted order and short-cutting early. This sort of detail isn't usually part of the contract of stock hash table implementations, so you probably still need to build your own.

Edit: People keep mentioning Cuckoo hashing for some reason, despite the fact that it's not a good open-hashing technique in general (Robin Hood hashes with linear probing are better). Thing is, any operation on a data structure that does not touch all of the memory in the data structure in exactly the same order regardless of input leaks cache timing information. That's the whole point of this article!

An alternative is to encode your data structure differently, for example for the "key" to itself contain the value, signed by some private key only known to the server. But this approach is limited by network capacity and the appropriateness of copying for the data in question. It's not appropriate for photos, for example, as they are just too big.

Edit: Forcing constant-time on the data structure via sleep() or similar calls is not a good mitigation. This either massively slows down your throughput, or leaks information via side channels. Remote attackers can measure throughput instead of latency to determine how long an operation takes.

Corrections appreciated from my knowledgeable readers :) I was quite disappointed when I realized that there were no good constant-time data structures and would be happy to be proven wrong. Thanks to Darius Bacon, Zooko Wilcox-O'Hearn, Jan Lehnardt, and Paul Khuong on Twitter for their insights; all mistakes are mine.

scheme workshop 2014

27 November 2014 5:48 PM (scheme | guile | igalia | gnu | adaptive optimization | javascript)

I just got back from the US, and after sleeping for 14 hours straight I'm in a position to type about stuff again. So welcome back to the solipsism, France and internet! It is good to see you on a properly-sized monitor again.

I had the enormously pleasurable and flattering experience of being invited to keynote this year's Scheme Workshop last week in DC. Thanks to John Clements, Jason Hemann, and the rest of the committee for making it a lovely experience.

My talk was on what Scheme can learn from JavaScript, informed by my work in JS implementations over the past few years; you can download the slides as a PDF. I managed to record audio, so here goes nothing:

55 minutes, vorbis or mp3

It helps to follow along with the slides. Some day I'll augment my slide-rendering stuff to synchronize a sequence of SVGs with audio, but not today :)

The invitation to speak meant a lot to me, for complicated reasons. See, Scheme was born out of academic research labs, and to a large extent that's been its spiritual core for the last 40 years. My way to the temple was as a money-changer, though. While working as a teacher in northern Namibia in the early 2000s, fleeing my degree in nuclear engineering, trying to figure out some future life for myself, for some reason I was recording all of my expenses in Gnucash. Like, all of them, petty cash and all. 50 cents for a fat-cake, that kind of thing.

I got to thinking "you know, I bet I don't spend any money on Tuesdays." See, there was nothing really to spend money on in the village besides fat cakes and boiled eggs, and I didn't go into town to buy things except on weekends or later in the week. So I thought that it would be neat to represent that as a chart. Gnucash didn't have such a chart but I knew that they were implemented in Guile, as part of this wave of Scheme consciousness that swept the GNU project in the nineties, and that I should in theory be able to write it myself.

Problem was, I also didn't have internet in the village, at least then, and I didn't know Scheme and I didn't really know Gnucash. I think what I ended up doing was just monkey-typing out something that looked like the rest of the code, getting terrible errors but hey, it eventually worked. I submitted the code, many years ago now, some of the worst code you'll read today, but they did end up incorporating it into Gnucash and to my knowledge that report is still there.

I got more into programming, but still through the back door, so to speak. I had done some free software work before going to Namibia, on GStreamer, and wanted to build a programmable modular synthesizer with it. I read about Supercollider, and decided I wanted to do something like that but with the "unit generators" defined in GStreamer and orchestrated with Scheme. If I knew then that Scheme could be fast, I probably would have started on an entirely different course of things, but that did at least result in gainful employment doing unrelated GStreamer things, if not a synthesizer.

Scheme became my dominant language for writing programs. It was fun, and the need to re-implement a bunch of things wasn't a barrier at all -- rather a fun challenge. After a while, though, speed was becoming a problem. It became apparent that the only way to speed up Guile would be to replace its AST interpreter with a compiler. Thing is, I didn't know how to write one! Fortunately there was previous work by Keisuke Nishida, jetsam from the nineties wave of Scheme consciousness. I read and read that code, mechanically monkey-typed it into compilation, and slowly reworked it into Guile itself. In the end, around 2009, Guile was faster and I found myself its co-maintainer to boot.

Scheme has been a back door for me for work, too. I randomly met Kwindla Hultman-Kramer in Namibia, and we found Scheme to be a common interest. Some four or five years later I ended up working for him with the great folks at Oblong. As my interest in compilers grew, and it grew as I learned more about Scheme, I wanted something closer there, and that's what I've been doing in Igalia for the last few years. My first contact there was a former Common Lisp person, and since then many contacts I've had in the JS implementation world have been former Schemers.

So it was a delight when the invitation came to speak (keynote, no less!) the Scheme Workshop, behind the altar instead of in the foyer.

I think it's clear by now that Scheme as a language and a community isn't moving as fast now as it was in 2000 or even 2005. That's good because it reflects a certain maturity, and makes the lore of the tribe easier to digest, but bad in that people tend to ossify and focus on past achievements rather than future possibility. Ehud Lamm quoted Nietzche earlier today on Twitter:

By searching out origins, one becomes a crab. The historian looks backward; eventually he also believes backward.

So it is with Scheme and Schemers, to an extent. I hope my talk at the conference inspires some young Schemer to make an adaptively optimized Scheme, or to solve the self-hosted adaptive optimization problem. Anyway, as users I think we should end the era of contorting our code to please compilers. Of course some discretion in this area is always necessary but there's little excuse for actively bad code.

Happy hacking with Scheme, and au revoir!

on yakshave, on color, on cosines, on glitchen

14 November 2014 4:49 PM (jpeg | scheme | guile | colorspaces | yaks | photos | dct | compression)

Hold on to your butts, kids, because this is epic.

on yaks

As in all great epics, our prideful, stubborn hero starts in a perfectly acceptable state of things, decides on a lark to make a small excursion, and comes back much much later to inflict upon you pictures from his journey.

So. I have a web photo gallery but I don't take many pictures these days. Dealing with photos is a bit of a drag, and the ways that are easier like Instagram or what-not give me the (peer, corporate, government: choose 3) surveillance hives. So, I had vague thoughts that I should update my web gallery. Yakpoint 1.

At the same time, my web gallery was written for mod_python on the server, and I don't like hacking in Python any more and kinda wanted to switch away from Apache. Yakpoint 2.

So I rewrote the server-side part in Scheme. (Yakpoint 3.) It worked fine but I found I needed the ability to get the dimensions of files on the server, so I wrote a quick-and-dirty JPEG parser. Yakpoint 4.

I needed EXIF data as well, as the original version displayed EXIF data, and for that I used a binding to libexif that I had written a few years ago when I thought about starting this project (Yakpoint -1). However I found some crashers in the library, because it had never really been tested in production, and instead of fixing them I said "what the hell, I'll just write an EXIF parser". (Yakpoint 5.) So I did and adapted the web gallery to use it (Yakpoint 6, for the adaptation.)

At this point, I looked back, and looked forward, and looked all around, and all was good, but what was with this uneasiness I was feeling? And indeed, I hadn't actually made anything better, and I wasn't taking more photos, and the workflow was the same.

I was also concerned about the client side of things, which was still in Python and using some breakage-prone legacy libraries to do the photo scaling and transformations and what-not, and relied on a desktop application (f-spot) of dubious future. So I started to look at what it would take to port that script to Scheme (Yakpoint 7). Well it used some legacy libraries to copy files over SSH (gnome-vfs; switching away from that would be Yakpoint 8) and I didn't want to make a Scheme GIO binding (Yakpoint 9, narrowly avoided), and I then -- and then, dear reader -- so then I said "well WTF my caching story on the server is crap anyway, I never know when the sqlite database has changed or not so I never know what responses I can cache, what I really want is a functional datastore" (Yakpoint 10), which is what I have with Git and Tekuti (Yakpoint of yore), and so why not just store my photos in Git like I do in Tekuti for blog posts and serve them from there, indexing as needed? Of course I'd need some other server software (Yakpoint of fore, by which I meantersay the future), but then I could just git push to update my photo gallery, and I wouldn't have to endure the horror that is GVFS shelling out to ssh in a FUSE daemon (Yakpoint of ne'er).

So. After mulling over these thoughts for a while I decided, during an autumnal walk on the Salève in which we had the greatest views of Mont Blanc everrrrr and yet where are the photos?, that really what I needed was new photo management software, not just a web gallery. I should be able to share photos from my phone or from my desktop, fix them up either place, tag and such, and OK woo hoo! Such is the future! And the present for many people? Thing is, I also needed good permissions management (Yakpoint what, 10 I guess?), because you know a dude just out of college is not the same as that dude many years later. Which means serving things over HTTPS (Yakpoints 11-47) in such a way that the app has some good control over who gets what.

Well. Anyway. My mind ran ahead, and runs ahead, and yet we haven't actually tasted the awesome sauce yet. So! The photo management software, whereever it lives, needs to rotate photos at least, and scale them down to a few resolutions. I smell a yak! I looked at jpegtran which can do some lossless rotations but it's not available as a library, which is odd; and really I don't like shelling out for core program functionality, because every time I deal with the file system it's the wild west of concurrent mutation. If naming things is one of the two hardest problems in computer science, the file system is the worst because you have to give a global name to every intermediate value.

At the same time to scale images, what was I to do? Make a binding to libjpeg? Well I started (Yakpoint 48) but for reals kids, libjpeg is not fun. It works great and is really clever but

  1. it's approximately impossible to use from a dynamic ffi; you want a compiler to verify that you are using the right structure definitions

  2. there has been an inane ABI and format break imposed by the official IJG libjpeg but which other implementations have not followed, but how could you know which one you are using?

  3. the error handling facility encourages longjmp in C programs; somewhat terrifying

  4. off-heap image manipulation libraries always interact poorly with GC, because the GC only sees the small pointer to the off-heap image, and so doesn't GC often enough

  5. I have zero guarantee that libjpeg won't change ABI in weird ways, and I don't want to touch this software for the next 10 years

  6. I want to do jpegtran-like lossless transformations, but that's not available as a library, and it's totes ridics that binding libjpeg does not help you out here

  7. it's still an unsafe C library, battle-tested yes, but terrifyingly unsafe, and I'd be putting it on my server and who knows?

Friends, I arrived at the pasture, and I, I chose the yak less shaven. I took my lame JPEG parser and turned it into a full decoder (Yakpoint 49), realized it wasn't much more work to do an encoder (Yakpoint 50), and implemented the lossless transformations (Yakpoint 51).

on haters

Before we go on, I know some people would think "what is this kid about". I mean, custom gallery software, a custom JPEG library of all things, all bespoke, why don't you just use off-the-shelf solutions? Why aren't you normal and use a normal language and what about the best practices and where's your business case and I can't go on about this because there's a technical term for people that say this kind of thing and it's "hater".

Thing is, when did a hater ever make anything cool? Come to think of it, when did a hater make anything at all? In my experience the most vocal haters have nothing behind their names except a long series of pseudonymous rants in other people's comment boxes. So friends, in the joyful spirit of earning-anew, let's talk about JPEG!

on color

JPEG is a funny thing. Photos are our lives and our memories, our first steps and our friends, and yet I for one didn't know very much about them. My mental model that "a JPEG is a rectangle of pixels" doesn't turn out to be quite right.

If you actually look in a normal JPEG, you see three planes of information. If I take this image, for example:

If I decode it, actually I get three images. Here's the first one:

This is just the greyscale version of the image. So, storytime! Remember black and white television? We had an old one that got moved around the house sometimes, like if Mom was working at something in the kitchen. We also had a color one in the living room, and you could watch one or the other and they showed the same stuff. Strange when you think about it though -- one being in color and the other not. Well it turns out that color was literally just added on, both historically and technically. The main broadcast was still in black and white, and then in one part of the frequency band there were separate color signals, which color TVs would pick up, mix with the black and white signal, and come out with color. Wikipedia notes that "color TV" was really just "colored TV", which is a phrase whose cleverness I respect. Big ups to the W P.

In the context of JPEG, this black-and-white signal is sometimes called "luma", but is more precisely called Y', where the "prime" (the apostrophe) indicates that the signal has gamma correction applied.

In the image above, I replaced the color planes (sometimes collectively called the "chroma") with zeroes, while losslessly keeping the luma. Below is the first color plane, with the Y' plane replaced with a uniform 50% luma, and the other color plane replaced with zeros.

This color signal is technically known as CB, which may be very imperfectly understood as the bluish component of the color. Well the original image wasn't very blue, so we don't see very much here.

Indeed, our eyes have a harder time seeing differences in color than differences in intensity. Apparently this goes all the way down to biology -- we have more receptors in our eyes for "black and white" and fewer for color.

Early broadcasters took advantage of this difference in perception by actually devoting more bandwidth in their broadcasts to luma than to chroma; if you check the Wikipedia page you will see that the area in the spectrum allocation devoted to color is much smaller than the area devoted to intensity. So it is in JPEG: the above image being half-width indicates that actually we're just encoding one CB sample for every two Y' samples.

Finally, here we have the CR color plane, which can loosely be thought of as the "redness" of the image.

These test images and crops preserve the actual encoding of this photo as it came from my camera, without re-encoding. That's partly why there's not much interesting going on; with the megapixels these days, it's hard to fit much of anything in a few hundred pixels square. This particular camera is sub-sampling in the horizontal direction, but it's also common to subsample vertically as well, producing color planes that are half-width and half-height. In my limited investigations I have found that cameras tend to sub-sample just in the X direction, producing what they call 4:2:2 images, and that standard software encoders subsample in both, producing 4:2:0.

Incidentally, properly scaling up the color planes is quite an irritating endeavor -- the standard indicates that the color is sampled between the locations of the Y' samples ("centered" chroma), but these images originally have EXIF data that indicates that the color samples are taken at the position of the first Y' sample ("co-sited" chroma). I'm pretty sure libjpeg doesn't delve into the EXIF to check this though, so it would seem that all renderings I have seen of these photos are subtly off.

But how do you get proper color out of these strange luma and chroma things? Well, the Y'CBCR colorspace is really just the same color cube as RGB, except rotated: the Y' axis traverses the diagonal from (0, 0, 0) (black) to (255, 255, 255) (white). CB and CR are perpendicular to that diagonal, pointing towards blue or red respectively. So to go back to RGB, you multiply by a matrix to rotate the cube.

It's not a very intuitive color system, as you can see from the images above. For one thing, at zero or full luma, the chroma axes have no meaning; black and white can have no hue. Indeed if you imagine trying to fit a cube corner-down into a similar-sized box, you end up either having empty space in the box, or you have to cut off corners from the cube, or both. Cut corners means that bits of the Y'CBCR signal are wasted; empty space means there are RGB colors that are not representable in Y'CBCR. I'm not sure, but I think both are true for the particular formulation of Y'CBCR used in JPEG.

There's more to say about color here but frankly I don't know enough to do so, even though I worked in digital video for many years. If this is something you are mildly interested in, I highly, highly recommend watching Wim Taymans' presentation at this year's GStreamer conference. He takes a look at color in video that is constructive, building up from biology through math to engineering. His is a principled approach rather than a list of rules. It really clarified a number of things for me (and opened doors to unknown unknowns beyond).

on cosines

Where were we? Right, JPEG. So the proper way to understand what JPEG is is to understand the encoding process. We've covered colorspace conversion from RGB to Y'CBCR and sub-sampling. Next, the image canvas is divided into equal-sized "macroblocks". (These are called "minimum coded units" (MCUs) in the JPEG context, but in video they are usually called macroblocks, and it's a better name.) Without sub-sampling, each macro-block will contain one 8-sample-by-8-sample block for each component (Y', CB, CR) of the image. In my images above, the canvas space corresponding to one chroma block is the space of two luma blocks, so the macroblocks will be 16 samples wide and 8 samples tall, and contain two Y' blocks and one each of CB and CR. If the image canvas can't be evenly divided into macroblocks, it is padded to fit, usually by duplicating the last column or row of samples.

Then to make a JPEG, each block is encoded separately, then the whole thing is just written out to a file, and you're done!

This description glosses over a couple of important points, but it's a good big-picture view to have in mind. The pipeline goes from RGB pixels, to a padded RGB canvas, to separate Y'CBCR planes, to a possibly subsampled set of those planes, to macroblocks, to encoded macroblocks, to the file. Decoding is the reverse. It's a totally doable, comprehensible thing, and that was one of the big takeaways for me from this project. I took photography classes in high school and it was really cool to see how to shoot, develop, and print film, and this is similar in many ways. The real "film" is raw-format data, which some cameras produce, but understanding JPEG is like understanding enlargers and prints and fixer baths and such things. It's smelly and dark but pretty cool stuff.

So, how do you encode a block? Well peoples, this is a kinda cool thing. Maybe you remember from some math class that, given n uniformly spaced samples, you can always represent that series as a sum of n cosine functions of equally spaced frequencies. In each litle 8-by-8 block, that's what we do: a "forward discrete cosine transformation" (FDCT), which is just multiplying together some matrices for every point in the block. The FDCT is completely separable in the X and Y directions, so the space of 8 horizontal coefficients multiplies by the space of 8 vertical coefficients at each column to yield 64 total coefficients, which is not coincidentally the number of samples in a block.

Funny thing about those coefficients: each one corresponds to a particular horizontal and vertical frequency. We can map these out as a space of functions; for example giving a non-zero coefficient to (0, 0) in the upper-left block of a 8-block-by-8-block grid, and so on, yielding a 64-by-64 pixel representation of the meanings of the individual coefficients. That's what I did in the test strip above. Here is the luma example, scaled up without smoothing:

The upper-left corner corresponds to a frequency of 0 in both X and Y. The lower-right is a frequency of 4 "hertz", oscillating from highest to lowest value in both directions four times over the 8-by-8 block. I'm actually not sure why there are some greyish pixels around the right and bottom borders; it's not a compression artifact, as I constructed these DCT arrays programmatically. Anyway. Point is, your lover's smile, your sunny days, your raw urban graffiti, your child's first steps, all of these are reified in your photos as a sum of cosine coefficients.

The odd thing is that what is reified into your pictures isn't actually all of the coefficients there are! Firstly, because the coefficients are rounded to integers. Mathematically, the FDCT is a lossless operation, but in the context of JPEG it is not because the resulting coefficients are rounded. And they're not just rounded to the nearest integer; they are probably quantized further, for example to the nearest multiple of 17 or even 50. (These numbers seem exaggerated, but keep in mind that the range of coefficients is about 8 times the range of the original samples.)

The choice of what quantization factors to use is a key part of JPEG, and it's subjective: low quantization results in near-indistinguishable images, but in middle compression levels you want to choose factors that trade off subjective perception with file size. A higher quantization factor leads to coefficients with fewer bits of information that can be encoded into less space, but results in a worse image in general.

JPEG proposes a standard quantization matrix, with one number for each frequency (coefficient). Here it is for luma:

(define *standard-luma-q-table*
  #(16 11 10 16 24 40 51 61
    12 12 14 19 26 58 60 55
    14 13 16 24 40 57 69 56
    14 17 22 29 51 87 80 62
    18 22 37 56 68 109 103 77
    24 35 55 64 81 104 113 92
    49 64 78 87 103 121 120 101
    72 92 95 98 112 100 103 99))

This matrix is used for "quality 50" when you encode an 8-bit-per-sample JPEG. You can see that lower frequencies (the upper-left part) are quantized less harshly, and vice versa for higher frequencies (the bottom right).

(define *standard-chroma-q-table*
  #(17 18 24 47 99 99 99 99
    18 21 26 66 99 99 99 99
    24 26 56 99 99 99 99 99
    47 66 99 99 99 99 99 99
    99 99 99 99 99 99 99 99
    99 99 99 99 99 99 99 99
    99 99 99 99 99 99 99 99
    99 99 99 99 99 99 99 99))

For chroma (CB and CR) we see that quantization is much more harsh in general. So not only will we sub-sample color, we will also throw away more high-frequency color variation. It's interesting to think about, but also makes sense in some way; again in photography class we did an exercise where we shaded our prints with colored pencils, and the results were remarkable. My poor, lazy coloring skills somehow rendered leaves lifelike in different hues of green; really though, they were shades of grey, colored in imprecisely. "Colored TV" indeed.

With this knowledge under our chapeaux, we can now say what the "JPEG quality" setting actually is: it's simply that pair of standard quantization matrices scaled up or down. Towards "quality 100", the matrix approaches all-ones, for no quantization, and thus minimal loss (though you still have some rounding, often subsampling as well, and RGB-to-Y'CBCR gamut loss). Towards "quality 0" they scale to a matrix full of large values, for harsh quantization.

This understanding also explains those wavey JPEG artifacts you get on low-quality images. Those artifacts look like waves because they are waves. They usually occur at sharp intensity transitions, which like a cymbal crash cause lots of high frequencies that then get harshly quantized. Incidentally I suspect (but don't know) that this is the same reason that cymbals often sound bad in poorly-encoded MP3s, because of harsh quantization in the frequency domain.

Finally, the coefficients are written out to a file as a stream of bits. Each file gets a huffman code allocated to it, which ideally is built from the distribution of quantized coefficient sizes seen in all of the blocks of an image. There are usually different encodings for luma and chroma, to reflect their different quantizations. Reading and writing this bitstream is a bit of a headache but the algorithm is specified in the JPEG standard, and all you have to do is implement it. Notably, though, there is special support for encoding a run of zero-valued coefficients, which happens often after quantization. There are rarely wavey bits in a blue blue sky.

on transforms

It's terribly common for photos to be wrongly oriented. Unfortunately, the way that many editors fix photo rotation is by setting a bit in the EXIF information of the JPEG. This is ineffectual, as web browsers don't look in the EXIF information, and silly, because it turns out you can losslessly rotate most JPEG images anyway.

Consider that the body of a JPEG is an array of macroblocks. To rotate an image, you just have to rearrange those macroblocks, then rearrange the blocks inside the macroblocks (e.g. swap the two Y' blocks in my above example), then transform the blocks themselves.

The lossless transformations that you can do on a block are transposition, vertical flipping, and horizontal flipping.

Transposition flips a block along its downward-sloping diagonal. To do so, you just swap the coefficients at (u, v) with the coefficients at (v, u). Easy peasey.

Flipping is trickier. Consider the enlarged DCT image from above. What would it take to horizontally flip the function at (0, 1)? Instead of going from light to dark, you want it to go from dark to light. Simple: you just negate the coefficients! But you only want to negate those coefficients that are "odd" in the X direction, which are those coefficients whose column is odd. And actually that's all there is to it. Flipping vertically is the same, but for coefficients whose row is odd.

I said "most images" above because those whose size is not evenly divided by the macroblock size can't be losslessly rotated -- you will end up seeing some of the hidden data that falls off the edge of the canvas. Oh well. Most raw images are properly dimensioned, and if you're downscaling, you already have to re-encode anyway.

But that's just flipping and transposition, you say! What about rotation? Well it turns out that you can express rotation in terms of these operations: rotating 90 degrees clockwise is just a transpose and a horizontal flip (in that order). Together, flipping horizontally, flipping vertically, and transposing form a group, in the same way that flipping and flopping form a group for mattresses. Yeah!

on scheme

I wrote this library in Scheme because that's my language of choice these days. I didn't run into any serious impedance mismatches; Guile has a generic multi-dimensional array facility that made it possible to express many of these operations as generic folds, unfolds, or maps over arrays. The huffman coding part was a bit irritating, but all in all things were pretty good. The speed is pretty bad, but I haven't optimized it at all, and it gives me a nice test case for the compiler. Anyway, it's been fun and it suits my needs. Check out the project page if you're interested. Yes, to shave a yak you have to get a bit bovine and smelly, but yaks live in awesome places!

Finally I will leave you with a glitch, one of many that I have produced over the last couple weeks. Comments and corrections welcome below. Happy hacking!

generators in firefox now twenty-two times faster

14 November 2014 8:41 AM (spidermonkey | firefox | mozilla | javascript | es6 | ecmascript | v8 | jandem | bloomberg | igalia)

It's with great pleasure that I can announce that, thanks to Mozilla's Jan de Mooij, the new ES6 generator functions are twenty-two times faster in Firefox!

Some back-story, for the unawares. There's a new version of JavaScript coming, ECMAScript 6 (ES6). Among the new features that ES6 brings are generator functions: functions that can suspend. Firefox's JavaScript engine, SpiderMonkey, has had support for generators for many years, long before other engines. This support was upgraded to the new ES6 standard last year, thanks to sponsorship from Bloomberg, and was shipped out to users in Firefox 26.

The generators implementation in Firefox 26 was quite basic. As you probably know, modern JavaScript implementations have a number of tiered engines. In the case of SpiderMonkey there are three tiers: the interpreter, the baseline compiler, and the optimizing compiler. Code begins execution in the interpreter, which is the quickest engine to start. If a piece of code is hot -- meaning that lots of time is being spent there -- then it will "tier up" to the next level, where it is analyzed, possibly optimized, and then compiled to machine code.

Unfortunately, generators in SpiderMonkey have always been stuck at the lowest tier, the interpreter. This is because of SpiderMonkey's choice of implementation strategy for generators. Generators were implemented as "floating interpreter stack frames": heap-allocated objects whose shape was exactly the same as a stack frame in the interpreter. This had the advantage of being fairly cheap to implement in the beginning, but ultimately it made them unable to take advantage of JIT compilation, as JIT code runs on its own stack which has a different layout. The previous strategy also relied on trampolining through a helper written in C++ to resume generators, which killed optimization opportunities.

The solution was to represent suspended generator objects as snapshots of the state of a stack frame, instead of as stack frames themselves. In order for this to be efficient, last year we did a number of block scope optimizations to try and reduce the amount of state that a generator frame would have to restore. Finally, around March of this year we were at the point where we could refactor the interpreter to implement generators on the normal interpreter stack, with normal interpreter bytecodes, with the vision of being able to JIT-compile those bytecodes.

I ran out of time before I could land that patchset; although the patches were where we wanted to go, they actually caused generators to be even slower and so they languished in Bugzilla for a few more months. Sad monkey. It was with delight, then, that a month or so ago I saw that SpiderMonkey JIT maintainer Jan de Mooij was interested in picking up the patches. Since then he has been hacking off and on at getting my old patches into shape, and ended up applying them all.

He went further, optimizing stack frames to not reserve space for "aliased" locals (locals allocated on the scope chain), speeding up object literal creation in the baseline compiler and finally has implemented baseline JIT compilation for generators.

So, after all of that perf nargery, what's the upshot? Twenty-two times faster! In this microbenchmark:

function *g(n) {
    for (var i=0; i<n; i++)
        yield i;
function f() {
    var t = new Date();
    var it = g(1000000);
    for (var i=0; i<1000000; i++);
    print(new Date() - t);

Before, it took SpiderMonkey 980 milliseconds to complete on Jan's machine. After? Only 43! It's actually marginally faster than V8 at this point, which has (temporarily, I think) regressed to 45 milliseconds on this test. Anyway. Competition is great and as a committer to both projects I find it very satisfactory to have good implementations on both sides.

As in V8, in SpiderMonkey generators cannot yet reach the highest tier of optimization. I'm somewhat skeptical that it's necessary, too, as you expect generators to suspend fairly frequently. That said, a yield point in a generator is, from the perspective of the optimizing compiler, not much different from a call site, in that it causes all locals to be saved. The difference is that locals may have unboxed representations, so we would have to box those values when saving the generator state, and unbox on restore.

Thanks to Bloomberg for funding the initial work, and big, big thanks to Mozilla's Jan de Mooij for picking up where we left off. Happy hacking with generators!

ffconf 2014

9 November 2014 5:36 PM (javascript | javascriptcore | spidermonkey | v8 | self-hosting | bootstrapping | igalia)

Last week I had the great privilege of speaking at ffconf in Brighton, UK. It was lovely. The town put on a full demonstration of its range of November weather patterns, from blue skies to driving rain to hail (!) to sea-spray to drizzle and back again. Good times.

The conference itself was quite pleasant as well, and from the speaker perspective it was amazing. A million thanks to Remy and Julie for making it such a pleasure. ffconf is mostly a front-end development conference, so it's not directly related with the practice of my work on JS implementations -- perhaps you're unaware, but there aren't so many browser implementors that actually develop content for their browsers, and indeed fewer JS implementors that actually write JS. Me, I sling C++ all day long and the most JavaScript I write is for tests. When in the weeds, sometimes we forget we're building an amazing runtime and that people do inspiring things with it, so it's nice to check in with front-end folks at their conferences to see what people are excited about.

My talk was about the part of JavaScript implementations that are written in JavaScript itself. This is an area that isn't so well known, and it has its amusing quirks. I think it can be interesting to a curious JS hacker who wants to spelunk down a bit to see what's going on in their browsers. Intrepid explorers might even find opportunities to contribute patches. Anyway, nerdy stuff, but that's basically how I roll.

The slides are here: without images (350kB PDF) or with images (3MB PDF).

I haven't been to the UK in years, and being in a foreign country where everyone speaks my native language was quite refreshing. At the same time there was an awkward incident in which I was reminded that though close, American and English just aren't the same. I made this silly joke that if you get a polyfill into a JS implementation, then shucks, you have a "gollyfill", 'cause golly it made it in! In the US I think "golly" is just one of those milquetoast profanities, "golly" instead of "god" like saying "shucks" instead of "shit". Well in the UK that's a thing too I think, but there is also another less fortunate connotation, in which "golly" as a noun can be a racial slur. Check the Wikipedia if you're as ignorant as I was. I think everyone present understood that wasn't my intention, but if that is not the case I apologize. With slides though it's less clear, so I've gone ahead and removed the joke from the slides. It's probably not a ball to take and run with.

However I do have a ball that you can run with though! And actually, this was another terrible joke that wasn't bad enough to inflict upon my audience, but that now chance fate gives me the opportunity to use. So never fear, there are still bad puns in the slides. But, you'll have to click through to the PDF for optimal groaning.

Happy hacking, JavaScripters, and until next time.

ffs ssl

17 October 2014 2:33 PM (ssl | tls | ffs | meta | https | http | hsts | pki | networking)

I just set up SSLTLS on my web site. Everything can be had via, and things appear to work. However the process of transitioning even a simple web site to SSL is so clownshoes bad that it's amazing anyone ever does it. So here's an incomplete list of things that can go wrong when you set up TLS on a web site.

You search "how to set up https" on the Googs and click the first link. It takes you here which tells you how to use StartSSL, which generates the key in your browser. Whoops, your private key is now known to another server on this internet! Why do people even recommend this? It's the worst of the worst of Javascript crypto.

OK so you decide to pay for a certificate, assuming that will be better, and because who knows what's going on with StartSSL. You've heard of RapidSSL so you go to WTF their price is 49 dollars for a stupid certificate? Your domain name was only 10 dollars, and domain name resolution is an actual ongoing service, unlike certificate issuance that just happens one time. You can't believe it so you click through to the prices to see, and you get this:


OK so I'm using Epiphany on Debian and I think that uses the system root CA list which is different from what Chrome or Firefox do but Jesus this is shaking my faith in the internet if I can't connect to an SSL certificate provider over SSL.

You remember hearing something on Twitter about cheaper certs, and oh ho ho, it's, not just RapidSSL. WTF. OK. It turns out Geotrust and RapidSSL and Verisign are all owned by Symantec anyway. So you go and you pay. Paying is the first thing you have to do on rapidsslonline, before anything else happens. Welp, cross your fingers and take out your credit card, cause SSLanta Clause is coming to town.

Recall, distantly, that SSL has private keys and public keys. To create an SSL certificate you have to generate a key on your local machine, which is your private key. That key shouldn't leave your control -- that's why the DigitalOcean page is so bogus. The certification authority (CA) then needs to receive your public key and then return it signed. You don't know how to do this, because who does? So you Google and copy and paste command line snippets from a website. Whoops!

Hey neat it didn't delete your home directory, cool. Let's assume that your local machine isn't rooted and that your server isn't rooted and that your hosting provider isn't rooted, because that would invalidate everything. Oh what so the NSA and the five eyes have an ongoing program to root servers? Um, well, water under the bridge I guess. Let's make a key. You google "generate ssl key" and this is the first result.

# openssl genrsa -des3 -out foo.key 1024

Whoops, you just made a 1024-bit key! I don't know if those are even accepted by CAs any more. Happily if you leave off the 1024, it defaults to 2048 bits, which I guess is good.

Also you just made a key with a password on it (that's the -des3 part). This is eminently pointless. In order to use your key, your web server will need the decrypted key, which means it will need the password to the key. Adding a password does nothing for you. If you lost your private key but you did have it password-protected, you're still toast: the available encryption cyphers are meant to be fast, not hard to break. Any serious attacker will crack it directly. And if they have access to your private key in the first place, encrypted or not, you're probably toast already.

OK. So let's say you make your key, and make what's called the "CRTCSR", to ask for the cert.

# openssl req -new -key foo.key -out foo.csr

Now you're presented with a bunch of pointless-looking questions like your country code and your "organization". Seems pointless, right? Well now I have to live with this confidence-inspiring dialog, because I left off the organization:

Don't mess up, kids! But wait there's more. You send in your CSR, finally figure out how to receive mail for because that's what "verification" means (not, god forbid, control of the actual web site), and you get back a certificate. Now the fun starts!

How are you actually going to serve SSL? The truly paranoid use an out-of-process SSL terminator. Seems legit except if you do that you lose any kind of indication about what IP is connecting to your HTTP server. You can use a more HTTP-oriented terminator like bud but then you have to mess with X-Forwarded-For headers and you only get them on the first request of a connection. You could just enable mod_ssl on your Apache, but that code is terrifying, and do you really want to be running Apache anyway?

In my case I ended up switching over to nginx, which has a startlingly underspecified configuration language, but for which the Debian defaults are actually not bad. So you uncomment that part of the configuration, cross your fingers, Google a bit to remind yourself how systemd works, and restart the web server. Haich Tee Tee Pee Ess ahoy! But did you remember to disable the NULL authentication method? How can you test it? What about the NULL encryption method? These are actual things that are configured into OpenSSL, and specified by standards. (What is the use of a secure communications standard that does not provide any guarantee worth speaking of?) So you google, copy and paste some inscrutable incantation into your config, turn them off. Great, now you are a dilettante tweaking your encryption parameters, I hope you feel like a fool because I sure do.

Except things are still broken if you allow RC4! So you better make sure you disable RC4, which incidentally is exactly the opposite of the advice that people were giving out three years ago.

OK, so you took your certificate that you got from the CA and your private key and mashed them into place and it seems the web browser works. Thing is though, the key that signs your certificate is possibly not in the actual root set of signing keys that browsers use to verify the key validity. If you put just your key on the web site without the "intermediate CA", then things probably work but browsers will make an additional request to get the intermediate CA's key, slowing down everything. So you have to concatenate the text files with your key and the one with the intermediate CA's key. They look the same, just a bunch of numbers, but don't get them in the wrong order because apparently the internet says that won't work!

But don't put in too many keys either! In this image we have a cert for with one intermediate CA:

And here is the same but with an a different root that signed the GeoTrust Global CA certificate. Apparently there was a time in which the GeoTrust cert hadn't been added to all of the root sets yet, and it might not hurt to include them all:

Thing is, the first one shows up "green" in Chrome (yay), but the second one shows problems ("outdated security settings" etc etc etc). Why? Because the link from Equifax to Geotrust uses a SHA-1 signature, and apparently that's not a good idea any more. Good times? (Poor Remy last night was doing some basic science on the internet to bring you these results.)

Or is Chrome denying you the green because it was RapidSSL that signed your certificate with SHA-1 and not SHA-256? It won't tell you! So you Google and apply snakeoil and beg your CA to reissue your cert, hopefully they don't charge for that, and eventually all is well. Chrome gives you the green.

Or does it? Probably not, if you're switching from a web site that is also available over HTTP. Probably you have some images or CSS or Javascript that's being loaded over HTTP. You fix your web site to have scheme-relative URLs (like // instead of, and make sure that your software can deal with it all (I had to patch Guile :P). Update all the old blog posts! Edit all the HTMLs! And finally, green! You're golden!

Or not! Because if you left on SSLv3 support you're still broken! Also, TLSv1.0, which is actually greater than SSLv3 for no good reason, also has problems; and then TLS1.1 also has problems, so you better stick with just TLSv1.2. Except, except, older Android phones don't support TLSv1.2, and neither does the Googlebot, so you don't get the rankings boost you were going for in the first place. So you upgrade your phone because that's a thing you want to do with your evenings, and send snarky tweets into the ether about scumbag google wanting to promote HTTPS but not supporting the latest TLS version.

So finally, finally, you have a web site that offers HTTPS and HTTP access. You're good right? Except no! (Catching on to the pattern?) Because what happens is that people just type in web addresses to their URL bars like "" and leave off the HTTP, because why type those stupid things. So you arrange for to redirect for users that have visited the HTTPS site. Except no! Because any network attacker can simply strip the redirection from the HTTP site.

The "solution" for this is called HTTP Strict Transport Security, or HSTS. Once a visitor visits your HTTPS site, the server sends a response that tells the browser never to fetch HTTP from this site. Except that doesn't work the first time you go to a web site! So if you're Google, you friggin add your name to a static list in the browser. EXCEPT EVEN THEN watch out for the Delorean.

And what if instead they go to instead of the that you configured? Well, better enable HSTS for the whole site, but to do anything useful with such a web request you'll need a wildcard certificate to handle the multiple URLs, and those run like 150 bucks a year, for a one-bit change. Or, just get more single-domain certs and tack them onto your cert, using the precision tool cat, but don't do too many, because if you do you will overflow the initial congestion window of the TCP connection and you'll have to wait for an ACK on your certificate before you can actually exchange keys. Don't know what that means? Better look it up and be an expert, or your wobsite's going to be slow!

If your security goals are more modest, as they probably are, then you could get burned the other way: you could enable HSTS, something could go wrong with your site (an expired certificate perhaps), and then people couldn't access your site at all, even if they have no security needs, because HTTP is turned off.

Now you start to add secure features to your web app, safe with the idea you have SSL. But better not forget to mark your cookies as secure, otherwise they could be leaked in the clear, and better not forget that your website might also be served over HTTP. And better check up on when your cert expires, and better have a plan for embedded browsers that don't have useful feedback to the user about certificate status, and what about your CA's audit trail, and better stay on top of the new developments in security! Did you read it? Did you read it? Did you read it?

It's a wonder anything works. Indeed I wonder if anything does.

high-performance packet filtering with pflua

2 September 2014 10:15 AM (lua | networks | packet filtering | luajit | trace compilation | jit | igalia | snabb | pcap | pflang | pflua)

Greets! I'm delighted to be able to announce the release of Pflua, a high-performance packet filtering toolkit written in Lua.

Pflua implements the well-known libpcap packet filtering language, which we call pflang for short.

Unlike other packet filtering toolkits, which tend to use the libpcap library to compile pflang expressions bytecode to be run by the kernel, Pflua is a completely new implementation of pflang.

why lua?

At this point, regular readers are asking themselves why this Schemer is hacking on a Lua project. The truth is that I've always been looking for an excuse to play with the LuaJIT high-performance Lua implementation.

LuaJIT is a tracing compiler, which is different from other JIT systems I have worked on in the past. Among other characteristics, tracing compilers only emit machine code for branches that are taken at run-time. Tracing seems a particularly appropriate strategy for the packet filtering use case, as you end up with linear machine code that reflects the shape of actual network traffic. This has the potential to be much faster than anything static compilation techniques can produce.

The other reason for using Lua was because it was an excuse to hack with Luke Gorrie, who for the past couple years has been building the Snabb Switch network appliance toolkit, also written in Lua. A common deployment environment for Snabb is within the host virtual machine of a virtualized server, with Snabb having CPU affinity and complete control over a high-performance 10Gbit NIC, which it then routes to guest VMs. The administrator of such an environment might want to apply filters on the kinds of traffic passing into and out of the guests. To this end, we plan on integrating Pflua into Snabb so as to provide a pleasant, expressive, high-performance filtering facility.

Given its high performance, it is also reasonable to deploy Pflua on gateway routers and load-balancers, within virtualized networking appliances.


Pflua compiles pflang expressions to Lua source code, which are then optimized at run-time to native machine code.

There are actually two compilation pipelines in Pflua. The main one is fairly traditional. First, a custom parser produces a high-level AST of a pflang filter expression. This AST is lowered to a primitive AST, with a limited set of operators and ways in which they can be combined. This representation is then exhaustively optimized, folding constants and tests, inferring ranges of expressions and packet offset values, hoisting assertions that post-dominate success continuations, etc. Finally, we residualize Lua source code, performing common subexpression elimination as we go.

For example, if we compile the simple Pflang expression ip or ip6 with the default compilation pipeline, we get the Lua source code:

return function(P,length)
   if not (length >= 14) then return false end
      local v1 = ffi.cast("uint16_t*", P+12)[0]
      if v1 == 8 then return true end
         do return v1 == 56710 end

The other compilation pipeline starts with bytecode for the Berkeley packet filter VM. Pflua can load up the libpcap library and use it to compile a pflang expression to BPF. In any case, whether you start from raw BPF or from a pflang expression, the BPF is compiled directly to Lua source code, which LuaJIT can gnaw on as it pleases. Compiling ip or ip6 with this pipeline results in the following Lua code:

return function (P, length)
   local A = 0
   if 14 > length then return 0 end
   A = bit.bor(bit.lshift(P[12], 8), P[12+1])
   if (A==2048) then goto L2 end
   if not (A==34525) then goto L3 end
   do return 65535 end
   do return 0 end
   error("end of bpf")

We like the independence and optimization capabilities afforded by the native pflang pipeline. Pflua can hoist and eliminate bounds checks, whereas BPF is obligated to check that every packet access is valid. Also, Pflua can work on data in network byte order, whereas BPF must convert to host byte order. Both of these restrictions apply not only to Pflua's BPF pipeline, but also to all other implementations that use BPF (for example the interpreter in libpcap, as well as the JIT compilers in the BSD and Linux kernels).

However, though Pflua does a good job in implementing pflang, it is inevitable that there may be bugs or differences of implementation relative to what libpcap does. For that reason, the libpcap-to-bytecode pipeline can be a useful alternative in some cases.


When Pflua hits the sweet spots of the LuaJIT compiler, performance screams.

(full image, analysis)

This synthetic benchmark runs over a packet capture of a ping flood between two machines and compares the following pflang implementations:

  1. libpcap: The user-space BPF interpreter from libpcap

  2. linux-bpf: The old Linux kernel-space BPF compiler from 2011. We have adapted this library to work as a loadable user-space module (source)

  3. linux-ebpf: The new Linux kernel-space BPF compiler from 2014, also adapted to user-space (source)

  4. bpf-lua: BPF bytecodes, cross-compiled to Lua by Pflua.

  5. pflua: Pflang compiled directly to Lua by Pflua.

To benchmark a pflang implementation, we use the implementation to run a set of pflang expressions over saved packet captures. The result is a corresponding set of benchmark scores measured in millions of packets per second (MPPS). The first set of results is thrown away as a warmup. After warmup, the run is repeated 50 times within the same process to get multiple result sets. Each run checks to see that the filter matches the the expected number of packets, to verify that each implementation does the same thing, and also to ensure that the loop is not dead.

In all cases the same Lua program is used to drive the benchmark. We have tested a native C loop when driving libpcap and gotten similar results, so we consider that the LuaJIT interface to C is not a performance bottleneck. See the pflua-bench project for more on the benchmarking procedure and a more detailed analysis.

The graph above shows that Pflua can stream in packets from memory and run some simple pflang filters them at close to the memory bandwidth on this machine (100 Gbit/s). Because all of the filters are actually faster than the accept-all case, probably due to work causing prefetching, we actually don't know how fast the filters themselves can run. At any case, in this ideal situation, we're running at a handful of nanoseconds per packet. Good times!

(full image, analysis)

It's impossible to make real-world tests right now, especially since we're running over packet captures and not within a network switch. However, we can get more realistic. In the above test, we run a few filters over a packet capture from, which mostly operates as a web server. Here we see again that Pflua beats all of the competition. Oddly, the new Linux JIT appears to fare marginally worse than the old one. I don't know why that would be.

Sadly, though, the last tests aren't running at that amazing flat-out speed we were seeing before. I spent days figuring out why that is, and that's part of the subject of my last section here.

on lua, on luajit

I implement programming languages for a living. That doesn't mean I know everything there is to know about everything, or that everything I think I know is actually true -- in particular, I was quite ignorant about trace compilers, as I had never worked with one, and I hardly knew anything about Lua at all. With all of those caveats, here are some ignorant first impressions of Lua and LuaJIT.

LuaJIT has a ridiculously fast startup time. It also compiles really quickly: under a minute. Neither of these should be important but they feel important. Of course, LuaJIT is not written in Lua, so it doesn't have the bootstrap challenges that Guile has; but still, a fast compilation is refreshing.

LuaJIT's FFI is great. Five stars, would program again.

As a compilation target, Lua is OK. On the plus side, it has goto and efficient bit operations over 32-bit numbers. However, and this is a huge downer, the result range of bit operations is the signed int32 range, not the unsigned range. This means that, x) might be negative. No one in the history of programming has ever wanted this. There are sensible meanings for negative results to bit operations, but only if an argument was negative. Grr. Otherwise, Lua shares the same concerns as other languages whose numbers are defined as 64-bit doubles.

Sometimes people get upset that Lua starts its indexes (in "arrays" or strings) with 1 instead of 0. It's foreign to me, so it's sometimes a challenge, but it can work as well as anything else. The problem comes in when working with the LuaJIT FFI, which starts indexes with 0, leading me to make errors as I forget which kind of object I am working on.

As a language to implement compilers, Lua desperately misses a pattern matching facility. Otherwise, a number of small gripes but no big ones; tables and closures abound, which leads to relatively terse code.

Finally, how well does trace compilation work for this task? I offer the following graph.

(full image, analysis)

Here the tests are paired. The first test of a pair, for example the leftmost portrange 0-6000, will match most packets. The second test of a pair, for example the second-from-the-left portrange 0-5, will reject all packets. The generated Lua code will be very similar, except for some constants being different. See for an example.

The Pflua performance of these filters is very different: the one that matches is slower than the one that doesn't, even though in most cases the non-matching filter will have to do more work. For example, a non-matching filter probably checks both src and dst ports, whereas a successful one might not need to check the dst.

It hurts to see Pflua's performance be less than the Linux JIT compilers, and even less than libpcap at times. I scratched my head for a long time about this. The Lua code is fine, and actually looks much like the BPF code. I had taken a look at the generated assembly code for previous traces and it looked fine -- some things that were not as good as they should be (e.g. a fair bit of conversions between integers and doubles, where these traces have no doubles), but things were OK. What changed?

Well. I captured the traces for portrange 0-6000 to a file, and dove in. Trace 66 contains the inner loop. It's interesting to see that there's a lot of dynamic checks in the beginning of the trace, although the loop itself is not bad (scroll down to see the word LOOP:), though with the double conversions I mentioned before.

It seems that trace 66 was captured for a packet whose src port was within range. Later, we end up compiling a second trace if the src port check fails: trace 67. The trace starts off with an absurd amount of loads and dynamic checks -- to a similar degree as trace 66, even though trace 66 dominates trace 67. It seems that there is a big penalty for transferring from one trace to another, even though they are both compiled.

Finally, once trace 67 is done -- and recall that all it has to do is check the destination port, and then update the counters from the inner loop) -- it jumps back to the top of trace 66 instead of the top of the loop, repeating all of the dynamic checks in trace 66! I can only think this is a current deficiency of LuaJIT, and not with trace compilation in general, although the amount of state transfer points to a lack of global analysis that you would get in a method JIT. I'm sure that values are being transferred that are actually dead.

This explains the good performance for the match-nothing cases: the first trace that gets compiled residualizes the loop expecting that all tests fail, and so only matching cases or variations incur the trace transfer-and-re-loop cost.

It could be that the Lua code that Pflua residualizes is in some way not idiomatic or not performant; tips in that regard are appreciated.


I was going to pass some possible slogans by our marketing department, but we don't really have one, so I pass them on to you and you can tell me what you think:

  • "Pflua: A Totally Adequate Pflang Implementation"

  • "Pflua: Sometimes Amazing Performance!!!!1!!"

  • "Pflua: Organic Artisanal Network Packet Filtering"

Pflua was written by Igalians Diego Pino, Javier Muñoz, and myself for Snabb Gmbh, fine purveyors of high-performance networking solutions. If you are interested in getting Pflua in a Snabb context, we'd be happy to talk; drop a note to the snabb-devel forum. For Pflua in other contexts, file an issue or drop me a mail at Happy hackings with Pflua, the totally adequate pflang implementation!

a wingolog user's manual

27 August 2014 8:37 AM (meta | comments)

Greetings, dear readers!

Welcome to my little corner of the internet. This is my place to share and write about things that are important to me. I'm delighted that you stopped by.

Unlike a number of other personal sites on the tubes, I have comments enabled on most of these blog posts. It's gratifying to me to hear when people enjoy an article. I also really appreciate it when people bring new information or links or things I hadn't thought of.

Of course, this isn't like some professional peer-reviewed journal; it's above all a place for me to write about my wanderings and explorations. Most of the things I find on my way have already been found by others, but they are no less new to me. As Goethe said, quoted in the introduction to The Joy of Cooking: "That which thy forbears have bequeathed to thee, earn it anew if thou wouldst possess it."

In that spirit I would enjoin my more knowledgeable correspondents to offer their insights with the joy of earning-anew, and particularly to recognize and banish the spectre of that moldy, soul-killing "well-actually" response that is present on so many other parts of the internet.

I've had a good experience with comments on this site, and I'm a bit lazy, so I take an optimistic approach to moderation. By default, comments are posted immediately. Every so often -- more often after a recent post, less often in between -- I unpublish comments that I don't feel contribute to the piece, or which I don't like for whatever reason. It's somewhat arbitrary, but hey, welcome to my corner of the internet.

This has the disadvantage that some unwanted comments end up published, then they go away. If you notice this happening to someone else's post, it's best to just ignore it, and in particular to not "go meta" and ask in the comments why a previous comment isn't there any more. If it happens to you, I'd ask you to re-read this post and refrain from unwelcome comments in the future. If you think I made an error -- it can happen -- let me know privately.

Finally, and it really shouldn't have to be said, but racism, sexism, homophobia, transphobia, and ableism are not welcome here. If you see such a comment that I should delete and have missed, let me know privately. However even among well-meaning people, and that includes me, there are ways of behaving that reinforce subtle bias. Please do point out such instances in articles or comments, either publicly or privately. Working on ableist language is a particular challenge of mine.

You can contact me via comments (anonymous or not), via email (, twitter (@andywingo), or IRC (wingo on freenode). Thanks for reading, and happy hacking :)

revisiting common subexpression elimination in guile

25 August 2014 9:48 AM (guile | compilers | cse | scheme | gnu | effects analysis | cps | ssa | scalar replacement)

A couple years ago I wrote about a common subexpression pass that I implemented in Guile 2.0.

To recap, Guile 2.0 has a global, interprocedural common subexpression elimination (CSE) pass.

In the context of compiler optimizations, "global" means that it works across basic block boundaries. Basic blocks are simple, linear segments of code without control-flow joins or branches. Working only within basic blocks is called "local". Working across basic blocks requires some form of understanding of how values can flow within the blocks, for example flow analysis.

"Interprocedural" means that Guile 2.0's CSE operates across closure boundaries. Guile 2.0's CSE is "context-insensitive", in the sense that any possible effect of a function is considered to occur at all call sites; there are newer CSE passes in the literature that separate effects of different call sites ("context-sensitive"), but that's not a Guile 2.0 thing. Being interprocedural was necessary for Guile 2.0, as its intermediate language could not represent (e.g.) loops directly.

The conclusion of my previous article was that although CSE could do cool things, in Guile 2.0 it was ultimately limited by the language that it operated on. Because the Tree-IL direct-style intermediate language didn't define order of evaluation, didn't give names to intermediate values, didn't have a way of explicitly representing loops and other kinds of first-order control flow, and couldn't precisely specify effects, the results, well, could have been better.

I know you all have been waiting for the last 27 months for an update, probably forgoing meaningful social interaction in the meantime because what if I posted a followup while you were gone? Be at ease, fictitious readers, because that day has finally come.

CSE over CPS

The upcoming Guile 2.2 has a more expressive language for the optimizer to work on, called continuation-passing style (CPS). CPS explicitly names all intermediate values and control-flow points, and can integrate nested functions into first-order control-flow via "contification". At the same time, the Guile 2.2 virtual machine no longer penalizes named values, which was another weak point of CSE in Guile 2.0. Additionally, the CPS intermediate language enables more fined-grained effects analysis.

All of these points mean that CSE has the possibility to work better in Guile 2.2 than in Guile 2.0, and indeed it does. The shape of the algorithm is a bit different, though, and I thought some compiler nerds might be interested in the details. I'll follow up in the next section with some things that new CSE pass can do that the old one couldn't.

So, by way of comparison, the old CSE pass was a once-through depth-first visit of the nested expression tree. As the visit proceeded, the pass built up an "environment" of available expressions -- for example, that (car a) was evaluated and bound to b, and so on. This environment could be consulted to see if a expression was already present in the environment. If so, the environment would be traversed from most-recently-added to the found expression, to see if any intervening expression invalidated the result. Control-flow joins would cause recomputation of the environment, so that it only held valid values.

This simple strategy works for nested expressions without complex control-flow. CPS, on the other hand, can have loops and other control flow that Tree-IL cannot express, so for it to build up a set of "available expressions" requires a full-on flow analysis. So that's what the pass does: a flow analysis over the labelled expressions in a function to compute the set of "available expressions" for each label. A labelled expression a is available at label b if a dominates b, and no intervening expression could have invalidated the results. An expression invalidates a result if it may write to a memory location that the result may have read. The code, such as it is, may be found here.

Once you have the set of available expressions for a function, you can proceed to the elimination phase. First, you start by creating an "eliminated variable" map, which initially maps each variable to itself, and an "equivalent expressions" table, which maps "keys" to a set of labels and bound variables. Then you visit each expression in a function, again in topologically sorted order. For each expression, you compute a "key", which is some unique representation of an expression that can be compared by structural equality. Keys that compare as equal are equivalent, and are subject to elimination.

For example, consider a call to the add primitive with variables labelled b and c as arguments. Imagine that b maps to a in the eliminated variable table. The expression as a whole would then have a key representation as the list (primcall add a c). If this key is present in the equivalent expression table, you check to see if any of the equivalent labels is available at the current label. If so, hurrah! You mark the outputs of the current label as being replaced by the outputs of the equivalent label. Otherwise you add the key to the equivalent table, associated with the current label.

This simple algorithm is enough to recursively eliminate common subexpressions. Sometimes the recursive aspect (i.e. noticing that b should be replaced by a), along with the creation of a common key, causes the technique to be called global value numbering (GVN), but CSE seems a better name to me.

The algorithm as outlined above eliminates expressions that bind values. However not all expressions do that; some are used as control-flow branches. For this reason, Guile also computes a "truthy table" with another flow analysis pass. This table computes a set of which branches have been taken to get to each program point. In the elimination phase, if a branch is reached that is equivalent to a previously taken branch, we consult the truthy table to see which continuation the previous branch may have taken. If it can be proven to have taken just one of the legs, the test is elided and replaced with a direct jump.

A few things to note before moving on. First, the "compute an analysis, then transform the function" sequence is quite common in this sort of problem. It leads to some challenges regarding space for the analysis; my last article deals with these in more detail.

Secondly, the rewriting phase assumes that a value that is available may be substituted, and that the result would be a proper CPS term. This isn't always the case; see the discussion at the end of the article on CSE in Guile 2.0 about CPS, SSA, dominators, and scope. In essence, the scope tree doesn't necessarily reflect the dominator tree, so not all transformations you might like to make are syntactically valid. In Guile 2.2's CSE pass, we work around the issue by concurrently rewriting the scope tree to reflect the dominator tree. It's something I am seeing more and more and it gives me some pause as to the suitability of CPS as an intermediate language.

Also, consider the clobbering part of analysis, where e.g. an expression that writes a value to memory has to invalidate previously read values. Currently this is implemented by traversing all available expressions. This is suboptimal and could be quadratic in the end. A better solution is to compute a dependency graph for expressions, which links together operations on the same regions of memory; see LLVM's memory dependency analysis for an idea of how to do this.

Finally, note that this algorithm is global but intraprocedural, meaning that it doesn't propagate values across closure boundaries. It's possible to extend it to be interprocedural, though it's less necessary in the presence of contification.

scalar replacement via fabricated expressions

Let's say you get to an expression at label L, (cons a b). It binds a result c. You determine you haven't seen it before, so you add (primcall cons a b) → L, c to your equivalent expressions set. Cool. We won't be able to replace a future instance of (cons a b) with c, because that doesn't preserve object identity of the newly allocated memory, but it's definitely a cool fact, yo.

What if we add an additional mapping to the table, (car c) → L, a? That way any expression at which L is available would replace (car c) with a, which would be pretty neat. To do so, you would have to add the &read effect to the cons call's effects analysis, but since the cons wasn't really up for elimination anyway it's all good.

Similarly, for (set-car! c d) we can add a mapping of (car c) → d. Again we have to add the &read effect to the set-car, but that's OK too because the write invalidated previous reads anyway.

The same sort of transformation holds for other kinds of memory that Guile knows how to allocate and mutate. Taken together, they form a sort of store-to-load forwarding and scalar replacement that can entirely eliminate certain allocations, and many accesses as well. To actually eliminate the allocations requires a bit more work, but that will be the subject of the next article.

future work

So, that's CSE in Guile 2.0. It works pretty well. In the future I think it's probably worth considering an abstract heap-style analysis of effects; in the end, the precision of CSE is limited to how precisely we can model the effects of expressions.

The trick of using CSE to implement scalar replacement is something I haven't seen elsewhere, though I doubt that it is novel. To fully remove the intermediate allocations needs a couple more tricks, which I will write about in my next nargy dispatch. Until then, happy hacking!