You probably shouldn't use a lookup table (2022) | Hacker News Reader

You probably shouldn't use a lookup table (2022)

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Eh, you should probably test it either way. Performance can be very unpredictable. I ran into a weird case years ago when I was writing a program that needed to calculate popcount (number of 1 bits in a number). My method using a 256-entry lookup table turned out to be faster than using GCC's popcount intrinsic. (See [1] for a question from someone who encountered a similar situation. The solution provided there was to compile with -march=native, but I think I tried that without success.)

I ran into a similar problem in another program where I needed 128-bit integers. I implemented them myself as a C struct containing two 64-bit integers. Then I discovered that GCC implemented its own 128-bit integer type. But that type was somehow slower than my implementation!

[1] https://stackoverflow.com/questions/52161596/why-is-builtin-...

Lookup tables can be insanely fast, if kept entirely in L[1|2] cache.

We found this out, when we were optimizing image processing pipelines (image processing uses lots of lookup tables).

We found that the best way to optimize was to avoid moving out of cache, so we had to rewrite a lot of our stuff, so it never broke cache.

That meant a lot of copy-and-paste repetition, strict (small) static functions, and hardcoded values, instead of properties or even constants.

I don't remember all the stuff we learned, but it wasn't pretty (and applied only to x86 architecture. Not sure how well it would work, these days, on ARM).

Regardless of the arguments this article makes, it can be surprising. One time back in the Core 2 days I was optimizing an alpha blend in software and I had something like x * y / 255. That operation was a tiny bit slower than table[(x << 8) | y].

Shift is one cycle. Or is one cycle. If your table is using a fast algorithm, it’s going to add a few more cycles and a couple very predictable branches.

Meanwhile, divide is insanely slow.

If your table is in L1 or L2 cache, it should be faster than the divide, but if not, I’d guess it would be slower. As the article says, that’s why you test then hope it doesn’t change later.

Sure, but my point is, how fast does the operation need to be and how slow does accessing the table need to be for the LUT to not be worth it, if a multiplication and a division is too slow?

This was a big thing in video game development in the mid 90's/early 2000's. So long as you can keep the code and data or at least manageable chunks of it in cache, that would give huge performance gains.

Things like the Ps2 VPU1 16KByte cache and the much more limited VPU0 with 4Kbyte cache. There were many titles that just did not use VPU0 for anything high performant simply because the cache limit killed its potential.

The Gamecube had a 'locked-cache' feature. You were able to reserve 16 KB of L1 data cache to use as scratchpad.

> hardcoded values, instead of properties or even constants.

What's the difference in the object code between a hardcoded value and a constant? Surely they should be the same?

I don’t remember, exactly.

It was C++ (LLVM, I think).

It was important that the PC never leave the cache address pool, and constants may have been in a table, somewhere.

With macros, it was almost the same.

Lookup tables can be competitive with SIMD https://darkcephas.blogspot.com/2018/10/validating-utf8-stri...

Was your problem perhaps because of the hardware bug where popcount unnecessarily stalled on the output as if it were an input?

Later compilers added an explicit zero of the output to work around this issue.

Interesting... I hadn't heard about that bug. Here's my current theory about what was happening. Back then, I was using an Intel Atom notebook, and some research tells me that the early Atom processors don't have the popcount instruction. This would make GCC fall back to its implementation. I looked at GCC's current implementation, and it's using a 256-entry lookup table. My implementation was faster... so either (1) I was using a larger lookup table than I remembered, maybe 65536-entry, or (2) GCC was doing something different back then.

Perhaps a wrong link? Your link shows a case where the compiler's implementation is better than a custom one.

Has the link been edited? And are you taking about the question or the answers? In the question, __builtin_popcount is the slowest of the 3 options on both compilers.

This is very long for something that's quite simple: If your input space is small enough that it fits into an 8- or 16-bit LUT, try it. If it's faster, use the LUT; if it's not, don't use it. Really, that's all that needs to be said. The cases where LUTs this small crop up are so rare that you lose nothing by trying. There's no use in trying to predict the performance when you can just measure it.

One challenge is that the table cutoff size in a microbenchmark will be higher than in an application that has other cache pressure.

So for example, you may have a bit of code that is rarely very hot unless you're being DOS attacked. If you are it's performance is limiting for the system, so very important.

Otherwise it just runs intermittently. A large table may win in a microbenchmark or under the dos load, but trash the application performance outside of attacks due to flushing out the cache relative to a slower implementation with a smaller table or no table.

It's often difficult to measure the overall application performance difference between changes to components (as effects from alignment may dominate). And even if you do know that you have a situation like I described the correct choice isn't always obvious.

Don't do a microbenchmark, test the entire application under expected usage with and without the LUT. If it's supposed to tolerate a DoS, test that as well. A LUT is a drop-in replacement; there's no need to rely on some synthetic benchmark that may not be representative when you can test on the real thing.

You can even have the code detect a usage/abusage pattern and switch implementations on the fly.

I agree. Do a benchmark end-to-end. Measuring the lookup alone and theorizing is worth nothing.

Another comment says bit shifting 128 bits, constructed ftom 2 64 bit lut results, still won over a simple division.

It's still a simple rule to find out by testing, but the simple rule is not so limited.

I ran into CPU cache issues in a slightly different application 15+ years ago. I was working on indexing gigabytes of text on a mobile CPU (before smart phones caused massive investment in such CPUs). Word normalization logic (e.g., sky/skies/sky's -> sky) was very slow, so I used a word cache which sped it up immensely.

The initial version of the word cache cleared the entire cache when it hit a certain number of entries, just as a placeholder. When I got around to adding some LRU eviction logic, it became faster on our desktop simulator, but far slower on the embedded device (slower than with no word cache at all). The difference came down to the CPU cache size / strategy differences between the desktop and mobile CPUs.

We ended up shipping the "dumb" word cache logic because it was so much faster in practice. The word cache eviction function was only two lines of code plus a large comment that acknowledged that "yes, this looks dumb" and imploring that the speed of any future improvements be compared to the dumb version on the target device. Testing real data on the hardware used in practice is incredibly important.

Not hugely convincing to put a toy model up against a micro benchmark and claim the toy model proves the micro benchmark wrong.

The correct way to compare these approaches is with real code.

The correct way to compare these two approaches is to measure the difference on your individual program and not rely on benchmarks that measure different programs.

But I also understand that you can't do that for every decision you need to make, so at least this article gives a hint that lookup tables are something that might be worth measuring.

Most of the time the solution that pollutes L1 caches more is going to lose in real life use. LUTs do that a lot, but of course ballooned code can hit L1C cache badly as well.

You can compute a ton on a modern CPU during what a memory access would take.

This is a lot of words about things that probably don't matter.

IMO: the bottleneck of lookup tables is concisely described as follows: 2 or 3 lookups in L1 cache per cycle on modern CPUs, and 10x fewer to 500x fewer depending on how far away (L2, L3, DDR near, or DDR remote).

Meanwhile, modern CPU instructions like AES, Multiply, XOR, ADD and more can effectively operate 3, 4, or even more times per clock tick regardless of circumstances.

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Don't even talk about cache hierarchies. You are already behind at the L1 cache level due to the relatively few load/store units in modern CPU (or GPU) cores. And hitting L2 or L3 cache gets exponentially worse.

> Meanwhile, modern CPU instructions like AES, Multiply, XOR, ADD and more can effectively operate 3, 4, or even more times per clock tick regardless of circumstances.

I don't think people are making lookup tables to adding or xoring 2 numbers...

Between BMI instructions (PEXT, PDEP, bit reverse, least significant 1s bit, etc. Etc), AES, SHA1, add, xor, rotate, shift, and, or, not, multiply, carryless multiply and...

Pshufb (4-bit / 16-byte lookup table)

You might be surprised at how many operations can be done without touching the load/store units on CPUs.

In my experience, it's usually worth the effort. Then again, it's a LOT of effort needed.

If you are just doing things simply and easily? Lookups are almost the easiest solution. But I probably wouldn't reach for lookup tables for a performance based problem today.

Here's an in-the-wild, long-standing example of a table used for bit reversals: https://gitlab.com/libtiff/libtiff/-/blob/master/libtiff/tif...

The function to do the same for a byte is... what? 3 or 4 lines long in C? I guess it takes a couple of temp variables, though, which may dissuade some devs.

That's not "A lookup table is faster than a native bit reversal instruction."; that's "There's no portable way to make the compiler emit a native bit reversal instruction, and a lookup table is (presumably) faster than a couple dozen instructions to do it manually (at least on most target architectures).".

What about something like https://github.com/abseil/abseil-cpp/blob/master/absl/string... ? ASCII lowercase can be something like

     auto is_upper= (x > '@') & (x < '[');
     return is_upper ? x+32 : x;

Which boils down to add, add, cmp, cmov on x86. It might save some cache traffic, but the cache traffic is less code since it's only a mov. The version that's code instead of lookups probably exacerbates register pressure problems in large programs? I don't have good intuition for which would be more efficient in practice.

Your 8-bit lookup can never be parellized, while the add/cmp/cmov is really easy AVX512 that probably auto-inlines and auto-vectorizes.

I dunno, it's ridiculously a benefit to the code by my instinct. While lookup table looks pretty bad.

> can never be parellized

I mean, I'm not skilled enough in those ISA extensions to stick my neck out. It's not totally obvious to me that there is not some shuffle or permute facility that can load 64 bytes at a time from LUTs.

> It's not totally obvious to me that there is not some shuffle or permute facility that can load 64 bytes at a time from LUTs.

You are talking about vgather and/or vscatter, which are well known to be very slow AVX2 or AVX512 instructions.

Maybe a future CPU will make these instructions high performance. But no modern 2023-era CPU has a high-speed vgather.

Like: the vgather does one-at-a-time slow. You basically lose parallelism even if the vgather instruction describes what you want to do, it's not an effective parallel operation today (and may never be)

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Pshufb as a 4-bit LUT is an exception and is effectively a high speed (but very very small) lookup table. Like every cycle 64 bytes at a time fast.

You are limited by the 16-byte lookup size (aka the size of an SSE register), maybe a bit bigger if there are new instructions I dunno about.

Vectorized gather loads can do just that. But currently are pretty underwhelming on x86 machines.

Although it can't be easily vectorized, it can be pipelined, that can help both hide the access latency and keep the lookup table hot. The code is not going to be pretty thorough.

> Which boils down to add, add, cmp, cmov on x86.

By using SIMD instructions like AVX2 you can do 32 characters in parallel. With AVX512, 64.

Pretty easy to write something way faster by not using a LUT.

Yes, this is a good example where LUTs are very likely to be slower, especially if you can avoid branch mispredictions with cmov.

Except that in Unicode, this doesn't work.

The example code is a 256-byte lookup table, meaning the original example won't work with Unicode either.

In fact, I'm pretty sure that Unicode cannot be solved with a lookup table due to its variable length, but maybe you can prove me wrong? (Assuming UTF8 here)

256 is indeed pretty limited.

Unicode does have a limited space, but it cannot be stored practically in single table. It currently runs up to 0x323AF, a bit over 200k, and most of the characters of course don't have a lower/uppercase mapping. The implementations I've seen do a few comparisons and then delegate to a table.

But: horses for courses. If you have to normalize a lot of Latin-1 text (such transform case, or strip diacritics), you can probably write some vector instructions that runs circles around a simple LUT. But it's not going to be as easy.

What the fuck you expect "bit reversal" to even do in unicode ?

I had the vague impression this was about lowercase. No need for expletives. Perhaps you should comment elsewhere.

Comedy: did you notice that the next static definition is for a 256 byte lookup table for the unreversed bits too:

  TIFFNoBitRevTable[256] = {
    0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, ... 0xFF }

Maybe PSHUFB/VTBL to reverse each nibble and then put the reversed nibbles together would be wayyy faster?

I'm guessing portability matters here, and there is not much commercial pressure to actually optimise this TIFF library?

Which is not simple add or xor, which is why lookup is used... I obviously wasn't talking about it.

The most used one is probably sin() on CPUs without hardware math

Why exponentially?

Interesting article but very in the weeds on it's usecases and I wish the caveats on when it applies were more clearly stated. There are many situations where the computation being done is prohibitively expensive compared to the time horizon required, LUTs are great for that sort of thing. IMO people should use LUTs MORE often.

Yes use LUTs.

But 4-LUT is also called pshufb and you never ever need to touch the relatively slow load/store units.

The space of computations you can do with 4-LUT PSHUFB instructions, followed up with simple bit instructions (add, or, not, xor, multiply) is rather insane.

The space you can cover in a table with n values is much, much larger, even for small values of n (say 100).

In my work LUTs are a reaction to really poor performance, not a matter of course. Every time I reach for one my inner dialog says “you (probably) should use a lookup table”.

I always used to use lookup tables for sin/cos in the days of software 3D rendering.

The developers of Mario 64 did the same, but this video dives into those LUTs and brings them into question:

https://www.youtube.com/watch?v=xFKFoGiGlXQ

A subset of (3) that is the reason for Hedgewars' sine lookup table. "When you want the results to be very predictable" Deterministic lockstep has always had issues with floating point variations across platforms, and I imagine that applies to other things as well...

Well, it always depends on what you lookup i.e. how much time one needs to compute entries of the given lookup table. If it takes O(2^n) time , then payback comes quickly, where n is the input size. It’s good advice to be very skeptical if one drops general statements like that. Look for algorithms with the best worst -case time complexity is a good start. It will always win. Theory works. Question is only of big the input has to be in order to see that. Here, the fun part starts I guess.

For the most part I agree. This can generalized with the observation that a) sometimes is faster to recompute a function than caching it, and b) cache is a limited resource usually more than CPU cycles.

Same. I've replaced a ton of LUTs with pure [vectorized] code and most of the time it's a big win. Some computations can of course be too heavy, but that's pretty rare nowadays.

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