Thursday, April 6, 2023

CRC64 in Redis is getting even faster

On Friday last week, I submitted this PR to Redis: .

In the PR, I make single-threaded CRC64 53-73% faster for a CPU that is 13 years old, and ~67% faster for a CPU that is 5 years old. I'll get into the details more as to how / why, but modern CPUs could see 2x+, and an update to the algorithm should allow for leveraging more CPU hardware as it scales. This is also generally applicable to all CRC polynomials, and brings software CRC within 2x of hardware CRC performance.

Oh, then I also made CRC concatenation >10,000x faster, but I suspect that was previously known, and just not reported for what it was.

I know, this is going to feel like "learn this one simple trick to make all your programs faster" clickbait, but for some algorithms, 2x faster is just the start. (and extrapolating to other CRCs

Computer Architecture Background

For folks who already know about the history of computers, and how / why CPUs do what they do, jump ahead to "Making it faster".

 Decades before I was born, Alan Turing and John von Neumann developed competing thoughts about how to conceptualize and build computers. Ultimately, the von Neuman architecture won out. It is best characterized by a central processing unit with control flow, arithmetic operations, along with an interface to memory, input devices, and output devices. To go a little further for our specific example, processors have been built to basically do a few things really well: read instructions, decode those instructions into sub-instructions, wait for data to arrive, then finally execute on any data that is available.

Fetching things can sometimes take a while, and execution isn't nearly an instant operation. Even with your 3 or 4 gigahertz PC, what's really going on is that most CPU instructions, especially complex mathematical functions like square root, division, and modulo, all take multiple steps. So perhaps if you are performing a division operation, you may only get a few bits each cycle, and you may need to wait tens of cycles to get your result. Normally this is all hidden, so you only get your final results, and not incomplete results.

In the specification manuals for most CPUs, you can look up information about how many instructions of what types can be dispatched in a cycle, and how many cycles each operation will take. Depending on the operation, and other things going on at the time, sometimes you can start multiple operations of the same type in adjacent "pipelines", like having multiple lines in a factory. Sometimes you can add items to the lines every cycle, and sometimes each step takes longer than a cycle and items to be added to the pipeline have to wait. Sometimes, there are groups of 2, 4, or 8 items that need to be processed at once, and we have instructions specifically designed to process these groups in what is called vectorization.

Making it faster

Back in 2013, Mark Adler released performance improvements to the CRC class of algorithms. I didn't learn of them until several years later, through Matt Standcliff's Redis work and optimizations around 2017 or 2018. Huge thank you to Mark for writing the code, Matt for making it work with Redis, and Madelyn Olson for finally getting it merged in 2020.

A friend and former coworker sent me a reference to the "hacker's delight CRC", which was posted in 2014. That looks to use the same techniques that Mark Adler released in 2013.

I don't know who originated the work, but I'm going to guess it was Mark Adler or one of his colleagues, being he is the creator of the Adler CRC32, and co-creator of the Zip format, among others.

What was done? Mark transformed the typically bit or byte-wise operations of CRC into what could be done up to 8 bytes at a time. CPUs are built to do many such operations at the same time, so this naturally sped up CRC from around 400-408 MB/second to ~1420 MB/second, at least on one of my daily-workhorse Intel Xeon 2670's. That's a ~3.5x speedup by switching from 1 byte at a time to 8 bytes. Quite incredible if I didn't compile, run, and compare the outputs myself.

Not used, and rarely mentioned, I noticed that Mark had provided a method to do CRC combining. Where normally if you had some data, you had to have one function run from start to finish over that one whole block of data. You could pause, but you had to do the first part first. This limitation is very common among hashing algorithms.

Again, I don't know the origination of the idea, but Mark determined a way to merge the crcs of conceptually adjacent segments. So you can cut your 1 segment into 2, compute over the segments in parallel, combine the results, and get the same result as if you had computed the value serially.

Normally, most folks would add some threads, build a thread scheduler, and work out how to make this faster with threads. I did this, but only because I already had a threaded snapshot engine for Redis (not a part of this PR), so my CRCs were naturally faster. But I wasn't just interested in threads, and Mark's improvements weren't from thread shuffling on one CPU, it was from putting more operations in the CPU from one thread.

Armed with the knowledge that I could extend a CRC, I pulled the CRC operation over 8 bytes at a time into a group of macros, then had the single thread run over 2 or 3 segments producing 2 or 3 concurrent 8-byte segment CRCs over the data, all in one thread.

I had difficulty making CRC64 faster for data smaller than about 2-3 megabytes until I noticed something important. The original CRC combine method was taking ~270 microseconds to staple ~1 meg CRCs together. After some vectorization, manual and automatic, I settled on a compiler-vectorized method that got me down to ~29 microseconds for the CRC combine operation back in spring 2018.

On Wednesday, March 29, after looking at the algorithm further while preparing the patch for what ultimately became this pull request, I noticed that if you were to cache a certain set of data, much like we had done with the CRC computation in the first place, you could eliminate much of that remaining ~29 microseconds. So I did.

After a quick cache initialization that takes around 140 microseconds, or just more than half the time of the original staple over 1 meg, a 32 kilobyte cache is populated for your polynomial that allows CRC64 stapling. Due to an apparent cycle in the CRC after 64 bits of merge, we can actually merge unlimited length segments. After initialization, calls to combine about a megabyte now take roughly 25 nanoseconds. Yes, nanoseconds. From 270 microseconds without vectorization and caching, to 29 microseconds with vectorization, then all the way to 25 nanoseconds with caching.

So at least in Redis-land, CRC64 combining is about 10,800 times faster overall with the use of a 32 kilobyte cache and some auto-vectorization.


While I am pretty sure that the caching portion is a well-known optimization, at least to Mark Adler, as I see a similar set of CRC combine optimizations in the most recent version of his codebase, which makes me think I should do a literature check before I write software. That said, Mark does not provide the additional vector operations, and without them, the cache speedup (at least in my version) is limited to getting us to 8 microseconds, instead of 50 nanoseconds typical worst-case.

So overall, the Redis CRC combine is about 160x faster than CRCany's combine, and nets >10,000x speedup from what I was originally working with, compared to around a 60x speedup with caching, or only 10x with vectorization (the combination is super effective).

Here are some benchmark outputs in a Github gist.

Overall, that gets us from 400-408 Megs/second for 1 byte at a time, to ~1420 megs/second for 8 bytes at a time, to up to ~2325 megs/second. So roughly 63% faster on an Intel Xeon E5-2670 v0 @ 2.60GHz with 20Mb of cache.

That is an old CPU, originally marketed Q1 2012. So it has a relatively smaller number of load, store, and arithmetic units compared to a more modern processor. I happen to have a slightly newer Intel Core i3-8130U @ 2.20 ghz, which was first listed for sale Q1 2018, and which I got in the summer of 2019, inside the laptop in which it currently runs.

Again, we see 400-408 Megs/second for 1 byte at a time processing. The 8-byte at a time version gets us up to ~1400 megs/second, or 3.5x faster, with the 24-byte at a time version seeing ~2350 megs/second on larger data. Ours gets us an approximate 68% speedup at 24 bytes, over the 8 byte at a time method.

In some benchmarks on ~10k of data (fitting inside L1 cache), I saw crc64 achieve upwards of 5670 megs/second on the 8130U.

Beating 1 byte/cycle

On my 5 year old mobile CPU, we see the 2.2ghz processor handling 2350 Megs/second, which is 1.068 bytes/cycle. If the data happens to already be loaded into cache after being created by another step, as is the case in many Redis snapshot operations, we see 2.6 bytes/cycle processed.

This speed puts us on par with the performance of "properly engineered" hashes that don't use any tables, and we are within a factor of 2 of the hardware CRC64 available in some more modern CPUs. For those about to ask, no we can't use that CRC in Redis or generally, it is not the right polynomial; if you run the functions on the data, you get different outputs.

I do not know if you can convert the output of CRC from one polynomial to another, but I suspect the answer is no. Might be an interesting question to ask a good mathematician.

Similar optimizations on 16 and 24-way (or more) processing can be done on CRC16 in Redis, or any other CRCs anywhere, as the 8 bytes at a time processing has already been implemented in CRCany. We skip this 16/24 byte optimization in Redis because CRC16 is typically used there for cluster slot identification, which is performed on keys that are generally in the tens to maybe hundreds of bytes in size, and there isn't a benefit to the optimization until 128 bytes for 16-way, and ~2k for 24-way. On the other hand, CRC64 is typically performed over snapshots of keys and data, which can reach to tens of gigabytes in size.

I'll try to get the optimizations upstream to crcany soon.


That's a lot of information, but CRC64 in Redis is getting about 60-70% faster for old machines, and likely 2x or faster on even newer hardware. For CRC combining, we achieve ~50ns worst-case time.


Pull request:

Banchmark outputs:

Mark Adler's crcany project:

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