Introduction and index of this series is here.

The previous post investigated some lossless filtering of data, before passing it to a regular compression library. Our result so far is: 94.5MB of data can get filtered+compressed down to 23.0MB in one second (split/shuffle bytes, delta encode, zstd or kraken compression). It decompresses back in about 0.15 seconds (which quite a bit slower than without data filtering, but that’s something for later day).

In this post, I’ll look at one open source library that does not feel like it would immediately be suitable for compressing my data set.

zeux/meshoptimizer

meshoptimizer by Arseny Kapoulkine is a very nice library for processing, optimizing, and compressing 3D model (“mesh”) data. It can do vertex and index reordering for efficiency of various GPU caches, mesh simplification, quantization and conversion of the vertex data, has index and vertex data compression utilities, and various tools to do all that on glTF2 geometry files.

Notice the “vertex data compression utilities” bit? We’re going to try that one. Since the meshoptimizer compression is an official glTF extension, there’s a specification for it even (EXT_meshopt_compression).

It’s not immediately obvious that it can also be used for anything else than actual 3D model vertex data compression. But look at it:

• It is completely lossless,
• It takes “size of each vertex in bytes” and “number of vertices” as an input. But who says these need to be vertices? It’s just some data.
• It assumes that there is some correllation / smoothness between neighboring vertices; that’s how it gets compression after all. We don’t have “vertices”, but our “data items” from water or snow simulation are nicely laid out in memory one after another, and their values do vary fairly smoothly.

In our case, water, snow simulation and float4 data files are all going to be “yeah, we are totally 16-byte vertices”, and the float3 data file is going to be “I’m full of 12-byte vertices, really”. And then we just use meshopt_encodeVertexBufferBound, meshopt_encodeVertexBuffer and meshopt_decodeVertexBuffer functions from the library.

So does it work?

The chart here shows our three regular compressors (zstd, lz4, kraken; dashed lines), as well as the same compressors with best filtering from previous post (solid lines). meshoptimizer is the large blue point, since it has no “compression levels” to speak of.

This is actually pretty impressive!

• Really fast to compress (0.2 seconds), and really fast to decompress (3.5GB/s, almost at lz4 speeds).
• For a “compress in under a second” task, it beats zstd on ratio, and achieves the same ratio as Oodle Kraken. 😮 We have a 29.5MB file.
• It does not quite achieve the compression ratio of regular compressors with filtering applied. But hey, we are mis-using “mesh” optimizer library for data that is almost certainly not meshes :)

Oh but hey, meshoptimizer readme says:

The result of the encoding is generally significantly smaller than initial data, and remains compressible with general purpose compressors

So let’s try just that: compress our data with meshoptimizer, and then try adding our old friends zstd/lz4/kraken on top of that.

• For compression under one second, this now achieves 24.4MB file size. Nice!
• Kraken and zstd are almost the same performance and ratio here.
• Still not as small as filtering + regular compression (which gets down to 23.0MB), but pretty close.
• Decompression is still very fast; 3x faster than with filtering + regular decompression. Nice!

I have also tried various filtering approaches before doing mesh optimizer compression (split floats, split bytes, delta, xor, rotate floats left by one bit, etc.). And these do not actually help; often making compression ratio worse. This makes sense; mesh optimizer vertex compression codec has a lot of similarities to a data filter itself, so additional filtering just gets in the way and “confuses” it. Or that’s my impression.

Conclusion and what’s next

My takeaway is that if you have structured data that is mostly floating point and inherently has some similarities / smoothness across it, then you should take a look at using meshoptimizer vertex compression codec. Even if your data is not meshes at all!

It makes the data smaller by itself, but you can also pass that down into any other regular data compression library for further compression.

And it’s really fast at both compression and decompression. There’s a pure-JavaScript version too in there, if you’re targeting the web platform.

Next up, I’ll look into several libraries specifically targeted at floating point data compression, that are mostly coming from the scientific community. And then after that, maybe at lossy compression.

Introduction and index of this series is here.

In the previous parts we saw that using generic data compression libraries, we can get our 94.5MB data down to 33.8MB (zstd level 7) or 29.6MB (oodle kraken level 2) size, if we’re not willing to spend more than one second compressing it.

That’s not bad, but is there something else we can do? Turns out, there is, and in fact it’s quite simple. Enter data filtering.

Prediction / filtering

We saw filtering in the past (EXR and SPIR-V), and the idea is simple: losslessly transform the data so that it is more compressible. Filtering alone does nothing to reduce the data size, but (hopefully!) it decreases data randomness. So the process is: filter the data, then compress that. Decompression is reverse: decompress, then un-filter it.

Here’s some simple filters that I’ve tried (there are many, many other filters possible, I did not try them all!).

Reorder floats array-of-structures style

Recall that in our data, we know that water simulation has four floats per “element” (height, velocity x, velocity y, pollution); snow simulation similarly has four floats per element; and other data is either four or three floats per element. Instead of having the data like that (“array of structures” style), we can try to reorder it into “structure of arrays” style. For water simulation, that would be all heights first, then all x velocities, then all y velocities, etc.

So this:

becomes this:

Completely unoptimized code to do that could look like this (and our data is floats, i.e. 4 bytes, so you’d call these templates with a 4-byte type e.g. uint32_t):

// channels: how many items per data element
// dataElems: how many data elements
template<typename T>
static void Split(const T* src, T* dst, size_t channels, size_t dataElems)
{
	for (size_t ich = 0; ich < channels; ++ich)
	{
		const T* ptr = src + ich;
		for (size_t ip = 0; ip < dataElems; ++ip)
		{
			*dst = *ptr;
			ptr += channels;
			dst += 1;
		}
	}
}
template<typename T>
static void UnSplit(const T* src, T* dst, size_t channels, size_t dataElems)
{
	for (size_t ich = 0; ich < channels; ++ich)
	{
		T* ptr = dst + ich;
		for (size_t ip = 0; ip < dataElems; ++ip)
		{
			*ptr = *src;
			src += 1;
			ptr += channels;
		}
	}
}

Does that help? The results are interesting (click for an interactive chart):

• It does help LZ4 to achieve a bit higher compression ratios.
• Makes zstd compress faster, and helps the ratio at lower levels, but hurts the ratio at higher levels.
• Hurts oodle kraken compression.
• Hurts the decompression performance quite a bit (for lz4 and kraken, slashes it in half). In all cases the data still decompresses under 0.1 seconds, so acceptable for my case, but the extra pass over memory is not free.

Ok, so this one’s a bit “meh”, but hey, now that the data is grouped together (all heights, then all velocities, …), we could try to exploit the fact that maybe neighboring elements are similar to each other?

Reorder floats + XOR

In the simulation data example, it’s probably expected that usually the height, or velocity, or snow coverage, does not vary “randomly” over the terrain surface. Or in an image, you might have a color gradient that varies smoothly.

“But can’t data compressors already compress that really well?!”

Yes and no. Usually generic data compressors can’t. Most of them are very much oriented at finding repeated sequences of bytes. So if you have a very smoothly varying surface height or image pixel color, e.g. a sequence of bytes 10, 11, 12, 13, 14, 15, well that is not compressible at all! There are no repeating byte sequences.

But, if you transform the sequence using some sort of “difference” between neighboring elements, then repeated byte sequences might start appearing. At first I tried XOR’ing the neighboring elements together (interpreting each float as an uint32_t), since at some point I saw that trick being mentioned in some “time series database” writeups (e.g. Gorilla).

A completely unoptimized code to do that:

template<typename T>
static void EncodeDeltaXor(T* data, size_t dataElems)
{
	T prev = 0;
	for (size_t i = 0; i < dataElems; ++i)
	{
		T v = *data;
		*data = v ^ prev;
		prev = v;
		++data;
	}
}
template<typename T>
static void DecodeDeltaXor(T* data, size_t dataElems)
{
	T prev = 0;
	for (size_t i = 0; i < dataElems; ++i)
	{
		T v = *data;
		v = prev ^ v;
		*data = v;
		prev = v;
		++data;
	}
}

And that gives (faint dashed line: raw compression, thin line: previous attempt (split floats), thick line: split floats + XOR):

• Compression ratio is way better for zstd and lz4 (for kraken, only at lower levels).
• zstd pretty much reaches kraken compression levels! The lines almost overlap in the graph.
• Decompression speed takes a bit of a hit, as expected. I might need to do something about it later.

So far we got from 33.8MB (zstd) / 29.6MB (kraken) at beginning of the post down to 28MB (zstd, kraken), while still compressing in under 1 second. Nice, we’re getting somewhere.

Reorder floats + Delta

The “xor neighboring floats” trick from Gorilla database was in the context of then extracting the non-zero sequences of bits from the result and storing that in less space than four bytes. I’m not doing any of that, so how about this: instead of XOR, do a difference (“delta”) between the neighboring elements? Note that delta is done by reinterpreting data as if it were unsigned integers, i.e. these templates are called with uint32_t type (you can’t easily do completely lossless floating point delta math).

template<typename T>
static void EncodeDeltaDif(T* data, size_t dataElems)
{
	T prev = 0;
	for (size_t i = 0; i < dataElems; ++i)
	{
		T v = *data;
		*data = v - prev;
		prev = v;
		++data;
	}
}
template<typename T>
static void DecodeDeltaDif(T* data, size_t dataElems)
{
	T prev = 0;
	for (size_t i = 0; i < dataElems; ++i)
	{
		T v = *data;
		v = prev + v;
		*data = v;
		prev = v;
		++data;
	}
}

And that gives (faint dashed line: raw compression, thin line: previous attempt (split floats + XOR), thick line: split floats + delta):

Now that’s quite an improvement! All three compressors tested get their compression ratio lifted up. Good! Let’s keep on going.

Reorder bytes

Hey, how about instead of splitting each data point into 4-byte-wide “streams”, we split into 1-byte-wide ones? After all, general compression libraries are oriented at finding byte sequences that would be repeating. This is also known as a “shuffle” filter elsewhere (e.g. HDF5). Exactly the same Split and UnSplit functions as above, just with uint8_t type.

Faint dashed line: raw compression, thin line: previous attempt (split floats + Delta), thick line: split bytes:

• kraken results are almost the same as with “split floats and delta”. Curious!
• zstd ratio (and compression speed) is improved a bit.
• lz4 ratio is improved a lot (it’s beating original unfiltered kraken at this point!).

I’ll declare this a small win, and let’s continue.

Reorder bytes + Delta

Split by bytes as previous, and delta-encode that. Faint dashed line: raw compression, thin line: previous attempt (split bytes), thick line: split bytes + delta:

Holy macaroni grated potato dumplings!

• Another compression ratio increase. Both zstd and kraken get our data to 23MB in about one second (whereas it was 33.8MB and 29.6MB at the start of the post).
• zstd actually slightly surpasses kraken at compression ratios in the area (“under 1 sec”) that I care about. 😮
• lz4 is not too shabby either, being well ahead of unfiltered kraken.
• Downside: decompression is slightly longer than 0.1 seconds now. Not “terrible”, but I’d want to look into whether all this reordering and delta could be sped up.

Conclusion and what’s next

There’s lots of other data filtering approaches and ideas I could have tried, but for now I’m gonna call “reorder bytes and delta” a pretty good win; it’s extremely simple to implement and gives a massive compression ratio improvement on my data set.

I did actually try a couple other filtering approaches. Split data by bits (using bitshuffle library) was producing worse ratios than splitting by bytes. Rotating each float left by one bit, to make the mantissa & exponent aligned on byte boundaties, was also not an impressive result. Oh well!

Maybe at some point I should also test filters specifically designed for 2D data (like the water and snow simulation data files in my test), e.g. something like PNG Paeth filter or JPEG-LS LOCO-I (aka “ClampedGrad”).

Next up, I’ll look at an open source library that does not advertise itself as a general data compressor, but I’m gonna try it anyway :) Until then!

Introduction and index of this series is here.

In the previous part I looked at generic lossless data compressors (zlib, lz4, zstd, brotli), and was thinking of writing about data filtering next. But then, libdeflate and Oodle entered the chat!

libdeflate

libdeflate is an independent implementation of zlib/deflate compression, that is heavily optimized. I’ve seen it before (EXR blog post), and indeed it is very impressive, considering it produces completely zlib-compatible data, but much faster and at a bit higher compression ratio too.

Here are the results (click for an interactive chart). The compressors from the previous post are faded out; libdeflate addition is dark green:

It is not better than zstd, but definitely way better than zlib (~3x faster compression, ~2x faster decompression, slightly higher ratio). If you need to produce or consume deflate/zlib/gzip formatted data, then absolutely look into libdeflate.

Oodle

Oodle is a set of compressors by Epic Games Tools (née RAD Game Tools). It is not open source or freely available, but the good people there graciously gave me the libraries to play around with.

There are several compressors available, each aiming at different ratio vs. performance tradeoff. It’s easiest to think of them as: “Kraken” is “better zstd” (great ratio, good decompression performance), “Selkie” is “better lz4” (ok ratio, very fast decompression), and “Mermaid” is in the middle of the two, with no clear open source competitor.

Here they are, additions in various shades of purple:

And… yeah. On the compression front, Mermaid leaves everyone else (zstd, brotli) in the dust on the Pareto front (remember: upper right is better). And then Kraken improves on top of that 🤯 Decompression performance is a similar story: everything (except lz4) is behind.

Wizardry! It’s a shame they are not freely available, eh :/

What’s next?

Next up, we’ll really look at some simple data filtering (i.e. fairly similar to EXR post from a while ago). Until then!

Introduction and index of this series is here.

We have 94.5MB worth of data, and we want to make it smaller. About the easiest thing to do: use one of existing lossless data compression libraries, or as us old people call it, “zip it up”.

There are tons of compression libraries out there, I certainly will not test all of them (there’s lzbench and others for that). I tried some popular ones: zlib, lz4, zstd and brotli.

Here are the results (click for an interactive chart):

This is running on Windows, AMD Ryzen 5950X, compiled with Visual Studio 2022 (17.4), x64 Release build. Each of the four data files is compressed independently one after another, serially on a single thread.

I also have results on the same Windows machine, compiled with Clang 15, and on an Apple M1 Max, compiled with Clang 14.

What can we see from this?

The compression charts have compression ratio (higher = better) on the vertical axis, and throughput on the horizontal axis (higher = better). Note that the horizontal axis is logarithmic scale; performance of the rightmost point is literally hundreds of times faster than the leftmost point. Each line on the graph is one compression library, with different settings that it provides (usually called “compression levels”).

Compression graph is the usual “Pareto front” situation - the more towards upper right a point is, the better (higher compression ratio, and better performance). The larger points on each compression curve are the “default” levels of each library (6 for zlib, 3 for zstd, “simple” for lz4).

Decompression graph, as is typical for many data compression algorithms, is much less interesting. Often decompression performance is more or less the same when using the same compression library; no matter what the compression level is. You can ballpark and say “lz4 decompresses at around 5GB/s” for this data set.

Anyway, some takeaway points:

• Generic data compression libraries can get this data set from 94.5MB down to 32-48MB, i.e. make it 2x-3x smaller.
• They would take between 0.1s and 1.0s to compress the data, and between 0.02s and 0.2s to decompress it.
  • With Brotli maximum level (11), you can go as low as 27MB data (3.5x ratio), but it takes over two minutes to compress it :/
• zstd is better than zlib in all aspects. You can get the same compression ratio, while compressing 10x faster; or spend same time compressing, and get better ratio (e.g. 2.6x -> 2.9x). Decompression is at least 2x faster too.
  • Current version of zstd (1.5.2, 2022 Jan) has some dedicated decompression code paths written in assembly, that are only used when compiling with clang/gcc compilers. On a Microsoft platform you might want to look into using Clang to compile it; decompression goes from around 1GB/s up to 2GB/s! Or… someone could contribute MSVC compatible assembly routines to zstd project :)
• If you need decompression faster than 2GB/s, use lz4, which goes at around 5GB/s. While zstd at level -5 is roughly the same compression ratio and compression performance as lz4, the decompression is still quite a bit slower. lz4 does not reach more than 2.2x compression ratio on this data set though.
• If you need best compression ratio out of these four, then brotli can do that, but compression will not be fast. Decompression will not be fast either; curiously brotli is slower to decompress than even zlib.
• There’s basically no reason to use zlib, except for the reason that it likely exists everywhere due to its age.

Which place exactly on the Pareto front is important to you, depends on your use case:

• If compression happens once on some server, and the result is used thousands/millions of times, then you much more care about compression ratio, and not so much about compression performance. A library like brotli seems to be targeted at exact this use case.
• On the completely opposite side, you might want to “stream” some data exactly once, for example some realtime application sending profiling data for realtime viewing. You are compressing it once, and decompressing it once, and all you care about is whether the overhead of compression/decompression saves enough space to transmit it faster. lz4 is primarily targeted at use cases like this.
• If your scenario is similar to a “game save”, then for each compression (“save”), there’s probably a handful of decompressions (“load”) expected. You care both about compression performance, and about decompression performance. Smaller file like with brotli level 11 would be nice, but if it means almost three minutes of user waiting (as opposed to “one second”), then that’s no good.

My use case here is similar to a “game save”; as in if compressing this data set takes longer than one or two seconds then it’s not acceptable. Later posts will keep this in mind, and I will not even explore the “slow” compression approaches much.

In general, know your use case! And don’t just blindly use “maximum” compression level; in many libraries it does not buy you much, but compression becomes much, much slower (brotli here seems to be an exception - while compression is definitely much slower, going from level 10 to the maximum level 11 does increase compression ratio quite a bit).

What’s next?

Next up, we’ll look at some simple data filtering (i.e. fairly similar to EXR post from a while ago) a couple more generic data compressors. Until then!

I was playing around with compression of some floating point data, and decided to write up my findings. None of this will be any news for anyone who actually knows anything about compression, but eh, did that ever stop me from blogging? :)

Situation

Suppose we have some sort of “simulation” thing going on, that produces various data. And we need to take snapshots of it, i.e. save simulation state and later restore it. The amount of data is in the order of several hundred megabytes, and for one or another reason we’d want to compress it a bit.

Let’s look at a more concrete example. Simulation state that we’re saving consists of:

Water simulation. This is a 2048x2048 2D array, with four floats per array element (water height, flow velocity X, velocity Y, pollution). If you’re a graphics programmer, think of it as a 2k square texture with a float4 in each texel.

Here’s the data visualized, and the actual 64MB size raw data file (link):

Snow simulation. This is a 1024x1024 2D array, again with four floats per array element (snow amount, snow-in-water amount, ground height, and the last float is actually always zero).

Here’s the data visualized, and the actual 16MB size raw data file (link):

A bunch of “other data” that is various float4s (mostly colors and rotation quaternions) and various float3s (mostly positions). Let’s assume these are not further structured in any way; we just have a big array of float4s (raw file, 3.55MB) and another array of float3s (raw file, 10.9MB).

Don’t ask me why the “water height” seems to be going the other direction as “snow ground height”, or why there’s a full float in each snow simulation data point that is not used at all. Also, in this particular test case, “snow-in-water” state is always zero too. 🤷

Anyway! So we do have 94.5MB worth of data that is all floating point numbers. Let’s have a go at making it a bit smaller.

Post Index

Similar to the toy path tracer series I did back in 2018, I generally have no idea what I’m doing. I’ve heard a thing or two about compression, but I’m not an expert by any means. I never wrote my own LZ compressor or a Huffman tree, for example. So the whole series is part exploration, part discovery; who knows where it will lead.

• Part 1: Generic Lossless Compression (zlib, lz4, zstd, brotli)
• Part 2: Generic Lossless Compression (libdeflate and Oodle entered the chat)
• Part 3: Data Filtering (simple data filtering to improve compression ratio)
• Part 4: Mesh Optimizer (mis-using mesh compression library on our data set)
• Part 5: Science! (zfp, fpzip, SPDP, ndzip, streamvbyte)
• Part 6: Optimize Filtering (optimizations for part 3 data filters)
• Part 7: More Filtering Optimization (better optimizations for part 3 data filters)
• Part 8: Blosc (testing Blosc compression library)
• Part 9: LZSSE and Lizard (lzsse8, lizard)