Making Gaussian Splats smaller

In the previous post I started to look at Gaussian Splatting. One of the issues with it, is that the data sets are not exactly small. The renders look nice:

But each of the “bike”, “truck”, “garden” data sets is respectively a 1.42GB, 0.59GB, 1.35GB PLY file. And they are loaded pretty much as-is into GPU memory as giant structured buffers, so at least that much VRAM is needed too (plus more for sorting, plus in the official viewer implementation the tiled splat rasterizer uses some-hundreds-of-MB).

I could tell you that I can make the data 19x smaller (78, 32, 74 MB respectively), but then it looks not that great. Still recognizable, but really not good (however, the artifacts are not your typical “polygonal mesh rendering at low LOD”, they are more like “JPG artifacts in space”):

However, in between these two extremes there are other configurations, that make the data 5x-10x smaller while looking quite okay.

So we are starting at 248 bytes for each splat, and we want to get that down. Note: everywhere here I will be exploring both storage and runtime memory usage, i.e. not “file compression”! Rather, I want to cut down on GPU memory consumption too. Getting runtime data smaller also makes the data on disk smaller as a side effect, but “storage size” is a whole another and partially independent topic. Maybe for some other day!

One obvious and easy thing to do with the splat data, is to notice that the “normal” (12 bytes) is completely unused. That does not save much though. Then you can of course try making all the numbers be Float16 instead of Float32, this is acceptably good but only makes the data 2x smaller.

You could also throw away all the spherical harmonics data and leave only the “base color” (i.e. SH0), and that would cut down 75% of the data size! This does change the lighting and removes some “reflections”, and is more visible in motion, but progressively dropping SH bands with lower quality levels (or progressively loading them in) is easy and sensible.

So of course, let’s look at what else we can do :)

Reorder and cut into chunks

The ordering of splats inside the data file does not matter; we are going to sort them by distance at rendering time anyway. In the PLY data file they are effectively random (each point here is one splat, and color is gradient based on the point index):

But we could reorder them based on “locality” (or any other criteria). For example, ordering them in a 3D Morton order, generally, makes nearby points in space be near each other inside the data array:

And then, I can group splats into chunks of N (N=256 was my choice), and hope that since they would generally be close together, maybe they have lower variance of their data, or at least their data can be somehow represented in fewer bits. If I visualize the chunk bounding boxes, they are generally small and scattered all over the scene:

This is pretty much slides 112-113 of “Learning from Failure” Dreams talk.

Future work: try Hilbert curve ordering instead of Morton. Also try “partially filled chunks” to break up large chunk bounds, that happen whenever the Morton curve flips to the other side.

By the way, Morton reordering can also make the rendering faster, since even after sorting by distance the nearby points are more likely to be nearby in the original data array. And of course, nice code to do Morton calculations without relying on BMI or similar CPU instructions can be found on Fabian’s blog, adapted here for 64 bit result case:

// Based on
// Insert two 0 bits after each of the 21 low bits of x
static ulong MortonPart1By2(ulong x)
    x &= 0x1fffff;
    x = (x ^ (x << 32)) & 0x1f00000000ffffUL;
    x = (x ^ (x << 16)) & 0x1f0000ff0000ffUL;
    x = (x ^ (x << 8)) & 0x100f00f00f00f00fUL;
    x = (x ^ (x << 4)) & 0x10c30c30c30c30c3UL;
    x = (x ^ (x << 2)) & 0x1249249249249249UL;
    return x;
// Encode three 21-bit integers into 3D Morton order
public static ulong MortonEncode3(uint3 v)
    return (MortonPart1By2(v.z) << 2) | (MortonPart1By2(v.y) << 1) | MortonPart1By2(v.x);

Make all data 0..1 relative to the chunk

Now that all the splats are cut into 256-splat size chunks, we can compute minimum and maximum data values of everything (positions, scales, colors, SHs etc.) for each chunk, and store that away. We don’t care about data size of that (yet?); just store them in full floats.

And now, adjust the splat data so that all the numbers are in 0..1 range between chunk minimum & maximum values. If that is kept in Float32 as it was before, then this does not really change precision in any noticeable way, just adds a bit of indirection inside the rendering shader (to figure out final splat data, you need to fetch chunk min & max, and interpolate between those based on splat values).

Oh, and for rotations, I’m encoding the quaternions in “smallest three” format (store smallest 3 components, plus index of which component was the largest).

And now that the data is all in 0..1 range, we can try representing it with smaller data types than full Float32!

But first, how does all that 0..1 data look like? The following is various data displayed as RGB colors, one pixel per splat, in row major order. With positions, you can clearly see that it changes within the 256 sized chunk (it’s two chunks per horizontal line):

Rotations do have some horizontal streaks but are way more random:

Scale has some horizontal patterns too, but we can also see that most of scales are towards smaller values:

Color (SH0) is this:

And opacity is often either almost transparent, or almost opaque:

There’s a lot of spherical harmonics bands and they tend to look like a similar mess, so here’s one of them:

Hey this data looks a lot like textures!

We’ve got 3 or 4 values per each “thing” (position, color, rotation, …) that are all in 0..1 range now. I know! Let’s put them into textures, one texel per splat. And then we can easily experiment with using various texture formats on them, and have the GPU texture sampling hardware do all the heavy lifting of turning the data into numbers.

We could even, I dunno, use something crazy like use compressed texture formats (e.g. BC1 or BC7) on these textures. Would that work well? Turns out, not immediately. Here’s turning all the data (position, rotation, scale, color/opacity, SH) into BC7 compressed texture. Data is just 122MB (12x smaller), but PSNR is a low 21.71 compared to full Float32 data:

However, we know that GPU texture compression formats are block based, e.g. on typical PC the BCn compression formats are all based on 4x4 texel blocks. But our texture data is laid out in 256x1 stripes of splat chunks, one after another. Let’s reorder them some more, i.e. lay out each chunk in a 16x16 texel square, again arranged in Morton order within it.

uint EncodeMorton2D_16x16(uint2 c)
    uint t = ((c.y & 0xF) << 8) | (c.x & 0xF); // ----EFGH----ABCD
    t = (t ^ (t << 2)) & 0x3333;               // --EF--GH--AB--CD
    t = (t ^ (t << 1)) & 0x5555;               // -E-F-G-H-A-B-C-D
    return (t | (t >> 7)) & 0xFF;              // --------EAFBGCHD
uint2 DecodeMorton2D_16x16(uint t)      // --------EAFBGCHD
    t = (t & 0xFF) | ((t & 0xFE) << 7); // -EAFBGCHEAFBGCHD
    t &= 0x5555;                        // -E-F-G-H-A-B-C-D
    t = (t ^ (t >> 1)) & 0x3333;        // --EF--GH--AB--CD
    t = (t ^ (t >> 2)) & 0x0f0f;        // ----EFGH----ABCD
    return uint2(t & 0xF, t >> 8);      // --------EFGHABCD

And if we rearrange all the texture data that way, then it looks like this now (position, rotation, scale, color, opacity, SH1):

And encoding all that into BC7 improves the quality quite a bit (PSNR 21.71→24.18):

So what texture formats should be used?

After playing around with a whole bunch of possible settings, here’s the quality setting levels I came up with. Formats indicated in the table below:

  • F32x4: 4x Float32 (128 bits). Since GPUs typically do not have a three-channel Float32 texture format, I expand the data quite uselessly in this case, when only three components are needed.
  • F16x4: 4x Float16 (64 bits). Similar expansion to 4 components as above.
  • Norm10_2: unsigned normalized (32 bits). GPUs do support this, and Unity almost supports it – it exposes the format enum member, but actually does not allow you to create texture with said format (lol!). So I emulate it by pretending the texture is in a single component Float32 format, and manually “unpack” in the shader.
  • Norm11: unsigned normalized 11.10.11 (32 bits). GPUs do not have it, but since I’m emulating a similar format anyway (see above), then why not use more bits when we only need three components.
  • Norm8x4: 4x unsigned normalized byte (32 bits).
  • Norm565: unsigned normalized 5.6.5 (16 bits).
  • BC7 and BC1: obvious, 8 and 4 bits respectively.
Quality Pos Rot Scl Col SH Compr PSNR
Very High F32x4 F32x4 F32x4 F32x4 F32x4 0.8x
High F16x4 Norm10_2 Norm11 F16x4 Norm11 2.9x 54.82
Medium Norm11 Norm10_2 Norm11 Norm8x4 Norm565 5.2x 47.82
Low Norm11 Norm10_2 Norm565 BC7 BC1 12.2x 34.79
Very Low BC7 BC7 BC7 BC7 BC1 18.7x 24.02

Here are the “reference” (“Very High”) images again (1.42GB, 0.59GB, 1.35GB data size):

The “Medium” preset looks pretty good! (280MB, 116MB, 267MB – 5.2x smaller; PSNR respectively 47.82, 48.73, 48.63):

At “Low” preset the color artifacts are more visible but not terribad (119MB, 49MB, 113MB – 12.2x smaller; PSNR respectively 34.72, 31.81, 33.05):

And the “Very Low” one mostly for reference; it kinda becomes useless at such low quality (74MB, 32MB, 74MB – 18.7x smaller; PSNR 24.02, 22.28, 23.1):

Oh, and I also recorded an awkwardly-moving-camera video, since people like moving pictures:

Conclusions and future work

The gaussian splatting data size (both on-disk and in-memory) can be fairly easily cut down 5x-12x, at fairly acceptable rendering quality level. Say, for that “garden” scene 1.35GB data file is “eek, sounds a bit excessive”, but at 110-260MB it’s becoming more interesting. Definitely not small yet, but way more within being usable.

I think the idea of arranging the splat data “somehow”, and then compressing them not by just individually encoding each spat into smaller amount of bits, but also “within neighbors” (like using BC7 or BC1), is interesting. Spherical Harmonics data in particular looks quite ok even with BC1 compression (it helps that unlike “obviously wrong” rotation or scale, it’s much harder to tell when your spherical harmonics coefficient is wrong :)).

There’s a bunch of small things I could try:

  • Splat reordering: reorder splats not only based on position, but also based on “something else”. Try Hilbert curve instead of Morton. Try using not-fully-256 size chunks whenever the curve flips to the other side.
  • Color/Opacity encoding: maybe it’s worth putting that into two separate textures, instead of trying to get BC7 to compress them both.
  • I do wonder how would reducing the texture resolution work, maybe for some components (spherical harmonics? color if opacity is separate?) you could use lower resolution texture, i.e. below 1 texel per splat.

And then of course there are larger questions, in a sense of whether this way looking at reducing data size is sensible at all. Maybe something along the lines of “Random-Access Neural Compression of Material Textures” (Vaidyanathan, Salvi, Wronski 2023) would work? If only I knew anything about this “neural/ML” thing :)

All my code for the above is in this PR on github (merged 2023 Sep).

In the followup post I look at making them even smaller!

Gaussian Splatting is pretty cool!

SIGGRAPH 2023 just had a paper “3D Gaussian Splatting for Real-Time Radiance Field Rendering” by Kerbl, Kopanas, Leimkühler, Drettakis, and it looks pretty cool! Check out their website, source code repository, data sets and so on (I should note that it is really, really good to see full source and full data sets being released. Way to go!).

I’ve decided to try to implement the realtime visualization part (i.e. the one that takes already-produced gaussian splat “model” file) in Unity. As well as maybe play around with looking at whether the data sizes could be made smaller (maybe use some of the learnings from float compression series too?).

What’s a few million badly rendered boxes among friends, anyway?

For the impatient: I got something working over at aras-p/UnityGaussianSplatting, and will tinker with things there some more. And since this post, I wrote several others:

Meanwhile, some quick random thoughts on this Gaussian Splatting thing.

What are these Gaussian Splats?

Watch the paper video and read the paper, they are pretty good!

I have seen quite many 3rd party explanations of the concept at this point, and some of them, uhh, get a thing or two wrong about it :)

  • This is not a NeRF (Neural Radiance Field)! There is absolutely nothing “neural” about it.
  • It is not somehow “fast, because it uses GPU rasterization hardware”. The official implementation does not use the rasterization pipeline at all; it is 100% done with CUDA. In fact, it is fast because it does not use the fixed function rasterization, as we’ll see below.


Gaussian Splats are, basically, “a bunch of blobs in space”. Instead of representing a 3D scene as polygonal meshes, or voxels, or distance fields, it represents it as (millions of) particles:

  • Each particle (“a 3D Gaussian”) has position, rotation and a non-uniform scale in 3D space.
  • Each particle also has an opacity, as well as color (actually, not a single color, but rather 3rd order Spherical Harmonics coefficients - meaning “the color” can change depending on the view direction).
  • For rendering, the particles are rendered (“splatted”) as 2D Gaussians in screen space, i.e. they are not rendered as scaled elongated spheres, actually! More on this below.

And that’s it. The “Gaussian Splatting” scene representation is just that, a whole bunch of scaled and colored blobs in space. The genius part of the paper is several things:

  • They found a way how to create these millions of blobs that would represent a scene depicted by a bunch of photos. This is using gradient descent and “differentiable rendering” and all the other things that are way over my head. This feels like the major contribution, like maybe previously people assumed that in order for gradient descent optimizer to work nicely, you need to use a continuous or connected scene representation (vs “just a bunch of blobs”), and this paper proved that wrong? Anyway, I don’t understand this area, so I won’t talk about it more :)
  • They have developed a fast way to render all these millions of scaled particles. This by itself is not particularly ground breaking IMHO, various people have noticed that using something like a tile-based “software, but on GPU” rasterizer is a good way to do this.
  • They have combined existing established approaches (like gaussian splatting, and spherical harmonics) in a nice way.
  • And finally, they have resisted the temptation to do “neural” anything ;)

Previous Building Blocks

The Gaussian Splatting seems to be invented around year 2001-2002, see for example “EWA Splatting” paper by Zwicker, Pfister, Van Baar, Gross. There they have scaled and oriented “blobs” in space, calculate how would they project onto screen, and then do the actual “blob shape” (a “Gaussian”) in 2D, in screen-space. A bunch of signal processing, sampling, aliasing etc. math presumably supports doing it that way.

Speaking of ellipsoids, Ecstatica game from 1994 had a fairly unique ellipsoid-based renderer.

Spherical Harmonics (a way to represent a function over a surface of a sphere) have been around for several hundred years in physics, but really were popularized in computer graphics around 2000 by Ravi Ramamoorthi and Peter-Pike Sloan. But actually, a 1984 “Ray tracing volume densities” paper by Kajiya & Von Herzen might be the first use of them in graphics. A nice summary of various things related to SH is at Patapom’s page.

Point-Based Rendering in various forms has been around for a long time, e.g. particle systems were used since “forever” (but typically used for vfx / non-solid phenomena). “The Use of Points as a Display Primitive” is from 1985. “Surfels” paper is from 2000.

Something closer to my heart, a whole bunch of demoscene demos are using non-traditional rendering approaches. Fairlight & CNCD have several notable examples, e.g. Agenda Circling Forth (2010), Ceasefire (all falls down..) (2010), Number One / Another One (2018):

Real-time VFX tools like Notch have pretty extensive features for creating, simulating and displaying point/blob based “things”.

Ideas of representing images or scenes with a bunch of “primitive shapes”, as well as tools to generate those, have been around too. E.g. fogleman/primitive (2016) is nice.

Media Molecule “Dreams” has a splat-based renderer (I think the shipped version is not purely splat-based but a combination of several techniques). Check out the most excellent “Learning from Failure” talk by Alex Evans: at SIGGRAPH 2015 (splats start at slide 109) or video from Umbra Ignite 2015 (splats start at 22:34).

Tiled Rasterization for particles has been around at least since 2014 (“Holy smoke! Faster Particle Rendering using Direct Compute” by Gareth Thomas). And the idea that dividing screen into tiles, doing a bunch of things “inside the tile” thus cutting on memory traffic, is how entire mobile GPU space operates, and has been operating since “forever”, tracing back to first PowerVR designs (1996) and even Pixel Planes 5 from 1989.

This is all great! Taking existing, developed, solid building blocks and combining them in a novel way is excellent work.

My Toy Playground

My current implementation (of just the visualizer of Gaussian Splat models) for Unity is over at github: aras-p/UnityGaussianSplatting. Current state is “it kinda works, but it is not fast”:

  • The rendering does not look horrible, but does not exactly match official implementation. Here is official vs my rendering of the same scene. Official one has more small detail, and lighting is slightly different Fixed!
  • Performance is not great. The scene above renders on NVIDIA RTX 3080 Ti at 1200x800 in 7.40ms (135FPS) in the official viewer, whereas my attempt is 23.8ms (42FPS) currently, i.e. 4x slower. For sorting I’m using some fairly simple GPU bitonic sort (official impl uses CUDA radix sort which is based on OneSweep algorithm). Rasterization in their case is tile-based and written in CUDA, whereas I’m “just” using regular GPU rasterization pipeline and rendering each splat as a screenspace quad.
    • On the plus side, my code is all regular HLSL within Unity, which means it also happens to work on e.g. Mac just fine. The scene above on Apple M1 Max renders in 108ms (9FPS) though :/
    • My implementation seems to use 2x less GPU memory right now too (official viewer: 4.8GB, mine: 2.2GB and that’s including whatever Unity editor takes).

So all of that could be improved and optimized quite a bit!

One thing I haven’t seen talked much about, by everyone super excited about Gaussian Splats, is data size and memory usage. Yeah, rendering is nice, but this bicycle scene above is 1.5GB of data on-disk, and then at runtime it needs some more (for sorting, tile based rendering etc.). That scene is six million blobs in space, with each of them taking about 250 bytes. There has to be some way to make that smaller! Actually the Dreams talk above has some neat ideas.

Maybe I should play around with that. Someday!

Float Compression 9: LZSSE and Lizard

Introduction and index of this series is here.

Some people asked whether I have tested LZSSE or Lizard. I have not! But I have been aware of them for years. So here’s a short post, testing them on “my” data set. Note that at least currently both of these compressors do not seem to be actively developed or updated.

LZSSE and Lizard, without data filtering

Here they are on Windows (VS2022, Ryzen 5950X). Also included Zstd and LZ4 for comparison, as faint dashed lines:

For LZSSE I have tested LZSSE8 variant, since that’s what readme tells to generally use. “Zero” compression level here is the “fast” compressor; other levels are the “optimal” compressor. Compression levels beyond 5 seem to not buy much ratio, but get much slower to compress. On this machine, on this data set, it does not look competetive - compression ratio is very similar to LZ4; decompression a bit slower, compression a lot slower.

For Lizard (née LZ5), it really is like four different compression algorithms in there (fastLZ4, LIZv1, fastLZ4 + Huffman, LIZv1 + Huffman). I have not tested the Huffman variants since they can not co-exist with Zstd in the same build easily (symbol redefinitions). The fastLZ4 is shown as lizard1x here, and LIZv1 is shown as lizard2x.

lizard1x (i.e. Lizard compression levels 10..19) seems to be pretty much the same as LZ4. Maybe it was faster than LZ4 back in 2019, but since then LZ4 gained some performance improvements?

lizard2x is interesting - better compression ratio than LZ4, a bit slower decompression speed. In the middle between Zstd and LZ4 when it comes to decompression parameter space.

What about Mac?

The above charts are on x64 architecture, and Visual Studio compiler. How about a Mac (with a Clang compiler)? But first, we need to get LZSSE working there, since it is very much written with raw SSE4.1 intrinsics and no fallback or other platform paths. Luckily, just dropping a sse2neon.h into the project and doing a tiny change in LZSSE source make it just work on an Apple M1 platform.

With that out of the way, here’s the chart on Apple M1 Max with Clang 14:

Here lzsse8 and lizard1x do get ahead of LZ4 in terms of decompression performance. lizard1x is about 40% faster than LZ4 at decompression at the same compression ratio. LZSSE is “a bit” faster (but compression performance is still a lot slower than LZ4).

LZSSE and Lizard, with data filtering and chunking

If there’s anything we’ve learned so far in this whole series, is that “filtering” the data before compression can increase the compression ratio a lot (which in turn can speed up both compression and decompression due to data being easier or smaller). So let’s do that!

Windows case, all compressors with “split bytes, delta” filter from part 7, and each 1MB block is compressed independently (see part 8):

Well, neither LZSSE nor Lizard are very good here – LZ4 with filtering is faster than either of them, with a slightly better compression ratio too. If you’d want higher compression ratio, you’d reach for filtered Zstd.

On a Mac things are a bit more interesting for lzsse8 case; it can get ahead of filtered LZ4 decompression performance at expense of some compression ratio loss:

I have also tested on Windows (same Ryzen 5950X) but using Clang 15 compiler. Neither LZSSE nor Lizard are on the Pareto frontier here:


On my data set, neither LZSSE nor Lizard are much competetive against (filtered or unfiltered) LZ4 or Zstd. They might have been several years ago when they were developed, but since then both LZ4 and Zstd got several speedup optimizations.

Lizard levels 10-19, without any data filtering, do get ahead of LZ4 in decompression performance, but only on Apple M1.

LZSSE is “basically LZ4” in terms of decompression performance, but the compressor is much slower (fair, the project says as much in the readme). Curiously enough, where LZSSE gets ahead of LZ4 is on an Apple M1, a platform it is not even supposed to work on outside the box :)

Maybe next time I’ll finally look at lossy floating point compression. Who knows!

Float Compression 8: Blosc

Introduction and index of this series is here.

Several people have asked whether I have tried Blosc library for compressing my test data set. I was aware of it, but have not tried it! So this post is fixing that.

In the graphics/vfx world, OpenVDB uses Blosc as one option for volumetric data compression. I had no idea until about two weeks ago!

What is Blosc?

Blosc is many things, but if we ignore all the parts that are not relevant for us (Python APIs etc.), the summary is fairly simple:

  • It is a data compression library geared towards structured (i.e. arrays of same-sized items) binary data. There’s a fairly simple C API to access it.
  • It splits the data into separate chunks, and compresses/decompresses them separately. This optionally allows multi-threading by putting each chunk onto a separate job/thread.
  • It has a built-in compression codec BloscLZ, based on FastLZ. Out of the box it also builds with support for Zlib, LZ4, and Zstd.
  • It has several built-in lossless data filtering options: “shuffle” (exactly the same as “reorder bytes” from part 3), “bitshuffle” and “delta”.

All this sounds pretty much exactly like what I’ve been playing with in this series! So, how does Blosc with all default settings (their own BloscLZ compression, shuffle filter) compare? The below is on Windows, VS2022 (thin solid lines are zstd and lz4 with byte reorder + delta filter optimizations from previous post; dashed lines are zstd and lz4 without any filtering; thick line is blosc defaults):

So, Blosc defaults are:

  • Better than just throwing zstd at the data set: slightly higher compression ratio, faster compression, way faster decompression.
  • Mostly better than just using lz4: much better compression ratio, faster compression, decompression slightly slower but still fast.
  • However, when compared to my filters from previous post, Blosc default settings do not really “win” – compression ratio is quite a bit lower (but, compression and decompression speed is very good).

Note that here I’m testing Blosc without using multi-threading, i.e. nthreads is set to 1 which is the default.

I’m not quite sure how they arrive at the “Blosc is faster than a memcpy()” claim on their website though. Maybe if all the data is literally zeroes, you could get there? Otherwise I don’t quite see how any LZ-like codec could be faster than just a memory copy, on any realistic data.

Blosc but without the Shuffle filter

Ok, how about Blosc but using LZ4 or Zstd compression, instead of the default BloscLZ? And for now, let’s also turn off the default “shuffle” (“reorder bytes”) filter:

  • Without “shuffle” filter, Blosc-Zstd basically is just Zstd, with a very small overhead and a tiny loss in compression ratio. Same for Blosc-LZ4; it is “just” LZ4, so to speak.
  • BloscLZ compressor without the shuffle filter is behind vanilla LZ4 both in terms of ratio and performance.

Blosc with Shuffle, and Zstd/LZ4

What if we turn the Shuffle filter back on, but also try LZ4 and Zstd?

For both zstd and lz4 cases, the compression ratio is below what “my” filter achieves. But the decompression performance is interesting: Blosc-Zstd is slightly ahead of “zstd + my filter”, and Blosc-LZ4 is quite a bit ahead of “lz4 + my filter”. So that’s interesting! So far, Blosc-LZ4 with Shuffle is on the Pareto frontier if you need that particular balance between ratio and decompression performance.

Blosc with Shuffle and Delta filters

Looks like Blosc default Shuffle filter is exactly the same as my “reorder bytes” filter. But in terms of best compression ratio, “reorder bytes + delta” was the best option so far. Oh hey, Blosc (since version 2.0) also has a filter named “Delta”! Let’s try that one out:

Huh. The Shuffle + Delta combination is, like, not great at all? The compression ratio is below 2.0 everywhere; i.e. worse than just zstd or lz4 without any data filtering? 🤔

Oh wait, looks like Blosc’ “Delta” filter is not a “delta” at all. Sometime in 2017 they changed it to be a XOR filter instead (commit). The commit message says “for better numerical stability”, no idea what that means since this is operating all on integers.

Ah well, looks like at least on this data set, the Delta filter does not do anything good, so we’ll forget about it. Update: look at “bytedelta” filter below, new in Blosc 2.8!

Input data chunking

The question remains, why and how is Blosc-LZ4 with Shuffle faster at decompression than “my” filter with LZ4? One reason could be that my filter is not entirely optimized (very possible). Another might be that Blosc is doing something differently…

And that difference is: by default, Blosc splits input data into separate chunks. The chunk sizes seem to be 256 kilobytes by default. Then each chunk is filtered and compressed completely independently from the other chunks. Of course, the smaller the chunk size, the lower is the compression ratio that you get, since the LZ compression codec can’t “see” data repetitions outside the chunk boundaries.

What if I added very similar “data chunking” to “my” tests, i.e. just zstd/lz4, my filters, and all that split into independent chunks? Here’s without chunks, plus graphs for 64KB, 256KB, 1MB, 4MB chunk sizes:

It is a bit crowded, but you can see how splitting data into 4MB chunks practically does not lose any compression ratio, yet manages to make LZ4 decoding quite a bit faster. With much smaller chunk sizes of 64KB, the compression ratio loss seems to be “maybe too large” (still way better than without any data filtering though). It feels like chunk size of 1MB is quite good: very small compression ratio loss, good decompression speedup:

So this is another trick that is not directly related to Blosc: splitting up your data into separate 256KB-1MB chunks might be worth doing. Not only this would enable operating on chunks in parallel (if you wish to do that), but also it speeds things up, especially decompression. The reason being that the working set memory needed to do decompression now neatly fits into CPU caches.

Update: “bytedelta” filter in Blosc 2.8

Something quite amazing happened: seemingly after reading this same blog post and the previous one, Blosc people added a new filter called “bytedelta”, that, well, does exactly what you’d think it would – it is delta encoding. Within Blosc, you would put a “shuffle” (“split bytes” in my posts) filter, followed by a “bytedelta” filter.

This just shipped in Blosc 2.8.0, and they have an in-depth blog post testing it on ERA5 data sets, a short video, and a presentation at LEAPS Innov WP7 (slides). That was fast!

So how does it compare?

  • Thick solid lines are Blosc shuffle+bytedelta, for the three bases of Blosc built-in BLZ compression, as well as Blosc using LZ4 and Zstd compression.
  • For comparison, Blosc with just shuffle filter are dashed lines of the same color.
  • There’s also “my own” filter from previous post using LZ4 and Zstd and splitting into 1MB chunks on the graph for comparison.

So, Blosc bytedelta filter helps compression ratio a bit in BLZ and LZ4 cases, but helps compression ratio a lot when using Zstd. It is a sligth loss of compression ratio compared to best result we have without Blosc (Blosc splits data into ~256KB chunks by default), and a bit slower too, probably because the “shuffle” and “bytedelta” are separate filters there instead of combined filter that does both in one go.

But it’s looking really good! This is a great outcome. If you are using Blosc, check whether “shuffle” + “bytedelta” combination works well on your data. It might! Their own blog post has way more extensive evaluation.

Aside: “reinventing the wheel”

Several comments I saw about this whole blog post series were along the lines of “what’s the point; all of these things were already invented”. And that is true! I am going down this rabbit hole mostly for my own learning purposes, and just writing them down because… “we don’t ask why, we ask why not”.

I have already learned a bit more about compression, data filtering and SIMD, so yay, success. But also:

  • The new “bytedelta” filter in Blosc 2.8 is very directly inspired by this blog post series. Again, this is not a new invention; delta encoding has been around for many decades. But a random post on the interwebs can make someone else go “wait, turns out we don’t have this trick, let’s add it”. Nice!
  • After writing part 7 of these series, I looked at OpenEXR code again, saw that while they do have Intel SSE optimizations for zip-compressed .exr files reading, they do not have ARM NEON paths. So I added those, and that makes loading .exr files that use zip compression almost 30% faster on a Mac M1 laptop. That shipped in OpenEXR 3.1.6, yay!

So I don’t quite agree with some random internet commenters saying “these posts are garbage, all of this has been invented before”. The posts might be garbage, true, but 1) I’ve learned something and 2) improvements based on these posts have landed into two open source software libraries by now.

Don’t pay too much attention to internet commenters.


Blosc is pretty good!

I do wonder why they only have a “shuffle” filter built-in though (there’s also “delta” but it’s really some sort of “xor”). At least on my data, “shuffle + actual delta” would result in much better compression ratio. Without having that filter, blosc loses to the filter I have at the end of previous post in terms of compression ratio, while being roughly the same in performance (after I apply 1MB data chunking in my code). Update: since 2.8 Blosc has a “bytedelta” filter; if you put that right after “shuffle” filter then it gets results really close to what I’ve got in the previous post.

Float Compression 7: More Filtering Optimization

Introduction and index of this series is here.

In the previous post I explored how to make data filters a bit faster, using some trivial merging of filters, and a largely misguided attempt at using SIMD.

People smarter than me pointed out that getting good SIMD performance requires a different approach. Which is kinda obvious, and another thing that is obvious is that I have very little SIMD programming experience, and thus very little intuition of what’s a good approach.

But to get there, first I’d need to fix a little poopoo I made.

A tiny accidental thing can prevent future things

Recall how in part 3 the most promising data filter seemed to be “reorder bytes + delta”? What it does, is first reorder data items so that all 1st bytes are together, then all 2nd bytes, etc. If we had three items of four bytes each, it would do this:

And then delta-encode the whole result:

i.e. first byte stays the same, and each following byte is difference from the previous one.

Turns out, this choice prevents some future optimizations. How? Because whole data reordering conceptually produces N separate byte streams, delta-encoding the whole result conceptually merges these streams together; the values in them become dependent on all previous values.

What if instead, we delta-encoded each stream separately?

In terms of code, this is a tiny change:

void Split8Delta(const uint8_t* src, uint8_t* dst, int channels, size_t dataElems)
    // uint8_t prev = 0; <-- WAS HERE
    for (int ich = 0; ich < channels; ++ich)
        uint8_t prev = 0; // <-- NOW HERE
        const uint8_t* srcPtr = src + ich;
        for (size_t ip = 0; ip < dataElems; ++ip)
            uint8_t v = *srcPtr;
            *dst = v - prev;
            prev = v;
            srcPtr += channels;
            dst += 1;

We will see how that is useful later. Meanwhile, this choice of “reorder, then delta the whole result” is what OpenEXR image format also does in the ZIP compression code :)

What the above change allows, is in the filter decoder to fetch from any number of byte streams at once and process their data (apply reverse delta, etc.). Something we could not do before, since values within each stream depended on the values of previous streams.

So, more (questionable) optimizations

Overall I did a dozen experiments, and they are all too boring to write about them here, so here are the main ones.

Note: in the previous post I made a mistake in timing calculations, where the time numbers were more like “average time it takes to filter one file”, not “total time it takes to filter whole data set”. Now the numbers are more proper, but don’t directly compare them with the previous post!

In the previous post we went from “A” to “D” variants, resulting in some speedups depending on the platform (un-filter for decompression: WinVS 106→75ms, WinClang 116→75ms, Mac 94→32ms):

Now that we can decode/unfilter all the byte streams independently, let’s try doing just that (no SIMD at all):

const size_t kMaxChannels = 64;
// Scalar, fetch a byte from N streams, write sequential
void UnFilter_G(const uint8_t* src, uint8_t* dst, int channels, size_t dataElems)
    uint8_t prev[kMaxChannels] = {};
    uint8_t* dstPtr = dst;
    for (size_t ip = 0; ip < dataElems; ++ip)
        const uint8_t* srcPtr = src + ip;
        for (int ich = 0; ich < channels; ++ich)
            uint8_t v = *srcPtr + prev[ich];
            prev[ich] = v;
            *dstPtr = v;
            srcPtr += dataElems;
            dstPtr += 1;

I did hardcode “maximum bytes per data element” to just 64 here. In our data set it’s always either 16 or 12, but let’s make the limit somewhat more realistic. It should be possible to not have a limit with some additional code, but “hey 64 bytes per struct should be enough for anyone”, or so the ancient saying goes.

So this is “G” variant: decompression WinVS 139ms, WinClang 125ms, Mac 104ms (“D” was: 75, 75, 32). This is not great at all! This is way slower! ☹️

But! See how this fetches a byte from all the “streams” of a data item, and has all the bytes of the previous data item? Doing the “un-delta” step could be done way more efficiently using SIMD now, by processing like 16 bytes at once (128 bit SSE/NEON registers are exactly 16 bytes in size).

A tiny SIMD wrapper, and Transpose

All the SSE and NEON code I scribbled in the previous post felt like I’m just repeating the same things for NEON after doing SSE part, just with different intrinsic function names. So, perhaps prematurely, I made a little helper to avoid having to do that: a data type Bytes16 that, well, holds 16 bytes, and then functions like SimdAdd, SimdStore, SimdGetLane and whatnot. It’s under 100 lines of code, and does just the tiny amount of operations I need: simd.h.

I will also very soon need a function that transposes a matrix, i.e. flips rows & columns of a rectangular array. As usual, turns out Fabian has written about this a decade ago (Part 1, Part 2). You can cook up a sweet nice 16x16 byte matrix transpose like this:

static void EvenOddInterleave16(const Bytes16* a, Bytes16* b)
    int bidx = 0;
    for (int i = 0; i < 8; ++i)
        b[bidx] = SimdInterleaveL(a[i], a[i+8]); bidx++; // _mm_unpacklo_epi8 / vzip1q_u8
        b[bidx] = SimdInterleaveR(a[i], a[i+8]); bidx++; // _mm_unpackhi_epi8 / vzip2q_u8
static void Transpose16x16(const Bytes16* a, Bytes16* b)
    Bytes16 tmp1[16], tmp2[16];
    EvenOddInterleave16(a, tmp1);
    EvenOddInterleave16(tmp1, tmp2);
    EvenOddInterleave16(tmp2, tmp1);
    EvenOddInterleave16(tmp1, b);

and then have a more generic Transpose function for any NxM sized matrix, with the faster SIMD code path for cases like “16 rows, multiple-of-16 columns”. Why? We’ll need it soon :)

Continuing with optimizations

The “G” variant fetched one byte from each stream/channel, did <something else>, and then fetched the following byte from each stream, and so on. Now, fetching bytes one by one is probably wasteful.

What we could do instead, for the un-filter: from each stream, fetch 16 (SIMD register size) bytes, and decode the deltas using SIMD prefix sum (very much like in “D” variant). Now we have 16 data items on stack, but they are still in the “split bytes” memory layout. But, doing a matrix transpose gets them into exactly the layout we need, and we can just blast that into destination buffer with a single memcpy.

// Fetch 16b from N streams, prefix sum SIMD undelta, transpose, sequential write 16xN chunk.
void UnFilter_H(const uint8_t* src, uint8_t* dst, int channels, size_t dataElems)
    uint8_t* dstPtr = dst;
    int64_t ip = 0;

    // simd loop: fetch 16 bytes from each stream
    Bytes16 curr[kMaxChannels] = {};
    const Bytes16 hibyte = SimdSet1(15);
    for (; ip < int64_t(dataElems) - 15; ip += 16)
        // fetch 16 bytes from each channel, prefix-sum un-delta
        const uint8_t* srcPtr = src + ip;
        for (int ich = 0; ich < channels; ++ich)
            Bytes16 v = SimdLoad(srcPtr);
            // un-delta via prefix sum
            curr[ich] = SimdAdd(SimdPrefixSum(v), SimdShuffle(curr[ich], hibyte));
            srcPtr += dataElems;

        // now transpose 16xChannels matrix
        uint8_t currT[kMaxChannels * 16];
        Transpose((const uint8_t*)curr, currT, 16, channels);

        // and store into destination
        memcpy(dstPtr, currT, 16 * channels);
        dstPtr += 16 * channels;

    // any remaining leftover
    if (ip < int64_t(dataElems))
        uint8_t curr1[kMaxChannels];
        for (int ich = 0; ich < channels; ++ich)
            curr1[ich] = SimdGetLane<15>(curr[ich]);
        for (; ip < int64_t(dataElems); ip++)
            const uint8_t* srcPtr = src + ip;
            for (int ich = 0; ich < channels; ++ich)
                uint8_t v = *srcPtr + curr1[ich];
                curr1[ich] = v;
                *dstPtr = v;
                srcPtr += dataElems;
                dstPtr += 1;

The code is getting more complex! But conceptually it’s not – half of the function is the SIMD loop that reads 16 bytes from each channel; and the remaining half of the function is non-SIMD code to handle any leftover in case data size was not multiple of 16.

For the compression filter it is similar idea, just the other way around: read 16 N-sized items from the source data, transpose which gets them into N channels with 16 bytes each. Now do the delta encoding with SIMD on that. Store each of these 16 bytes into N separate locations. Again half of the code is just for handling non-multiple-of-16 data size leftovers.

// Fetch 16 N-sized items, transpose, SIMD delta, write N separate 16-sized items
void Filter_H(const uint8_t* src, uint8_t* dst, int channels, size_t dataElems)
    uint8_t* dstPtr = dst;
    int64_t ip = 0;
    const uint8_t* srcPtr = src;
    // simd loop
    Bytes16 prev[kMaxChannels] = {};
    for (; ip < int64_t(dataElems) - 15; ip += 16)
        // fetch 16 data items
        uint8_t curr[kMaxChannels * 16];
        memcpy(curr, srcPtr, channels * 16);
        srcPtr += channels * 16;
        // transpose so we have 16 bytes for each channel
        Bytes16 currT[kMaxChannels];
        Transpose(curr, (uint8_t*)currT, channels, 16);
        // delta within each channel, store
        for (int ich = 0; ich < channels; ++ich)
            Bytes16 v = currT[ich];
            Bytes16 delta = SimdSub(v, SimdConcat<15>(v, prev[ich]));
            SimdStore(dstPtr + dataElems * ich, delta);
            prev[ich] = v;
        dstPtr += 16;
    // any remaining leftover
    if (ip < int64_t(dataElems))
        uint8_t prev1[kMaxChannels];
        for (int ich = 0; ich < channels; ++ich)
            prev1[ich] = SimdGetLane<15>(prev[ich]);
        for (; ip < int64_t(dataElems); ip++)
            for (int ich = 0; ich < channels; ++ich)
                uint8_t v = *srcPtr;
                dstPtr[dataElems * ich] = v - prev1[ich];
                prev1[ich] = v;

Now that is a lot of code indeed, relatively speaking. Was it worth it? This is variant “H”: decompression unfilter WinVS 21ms, WinClang 20ms, Mac 28ms (previous best “D” was 75, 75, 32). Compression filter WinVS 24ms, WinClang 23ms, Mac 31ms (“D” was 63, 54, 32).

Hey look, not bad at all!

Is it cheating if you optimize for your data?

Next up is a step I did only for the decoding unfilter. It’s not all that interesting, but raises a good question: is it “cheating”, if you optimize/specialize your code for your data?

The answer is, of course, “it depends”. In my particular case, I’m testing on four data files, and three of them use data items that are 16 bytes in size (the 4th one uses 12 byte items). The UnFilter_H function above is written for generic “any, as long as <64 bytes item size” data. What I used that exact code for all non-16 sized data, but did “something better” for 16-sized data?

In particular, the transpose step becomes exact 16x16 matrix transpose, for which we have a sweet nice function already. And the delta decoding could be done after the transpose, using way more efficient “just add SIMD registers” operation instead of trying to cram that into SIMD prefix sum. The interesting part of the SIMD inner loop becomes this then:

// fetch 16 bytes from each channel
Bytes16 curr[16];
const uint8_t* srcPtr = src + ip;
for (int ich = 0; ich < 16; ++ich)
    Bytes16 v = SimdLoad(srcPtr);
    curr[ich] = v;
    srcPtr += dataElems;

// transpose 16xChannels matrix
Bytes16 currT[16];
Transpose((const uint8_t*)curr, (uint8_t*)currT, 16, channels);

// un-delta and store
for (int ib = 0; ib < 16; ++ib)
    prev = SimdAdd(prev, currT[ib]);
    SimdStore(dstPtr, prev);
    dstPtr += 16;

Does that help? “I” case: decompression unfilter WinVS 18ms, WinClang 14ms, Mac 24ms (“H” was 21, 20, 28). Yeah, it does help.

Groups of four

Fabian pointed out that fetching from “lots” (e.g. 16) separate streams at once can get into an issue of CPU cache trashing. If the streams spaced apart at particular powers of two, and you are fetching from more than 4 or 8 (typical CPU cache associativity) streams at once, it’s quite likely that many of your memory fetches will be landing into the same physical CPU cache lines.

One possible way to avoid this is also “kinda cheating” (or well, “using knowledge of our data”) – we know we are operating on floating point (4-byte) things, i.e. our data structure sizes are always a multiple of four. We could be fetching not all N (N = data item size) streams at once, but rather do that in groups of 4 streams. Why four? Because we know the number of streams is multiple of four, and most CPU caches are at least 4-way associative.

So conceptually, decompression unfilter would be like (straight pseudo-code paste from Fabian’s toot):

for (chunks of N elements) {
  for groups of 4 streams {
    read and interleave N values from 4 streams each
    store to stack
  for elements {
    read and interleave groups of 4 streams from stack
    sum into running total
    store to dest

This hopefully avoids some CPU cache trashing, and also fetches more than 16 bytes from each stream in one go. Ideally we’d want to fetch as much as possible, while making sure that everything we’re working with stays in CPU L1 cache.

I’ve tried various sizes, and in my testing size of 384 bytes per channel worked best. The code is long though, and kind of a mess; the “we effectively achieve a matrix transpose, but in two separate steps” is not immediately clear at all (or not clear at my lacking experience level :)). In the code I have separate path for 16-sized data items, where the 2nd interleave part is much simpler.

Anyhoo, here it is:

void UnFilter_K(const uint8_t* src, uint8_t* dst, int channels, size_t dataElems)
    assert((channels % 4) == 0); // our data is floats so channels will always be multiple of 4

    const int kChunkBytes = 384;
    const int kChunkSimdSize = kChunkBytes / 16;
    static_assert((kChunkBytes % 16) == 0, "chunk bytes needs to be multiple of simd width");
    uint8_t* dstPtr = dst;
    int64_t ip = 0;
    alignas(16) uint8_t prev[kMaxChannels] = {};
    Bytes16 prev16 = SimdZero();
    for (; ip < int64_t(dataElems) - (kChunkBytes - 1); ip += kChunkBytes)
        // read chunk of bytes from each channel
        Bytes16 chdata[kMaxChannels][kChunkSimdSize];
        const uint8_t* srcPtr = src + ip;
        // fetch data for groups of 4 channels, interleave
        // so that first in chdata is (a0b0c0d0 a1b1c1d1 a2b2c2d2 a3b3c3d3) etc.
        for (int ich = 0; ich < channels; ich += 4)
            for (int item = 0; item < kChunkSimdSize; ++item)
                Bytes16 d0 = SimdLoad(((const Bytes16*)(srcPtr)) + item);
                Bytes16 d1 = SimdLoad(((const Bytes16*)(srcPtr + dataElems)) + item);
                Bytes16 d2 = SimdLoad(((const Bytes16*)(srcPtr + dataElems * 2)) + item);
                Bytes16 d3 = SimdLoad(((const Bytes16*)(srcPtr + dataElems * 3)) + item);
                // interleaves like from
                Bytes16 e0 = SimdInterleaveL(d0, d2); Bytes16 e1 = SimdInterleaveR(d0, d2);
                Bytes16 e2 = SimdInterleaveL(d1, d3); Bytes16 e3 = SimdInterleaveR(d1, d3);
                Bytes16 f0 = SimdInterleaveL(e0, e2); Bytes16 f1 = SimdInterleaveR(e0, e2);
                Bytes16 f2 = SimdInterleaveL(e1, e3); Bytes16 f3 = SimdInterleaveR(e1, e3);
                chdata[ich + 0][item] = f0;
                chdata[ich + 1][item] = f1;
                chdata[ich + 2][item] = f2;
                chdata[ich + 3][item] = f3;
            srcPtr += 4 * dataElems;

        if (channels == 16)
            // channels == 16 case is much simpler
            // read groups of data from stack, interleave, accumulate sum, store
            for (int item = 0; item < kChunkSimdSize; ++item)
                for (int chgrp = 0; chgrp < 4; ++chgrp)
                    Bytes16 a0 = chdata[chgrp][item];
                    Bytes16 a1 = chdata[chgrp + 4][item];
                    Bytes16 a2 = chdata[chgrp + 8][item];
                    Bytes16 a3 = chdata[chgrp + 12][item];
                    // now we want a 4x4 as-uint matrix transpose
                    Bytes16 b0 = SimdInterleave4L(a0, a2); Bytes16 b1 = SimdInterleave4R(a0, a2);
                    Bytes16 b2 = SimdInterleave4L(a1, a3); Bytes16 b3 = SimdInterleave4R(a1, a3);
                    Bytes16 c0 = SimdInterleave4L(b0, b2); Bytes16 c1 = SimdInterleave4R(b0, b2);
                    Bytes16 c2 = SimdInterleave4L(b1, b3); Bytes16 c3 = SimdInterleave4R(b1, b3);
                    // c0..c3 is what we should do accumulate sum on, and store
                    prev16 = SimdAdd(prev16, c0); SimdStore(dstPtr, prev16); dstPtr += 16;
                    prev16 = SimdAdd(prev16, c1); SimdStore(dstPtr, prev16); dstPtr += 16;
                    prev16 = SimdAdd(prev16, c2); SimdStore(dstPtr, prev16); dstPtr += 16;
                    prev16 = SimdAdd(prev16, c3); SimdStore(dstPtr, prev16); dstPtr += 16;
            // general case: interleave data
            uint8_t cur[kMaxChannels * kChunkBytes];
            for (int ib = 0; ib < kChunkBytes; ++ib)
                uint8_t* curPtr = cur + ib * kMaxChannels;
                for (int ich = 0; ich < channels; ich += 4)
                    *(uint32_t*)curPtr = *(const uint32_t*)(((const uint8_t*)chdata) + ich * kChunkBytes + ib * 4);
                    curPtr += 4;
            // accumulate sum and store
            // the row address we want from "cur" is interleaved in a funky way due to 4-channels data fetch above.
            for (int item = 0; item < kChunkSimdSize; ++item)
                for (int chgrp = 0; chgrp < 4; ++chgrp)
                    uint8_t* curPtrStart = cur + (chgrp * kChunkSimdSize + item) * 4 * kMaxChannels;
                    for (int ib = 0; ib < 4; ++ib)
                        uint8_t* curPtr = curPtrStart;
                        // accumulate sum w/ SIMD
                        for (int ich = 0; ich < channels; ich += 16)
                            Bytes16 v = SimdAdd(SimdLoadA(&prev[ich]), SimdLoad(curPtr));
                            SimdStoreA(&prev[ich], v);
                            SimdStore(curPtr, v);
                            curPtr += 16;
                        // store
                        memcpy(dstPtr, curPtrStart, channels);
                        dstPtr += channels;
                        curPtrStart += kMaxChannels;

    // any remainder
    if (channels == 16)
        for (; ip < int64_t(dataElems); ip++)
            // read from each channel
            alignas(16) uint8_t chdata[16];
            const uint8_t* srcPtr = src + ip;
            for (int ich = 0; ich < 16; ++ich)
                chdata[ich] = *srcPtr;
                srcPtr += dataElems;
            // accumulate sum and write into destination
            prev16 = SimdAdd(prev16, SimdLoadA(chdata));
            SimdStore(dstPtr, prev16);
            dstPtr += 16;
        for (; ip < int64_t(dataElems); ip++)
            const uint8_t* srcPtr = src + ip;
            for (int ich = 0; ich < channels; ++ich)
                uint8_t v = *srcPtr + prev[ich];
                prev[ich] = v;
                *dstPtr = v;
                srcPtr += dataElems;
                dstPtr += 1;

I told you it is getting long! Did it help? “K” case: decompression unfilter WinVS 15ms, WinClang 15ms, Mac 16ms (“H” was 18, 14, 24)

Ok, it does significantly help Mac (Apple M1/NEON) case; helps a bit on Windows PC too.


All in all, for the decompression unfilter we went from super simple code in part 3 (“A”) to a naïve attempt at SIMD (“D”) to this fairly involved “K” variant, and their respective timings are:

  • Ryzen 5950X, Windows, VS2022: 1067515ms. Clang 15: 1167515ms.
  • Apple M1, Clang 14: 943216ms.

The performance is 5-8 times faster, which is nice. Note: it’s entirely possible that I have misunderstood Fabian’s advice, and/or did it wrong, or just left some other speedup opportunities lying on the floor.

The filtering part is faster now, great. How does this affect the overall process, when we put it next to the actual data compression & decompression? After all, this is what we are really interested in.

Here they are (click for interactive chart; solid thick line: this post, solid thin line: “D” from previous post). Windows MSVC, Windows Clang, Mac Clang:

Hey look! If you are using zstd, both compression and decompression is faster and better ratio with the data filtering applied. For LZ4 the decompression does not quite reach the 5GB/s that it can do without data filtering, but it does go up to 2.5GB/s which is way faster than 0.7GB/s that it was going on in the “A” approach. And the compression ratio is way better than just LZ4 can achieve.

The code is quite a bit more complex though. Is all that code complexity worth it? Depends.

  • The code is much harder to follow and understand.
  • However, the functionality is trivial to test, and to ensure it keeps on working via tests.
  • This is not one of those “oh but we need to keep it simple if it needs to get changed later” cases. You either do “combine streams, decode delta”, or you do something else. Once or if you settled onto that data format, the code to achieve that un-filtering step needs to do exactly just that. If you need to do something else, throw away this code and write code to do that other thing!
  • If “data un-filtering” (transpose, decode delta) is critical part of your library or product, or just a performance critical area, then it might be very well worth it.

Nothing in the above is “new” or noteworthy, really. The task of “how to filter structured data” or “how to transpose data fast” has been studied and solved quite extensively. But, it was a nice learning experience for me!

What’s next

I keep on saying that I’d look into lossy compression options, but now many (read: more than one!) people have asked “what about Blosc?” and while I was aware of it for a number of years, I have never actually tested it. So I’m gonna do that next!