cbloom rants


Rate allocation in Oodle Texture

Oodle Texture does rate-distortion optimization (RDO) BCN encoding, optimizing the BCN encoding for an R-D two axis score such that the size of the BCN texture after a following lossless compression is reduced while the distortion (difference from original) is not increased too much.

One way to think about RDO conceptually is as rate allocation. Rate allocation is when an encoder intentionally puts more or fewer bits in parts of the data to control what the decoder will receive, so that it can use more bits where it helps more, and the result is a better quality for a given output size. I want to talk a bit about that viewpoint and how it works in Oodle Texture.

Traditional lossy encoders like JPEG didn't have active rate allocation; they used a fixed scheme (DCT and quantize) that did a fixed rate allocation (give more bits to the lower frequencies) and didn't try to optimize that based on image contents. Modern codecs like H264 use rate allocating encoders and furthermore have explicit tools in the format to make rate allocation more flexible, such as variable quantizers. Formats without explicit rate allocation controls can still be rate adjusted, which is what we do in Oodle Texture, but it's not as easy to dial.

In that context, we think of a traditional non-RDO BCN encoder as allocating rate evenly to all blocks; it doesn't care where the rate goes and just tries to minimize distortion. The BCN encoder itself produces fixed size blocks (8 bytes per block for BC1 or 16 bytes per block for BC7), but the "rate" we care about is the size of the block after subsequent LZ compression (eg. with Kraken or Zip/deflate).

In Oodle Texture, we use the Lagrange parameter method for RDO. Specifically we construct a Lagrange cost :

J = D + lambda * R
and then we can just minimize a single number, J, rather than a two-axis score of {R,D}. Obviously when lambda=0 this reduces to J=D , minimize D, which is a non-RDO encoding that only cares about quality and not rate. As lambda increases your score is more and more a balance of minimizing both distortion and rate.

We sometimes think of D(R) , distortion just being a function of R, but that's not how it works in an implementation, you don't actually know the functions for how R and D relate.

In practice there is some encoding, which I will index by "i" , and you have two separate functions :

R(i) and D(i)
That is, you just choose various encodings that look promising, and measure R and D of each. This will give you a scattering of points on an R-D plot. Some points are off the Pareto Frontier - strictly worse in terms of R & D and we just reject those points. See Fabian's blog on RDO for some pictures of this.

Henceforth I will assume that points off the Pareto Frontier have been rejected and we now only are looking at encodings on the Pareto R-D curve. Also I will sort the index of encodings "i" by rate.

The R(i) and D(i) curves both tend to be hyperbolic-shaped, with minima at opposite ends of the "i" spectrum. If you minimized either one on their own, they don't have any local minima so you would just go to the edge of what the encoding format is capable of doing. By adding them together with lambda, it makes a trough somewhere in the middle :

High D, low R on the left (very lossy), low D high R (non-RDO) on the right.

At low lambda, the minimum of J is in the high-R, low-D domain. As lambda increases it shifts the minimum of J to lower R. In the example chart, the red low-lambda curve has minimum at i=14, the teal medium-lambda curve has minimum at i=12, the gold high-lambda curve has minimum at i=10. In this way, lambda can be used to dial rate, but indirectly.

Concretely, if we reparameterize to imagine we have a function D(R) (Distortion as a function of R; there is only one encoding for each R because we discard non-Pareto encodings), we have :

J(R) = D(R) + lambda * R

minimum is at d/dR J = 0

d/dR J = 0 = d D /dR + lambda

lambda = - dD / dR

lambda is the slope on the D(R) curve.

Because the D(R) curve is hyperbolic-shaped, the slope acts like a parameter of D itself. That is, where D is higher, the curve is also steeper, so by dialing the slope we have control over the principle value D as well.

Aside for experts : we are assuming that D(R) is continuous and monotonic AND dD/dR is continuous and monotonic; that is, the slope steadily increases from low to high. The whole idea of lambda as a slope of D(R) only really works if these curves are smooth and hyperbolic shaped as expected. We also need J to only have one local minimum. If these assumptions fail (which in practice they do!) you can wind up at a minimum that's not where you want, and the lambda-dials-D relationship can break down. There are some tricks to avoid these pitfalls. Try to avoid large steps of R/D in your encoding choices; provide the encoder with a fine grained series of steps; don't use the true R which can have strange non-monotonic wiggles, instead use an approximation of R which tends to smooth things out; you generally want to pre-classify the encodings that you think are low R vs high R and force them to be monotonic rather than measuring true R.

Now, "lambda is the slope on the D(R) curve" sounds a bit unintuitive and abstract, but in fact it is a concrete simple thing.

Lambda is a price. It is the gain in D that you must get for a gain in R to be worth it.

By using lambda as your control parameter instead of D, you are dialing quality via the *cost* of quality in terms of rate. You are saying "this much gain in quality is worth this much rate to me". We typically measure R in bits, so let's say lambda is quality per bit. In order to make a file bigger by 1 bit, it must provide at least "lambda" quality gain. Smaller quality gain, it's not worth it, don't do it.

Having our control paramter be price instead of directly controlling R or D turns out to be very beneficial, both for us internally and for you externally.

First why it's right externally : lambda control (slope control) lets you set a single parameter that works for all kinds of data or images. It automatically gives more rate to images that are harder to compress ("harder" here very concretely means a steeper slope - they give up more distortion than average for each step or rate). So you can have a mix of very vastly different data, lightmaps and normal maps and cartoon drawings, and they automatically rate adjust to send bits where they help the most. Many novices prefer to think of "rate reduction" or a "constant quality" kind of setting, like "I want to RDO all my images to 30% rate reduction", but that's really wrong. On some images, getting to 30% rate reduction would do lots of quality damage, while on others you could easily get more rate reduction (say 50%) without much quality loss at all. Lambda does that for you automatically.

Internally it's important because it lets us make each coding decision in isolation, just by looking at the J cost of that one decision in isolation. It makes the problem separable (which is also great for parallelism), but still achieve a global minimum. Lagrange optimization automatically does rate allocation within the image to different blocks and decisions.

I think it helps to compare to an alternative manual rate allocation method to see how advantageous it is :

Algorithm Manual Rate Allocation :

you have an image of N BCN 4x4 blocks
for each block, find the lowest D (non-RDO) encoding
measure R of that encoding - this is the max rate for each block

now incrementally reduce total rate
you want to take rate from the best block to take rate from of the N

for all N blocks
find the next smaller encoding 
measure the D increase for that step down of R
slope(n) = delta(D) / delta(R)

take the one block change n with the lowest slope(n)

repeat until all slopes(n) are > max_desired_slope


Algorithm Lagrange Rate Allocation :

for all N blocks in parallel :

try various encodings of the block
compute J = D + lambda * R for each encoding
take the encoding on that block with the best J

In "Manual Rate Allocation" we have this palette of various bins (the blocks) to choose to take rate from, and you take it from the one that does the least damage to D, if you keep repeating that the slopes will converge until they are all roughly equal.

The powerful thing is that these two algorithms converge to exactly the same solution (caveat: assuming monotonic and smooth R/D curves, which in fact they are not). The Lagrange method is actually doing rate allocation between the blocks, even though it's not explicit, and each block can be considered in isolation. In an RDO encoder, rate is like water, it flows away from high ground (dD/dR is high) to low ground, until level is reached. The Lagrange method is able to do this separably because the total amount of water (rate) is not conserved.

We can control exactly what the rate allocation does through the choice of the D function. The R function for rate is relatively inflexible - we're counting bits of output size (though in practice we may want to use a smoothed rate rather than true rate), we don't have much choice in R - in contrast, the D function is not absolutely specified and there are lots of options there. The choice of D changes where rate flows.

For example consider the common choices of D = L1 norm (SAD) vs L2 norm (SSD). These metric score different errors differently, which causes rate to flow. In particular L2 (squaring) puts a very big weight on single large errors vs. smaller multiple errors.

Source data   = { 10, 10 }
Approximation = {  8, 12 }

SAD error = 2 + 2 = 4
SSD error = 2^2 + 2^2 = 8

Source data   = { 10, 10 }
Approximation = { 10, 14 }

SAD error = 0 + 4 = 4
SSD error = 0^2 + 4^2 = 16

Choosing D = SSD would cause rate to flow from the {8,12} approximation to the {10,14} approximation because the error is much bigger there (relative to where it is with SAD). All reasonable D functions will be zero for an exact match, and increase as the approximation gets further from the source data, but they can increase at different rates for different types of distortions. In a non-RDO encoding, these different D functions might find very similar encodings, but with RDO by choosing different D you get rate to flow between blocks to different characters of error.

With no further ado, we can get to the fun part : pictures of how rate allocation plays out in practice in Oodle Texture.

These images show the original image, followed by gray scale images of the rate allocation. These are for BC7 encodings with Oodle Texture. The non-RDO encoding is Oodle Texture at lambda=0 ; the RDO encodings are at lambda=40 (typical medium quality setting).

In the rate allocation images, each pixel represents one 4x4 block. White is full rate (16 bytes per block) and black is zero bits. These encodings are not normalized to the same total rate (in particular the non-RDO is of course much larger). The images are gamma corrected so that linear light intensity corresponds to bits per block. The original images are halved in size for display here. So for example "mysoup" was 1024x512, the original shown here is 512x256, and rate map is one pixel per block, so 256x128.

The "rmse" and "perceptual" images use the exact same coding procedure at the same lambda, they differ only in the D function used to measure distortion. "rmse" tries to minimize simple L2 norm, while "perceptual" has some estimation of visual quality (trying to avoid blocking artifacts, for example).

The R measured for these maps is the size of each block after subsequent compression by Oodle's LZA compressor.

non-RDORDO rmseRDO perceptual

The non-RDO "mysoup" has very high entropy, the BC7 blocks are nearly incompressible by the LZ (7.759 bpb). The RDO with D=rmse keeps very high bit rate in the blocks of the bowl rim, but allocates lots of bits away from the smooth regions in the egg and pumpkin. In the "perceptual" allocation, the bits in the rim are reduced, allowing more error there, and the bit rate of the smooth regions come up to avoid blocking artifacts.

non-RDORDO rmseRDO perceptual

In the house image "test6" the bit rate of the "rmse" allocation goes nearly to zero in the smooth dark areas of the beams under the eaves. That's a mistake perceptually and causes bad blocking artifacts, so the "perceptual" allocator shifts rate back to those blocks.

non-RDORDO rmseRDO perceptual

We can see that Oodle Texture is changing near-even rate allocation to very variable rate per block. Even though the BC7 blocks are always 16 bytes, we have made some more compressible than others, shifting rate to where it is needed. On many blocks, 16 bytes is just too much, that much rate is not needed to get a good encoding, and the difference in D to a reduced-size encoding is small; these are low slope blocks and will lose rate in RDO. After rate allocation, the blocks all have the same dD/dR slope; they reach an equilibrium where you can't take bits from one block and move it to another block and improve total quality.

Something you may notice in all the rate allocation maps is there are horizontal lines of higher rate going through the image. This is where we slice the images into chunks for parallelism of some operations that have to work per-chunk instead of per-block. The stripes of higher rate show that we could find some improvement there.

Links :

Oodle Texture at radgametools.com
Lagrange space-speed optimization - cbloom blog
Leviathan is a market trader - cbloom blog
Rate-Distortion Optimisation in Dirac
Rate-distortion optimization The ryg blog


Oodle 2.8.14 with Mac ARM64

Oodle 2.8.14 is out. The full changelog is at RAD. The highlights are :
## Release 2.8.14 - February 15, 2021

$* *enhancement* : BC7 encoding is faster ; slightly different encodings at higher speed with similar quality

$* *new* : Mac ARM64 build now provided ; Mac example exes are fat x64+arm64
$* *new* : Apple tvOS build now provided

$* *deprecation* : Mac 32 bit x86 build no longer provided
We're also now shipping plugin integrations for Unreal 4.26

Kraken decompression is wicked fast on the M1 :

Kraken, Win-x64 msvc-1916, lzc99.kraken.zl6
lzt99 : 24,700,820 ->10,013,788 =  3.243 bpb =  2.467 to 1
decode           : 16.444 millis, 2.26 c/B, rate= 1502.09 MB/s

Kraken, Mac-x64 xcode-12.0.0, lzc99.kraken.zl6
lzt99 : 24,700,820 ->10,013,788 =  3.243 bpb =  2.467 to 1
decode           : 16.183 millis, 2.10 c/B, rate= 1526.36 MB/s

Kraken, Mac-ARM64 xcode-12.0.0, lzc99.kraken.zl6
lzt99 : 24,700,820 ->10,013,788 =  3.243 bpb =  2.467 to 1
decode           : 11.967 millis, 1.55 c/B, rate= 2064.13 MB/s

Win64 run is :
AMD Ryzen 9 3950X (CPU locked at 3393 MHz, no turbo)
Zen2, 16 cores (32 hyper), TSC at 3490 MHz 

Mac runs on Macbook Mini M1 at 3205 MHz

Mac x64 is emulated on the M1
c/B = cycles per byte should be taken with some salt as we have trouble finding real clock rates, but it's clear the M1 has superior IPC (instructions per clock) to the Zen2. It seems to be about the same speed as the Zen2 in emulated x64!

It will be interesting to see what the M1 high performance variants can do.

Some more speeds cuz I like big numbers :

Macbook Mini M1 ARM64 :

Mermaid, Normal, lzt99 :
24,700,820 ->11,189,930 =  3.624 bpb =  2.207 to 1
encode (x1)      : 299.154 millis, 37.21 c/B, rate= 82.57 MB/s
decode (x30)     : 6.438 millis, 0.80 c/B, rate= 3836.60 MB/s

Mermaid, Optimal2, lzt99 :
24,700,820 ->10,381,175 =  3.362 bpb =  2.379 to 1
encode (x1)      : 3.292 seconds, 409.43 c/B, rate= 7.50 MB/s
decode (x30)     : 7.134 millis, 0.89 c/B, rate= 3462.57 MB/s

Selkie, Normal, lzt99 :
24,700,820 ->13,258,742 =  4.294 bpb =  1.863 to 1
encode (x1)      : 213.197 millis, 26.51 c/B, rate= 115.86 MB/s
decode (x30)     : 3.126 millis, 0.39 c/B, rate= 7901.52 MB/s

Selkie, Optimal2, lzt99 :
24,700,820 ->12,712,659 =  4.117 bpb =  1.943 to 1
encode (x1)      : 1.861 seconds, 231.49 c/B, rate= 13.27 MB/s
decode (x30)     : 3.102 millis, 0.39 c/B, rate= 7962.55 MB/s



AVIF is an image format derived from I-frames of AV1 video (similar to HEIC/HEIF from H265/HEVC). See also my 2014 Test of BPG , which is an H265 I-frame image format.

Here are some links I've found on AVIF :

AVIF image format supported by Cloudflare Image Resizing
GitHub - AOMediaCodeclibavif libavif - Library for encoding and decoding .avif files
GitHub - googlebrunsli Practical JPEG Repacker
Releases · kornelskicavif-rs · GitHub
GitHub - link-ucavif avif encoder, using libaom directly.
GitHub - xiphrav1e The fastest and safest AV1 encoder.
AVIF for Next-Generation Image Coding by Netflix Technology Blog Netflix TechBlog
Submissions from xiph.org Hacker News
Image formats for the web HEIC and AVIF – The Publishing Project
Comparing AVIF vs WebP file sizes at the same DSSIM
AV1 Codec
AVIF images color losschange AV1

Unfortunately I have not found a standard encoder with recommended settings. There appears to be zero guidance on settings anywhere. Because of that I am using the simplest encoder I could find, Kornelski's "cavif" which has a simple --quality parameter. I run thusly :

cavif --quality=X -o out.avif in.png
avifdef out.avif dec.png
imdiff in.png dec.png 
CALL FOR HELP : if you know better programs/settings for encoding AVIF, please let me know ; in avifenc , what is the min max Q parameter? adaptive quantization appears to be off by default, don't we want that on?

I measure results using my imdiff

I will compare AVIF to what I call "JPEG++" which is JPEG with the packjpg/Lepton back end, and a deblocking decoder (my "jpegdec"). This a rough stand-in for what I think a real JPEG++ should be (it should really have an R-D front-end and chroma-from-luma as well; that's all very easy and unequivocably good).

With no further ado, some results :

(imdiff "fit" is a quality in 0-10 , higher is better)

porsche640.bmp :

PDI_1200 :

Results are a bit disappointing. AVIF is much beter on RMSE but slightly worse on my other two scores. Overall that means it's most likely better overall, but it's not a huge margin.

(I'm sure AVIF is a big win on graphic/text images where JPEG does poorly)

AVIF results here look worse than what I saw from BPG (HEIC). Perhaps better encoders/settings will fix that.

Looking at the results visually, AVIF preserves sharp lines much better, but is completely throwing away detail in some places. There are some places where I see AVIF actually *change* the image, whereas JPEG is always just making the same image but slightly worse.

7z of encoded images to compare (2 MB)

NOTE : the fact that AVIF wins strongly in RGB RMSE but not in my other perceptual metrics indicates that is is not optimizing for those metrics. Perhaps in other perceptual metrics it would show a strong win. The metrics I use here from imdiff were chosen because I found them to be the best fit to human quality scores. Lots of the standard scores that people use (like naive SSIM) I have found to be utter junk, with no better correlation to human quality than RMSE. MS-SSIM-IW is the best variant of SSIM I know, but I haven't tested some of the newer metrics that have come out in the last few years.


Some JPEG Tools

A couple of tips and tools for working with JPEG files. I use :


Of course you can use exiftool and jpegtran but these are rather simpler.

1. Strip all personal data before uploading images to the web.

JPEG EXIF headers contain things like date shot and location. If you don't want Google to scrape that and use it to track your movements and send drones to follow you carrying advertisements, you might want to strip all that private data before you upload images to the net. I use :

jhead -purejpg %*
jhead -mkexif %*
jhead -dsft %*
with the very handy jhead tool. This removes all non-image headers, then makes a blank exif, then sets the exif time from the mod time. The last two steps are optional, if you want to preserve the shot time (assuming the mod time of the file was equal to the exif time). Note if the times are not equal you can use "jhead -ft" to set modtime from exif time before this.

Also note that if you use tools to modify images (resizing, changing exposure, what have you), they may or may not carry through the old exif data; whether that's good or bad is up to you, but it's very inconsistent. They also will probably set the modtime to now, whereas I prefer to keep the modtime = shot time so that I can find files by date more easily.

2. Remove orientation tags

iPhones are the only device I know of that consistently make use of the JPEG orientation tags rather than actually rotate the pixels. Unfortunately lots of loaders don't support these tags right, so if you load the image in a non-compliant loader it will appear sideways or upside down.

(this is a classic problem with data formats that have too many features; inevitabily many implementers only support a subset of the features which they deem to be the necessary ones; then some bone-head says "oh look the format has this weird feature, let's use it", and they output data which most loaders won't load right (then they blame the loaders). This is a mistake of the people defining the format; don't include unnecessary features, and make the practical subset a well-defined subset, not something that forms ad-hoc from use.)

To fix this, you want to read the orientation tag, rotate the pixels, then blank out the orientation tag (you have to do the last step or compliant loaders will doubly rotate). I used to have scripts to do all that with jpegtran, but it's super easy to do with jhead, you just :

jhead -autorot %*

3. Lossless crop

Avoid loading a JPEG, modifying it, and saving it out again. It destroys the image by re-applying the lossy quantization. I think by far the most common modification people do is cropping and there's no damn reason to re-encode for a crop. You can crop at 8x8 granularity losslessly, and you should. (all the web image uploaders that give you a crop tool need to do this, please, stop sucking so bad).

jpegcrop is a GUI tool that provides a decent lossless crop.

FreeVimager is okay too. Lossless crop is hidden in "JPEG Advanced".

We've got JPEG-XL coming soon, which looks great, but all the tech in the world won't help if people like Instagram & Youtube keep re-encoding uploads, and re-encoding every time you modify.


Oodle 2.8.13 Release

Oodle 2.8.13 fixes an issue in Oodle Texture with consistency of encodings across machine architectures.

We try to ensure that Oodle Texture creates the same encodings regardless of the machine you run on. So for example if you run on machines that have AVX2 or not, our optional AVX2 routines won't change the results, so you get binary identical encodings.

We had a mistake that was causing some BC1 RDO encodings to be different on AMD and Intel chips. This is now fixed.

The fixed encoding (for BC1 RDO) made by 2.8.13 can be different than either of the previous (AMD or Intel) encodings. I want to use this announcement as an opportunity to repeat I point I am trying to push :

Do not use the binary output of encodings to decide what content needs to be patched!

This is widespread practice in games and it is really a bad idea. The problem is that any changes to the encoders you use (either Oodle Texture, your compressor, or other), can cause you to patch all your content unnecessarily. We do NOT gaurantee that different versions of Oodle Texture produce the same output, and in fact we can specifically promise they won't (always produce the same encodings) because we will continue to improve the encoder and find better encodings over time. Aside from version changes causing binary diffs, you might want to change settings, quality or speed levels, etc. and that shouldn't force a full patch down to customers.

The alternative to using binary output to make patches is to check if the pre-encoding content has changed, and don't patch if that is the same. I know there are difficult issues with that, often for textures you do something like load a bitmap, apply various transforms, then do the BCN encoding, and there's not a snapshot taken of the fully processed texture right before the BCN encoding.

If you are shipping a game with a short lifespan, your intention is to only ship it and only patch for bugs, then patching based on binary compiled content diffs is probably fine. But if you are shipping a game that you intend to have a long lifetime, with various generations of DLC, or a long term online player base, then you seriously need to consider patching based on pre-compression content diffs. It is very likely you will at some point in the life time of the game have to face OS version changes, compiler changes, or perhaps bugs in the encoder which force you to get on a newer version of the compression tools. You don't want to be in a situation where that's impossible because it would generate big patches.

One elegant way to solve this, and also speed up your content cooking, is to implement a cooked content cache.

Take the source bitmap, and all the texture cooking & encoding options, and use those as a key to look up pre-cooked content from a network share or similar. If found, don't re-encode.

Every time you export a level, you don't want to have to re-encode all the textures with Oodle Texture. With huge art teams, when someone edits a texture, everyone else on the team can just fetch from the cook cache rather than encode it locally.

The same kind of system can be used to avoid unnecessary patches. If you then populate your cook-cache with the content from the last shipped version, you won't make new encodings unless the source art or options change, even if the encoder algorithm changes.

For the lossless package compressor, ideally the patch generator would be able to decode the compression and wouldn't generate patches if only the compressed version changed.

To be clear, I'm assuming here that you are compressing assets individually, or even in smaller sub-asset chunks, or some kind of paging unit. I'm assuming you are NOT compressing whole packages as single compression units; if you did that any a single byte changing in any asset could change the entire compressed unit, that's a bad idea for patching.

(note that encryption also has the same property of taking a single byte change and spreading it around the chunk, so encryption should usually be done on the same or smaller chunk than the compression)

With most existing patchers that are not compression-aware, if you change the compressor (for example by changing the encode level option, or updating to a newer version), the compressed bytes will change and generate large patches. What they should ideally do is see that while the compressed bytes changed, the decompressed bytes are the same, so no patch is needed, and the old version of the compressed bytes can be retained. This would allow you to deploy new compressors and have them used for all new content and gradually roll out, without generating unnecessary large patches.


How Oodle Kraken and Oodle Texture supercharge the IO system of the Sony PS5

The Sony PS5 will have the fastest data loading ever available in a mass market consumer device, and we think it may be even better than you have previously heard. What makes that possible is a fast SSD, an excellent IO stack that is fully independent of the CPU, and the Kraken hardware decoder. Kraken compression acts as a multiplier for the IO speed and disk capacity, storing more games and loading faster in proportion to the compression ratio.

Sony has previously published that the SSD is capable of 5.5 GB/s and expected decompressed bandwidth around 8-9 GB/s, based on measurements of average compression ratios of games around 1.5 to 1. While Kraken is an excellent generic compressor, it struggled to find usable patterns on a crucial type of content : GPU textures, which make up a large fraction of game content. Since then we've made huge progress on improving the compression ratio of GPU textures, with Oodle Texture which encodes them such that subsequent Kraken compression can find patterns it can exploit. The result is that we expect the average compression ratio of games to be much better in the future, closer to 2 to 1.

Oodle Kraken is the lossless data compression we invented at RAD Game Tools, which gets very high compression ratios and is also very fast to decode. Kraken is uniquely well suited to compress game content and keep up with the speed requirements of the fast SSD without ever being the bottleneck. We originally developed Oodle Kraken as software for modern CPUs. In Kraken our goal was to reformulate traditional dictionary compression to maximize instruction level parallelism in the CPU with lots independent work running at all times, and a minimum of serial dependencies and branches. Adapting it for hardware was a new challenge, but it turned out that the design decisions we had made to make Kraken great on modern CPUs were also exactly what was needed to be good in hardware.

The Kraken decoder acts as an effective speed multiplier for data loading. Data is stored compressed on the SSD and decoded transparently at load time on PS5. What the game sees is the rate that it receives decompressed data, which is equal to the SSD speed multiplied by the compression ratio.

Good data compression also improves game download times, and lets you store more games on disk. Again the compression ratio acts as an effective multiplier for download speed and disk capacity. A game might use 80 GB uncompressed, but with 2 to 1 compression it only take 40 GB on disk, letting you store twice as many games. A smaller disk with better compression can hold more games than a larger disk with worse compression.

When a game needs data on PS5, it makes a request to the IO system, which loads compressed data from the SSD; that is then handed to the hardware Kraken decoder, which outputs the decompressed data the game wanted to the RAM. As far the game is concerned, they just get their decompressed data, but with higher throughput. On other platforms, Kraken can be run in software, getting the same compression gains but using CPU time to decode. When using software Kraken, you would first load the compressed data, then when that IO completes perform decompression on the CPU.

If the compression ratio was exactly 1.5 to 1, the 5.5 GB/s peak bandwidth of the SSD would decompress to 8.25 GB/s uncompressed bytes output from the Kraken decoder. Sony has estimated an average compression ratio of between 1.45 to 1 and 1.64 to 1 for games without Oodle Texture, resulting in expected decompressed bandwidth of 8-9 GB/s.

Since then, Sony has licensed our new technology Oodle Texture for all games on the PS4 and PS5. Oodle Texture lets games encode their textures so that they are drastically more compressible by Kraken, but with high visual quality . Textures often make up the majority of content of large games and prior to Oodle Texture were difficult to compress for general purpose compressors like Kraken.

The combination of Oodle Texture and Kraken can give very large gains in compression ratio. For example on a texture set from a recent game :

Zip 1.64 to 1
Kraken 1.82 to 1
Zip + Oodle Texture 2.69 to 1
Kraken + Oodle Texture 3.16 to 1

Kraken plus Oodle Texture gets nearly double the compression of Zip alone on this texture set.

Oodle Texture is a software library that game developers use at content creation time to compile their source art into GPU-ready BC1-7 formats. All games use GPU texture encoders, but previous encoders did not optimize the compiled textures for compression like Oodle Texture does. Not all games at launch of PS5 will be using Oodle Texture as it's a very new technology, but we expect it to be in the majority of PS5 games in the future. Because of this we expect the average compression ratio and therefore the effective IO speed to be even better than previously estimated.

How does Kraken do it?

The most common alternative to Kraken would be the well known Zip compressor (aka "zlib" or "deflate"). Zip hardware decoders are readily available, but Kraken has special advantages over Zip for this application. Kraken gets more compression than Zip because it's able to model patterns and redundancy in the data that Zip can't. Kraken is also inherently faster to decode than Zip, which in hardware translates to more bytes processed per cycle.

Kraken is a reinvention of dictionary compression for the modern world. Traditional compressors like Zip were built around the requirement of streaming with low delay. In the past it was important for compressors to be able to process a few bytes of input and immediately output a few bytes, so that encoding and decoding could be done incrementally. This was needed due to very small RAM budgets and very slow communication channels, and typical data sizes were far smaller than they are now. When loading from HDD or SSD, we always load data in chunks, so decompressing in smaller increments is not needed. Kraken is fundamentally built around decoding whole chunks, and by changing that requirement Kraken is able to work in different ways that are much more efficient for hardware.

All dictionary compressors send commands to the decoder to reproduce the uncompressed bytes. These are either a "match" to a previous substring of a specified length at an "offset" from the current output pointer in the uncompressed stream, or a "literal" for a raw byte that was not matched.

Old fashioned compressors like Zip parsed the compressed bit stream serially, acting on each bit in different ways, which requires lots of branches in the decoder - does this bit tell you it's a match or a literal, how many bits of offset should I fetch, etc. This is also creates an inherent data dependency, where decoding each token depends on the last, because you have to know where the previous token ends to find the next one. This means the CPU has to wait for each step of the decoder before it begins the next step. Kraken can pre-decode all the tokens it needs to form the output, then fetch them all at once and do one branchless select to form output bytes.

Kraken creates optimized streams for the decoder

One of the special things about Kraken is that the encoded bit stream format is modular. Different features of the encoder can be turned on and off, such as entropy coding modes for the different components, data transforms, and string match modes. Crucially the Kraken encoder can choose these modes without re-encoding the entire stream, so it can optimize the way the encoder works for each chunk of data it sees. Orthogonality of bit stream options is a game changer; it means we can try N boolean options in only O(N) time by measuring the benefit of each option independently. If you had to re-encode for each set of options (as in traditional monolithic compressors), it would take O(2^N) time to find the best settings.

The various bit stream options do well on different types of data, and they have different performance trade offs in terms of decoder speed vs compression ratio. On the Sony PS5 we use this to make encoded bit streams that can be consumed at the peak SSD bandwidth so that the Kraken decoder is never the bottleneck. As long as the Kraken decoder is running faster than 5.5 GB/s input, we can turn on slower modes that get more compression. This lets us tune the stream to make maximum use of the time budget, to maximize the compression ratio under the constraint of always reading compressed bits from the SSD at full speed. Without this ability to tune the stream you would have very variable decode speed, so you would have to way over-provision the decoder to ensure it was never the bottleneck, and it would often be wasting computational capacity.

There are a huge number of possible compressed streams that will all decode to the same uncompressed bytes. We think of the Kraken decoder as a virtual machine that executes instructions to make output bytes, and the compressed streams are programs for that virtual machine. The Kraken encoder is then like an optimizing compiler that tries to find the best possible program to run on that virtual machine (the decoder). Previous compressors only tried to minimize the size of the compressed stream without considering how choices affect decode time. When we're encoding for a software decoder, the Kraken encoder targets a blend of decode time and size. When encoding for the PS5 hardware decoder, we look for the smallest stream that meets the speed requirement.

We designed Kraken to inherently have less variable performance than traditional dictionary compressors like Zip. All dictionary compressors work by copying matches to frequently occurring substrings; therefore they have a fast mode of decompression when they are getting lots of long string matches, they can output many bytes per step of the decoder. Prior compressors like Zip fall into a much slower mode on hard to compress data with few matches, where only one byte at a time is being output per step, and another slow mode when they have to switch back and forth between literals and short matches. In Kraken we rearrange the decoder so that more work needs to be done to output long matches, since that's already a super fast path, and we make sure the worst case is faster. Data with short matches or no matches or frequent switches between the two can still be decoded in one step to output at least three bytes per step. This ensures that our performance is much more stable, which means the clock rate of the hardware Kraken decoder doesn't have to be as high to meet the minimum speed required.

Kraken plus Oodle Texture can double previous compression ratios

Kraken is a powerful generic compressor that can find good compression on data with repeated patterns or structure. Some types of data are scrambled in such a way that the compressability is hard for Kraken to find unless that data is prepared in the right way to put it in a usable form. An important case of this for games is in GPU textures.

Oodle Kraken offers even bigger advantages for games when combined with Oodle Texture. Often the majority of game content is in BC1-BC7 textures. BC1-7 textures are a lossy format for GPU that encodes 4x4 blocks of pixels into 8 or 16 byte blocks. Oodle Kraken is designed to model patterns in this kind of granularity, but with previous BC1-BC7 texture encoders, there simply wasn't any pattern there to find, they were nearly incompressible with both Zip and Kraken. Oodle Texture creates BC1-7 textures in a way that has patterns in the data that Kraken can find to improve compression, but that are not visible to the human eye. Kraken can see that certain structures in the data repeat, the lengths of matches and offsets and space between matches, and code them in fewer bits. This is done without expensive operations like context coding or arithmetic coding.

It's been a real pleasure working with Sony on the hardware implementation of Kraken for PS5. It has long been our mission at RAD to develop the best possible compression for games, so we're happy to see publishers and platforms taking data loading and sizes seriously.


Topics in Quantization for Games

I want to address some topics in quantization, with some specifics for games.

We do "quantization" any time we take a high precision value (a floating point, or higher-bit integer) and store it in a smaller value. The quantized value has less precision. Dequantization takes you back to the space of the input and should be done to minimize the desired error function.

I want to encourage you to think of quantization like this :

quantization takes some interval or "bucket" and assigns it to a label

dequantization restores a given label to a certain restoration point

"quantization" does not necessarily take you to a linear numeric space with fewer bits

The total expected error might be what we want to minimize :

Total_Error = Sum_x P(x) * Error( x,  dequantization( quantization(x) ) )
Note that in general the input values x do not have uniform probability, and the Error is not just linear L1 or L2 error, you might care about some other type of error. (you might also care more about minimizing the maximum rather than the average error).

I like to think of the quantized space as "labels" because it may not be just a linear numerical space where you can do distance metrics - you always dequantize back to your original value space before you do math on the quantization labels.

I started thinking about this because of my recent posts on Widespread error in RGBE and Alternative quantizers for RGBE, and I've been looking in various game-related code bases and found lots of mistakes in quantization code. These are really quite big errors compared to what we work very hard to reduce. I've found this kind of thing before outside of games too. For example it's very common for the YUV conversions in video and image codecs to be quite crap, giving up lots of error for no good reason. Common errors I have seem in the YUV conversions are : using the terribad 16-235 range, using the rec601/bt709 matrix so that you encode with one and decode with the other, using terribad down and/or up filters for the chroma downsample). It's frustrating when the actual H264 layer works very hard to minimize error, but then the YUV-RGB layer outside it adds some that could be easily avoided.

We do quantization all the time. A common case is for 8-bit RGB colors to float colors, and vice versa. We do it over and over when we do rendering passes; every time you write values out to a render target and read them back, you are quantizing and dequantizing. It is important to take care to make sure that those quantization errors are not magnified by later passes. For example when writing something like normals or lighting information, a quantization error of 1/256 can become much larger in the next stage of rendering.

(a common example of that is dot products or cosines; if you have two vectors and store something that acts like a dot product between them (or a cosine of an angle), the quantization bucket around 1.0 for the two vectors being parallel corresponds to a huge amount of angular variation, and this often right where you care most about having good precision, it's much better to store something that's like the acos of the dot product)

If you aren't going to do the analysis about how quantization errors propagate through your pipeline, then the easiest thing to do is to only quantize once, at the very end, and keep as much precision through the stages as possible. If you do something like a video codec, or an image processing pipeline, and try to work in limited precision (even 16 bit), it is important to recognize that each stage is an implicit quantization and to look at how those errors propagate through the stages.

(aside: I will mention just briefly that we commonly talk about a "float" as being the "unquantized" result of dequantization; of course that's not quite right. A "float" is a quantized representation of a real number, it just has variable size quantization bins, smaller bins for smaller numbers, but it's still quantized with steps of 1 ulp (unit in last place). More correctly, going to float is not dequantization, but rather requantization to a higher precision quantizer. The analysis of propagating through quantization error to work in 8 bits or whatever is the same you should do for how float error propagates through a series of operations. That said I will henceforth be sloppy and mostly talk about floats as "dequantized" and assume that 1 ulp is much smaller than precision that we care about.)

So lets go back and start at the beginning :

Linear uniform scalar quantization

If our input values x are all equally probable ( P(x) is a constant ), and the error metric we care about is linear L1 or L2 norm, then the optimal quantizer is just equal size buckets with restoration to center of bucket.

(for L1 norm the total error is actually the same for any restoration point in the bucket; for L2 norm total error is minimized at center of bucket; for L1 norm the maximum error is minimized at center of bucket)

We'll now specifically look at the case of an input value in [0,1) and quantizing to N buckets. The primary options are :

int quantize_floor( float x , int N )
    return (int)( x * N );
    // or floor( x * N );
    // output is in [0, N-1] , input x in [0,1) not including 1.0

float dequantize_floor( int q, int N )
    return (q + 0.5f ) * (1.f / N);

int quantize_centered( float x, int N )
    return (int)( x * (N-1) + 0.5f );
    // or round( x * (N-1) )
    // output is in [0, N-1] , input x in [0,1] , including 1.0 is okay

float dequantize_centered( int q, int N )
    return q * (1.f / (N-1));

The rule of thumb for these quantizers is you either bias by 0.5 in the quantizer, or in the dequantizer. You must bias on one side or the other, not both and not neither! The "floor" quantizer is "bias on dequant", while the "centered" quantizer is "bias on quant".

Visually they look like this, for the case of N = 4 :

(the top is "floor" quantization, the bottom is "centered")

(the top is "floor" quantization, the bottom is "centered")

In both cases we have 4 buckets and 4 restoration points. In the "floor" case the terminal bucket boundaries correspond to the boundaries of the [0,1) input interval. In the "centered" case, the terminal buckets are centered on the [0,1) endpoint, which means the bucket boundaries actually go past the end, but they restore exactly to the endpoints.

If your input values are actually all equally likely and the error metric that you care about is just L2 norm, then "floor" quantization is strictly better. You can see that the bucket size for "floor" quantization is 1/4 vs. 1/3 for "centered", which means the maximum error after dequantization is 1/8 vs. 1/6.

In practice we often care more about the endpoints or the integers, not just average or maximum error; we suspect the probability P(x) for x = 0 and 1 is higher, and the error metric Error( dequantization( quantization(x) ) - x ) may also be non-linear, giving higher weight to the error when x = 0 and 1.

"centered" quantization also has the property of preserving integers. For example say your input range was [0,255) in floats. If you quantize to N=256 buckets with "centered" quantization, it will restore exactly to the integers.

Games should only be using centered quantization!

While in theory there are cases where you might want to use either type of quantization, if you are in games don't do that!

The reason is that the GPU standard for UNORM colors has chosen "centered" quantization, so you should do that too. Certainly you need to do that for anything that interacts with the GPU and textures, but I encourage you to just do it for all your quantization, because it leads to confusion and bugs if you have multiple different conventions of quantizer in your code base.

The GPU UNORM convention is :

float dequantize_U8_UNORM( unsigned char u8 )
  return u8 * (1.f/255);
which implies centered quantization, so please use centered quantization everywhere in games. That means : bias 0.5 on quantize, no bias on dequantize.

While on the topic of UNORM, let's look at conversion between quantized spaces with different precision. Let's do U8 UNORM to U16 UNORM for example.

The way to get that right is to think about it as dequantization followed by quantization. We dequantize the U8 UNORM back to real numbers, then quantize real numbers back to U16 :

dequant = u8 * (1.f/255);

u16 = round( dequant * 65535 );

u16 = round( u8 * (1.f/255) * 65535 );

u16 = round( u8 * 257 );

u16 = u8 * 257;

u16 = u8 * (256 + 1);

u16 = (u8<<8) + u8;

So U8 to U16 re-quantization for UNORM is : take the U8 value, and replicate it shifted up by 8.
requantize U8 UNORM to U16 UNORM :

0xAB -> 0xABAB

This obviously has the necessary property that 00 stays zero, and 0xFF becomes 0xFFFF, so 1.0 is preserved.

This is something we call "bit replication". Let's take a moment to see why it works exactly in some cases and only approximately in others.

Bit Replication for re-quantization to higher bit counts

Bit replication is often used in games to change the bit count of a quantized value (to "requantize" it).

For example it's used to take 5-bit colors in BC1 to 8-bit :

The top 3 bits of the 5-bit value are replicated to the bottom :

abcde -> abcde|abc

giving an 8 bit value

Bit replication clearly gets the boundary cases right : all 0 bits to all 0's (dequantizes to 0.0), and all 1 bits to all 1 bits (dequantizes to 1.0); in between bit replication linearly increases the low bits between those endpoints, so it's obviously sort of what you want. In some cases bit replication corresponds exactly to requantization, but not in others.

With a B-bit UNORM value, it has N = 2^B values. The important thing for quantization is the denominator (N-1). For example with a 5-bit value, (N-1) = 31 is the denominator. It becomes clear if we think about requantization as changing the *denominator* of a fraction.

Requantization from 5 bits to 10 bits is changing the denominator from 31 to 1023 :

dequant( 5b ) = 5b / 31.0;
requant_10( x ) = round( x * 1023.0 );

requant_5_to_10 = round( x * 1023 / 31 );

1023/31 = 33 exactly, so :

requant_5_to_10 = x * 33

in integers.  And 33 = (32 + 1) = shift up 5 and replicate

requantization from 5 to 10 bits is just duplicating the bits shifted up
abcde -> abcde|abcde

What that means is bit replication from B to 2B is exactly equal to what you would get if you dequantized that number to UNORM and requantized it again.

This is of course general for any B :

denominator for B is (N-1)
denominator for 2B is (N^2 - 1)

requantiztion is *= (N^2 - 1) / (N-1)

(N^2 - 1) = (N-1) * (N+1)


requantization is *= (N+1)

which is bit replication

Now more generally for bit replication to some number of bits that's not just double (but <= double, eg. between B and 2B) :

b between B and 2B
n = 2^b

requant_B_to_b(x) = round( x * (n-1) / (N-1) )

requant_B_to_b(x) = round( x * (N+1) * (n-1) / (N^2-1) )

requant_B_to_b(x) = round( (x bit replicated to 2B) * ( scale down ) )

bit replication from B to b is :

bitrep(x) = (x bit replicated to 2B) >> (2B - b)

that is, just replicate to 2B and then truncate low bits to get to b

when b = 2B , these are exactly equal as we showed above

obviously also at b = B (NOP)
and also at b = B+1 (adding one bit)

in the range b = [B+2, 2B-1] they are not quite exactly equal, but close

Let's look at an example, 5 bits -> 8 bits :

bitdouble( 5b ) = (5b * 33)

requant_5_to_8(5b) = round( (5b * 33) * ( 255.0 / 1023.0 ) )

bitrep_5_to_8(5b) = (5b * 33) >> 2

we can see where the small difference comes from :

bit replication just truncates off the 2 bottom bits

requantization does * (255/1023) , which is almost a /4 (like >>2) but not quite
and the requantization also rounds instead of truncating

so we should see how bit replication is similar to centered UNORM requantization, but not quite the same.

Now, bit replication is used in BC7, ASTC, etc. Is it a source of error? No, not if you do your encoder right. What it does mean is that you can't just find the 5-bit color value by doing a centered quantizer to 5 bits. Instead you have to ask what does the 5-bit value bit-replicate to, and find the closest value to your input.

Quantizing infinite signed values and the deadzone quantizer

So far we've talked about quantizing finite ranges, specifically [0,1) but you can map any other finite range to that interval. Let's have a brief look at quantizing infinite ranges.

If you just quantize a signed number to a signed quantized number, then you can use the above _floor or _centered quantizers without thinking any more about it. You will have uniform buckets across the whole number line. But what we often want to do is take a signed input number and quantize it to *unsigned* and separate out the sign bit, to create a sign+magnitude representation. (this makes the most sense with values whose probability P(x) is symmetric about zero and whose mean is at zero; eg. after a transform that subtracts off the mean)

One reason we might want to do that is because most of our schemes for sending unbounded (variable length) numbers work on unsigned numbers. For example : Encode Mod and Exp Golomb .

Now one option would be to quantize to signed ints and then Fold up Negatives to make an unsigned number to feed to your variable length scheme.

There are reasons we don't like that in data compression. Folded up negatives have a number line like : {0, -1, 1, -2, 2, -3 ... }

The annoying thing about that for data compression is that if you have a probability model like a Laplacian that decreases with absolutely value of x, the probabilities have these steps where values are repeated : { P(0), P(1), P(1), P(2), P(2), ... } and coding them with something like exp-golomb is no longer quite correct as they don't progressively fall off. Some codecs in the past have used tricks to reduce this (eg. JPEG-LS and CALIC) by doing things like being able to flip the sign so that you get either {0, -1, 1, -2, ... } or {0, 1, -1, 2, ... } depending on whether positive or negative is more probable.

Rather than do all that, let's assume you want to extract the sign bit and send it separately. So you are sending only the magnitude.

So we have taken the sign out and now only have a one sided interval [0, inf) to quantize. You can take that one-sided interval and just apply floor or centered quantization to it :

unsigned half_line_quantize( float x )
    ASSERT( x >= 0.f );
    //return floor( x ); // floor quantizer
    //return round( x ); // centered quantizer
    float bias = 0.f for floor and 0.5 for centered;
    return (unsigned) ( x + bias );

but something a bit funny has happened.

Floor and centered quantization now just act to shift where the boundary of the 0 bin is. But the 0 bin now occurs on both sides of the half interval, so to make the 0 bin the same size as the other bins, it should have a boundary at 0.5 (half the size of the other bins on the half interval). (I'm assuming here that your quantization bucket size is 1.0 ; for general sized quantization buckets just scale x before it gets here).

It's clear that the zero bin is a bit special, so we usually just go ahead and special case it :

pseduocode signed_line_quantizer( float x )
    // x signed

    float ax = fabsf(x);

    if ( ax < deadzone )
        // special bucket for zero :
        // don't send sign bit
        return 0;
        // do send sign bit of x
        // do floor quantizer above the zero bucket :
        return floor(ax - deadzone);

Now if you want the zero bucket to have the same size as all others, you would set deadzone = 0.5 (it's half the zero bucket size on the full line). If you want to use a uniform floor quantizer on the half line, that would correspond to deadzone = 1.0 (making the zero bucket actually twice the size of others after mirroring to the negative half of the line).

What's been found in data compression is that a "deadzone" larger than equal size buckets (larger than 0.5) is beneficial. There are two primary reasons :

We use codecs where coding zeros is especially cheap, so sending more zeros is very desirable. So larger deadzone in the quantizer will give you more zeros, hence cheaper coding, and this is a greater benefit than the loss in quality. This is sort of a hacky way of doing some rate-distortion optimization, like trellis quantization but without any work.

The other reason is perceptual modeling; many human perception systems (eyes and ears) are less sensitive to the initial onset of a signal than they are to variations once the signal is present. Signals near zero are not detected by humans at all until they reach some threshold, and then once they pass the threshold there's a finer discrimination of level. For example the human ear might not detect a harmonic until it is 10 dB, but then distinguish volume levels at 1 dB changes after that.

Essentially your quantizer has two parameters, the bucket size for zero, and then the bucket size for values above zero. This is a very simple form of a more general variable quantizer.

In theory you would like to have variable size bins, such that each bin corresponds to an equal amount of perceptual importance (eg. larger bins where the values are less important). For the most part we now do that by applying a nonlinear transformation to the value before it reaches the uniform quantizer, rather than trying to do variable size bins. For example you might take log(x) before quantizing if you think precision of high values is less important. Another common example is the "gamma corrected" color space (or sRGB) for images; that's a non-linear transform applied to the signal (roughly pow 2.2) to map it to a space that's more perceptually uniform so that the quantization buckets give more precision where it's needed.

Something to watch out for is that a lot of code uses a deadzone quantizer without being clear about it. If you see something like :

int half_line_quantizer_thats_actually_a_deadzone( float x )
  ASSERT( x >= 0.f );
  return (int) x;
That's actually a deadzone quantizer with a 2x sized bin zero, if it's being used after sign removal.

In the olden days, variable-size quantization buckets were used as a kind of entropy coder. They would have smaller buckets in higher probability regions and larger buckets in lower probability regions, so that the quantized output value had equal probability for all bins. Then you could send the quantized value with no entropy coding. This is now almost never done, it's better to use quantization purely for error metric optimization and use a separate entropy coder on the output.

Topics in dequantization

Just briefly some topics in dequantization.

For values that are all equally likely, under an L2 (SSD/RMSE) error norm, dequantization to the center of the bucket is optimal. More generally the restoration point for each bucket should minimize the error metric weighted by the probability of that input value.

An easy case is with an L2 error metric but a non-uniform probability. Then the error in a given bucket for a restoration point is :

L2 error of restoring to r in this bucket :

E = Sum_x P(x) * ( r - x )^2

( Sum_x for x's in this bucket )

find r that minimizes E by taking d/dr and setting to zero :

d/dr E = 0

d/dr E = Sum_x P(x) * ( r - x ) * 2

Sum_x P(x) * ( r - x ) = 0

Sum_x P(x) * r = Sum_x P(x) * x

r = ( Sum_x P(x) * x ) / ( Sum_x P(x) )

that's just the expectation value of x in the bucket

we should restore to the average expected 'x' value in the bucket.

A common case of that is for a skewed probability distribution - something like Laplacian or Poisson with a falloff of probabilities away from the peak - we should restore each bucket to a value that's skewed slightly towards the peak, rather than restoring the center.

Now if you have a mathematical model of P(x) then you could compute where these centers should be, and perhaps store them in a table.

What's often better in practice is just to measure them experimentally. Do trial runs and record all the values that fall into each quantization bucket and take their mean - that's your restoration point.

Then you could store those measured restoration points in constants in your code, OR you could measure them and store them per-data item. (for example an image compressor could transmit them per image - maybe not all but a few of the most important ones).

Another thing you can do in dequantization is to not always restore to the same point. I noted briefly previously that if what you care about is L1 norm, then any restoration point in the bucket has the same error. Rather than just pick one, you could restore to any random point in the bucket and that would give the same expected L1 norm.

L2 norm strongly prefers the mean (minimizing L2 is blurring or smoothing, while L1 allows lots of noise), but perceptually it may be better to add some randomness. You could restore to mean in the bucket plus a small amplitude of noise around there. Again this noise could be global constant, or could be sent per-image, or per-band; it could also be predicted from local context so you could have more or less noisy areas.

Note that adding noise in dequantization is not the same as just adding noise arbitrarily after the fact. The values are still within the quantization bucket, so they could have been the true source values. That is, we can reframe dequantization as trying to guess the source given the quantized version :

Encoder had original image I

made Q = quant( I )

Q was transmitted

rather than just run I' = dequant( Q )

we instead pose it as :

we want to find I'
such that
Q = quant( I' )
and I' has the maximum probability of being the original I
or I' has the most perceptual similarity to our guess of I

The key thing here is that noise within the quantization bucket keeps the constraint Q = quant(I') satisfied.

As an example I'll mention something I've done in the past for wavelet bit-plane truncation.

Wavelet coding converts an image into activity residuals at various frequency subbands. These are initially quantized with a uniform+deadzone quantizer (if a floating point wavelet transform was used). Then in many codecs they are sent progressively in bit planes, so the highest bits are sent first, then lower bits, so that you get the most important bits first. You can then truncate the stream, cutting off transmission of lower bits in the higher subbands, effectively increasing the quantizer there. This is done in JPEG2000 with the EBCOT scheme for example.

So a given wavelet residual might be sent like :

value 45

= 101101

only top 2 bits sent :


the others are cut off.

In the decoder you know which bits you got and which are missing, which is equivalent to a larger quantization bucket.

The classic option (eg. SPIHT) was just to fill the lost xx bits with zeros :

10xxxx -> 100000

This makes values that are too low and is generally very smoothing (high frequency detail just goes away)

You might think, it's a quantization bucket, we should restore to the middle, which is 0.5 which is the
next bit on :

10xxxx -> 101000 or 100111

That is much too high, it's larger than the expectation and actually looks like a sharpen filter.
The reason is that wavelet amplitudes have P(x) strongly skewed towards zero, so the mean value is
way below the middle of the bucket.

Restoring to 0.25 is a bit better :

10xxxx -> 100100

but even better is to just measure what is the mean in the image for each missing bit count; that
mean depends on how large our value was (the part that's not truncated).

Finally in addition to restoring the missing bits to mean, you could add randomness in the dequantization, either within the quantization bucket (below the bottom bit), or in the low part of the missing bits (eg. if 4 bits are missing the bottom 2 might get some randomness). You can compute the amount of randomness desired such that the decompressed image matches the high frequency energy of the original image.

And that's enough on quantization for now!


Oodle 2.8.11 with RDO for BC1_WithTransparency

Oodle Texture 2.8.11 adds support for RDO encoding of "BC1_WithTransparency" and BC2. We now support RDO encoding of all BC1-7 variants.

In Oodle, "BC1_WithTransparency" doesn't necessarily mean that the texture has any 1-bit transparency. (for background: BC1 can encoding alpha values of 0 or 255 (1.0), which binary on/off alpha; when alpha is 0 the color is always 0 or black). It means that the transparency bit is preserved. In our normal "BC1" encoder, we assume that the alpha value will not be read, so we are free to choose the encoding to maximize RGB quality.

The choice of "BC1_WithTransparency" vs "BC1" should not be made based on whether the source has alpha or not, it should be made based on whether your shader will *consume* alpha or not. So for example if you just have opaque RGB textures and you need to be able to pipe them to a shader that reads A to do alpha blending, and you are unable to manage the book-keeping to pipe constant 1.0 as a shader source for the A channel, then you must use "BC1_WithTransparency" to encoding opaque alpha in the texture.

When possible, we think it is best to use the "BC1" format which does not preserve alpha. Most people do not actually use binary transparency in BC1 (even for textures where the alpha is binary in the top mip, you typically need full alpha to make decent mips, so you should use BC7), they use BC1 for opaque textures. On opaque textures the "BC1" format that is free to change alpha can give much higher quality. You can then just map constant 1.0 as the A value source for the shader when binding a texture that is marked as opaque.

We understand that is not always practical in your pipeline, so we are trying to make "BC1_WithTransparency" work as well as possible.

Our RDO for "BC1_WithTransparency" will never change the binary alpha state of a pixel. Because of this the RMSE is actually only RGB, the A values will never differ from the original, assuming the original only had alpha values of 0 and 255 in U8.

An example of the quality of "BC1_WithTransparency" RDO on the "mysoup" image available in the Oodle Texture sample run :

otexdds bc1 mysoup1024.png r:\mysoup1024.dds --verbose
OodleTex_BC1 RMSE per texel: 7.0511

otexdds bc1a mysoup1024.png r:\mysoup1024.dds --verbose
OodleTex_BC1_WithTransparency RMSE per texel: 7.0510

otexdds bc1 mysoup1024.png r:\mysoup1024.dds --verbose --rdo
OodleTex_BC1 RMSE per texel: 7.5995

otexdds bc1a mysoup1024.png r:\mysoup1024.dds --verbose --rdo
OodleTex_BC1_WithTransparency RMSE per texel: 7.6006
On photographic images like this without a lot of opaque-black, the quality of "BC1_WithTransparency" is almost identical to "BC1".

On images that mix opaque black and other colors, the quality difference can be severe :

otexdds bc1 frymire.png r:\out.dds --verbose
OodleTex_BC1 RMSE per texel: 6.1506

otexdds bc1a frymire.png r:\out.dds --verbose
OodleTex_BC1_WithTransparency RMSE per texel: 12.1483
On "Frymire" from the Waterloo Bragzone set, the RMSE is nearly double with "BC1_WithTransparency".

We have also updated the Unreal integration for Oodle Texture to use "BC1_WithTransparency", as Unreal expects to be able to fetch opaque A from the texture on all BC1 encodings. Prior to 2.8.11 we were incorrectly using our "BC1" format in Unreal, which could change opaque black texels to transparent black.

Note that "BC1_WithTransparency" RDO's roughly the same as "BC1", so we expect compressed sizes to stay roughly the same.


Performance of various compressors on Oodle Texture RDO data

Oodle Texture RDO can be used with any lossless back-end compressor. RDO does not itself make data smaller, it makes the data more compressible for the following lossless compressor, which you use for package compression. For example it works great with the hardware compressors in the PS5 and the Xbox Series X.

I thought I'd have a look at how various options for the back end lossless compressor do on BCN texture data after Oodle Texture RDO. (Oodle 2.8.9)

127,822,976 bytes of BC1-7 sample data from a game. BC1,3,4,5, and 7. Mix of diffuse, normals, etc. The compressors here are run on the data cut into 256 KB chunks to simulate more typical game usage.

"baseline" is the non-RDO encoding to BCN by Oodle Texture. "rdo lambda 40" is a medium quality RDO run; at that level visual degradation is just starting to become easier to spot (lambda 30 and below is high quality).


by ratio:
ooLeviathan8    :  1.79:1 ,    1.4 enc MB/s , 1069.7 dec MB/s
lzma_def9       :  1.79:1 ,    8.7 enc MB/s ,   34.4 dec MB/s
ooKraken8       :  1.76:1 ,    2.2 enc MB/s , 1743.5 dec MB/s
ooMermaid8      :  1.71:1 ,    4.9 enc MB/s , 3268.7 dec MB/s
zstd22          :  1.70:1 ,    4.5 enc MB/s ,  648.7 dec MB/s
zlib9           :  1.64:1 ,   15.1 enc MB/s ,  316.3 dec MB/s
lz4hc1          :  1.55:1 ,   72.9 enc MB/s , 4657.8 dec MB/s
ooSelkie8       :  1.53:1 ,    7.4 enc MB/s , 7028.2 dec MB/s

rdo lambda=40:

by ratio:
lzma_def9       :  3.19:1 ,    7.7 enc MB/s ,   60.7 dec MB/s
ooLeviathan8    :  3.18:1 ,    1.1 enc MB/s , 1139.3 dec MB/s
ooKraken8       :  3.13:1 ,    1.7 enc MB/s , 1902.9 dec MB/s
ooMermaid8      :  3.01:1 ,    4.2 enc MB/s , 3050.6 dec MB/s
zstd22          :  2.88:1 ,    3.3 enc MB/s ,  733.9 dec MB/s
zlib9           :  2.69:1 ,   16.5 enc MB/s ,  415.3 dec MB/s
ooSelkie8       :  2.41:1 ,    6.6 enc MB/s , 6010.1 dec MB/s
lz4hc1          :  2.41:1 ,  106.6 enc MB/s , 4244.5 dec MB/s

If you compare the log-log charts before & after RDO, it's easy to see that the relative position of all the compressors is basically unchanged, they just all get more compression.

The output size from baseline divided by the output size from post-RDO is the compression improvement factor. For each compressor it is :

ooLeviathan8    : 1.7765
ooKraken8       : 1.7784
ooMermaid8      : 1.7602
ooSelkie8       : 1.5548

lzma_def9       : 1.7821
zstd22          : 1.6941
zlib9           : 1.6402
lz4hc1          : 1.5751
Leviathan, Kraken, Mermaid and LZMA all improve around 1.77 X ; ZStd and Zlib a little bit less (1.65-1.70X), LZ4 and Selkie by less (1.55X - 1.57X). Basically the stronger compressors (on this type of data) get more help from RDO and their advantage grows. ZStd is stronger than Mermaid on many types of data, but Mermaid is particularly good on BCN.

* : Caveat on ZStd & LZ4 speed here : this is a run of all compressors built with MSVC 2017 on my AMD reference machine. ZStd & LZ4 have very poor speed in their MSVC build, they do much better in a clang build. Their clang build can be around 1.5X faster; ZStd-clang is usually slightly faster to decode than Leviathan, not slower. LZ4-clang is probably similar in decode speed to Selkie. The speed numbers fo ZStd & LZ4 here should not be taken literally.

It is common that the more powerful compressors speed up (decompression) slightly on RDO data because they speed up with higher compression ratios, while the weaker compressors (LZ4 and Selkie) slow down slightly on RDO data (because they are often in the incompressible path on baseline BCN, which is a fast path).

Looking at the log-log plots some things stand out to me as different than generic data :

Leviathan, Kraken & Mermaid have a smaller gap than usual. Their compression ratio on this data is quite similar, usually there's a bigger step, but here the line connecting them in log-log space is more horizontal. This makes Mermaid more attractive because you're not losing much compression ratio for the speed gains. (for example, Mermaid + BC7Prep is much better for space & speed than Kraken alone).

ZStd is relatively poor on this type of data. Usually it has more compression than Mermaid and is closer to Kraken, here it's lagging quite far behind, and Mermaid is significantly better.

Selkie is relatively poor on this type of data. Usually Selkie beats LZ4 for compression ratio (sometimes it even beats zlib), but here it's just slightly worse than LZ4. Part of that is the 256 KB chunking is not allowing Selkie to do long-distance matches, but that's not the main issue. Mermaid looks like a much better choice than Selkie here.

Another BCN data set :

358,883,720 of BCN data. Mostly BC7 with a bit of BC6. Mix of diffuse, normals, etc. The compressors here are run on the data cut into 256 KB chunks to simulate more typical game usage.

baseline :

by ratio:
ooLeviathan8    :  1.89:1 ,    1.1 enc MB/s ,  937.0 dec MB/s
lzma_def9       :  1.88:1 ,    7.6 enc MB/s ,   35.9 dec MB/s
ooKraken8       :  1.85:1 ,    1.7 enc MB/s , 1567.5 dec MB/s
ooMermaid8      :  1.77:1 ,    4.3 enc MB/s , 3295.8 dec MB/s
zstd22          :  1.76:1 ,    3.9 enc MB/s ,  645.6 dec MB/s
zlib9           :  1.69:1 ,   11.1 enc MB/s ,  312.2 dec MB/s
lz4hc1          :  1.60:1 ,   73.3 enc MB/s , 4659.9 dec MB/s
ooSelkie8       :  1.60:1 ,    7.0 enc MB/s , 8084.8 dec MB/s

rdo lambda=40 :

by ratio:
lzma_def9       :  4.06:1 ,    7.2 enc MB/s ,   75.2 dec MB/s
ooLeviathan8    :  4.05:1 ,    0.8 enc MB/s , 1167.3 dec MB/s
ooKraken8       :  3.99:1 ,    1.3 enc MB/s , 1919.3 dec MB/s
ooMermaid8      :  3.69:1 ,    3.9 enc MB/s , 2917.8 dec MB/s
zstd22          :  3.65:1 ,    2.9 enc MB/s ,  760.0 dec MB/s
zlib9           :  3.36:1 ,   19.1 enc MB/s ,  438.9 dec MB/s
ooSelkie8       :  2.93:1 ,    6.2 enc MB/s , 4987.6 dec MB/s
lz4hc1          :  2.80:1 ,  114.8 enc MB/s , 4529.0 dec MB/s

On this data set, Mermaid lags between the stronger compressors more, and it's almost equal to ZStd. On BCN data, the strong compressors (LZMA, Leviathan, & Kraken) have less difference in compression ratio than they do on some other types of data. On this data set, Selkie pulls ahead of LZ4 after RDO, as the increased compressibility of post-RDO data helps it find some gains. Zlib, LZ4, and Selkie are almost identical compression ratios on the baseline pre-RDO data but zlib pulls ahead post-RDO.

The improvement factors are :

ooLeviathan8   :    2.154
ooKraken8      :    2.157
ooMermaid8     :    2.085
ooSelkie8      :    1.831

lzma_def9      :    2.148
zstd22         :    2.074
zlib9          :    1.988
lz4hc1         :    1.750
Similar pattern, around 2.15X for the stronger compressors, around 2.08X for the medium ones, and under 2.0 for the weaker ones.


Oodle Texture works great with all the lossless LZ coders tested here. We expect it to work well with all packaging systems.

The compression improvement factor from Oodle Texture is similar and good for all the compressors, but stronger compressors like Oodle Kraken are able to get even more benefit from the entropy reduction of Oodle Texture. Not only do they start out with more compression on baseline non-RDO data, they also improve by a larger multiplier on RDO data.

The Oodle Data lossless compressors are particularly good on BCN data, even relatively stronger than alternatives like zlib and ZStd than they are on some other data types. For example Oodle Mermaid is often slightly lower compression than ZStd on other data types, but is slightly higher compression than ZStd on BCN.

Mermaid has a substantial compression advantage over zlib on post-RDO BCN data, and decompresses 5-10X faster, making Mermaid a huge win over software zlib (zip/deflate/inflate).


Oodle 2.8.9 with Oodle Texture speed fix and UE4 integration

Oodle 2.8.9 is now shipping, with the aforementioned speed fix for large textures.

Oodle Texture RDO is always going to be slower than non-RDO encoding, it simply has to do a lot more work. It has to search many possible encodings of the block to BCN, and then it has to evaluate those possible encodings for both R & D, and it has to use more sophisicated D functions, and it has to search for possible good encodings in a non-convex search space. It simply has to be something like 5X slower than non-RDO encoding. But previously we just had a perf bug where working set got larger than cache sized that caused a performance cliff, and that shouldn't happen. If you do find any performance anomalies, such as encoding on a specific texture or with specific options causes much slower performance, please contact RAD.

timerun 287 vs 289

hero_xxx_n.png ; 4096 x 4096
timerun textest bcn bc7 r:\hero_xxx_n.png r:\out.dds -r40 --w32
got opt: rdo_lagrange_parameter=40

Oodle 2.8.7 :

encode time: ~ 8.9 s
per-pixel rmse (bc7): 0.8238
timerun: 10.881 seconds

Oodle 2.8.9 :

encode time: 4.948s
per-pixel rmse (bc7): 0.8229
timerun: 6.818 seconds
the "timerun" time includes all loading and saving and startup, which appears to be about 1.9s ; the RDO encode time has gone from about 8.9s to 4.95 s

(Oodle 2.8.7 textest bcn didn't log encode time so that's estimated; the default number of worker threads has changed, so use --w32 to make it equal for both runs)

We are now shipping a UE4 integration for Oodle Texture!

The Oodle Texture integration is currently only for Oodle Texture RDO/non-RDO BCN encoders (not BC7Prep). It should be pretty simple, once you integrate it your Editor will just do Oodle Texture encodes. The texture previews in the Editor let you see how the encodings look, and that's what you pack in the game. It uses the Unreal Derived Data Cache to avoid regenerating the encodings.

We expose our "lambda" parameter via the "LossyCompressionAmount" field which is already in the Editor GUI per texture. Our engine patches further make it so that LossyCompressionAmount inherits from LODGroup, and if not set there, it inherits from a global default. So you can set lambda at :

per texture LossyCompressionAmount

if Default then look at :

LODGroup LossyCompressionAmount

if Default then look at :

global lambda
We believe that best practice is to avoid having artists tweaking lambda a lot per-texture. We recommend leaving that at "Default" (inherit) as much as possible. The tech leads should set up the global lambda to what's right for your game, and possibly set up the LODGroups to override that for specific texture classes. Only rarely should you need to override on specific textures.


Currently our Oodle Texture for UE4 integration only works for non-console builds. (eg. Windows,Linux,Mac, host PC builds). It cannot export content for PS4/5/Xbox/Switch console builds. We will hopefully be working with Epic to fix this ASAP.

If you are a console dev, you can still try Oodle Texture for UE4, and it will work in your Editor and if you package a build for Windows, but if you do "package for PS4" it won't be used.

Sample package sizes for "InfiltratorDemo" :


No compression :                            2,536,094,378

No Oodle Data (Zlib), no Oodle Texture :    1,175,375,893

Yes Oodle Data,  no Oodle Texture :           969,205,688

No Oodle Data (Zlib), yes Oodle Texture :     948,127,728

Oodle Data + Oodle Texture lambda=40 :        759,825,164

Oodle Texture provides great size benefit even with the default Zlib compression in Unreal, but it works even better when combined with Oodle Data.

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