05-19-17 | Gorge Life

Truly one of the most magical places I've ever been in the world. Many a day I find myself thinking "what an eden, what a feliticous confluence of natural forces has made this land". Here's a few shots from the past few months.

Much of glory of this area is due to the remarkably sane preservation of its beauty by the Columbia River Gorge National Scenic Area.

Some background reading :

Columbia River Gorge balancing act : After 25 years, how are Gorge Scenic Area Act's goals of preserving the landscape and promoting economic growth in the towns it encompasses working?

Friends of the Gorge

Gorge Commission

05-13-17 | How we used Exceptions on Oddworld : Stranger's Wrath

Apparently I talked about this before in my Game Tech talk in 2004, but I never wrote it on my bloggy blog, so here goes.

On Stranger we used exceptions as a last gasp measure during dev to try to keep the game running for our content creation team. It worked great and I think everyone should use a similar system in game development.

We did not ship with exceptions. They were only used during development. To be clear, what we did NOT do :

We did NOT :

Use C++ exceptions (we used SEH with __try , __throw , __except)

Try to do proper "exception-safe" C++ ala Herb Sutter
  (this is a bizarre and very tricky complex way of writing C++ that requires
  doing everything in a different way than the normal linear imperative code; it
  uses lots of swaps and temp objects)

Return every error with exceptions ; most errors were via return value

Try to unwind excpetions cleanly/robustly

Any error that we expected to happen, or could happen in ship, such as files not found, media errors, etc. were handled with return codes. The standard way of functions returning codes and the calling code checking it and handling it somehow.

Also, errors that we could detect and just fix immediately, but not return a code, we would just fix. So, like say you tried to create an Actor and the pref file describing that actor didn't exist, we'd just print an error (and automatically email it to dev@oddworld) and just not create that Actor. Hey, shit's wrong, but you can continue.

The principle is : don't block artist A from working on their stuff just because the programmers or some other artist checked in other broken stuff. If possible, just disable the broken stuff, because artist A can probably continue.

Say the guys working on particle systems keep checking in broken stuff that would crash the game or cause lots of errors - fine. The rest of the art team can still be syncing to new builds, and they will just see an error printed about "particle system XX failed ; disabled" and then they can continue working on their other stuff.

Blocking the art/design team (potentially a lot of people) for even 5 minutes while you try to roll things back or whatever to fix it is really a HUGE HUGE disaster and should never ever happen.

Any time your artists/designers have to get up and go get coffee/snacks in the kitchen because things are broken and they can't work - you massively fucked up and you should endeavor to never do that again.

But there are inevitably problems that we didn't just detect and disable the object (like the pref not found above). Maybe you just get a crash in some code due to an array ref out of bounds, or somewhere deep in the code you detect a bad fault that you can't fix.

So, as a catch of last measure we used exceptions. The way we did it was to wrap a try/catch around each game object update, and if it caught an exception, that object was removed.

for each object O in the world list

  show & email error about O throwing
  remove O from world list
  // don't delete the object O since it could still be pointed at by the world, or could be corrupt


Removing O prevents it from trying to Update again and thus spamming. We assume that once it throws, something is badly broken there and we'll just get rid of it.

As I said before, this is NOT trying to catch every error and handle it in a robust way. Obviously O may have been partially through with its Update and put the world in a weird state, it may not keep the game from crashing to just remove O, there are lots of possible problems and we don't try to handle them. It's "optimistic" in that sense that we sort of expect it to fail and cause problems, but if it ever does work, then awesome, great, it saved an artist from crashing. In practice it actually works fine 90% of the time.

We specifically do *not* want to be robust, because writing fully robust exception-safe code (that would have to roll back all the partial changes to the world if there was a throw somewhere through the update) is too onerous. The idea of this system is that it imposes *zero* extra work on programmers writing normal game code.

We could also manually __throw in some places where appropriate. The criterion for doing that is : not an error you should ever get in the final game, it's a spot where you can't return an error code or just show a failure measure and do some kind of default fallback. You also don't need to __throw if it's a spot where the CPU will throw an interrupt for you.

For example, places where we might manually __throw : inside a vector push_back if the malloc to extend failed. In an array out of bounds deref. In the smart-pointer deref if the pointer is null.

Places where we don't __throw : trying to normalize a zero vector or orthonormalize a degenerate frame. These are better to detect, log an error measure, and just stuff in unitZ or something, because while that is broken it's a better way to break than the throw-catch mechanism which should only be used if there's no nicer way to stub-out the broken behavior.

Some (not particularly related) links :

cbloom rants 02-04-09 - Exceptions
cbloom rants 06-07-10 - Exceptions
cbloom rants 11-09-11 - Weird shite about Exceptions in Windows

04-18-17 | Context on Chroma Subsampling

Poked by Guetzli into thinking about pros/cons of chroma subsampling -

Chroma downsampling (as in standard JPEG YCbCr 420) is a big ugly hammer. It just throws away a ton of bits of information. That's pretty much always a bad thing in compression.

Now, preferring to throw away chroma detail before luma detail is valid and good. So if you are not chroma subsampling, then you need a perceptually optimizing encoder that knows to give fewer bits to high frequency chroma. You have much more control doing this through bit allocation than you do by just smashing the chroma planes. (for example, on blocks where there is almost no luma signal, then you might keep more of the high frequency chroma, on blocks with luma masking you can throw away lots of the high chroma AC bits - you just have way more precise control).

The chroma subsample is just a convenient way to get decent perceptual tradeoffs in a *non* optimizing encoder.

Chroma subsample is of course an R-D choice. It throws away signal, giving a certain disortion, in exchange it saves you some rate. This particular move is a good R-D choice at some tradeoff zone. Generally at high bit rate, it's a bad move. In most encoders, it becomes a good move at some lower quality. (in JPEG the tradeoff point is usually somewhere around 85). Measuring this D in RMSE is easy, but measuring it perceptually is rather tricky (when luma masking is present it may be near zero D perceptually, but without luma masking it can be much worse).

There are other issues.

In non-subsampled world, the approximate important weights for YCbCr are something like {0.7,0.13,0.17} . If you do subsample, then the chroma weights per-pixel need to go up by 4X , in which case they become pretty close to all being the same.

Many people mistakenly say the "eye does not see blue levels well". Not true, the eye can see the overall level of blue perfectly well, just as well as red or green. (eg for images where the whole thing is a single solid color). What the eye has is very poor spatial resolution in blue.

One of the issues is that chroma subsample is a nice win for *speed*. It gives you 4X less pixels to work on in two of your planes, half as many pixels overall. This means that subsampled chroma images are almost 2X faster to decode.

I used to be anti-chroma-subsample in my early years. For example in wavelets it's much neater to keep all your color planes full res, but send your bitplanes in [YUV] order. That way when you truncate the bottom bit planes, you drop the highest frequency chroma first. But then I realized that the 2X speedup from chroma subsample was nothing to sneeze at, and in general I'm now pro-chroma-subsample.

Another reminder : if you don't chroma subsample, then you may as well do a KLT on the color planes, rather than just use YUV or whatever. (maybe even KLT per region). The advantage of using standard YUV is that the chroma are known to be perceptually okay to downsample (you can't downsample the two minor components of the KLT transformed planes because you have no guarantee that they are of a type that the eye can't perceive high frequency data).

You can obviously construct adversarial images where the detail is all in chroma (the whole image has a constant luma). In that case chroma downsampling looks really bad and is perceptually a big mistake.

Chroma-from-luma in the decoder fixes all the color fringing that people associate with JPEG, but obviously it doesn't help in the adversarial cases where there is no luma detail to boost the chroma with.

I should also note while I'm at it that there are many codecs out there that just have bugs and/or mistakes in their downsamplers and/or upsamplers that cause this operation to produce way more error than it should.

04-15-17 | Tunstall in an arithmetic way

You can think of the Tunstall dictionary build in an arithmetic codery way.

Your dictionary is like the probability interval. You start with a full interval [0,1]. You put in all the single-character words, with P(c) for each char, so that all sums to one. You iteratively split the largest interval, and subdivide the range.

In binary the "split" operation is :

W -> W0 , W1

P(W) = P(W)*P(0) + P(W)*P(1)

In N-ary the split is :

W -> Wa , W[b+]

P(W) = P(W)*P(a) + P(w)*Ptail(b)

W[b+] means just the word W, but in the state "b+" (aka state "1"), following sym must be >= b
(P(w) here means P_naive(w), just the char probability product)

W[b+] -> Wb , W[c+]

P(w)*Ptail(b) = P(w)*P(b) + P(w)*Ptail(c)

(recall Ptail(c) = tail cumprob, sum of P(char >= c))
(Ptail(a) = 1.0)

So we can draw a picture like an arithmetic coder does, spliting ranges and specifying cumprob intervals to choose our string :

You just keep splitting the largest interval until you have a # of intervals = to the desired number of codes. (8 here for 3-bit Tunstall).

At that point, you still have an arithmetic coder - the intervals are fractional sizes and are correctly sized to the probabilities of each code word. eg. the interval for 01 is P(0)*P(1).

In the final step, each interval is just mapped to a dictionary codeword index. This gives each codeword an equal 1/|dictionary_size| probability interval, which in general is not quite right.

This is where the coding inefficiency comes from - it's the difference between the correct interval sizes and the size that we snap them to.

(ADD : in the drawing I wrote "snap to powers of 2" ; that's not the best way of describing that; they're just snapping to the subsequent i/|dictionary_size|. In this case with dictionary_size = 8 those points are {0,1/8,1/4,3/8,1/2,..} which is why I was thinking about powers of 2 intervals.)

04-14-17 | Marlin Summary

Sum up with simple take-away.

Plural Tunstall VTF coding in general is extremely fast to decode. It works best with 12-bit tables (must stay in L1), which means it only works well at entropy <= 4 bpb.

Marlin introduces an improved word probability model that captures the way the first letter probability is skewed by the longer-string exclusion. (this is just like the LAM exclusion in LZ)

That is, after coding with word W, subsequent chars that exist in the dictionary (Wa,Wb) cannot then be the next character to start a word, so the probably of the first char of the word being >= c is increased.

The Marlin word probability middle improves compression by 1-4% over naive plural Tunstall.

The simplest implementation of the Marlin probability adjustment is like this :

P_naive(W) = Prod[chars c in W] P('c')

P_word(W) = P_scale_first_char( W[0] ) * P_naive(W) * Ptail( num_children(W) )

(where Ptail is the tail-cumulative-proability :
Ptail(x) = Sum[ c >= x ] P('c')  (sum of character probabilities to end)

(instead of scaling by Ptail you can subtract off the child node probabilities as you make them)

on the first iteration of dictionary building, set P_scale_first_char() = 1.0

this is "naive plural Tunstall"

after building the dictionary, you now have a set of words and P(W) for each
compute :

P_state(i) = Sum[ words W with i children ] P(W)

(state i means only chars >= i can follow)

(iterating P_state -> P(W) a few times here is optional but unnecessary)

P_scale_first_char(c) = Sum[ i <= c ] P_state(i) / P_tail(i)

(P_scale_first_char = P_state_tail)

then repeat dic building one more time
(optionally repeat more but once seems fine)

And that's it!

What do these values actually look like? I thought it might be illuminating to dump them. This is on a pretty skewed file so the effect is large, the larger the MPS probability the bigger the effect.

filelen = 1572918
H = 2.917293

P of chars =

        [0] 0.46841475525106835 double
        [1] 0.11553621994280693 double
        [2] 0.11508546535801611 double
        [3] 0.059216055763873253    double
        [4] 0.058911526220693004    double
        [5] 0.036597584870921435    double
        [6] 0.036475518749229136    double
        [7] 0.018035269480036465    double
        [8] 0.017757441900976400    double
        [9] 0.010309501194595012    double
        [10]    0.0097379520102128646   double

P_state =

        [0] 0.62183816678155190 double
        [1] 0.15374679894466811 double
        [2] 0.032874234239563829    double
        [3] 0.063794018822874776    double
        [4] 0.026001940955215786    double
        [5] 0.011274295764837820    double
        [6] 0.028098911350290755    double
        [7] 0.012986055279597277    double
        [8] 0.0013397794289329405   double
        .. goes to zero pretty fast ..

P_scale_first_char =

        [0] 0.62183816678155202 double
        [1] 0.91106139196208336 double
        [2] 0.99007668169839014 double
        [3] 1.2020426052137052  double
        [4] 1.3096008656256881  double
        [5] 1.3712643080249607  double
        [6] 1.5634088663186672  double
        [7] 1.6817189544649160  double
        [8] 1.6963250203077103  double
        [9] 1.9281295477496172  double
        [10]    1.9418127462353780  double
        [11]    2.0234438458996773  double
        [12]    2.0540542047979415  double
        [13]    2.1488636999462676  double
        [14]    2.2798060244386895  double
        [15]    2.2798060244386895  double
        [16]    2.2798060244386895  double
        [17]    2.3660205062350039  double
        [18]    2.3840557757150402  double
        [19]    2.3840557757150402  double
        [20]    2.3840557757150402  double
        [21]    2.4066061022686838  double
        [22]    2.5584098628550294  double
        [23]    2.5584098628550294  double
        [24]    2.6690752676624321  double
        .. gradually goes up to 4.14

estimate real first char probability 
= P(c) * P_scale_first_char(c) =

        [0] 0.29127817269875372 double
        [1] 0.10526058936313110 double
        [2] 0.11394343565337962 double
        [3] 0.071180221940886246    double
        [4] 0.077150585733949978    double
        [5] 0.050184961893408854    double
        [6] 0.057026149416117611    double
        [7] 0.030330254533459933    double

the effect is to reduce the skewing of the probabilities in the post-word alphabet.

I think this problem space is not fully explored yet and I look forward to seeing more work in this domain in the future.

I'm not convinced that the dictionary building scheme here is optimal. Is there an optimal plural VTF dictionary?

I think maybe there's some space between something like RANS and Tunstall. Tunstall inputs blocks of N bits and doesn't carry any state between them. RANS pulls blocks of N bits and carries full state of unused value range between them (which is therefore a lot slower because of dependency chains). Maybe there's something in between?

Another way to think about this Marlin ending state issue is a bit like an arithmetic coder. When you send the index of a word that has children, you have not only sent that word, you've also sent information about the *next* word. That is some bits or fractional bits of information that you'd like to carry forward.

Say you have {W,Wa,Wb} in the dictionary and you send a W. You've also sent that the next word start with >= c. That's like saying your arithmetic coder cumprob is >= (Pa+Pb). You've refined the range of the next interval.

This could be done with Tunstall by doing the multi-table method (separate tables for state 0,1, and 2+), but unfortunately that doesn't fit in L1.

BTW you can think of Tunstall in an arithmetic codey way. Maybe I'll draw a picture because it's easier to show that way...

04-14-17 | Some commentary on Marlin and the code

WARNING : I'm a bit delirious with flu and lack of sleep at the moment so I'm not entirely sure what I'm writing. Apologies if it's a mess!

First, there's no point in making the T_ij transition matrix they talk about.

Back in "Understanding Marlin" you may recall I presented the algorithm thusly :

P_state(i) is given from a previous iteration and is constant

build dictionary using Marlin word model

we now have P(W) for all words in our dic

Use P(W) to compute new P_state(i)

optionally iterate a few times (~ 10 times) :
  use that P_state to compute adjusted P(W)
  use P(W) to compute new P_state

iteration dictionary building again (3-4 times)

in the paper (and code) they do it a bit differently. They compute the state transition matrix, which is :

T_ij = Sum[ all words W that end in state S_i ] P(W|S_j)

this is the probability that if you started in state j you will wind up in state i

instead of iterating P_state -> P(W) , they iterate :

T <- T * T

and then P_state(i) = T_i0

I tested both ways and they produce the exact same result, but just doing it through the P(W) computation is far simpler and faster. The matrix multiply is O(alphabet^3) while the P way is only O(alphabet+dic_size)

Also for the record - I have yet to find a case where iterating to convergence here actually helps. If you just make P_State from PW once and don't iterate, you get 99% of the win. eg :

laplacian distribution :

no iteration :

     0.67952             :  1,000,000 ->   503,694 =  4.030 bpb =  1.985 to 1 

iterate 10X :

     0.67952             :  1,000,000 ->   503,688 =  4.030 bpb =  1.985 to 1 

You *do* need to iterate the dictionary build. I do it 4 times. 3 times would be fine though, heck 2 is probably fine.

4: 0.67952             :  1,000,000 ->   503,694 =  4.030 bpb =  1.985 to 1 

3: 0.67952             :  1,000,000 ->   503,721 =  4.030 bpb =  1.985 to 1 

2: 0.67952             :  1,000,000 ->   503,817 =  4.031 bpb =  1.985 to 1 

The first iteration builds a "naive plural Tunstall" dictionary; the P_state is made from that, second iteration does the first "Marlin" dictionary build.

In general I think they erroneously come to the conclusion that plural Tunstall dictionaries are really slow to create. They're only 1 or 2 orders of magnitude slower than building a Huffman tree, certainly not slow compared to many encoder speeds. Sure sure if you want super fast encoding you wouldn't want to do it, but otherwise it's totally possible to build the dictionaries for each use.

There's a lot of craziness in the Marlin code that makes their dic build way slower than it should be. Some is just over-C++ madness, some is failure to factor out constant expressions.

the word is :

        struct Word : public std::vector<uint8_t> {

and the dictionary is :

std::vector<Word> W;

 (with no reserves anywhere)
yeah that's a problem.  May I suggest :

struct Word {
    uint64 chars;
    int len;

also reserve() is good and calling size() in loops is bad.

This is ouchy :

        virtual double phi(const Word &) const = 0;

and this is even more ouchy :

        virtual std::vector<Word> split(const Word &) const = 0;

The P(w) function that's used frequently is bad.

The key part is :

    for (size_t t = 0; t<=w[0]; t++) {
        double p = PcurrState[t]; 
        p *= P[w[0]]/PnextState[t];
        ret += p;

which you can easily factor out the common P[w[0]] from :

    int c0 = w[0];
    for (size_t t = 0; t<= c0; t++) {
        ret += PcurrState[t]/PnextState[t];
    ret *= P[c0]

but even more significant would be to realize that PcurrState (my P_state) and
PnextState (my P_tail) are not updated during dic building at all!  They're constant
during that phase, so that whole thing can be precomputed and put in a table.
Then this is just :

    int c0 = w[0];
    ret = PcurrState_over_PnextState_partial_sum[c0];
    ret *= P[c0]

that also gives us a chance to state clearly (again) the difference between "Marlin" and naive plural Tunstall. It's that one table right there.

    int c0 = w[0];
    ret = 1.0;
    ret *= P[c0]

this is naive plural Tunstall. It comes down to a modifed probability table for the first letter in the word.

Recall that :

P_naive(W) = Prod[ chars c in W ] P(c)

simple P_word(W) = P_naive(W) * Ptail( num_children(W) )

Reading Yamamoto and Yokoo "Average-Sense Optimality and Competitive Optimality for Almost Instantaneous VF Codes".

They construct the naive plural Tunstall VF dictionary. They are also aware of the Marlin-style state transition problem. (that is, partical nodes leave you in a state where some symbols are excluded).

They address the problem by constructing multiple parse trees, one for each initial state S_i. In tree T_i you know that the first character is >= i so all words that start with lower symbols are excluded.

This should give reasonably more compression than the Marlin approach, obviously with the cost of having multiple dictionaries.

In skewed alphabet cases where the MPS is very probable, this should be significant because words that start with the MPS dominate the dictionary, but in all states S_1 and higher those words cannot be used. In fact I conjecture that even having just 2 or 3 trees should give most of the win. One tree for state S_0, one for S_1 and the last for all states >= S_2. In practice this problematic because the multiple code sets would fall out of cache and it adds a bit of decoder complexity to select the following tree.

There's also a continuity between VTF codes and blocked arithmetic coders. The Yamamoto-Yokoo scheme is like a way of carrying the residual information between blocked transmissions, similar to multi-table arithmetic coding schemes.


I just went and got the marlin code to compile in VS 2015. Bit of a nightmare. I wanted to confirm I didn't screw anything up in my implementation.

two-sided Laplacian distribution centered at 0
(this is what the Marlin code assumes)

r = 0.67952

H = 3.798339

my version of Marlin-probability plural Tunstall :

0.67952             :  1,000,000 ->   503,694 =  4.030 bpb =  1.985 to 1 

Marlin reference code : 1,000,000 -> 507,412

naive plural Tunstall :

0.67952             :  1,000,000 ->   508,071 =  4.065 bpb =  1.968 to 1 

I presume the reason they compress worse than my version is because they make dictionaries for a handfull of Laplacian distributions and then pick the closest one. I make a dictionary for the actual char counts in the array, so their dictionary is mis-matching the actual distribution slightly.

04-14-17 | Tunstall vs Marlin Results Part 2

Testing on some real files.

Marlin :

loading : R:\tunstall_test\lzt24.literals
filelen = 1111673
H = 7.452694
sym_count = 256
lzt24.literals      :  1,111,673 -> 1,286,166 =  9.256 bpb =  0.864 to 1 
decode_time2 : seconds:0.0022 ticks per: 3.467 b/kc : 288.41 mbps : 498.66
loading : R:\tunstall_test\monarch.tga.rrz_filtered.bmp
filelen = 1572918
H = 2.917293
sym_count = 236
monarch.tga.rrz_filtered.bmp:  1,572,918 ->   618,447 =  3.145 bpb =  2.543 to 1 
decode_time2 : seconds:0.0012 ticks per: 1.281 b/kc : 780.92 mbps : 1350.21
loading : R:\tunstall_test\paper1
filelen = 53161
H = 4.982983
sym_count = 95
paper1              :     53,161 ->    35,763 =  5.382 bpb =  1.486 to 1 
decode_time2 : seconds:0.0001 ticks per: 1.988 b/kc : 503.06 mbps : 869.78
loading : R:\tunstall_test\PIC
filelen = 513216
H = 1.210176
sym_count = 159
PIC                 :    513,216 ->   140,391 =  2.188 bpb =  3.656 to 1 
decode_time2 : seconds:0.0002 ticks per: 0.800 b/kc : 1250.71 mbps : 2162.48
loading : R:\tunstall_test\tabdir.tab
filelen = 190428
H = 2.284979
sym_count = 77
tabdir.tab          :    190,428 ->    68,511 =  2.878 bpb =  2.780 to 1 
decode_time2 : seconds:0.0001 ticks per: 1.031 b/kc : 969.81 mbps : 1676.80
total bytes out : 1974785
naive plural Tunstall :
loading : R:\tunstall_test\lzt24.literals
filelen = 1111673
H = 7.452694
sym_count = 256
lzt24.literals      :  1,111,673 -> 1,290,015 =  9.283 bpb =  0.862 to 1 
decode_time2 : seconds:0.0022 ticks per: 3.443 b/kc : 290.45 mbps : 502.18
loading : R:\tunstall_test\monarch.tga.rrz_filtered.bmp
filelen = 1572918
H = 2.917293
sym_count = 236
monarch.tga.rrz_filtered.bmp:  1,572,918 ->   627,747 =  3.193 bpb =  2.506 to 1 
decode_time2 : seconds:0.0012 ticks per: 1.284 b/kc : 779.08 mbps : 1347.03
loading : R:\tunstall_test\paper1
filelen = 53161
H = 4.982983
sym_count = 95
paper1              :     53,161 ->    35,934 =  5.408 bpb =  1.479 to 1 
decode_time2 : seconds:0.0001 ticks per: 1.998 b/kc : 500.61 mbps : 865.56
loading : R:\tunstall_test\PIC
filelen = 513216
H = 1.210176
sym_count = 159
PIC                 :    513,216 ->   145,980 =  2.276 bpb =  3.516 to 1 
decode_time2 : seconds:0.0002 ticks per: 0.826 b/kc : 1211.09 mbps : 2093.97
loading : R:\tunstall_test\tabdir.tab
filelen = 190428
H = 2.284979
sym_count = 77
tabdir.tab          :    190,428 ->    74,169 =  3.116 bpb =  2.567 to 1 
decode_time2 : seconds:0.0001 ticks per: 1.103 b/kc : 906.80 mbps : 1567.86
total bytes out : 1995503

About the files :

lzt24.literals are the literals left over after LZ-parsing (LZQ1) lzt24
  like all LZ literals they are high entropy and thus do terribly in Tunstall

monarch.tga.rrz_filtered.bmp is the image residual after filtering with my DPCM
  (it actually has a BMP header on it which is giving Tunstall a harder time
   than if I stripped the header)

paper1 & pic are standard

tabdir.tab is a text file of a dir listing with lots of tabs in it

For speed comparison, this is the Oodle Huffman on the same files :
loading file (0/5) : lzt24.literals
ooHuffman1 : ed...........................................................
ooHuffman1 :  1,111,673 -> 1,036,540 =  7.459 bpb =  1.072 to 1
encode           : 8.405 millis, 13.07 c/b, rate= 132.26 mb/s
decode           : 1.721 millis, 2.68 c/b, rate= 645.81 mb/s
loading file (1/5) : monarch.tga.rrz_filtered.bmp
ooHuffman1 : ed...........................................................
ooHuffman1 :  1,572,918 ->   586,839 =  2.985 bpb =  2.680 to 1
encode           : 7.570 millis, 8.32 c/b, rate= 207.80 mb/s
decode           : 2.348 millis, 2.58 c/b, rate= 669.94 mb/s
loading file (2/5) : paper1
ooHuffman1 :     53,161 ->    33,427 =  5.030 bpb =  1.590 to 1
encode           : 0.268 millis, 8.70 c/b, rate= 198.67 mb/s
decode           : 0.080 millis, 2.60 c/b, rate= 665.07 mb/s
loading file (3/5) : PIC
ooHuffman1 :    513,216 ->   106,994 =  1.668 bpb =  4.797 to 1
encode           : 2.405 millis, 8.10 c/b, rate= 213.41 mb/s
decode           : 0.758 millis, 2.55 c/b, rate= 677.32 mb/s
loading file (4/5) : tabdir.tab
ooHuffman1 :    190,428 ->    58,307 =  2.450 bpb =  3.266 to 1
encode           : 0.926 millis, 8.41 c/b, rate= 205.70 mb/s
decode           : 0.279 millis, 2.54 c/b, rate= 681.45 mb/s

Tunstall is crazy fast. And of course that's a rather basic implementation of the decoder, I'm sure it could get faster.

Is there an application for plural Tunstall? I'm not sure. I tried it back in 2015 as an idea for literals in Mermaid/Selkie and abandoned it as not very relevant there. It works on low-entropy order-0 data (like image prediction residuals).

Of course if you wanted to test it against the state of the art you should consider SIMD Ryg RANS or GPU RANS. You should consider something like TANS with multiple symbols in the output table. You should consider merged-symbol codes, perhaps using escapes, perhaps runlen transforms. See for examples crblib/huffa.c for a survey of Huffman ideas from 1996 (pre-runtransform, blocking MPS's, order-1-huff, multisymbol output, etc.)

04-14-17 | Tunstall vs Marlin Results Part 1

For some reason I keep trying to type "marling". Anyway...

Geometric distribution , P(n) = r^n

I am comparing "Marlin" = plural Tunstall with P_state word probability model vs. naive plural Tunstall (P_word = P_naive). In both cases 8-byte output words, 12-bit codes.

Marlin :

filelen = 1000000
H = 7.658248
sym_count = 256
r=0.990             :  1,000,000 -> 1,231,686 =  9.853 bpb =  0.812 to 1 
decode_time2 : seconds:0.0018 ticks per: 3.064 b/kc : 326.42 mbps : 564.38
filelen = 1000000
H = 7.345420
sym_count = 256
r=0.985             :  1,000,000 -> 1,126,068 =  9.009 bpb =  0.888 to 1 
decode_time2 : seconds:0.0016 ticks per: 2.840 b/kc : 352.15 mbps : 608.87
filelen = 1000000
H = 6.878983
sym_count = 256
r=0.978             :  1,000,000 ->   990,336 =  7.923 bpb =  1.010 to 1 
decode_time2 : seconds:0.0014 ticks per: 2.497 b/kc : 400.54 mbps : 692.53
filelen = 1000000
H = 6.323152
sym_count = 256
r=0.967             :  1,000,000 ->   862,968 =  6.904 bpb =  1.159 to 1 
decode_time2 : seconds:0.0013 ticks per: 2.227 b/kc : 449.08 mbps : 776.45
filelen = 1000000
H = 5.741045
sym_count = 226
r=0.950             :  1,000,000 ->   779,445 =  6.236 bpb =  1.283 to 1 
decode_time2 : seconds:0.0012 ticks per: 2.021 b/kc : 494.83 mbps : 855.57
filelen = 1000000
H = 5.155050
sym_count = 150
r=0.927             :  1,000,000 ->   701,049 =  5.608 bpb =  1.426 to 1 
decode_time2 : seconds:0.0011 ticks per: 1.821 b/kc : 549.09 mbps : 949.37
filelen = 1000000
H = 4.572028
sym_count = 109
r=0.892             :  1,000,000 ->   611,238 =  4.890 bpb =  1.636 to 1 
decode_time2 : seconds:0.0009 ticks per: 1.577 b/kc : 633.93 mbps : 1096.07
filelen = 1000000
H = 3.986386
sym_count = 78
r=0.842             :  1,000,000 ->   529,743 =  4.238 bpb =  1.888 to 1 
decode_time2 : seconds:0.0008 ticks per: 1.407 b/kc : 710.53 mbps : 1228.51
filelen = 1000000
H = 3.405910
sym_count = 47
r=0.773             :  1,000,000 ->   450,585 =  3.605 bpb =  2.219 to 1 
decode_time2 : seconds:0.0007 ticks per: 1.237 b/kc : 808.48 mbps : 1397.86
filelen = 1000000
H = 2.823256
sym_count = 36
r=0.680             :  1,000,000 ->   373,197 =  2.986 bpb =  2.680 to 1 
decode_time2 : seconds:0.0006 ticks per: 1.053 b/kc : 950.07 mbps : 1642.67
filelen = 1000000
H = 2.250632
sym_count = 23
r=0.560             :  1,000,000 ->   298,908 =  2.391 bpb =  3.346 to 1 
decode_time2 : seconds:0.0005 ticks per: 0.891 b/kc : 1122.53 mbps : 1940.85

vs. plural Tunstall :

filelen = 1000000
H = 7.658248
sym_count = 256
r=0.99000           :  1,000,000 -> 1,239,435 =  9.915 bpb =  0.807 to 1 
decode_time2 : seconds:0.0017 ticks per: 2.929 b/kc : 341.46 mbps : 590.39
filelen = 1000000
H = 7.345420
sym_count = 256
r=0.98504           :  1,000,000 -> 1,130,025 =  9.040 bpb =  0.885 to 1 
decode_time2 : seconds:0.0016 ticks per: 2.814 b/kc : 355.36 mbps : 614.41
filelen = 1000000
H = 6.878983
sym_count = 256
r=0.97764           :  1,000,000 ->   990,855 =  7.927 bpb =  1.009 to 1 
decode_time2 : seconds:0.0014 ticks per: 2.416 b/kc : 413.96 mbps : 715.73
filelen = 1000000
H = 6.323152
sym_count = 256
r=0.96665           :  1,000,000 ->   861,900 =  6.895 bpb =  1.160 to 1 
decode_time2 : seconds:0.0012 ticks per: 2.096 b/kc : 477.19 mbps : 825.07
filelen = 1000000
H = 5.741045
sym_count = 226
r=0.95039           :  1,000,000 ->   782,118 =  6.257 bpb =  1.279 to 1 
decode_time2 : seconds:0.0011 ticks per: 1.898 b/kc : 526.96 mbps : 911.12
filelen = 1000000
H = 5.155050
sym_count = 150
r=0.92652           :  1,000,000 ->   704,241 =  5.634 bpb =  1.420 to 1 
decode_time2 : seconds:0.0010 ticks per: 1.681 b/kc : 594.73 mbps : 1028.29
filelen = 1000000
H = 4.572028
sym_count = 109
r=0.89183           :  1,000,000 ->   614,061 =  4.912 bpb =  1.629 to 1 
decode_time2 : seconds:0.0008 ticks per: 1.457 b/kc : 686.27 mbps : 1186.57
filelen = 1000000
H = 3.986386
sym_count = 78
r=0.84222           :  1,000,000 ->   534,300 =  4.274 bpb =  1.872 to 1 
decode_time2 : seconds:0.0007 ticks per: 1.254 b/kc : 797.33 mbps : 1378.58
filelen = 1000000
H = 3.405910
sym_count = 47
r=0.77292           :  1,000,000 ->   454,059 =  3.632 bpb =  2.202 to 1 
decode_time2 : seconds:0.0006 ticks per: 1.078 b/kc : 928.04 mbps : 1604.58
filelen = 1000000
H = 2.823256
sym_count = 36
r=0.67952           :  1,000,000 ->   377,775 =  3.022 bpb =  2.647 to 1 
decode_time2 : seconds:0.0005 ticks per: 0.935 b/kc : 1069.85 mbps : 1849.77
filelen = 1000000
H = 2.250632
sym_count = 23
r=0.56015           :  1,000,000 ->   304,887 =  2.439 bpb =  3.280 to 1 
decode_time2 : seconds:0.0004 ticks per: 0.724 b/kc : 1381.21 mbps : 2388.11

Very very small difference. eg :

plural Tunstall :

H = 3.986386
sym_count = 78
r=0.84222           :  1,000,000 ->   534,300 =  4.274 bpb =  1.872 to 1 

Marlin :

H = 3.986386
sym_count = 78
r=0.842             :  1,000,000 ->   529,743 =  4.238 bpb =  1.888 to 1 
decode_time2 : seconds:0.0008 ticks per: 1.407 b/kc : 710.53 mbps : 1228.51

Yes the Marlin word probability estimator helps a little bit, but it's not massive.

I'm not surprised but a bit sad to say that once again the Marlin paper compares to ridiculous straw men and doesn't compare to the most obvious, naive, and well known (see Savari for example, or Yamamoto & Yokoo) similar alternative - just doing plural Tunstall/VTF without the Marlin word probability model.

Entropy above 4 or so is terrible for 12-bit VTF codes.

The Marlin paper uses a "percent efficiency" scale which I find rather misleading. For example, this :

H = 3.986386
sym_count = 78
r=0.842             :  1,000,000 ->   529,743 =  4.238 bpb =  1.888 to 1 

is what I would consider pretty poor entropy coding. Entropy of 3.98 -> 4.23 bpb is way off. But as a "percent efficiency" it's 94% , which is really high on their graphs.

The more standard and IMO useful way to show this is a delta of your output bits minus the entropy, eg.

excess = 4.238 - 3.986 = 0.252

half a bit per byte wasted. A true arithmetic coder has an excess of less than 0.01 bpb typically. The worst you can ever do is an excess of 1.0 which occurs in any integer-bit entroy coder as the probability of the MPS goes towards 1.0

Part of my hope / curiosity in investigating this was wondering whether the Marlin procedure would help at all with the way Tunstall VTF codes really collapse in the H > 4 range , and the answer is - no , it doesn't help with that problem at all.

Anyway, on to more results.

04-14-17 | Classical Tunstall

Before continuing with Marlin, I want to take a brief digression to review "classical" or "true" Tunstall.

The classical Tunstall algorithm constructs VTF (variable to fixed) codes for binary memoryless (order-0) sources. It constructs the optimal code.

You start with dictionary = { "0","1" } , the single bit binary strings. (or dictionary = the null string if you prefer)

You then split one word W in the dictionary to make two new words "W0" and "W1" ; when you split W, it is removed since all possible following symbols now have words in the dictionary.

The algorithm is simple and iterative :

while dic size < desired
find best word W to split
remove W
add W0 and W1

each step increments dictionary size by +1

What is the best word to split?

Our goal is to maximize average code length :

A = Sum[words] P(W) * L(W)

under the split operation, what happens to A ?

W -> W0, W1

delta(A) = P(W0) * L(W0) + P(W1) * L(W1) - P(W) * L(W)

P(W0) = P(W)*P(0)
P(W1) = P(W)*P(1)
L(W0) = L(W)+1

.. simplify ..

delta(A) = P(W)

so to get the best gain of A, you just split the word with maximum probability. Note of course this is just greedy optimization of A and that might not be the true optimum, but in fact it is and the proof is pretty neat but I won't do it here.

You can naively build the optimal Tunstall code in NlogN time with a heap, or slightly more cleverly you can use two linear queues for left and right children and do it in O(N) time.

Easy peasy, nice and neat. But this doesn't work the same way for the large-alphabet scenario.

Now onto something that is a bit messy that I haven't figured out.

For "plural Tunstall" we aren't considering adding all children, we're only considering adding the next child.

A "split" operation is like :

start with word W with no children
W ends in state 0 (all chars >= 0 are possible)

the next child of W to consider is "W0"
(symbols sorted so most probable is first)

if we add "W0" then W goes to state 1 (only chars >= 1 possible)

W_S0 -> "W0" + W_S1

W_S1 -> "W1" + W_S2


again, we want to maximize A, the average codelen. What is delta(A) under a split operation?

delta(A) = P("W0") * L("W0") + P(W_S1) * L(W) - P(W_S0) * L(W)

delta(A) = P("W0") + (P("W0") + P(W_S1) - P(W_S0)) * L(W)

P("W0") + P(W_S1) - P(W_S0) = 0


delta(A) = P("W0") 

it seems like in plural Tunstall you should "split" the word that has maximum P("W0") ; that is maximize the probability of the word you *create* not the one you *remove*. This difference arises from the fact that we are only making one child of longer length - the other "child" in the pseudo-split here is actually the same parent node again, just with a reduced exit state.

In practice that doesn't seem to be so. I experimentally measured that choosing to split the word with maximum P(W) is better than splitting the word with maximum P(child).

I'm not sure what's going wrong with this analysis. In the Marlin code they just split the word with maximum P(W) by analogy to true Tunstall, which I'm not convinced is well justified in plural Tunstall.

While I'm bringing up mysteries, I tried optimal-parsing plural Tunstall. Obviously with "true tunstall" or any prefix-free code that's silly, the greedy parse is the only parse. But with plural Tunstall, you might have "aa" and also "aaa" in the tree. In this scenario, by analogy to LZ, the greedy parse is usually imperfect because it is sometimes better to take a shorter match now to get a longer one on the next work. So maybe some kind of lazy , or heck full optimal parse. (the trivial LZSS backward parse works well here).

Result : optimal-parsed plural Tunstall is identical to greedy. Exactly, so it must be provable. I don't see an easy way to show that the greedy parse is optimal in the plural case. Is it true for all plural dictionaries? (I doubt it) What are the conditions on the dictionary that guarantee it?

I think that this is because for any string in the dictionary, all shorter substrings of that string are in the dictionary too. This makes optimal parsing useless. But I think that property is a coincidence/bug of how Marlin and I did the dictionary construction, which brings me to :

Marlin's dictionary construction method and the one I was using before, which is slightly different, both have the property that they never remove parent nodes when they make children. I believe this is wrong but I haven't been able to make it work a different way.

The case goes like this :

you have word W in the dictionary with no children

you have following chars a,b,c,d.  a and b are very probable, c and d are very rare.

P(W) initially = P_init(W)

you add child 'a' ; W -> Wa , W(b+)
P(W) -= P(Wa)
add child 'b'
W(b+) -> Wb , W(c+)
P(W) -= P(Wb)

now the word W in the dictionary has
P(W) = P(Wc) + P(Wd)

these are quite rare, so P(W) now is very small

W is no longer a desirable dictionary entry.

We got all the usefulness of W out in Wa and Wb, we don't want to keep W in the dictionary just to be able to code it with rare following c's and d's - we'd like to now remove W.

In particular, if the current P(W) of the parent word is now lower than a child we could make somewhere else by splitting, remove W and split the other node. Or something like that - here's where I haven't quite figured out how to make this idea work in practice.

So I believe that both Marlin and my code are NOT making optimal general VTF plural dictionaries, they are making them under the (unnecessary) constraint of the shorter-substring-is-present property.

04-13-17 | Understanding Marlin

I will be using "Tunstall" to mean any variable to fixed coder. I am considering large alphabet (eg. 8-bit input alphabet), "plural" (eg. non-prefix-free dictionary). I am also considering only modeling order-0 statistics.

I label the symbols 'a','b','c' from most probable to least probable. I will use single quotes for symbols, and double quotes for words in the dictionary. So :

P('a') , P('b'), etc. are given

P('a') >= P('b') >= P('c') are ordered

I will use the term "Marlin" to describe the way they estimate the probability of dictionary words. (everything else in the paper is either obvious or well known (eg. the way the decoder works), so the innovation and interesting part is the word probability estimation, so that is what I will call "Marlin" , the rest is just "Tunstall").

Ok. To build a Tunstall dictionary your goal is to maximize the average input length, which is :

average input length = Sum[words] { P(word) * L(word) }

since the output length is fixed, maximizing the input length maximizes compression ratio.

In the original Tunstall algorithm on binary input alphabet, this is easily optimized by splitting the most probable word, and adding its two children. This can be done in linear time using two queues for left and right (0 and 1) children.

The Marlin algorithm is all about estimating P(word).

The first naive estimate (what I did in my 12/4/2015 report) is just to multiply the character probabilities :

P(word) = Prod[c in word] P('c')

that is

P("xyz") = P('x') * P('y') * P('z')

but that's obviously not right. The reason is that the existence of words in the dictionary affects the probability of other words.

In particular, the general trend is that the dictionary will accumulate words with the most probable characters (a,b,c) which will make the effective probability of the other letters in the remainder greater.

For example :

Start the dictionary with the 256 single-letter words

At this point the naive probabilities are exact, that is :

P("a") (the word "a") = P('a') (the letter 'a')

Now add the most probable bigram "aa" to the dictionary.

We now have a 257-word dictionary.  What are the probabilities when we code from it ?

Some of the occurrances of the letter 'a' will now be coded with the word "aa"

That means P("a") in the dictionary is now LESS than P('a')

Now add the next most probable words, "ab" and "ba"

The probability of "a" goes down more, as does P("b")

Now if we consider the choice of what word to add next - is it "ac" or "bb" ?

The fact that some of the probability of those letters has been used by words in the dictionary affects
our estimate, which affects our choice of how to build the dictionary.

so that's the intuition of the problem, and the Marlin algorithm is one way to solve it.

Let's do it intuitively again in a bit more detail.

There are two issues : the way the probability of a shorter word is reduced by the presence of longer words, and the way the probability of raw characters that start words is changed by the probability of them coming after words in the dictionary.

Say you have word W in your dictionary

and also some of the most probable children.

W, Wa, Wb are in dictionary

Wc, Wd are not

We'll say word "W" has 2 children (Wa and Wb).

So word "W" will only be used from the dictionary if the children are NOT a or b
(since in that case the longer word would be used).

So if you have seen word "W" so far, to use word W, the next character must be terminal,
eg. one that doesn't correspond to another child.

So the probability of word W should be adjusted by :

P(W) *= P(c) + P(d)

Because we are dealing with sorted probability alphabets, we can describe the child set with just one integer to indicate which ones are in the dictionary. In Marlin terminology this is c(w), and corresponds to the state Si.

If we make the tail cumulative probability sum :

Ptail(x) = Sum[ c >= x ] P('c')  (sum of character probabilities to end)
Ptail(255) = P(255)
Ptail(254) = P(254) + P(255)
Ptail(0) = sum of all P('c')  = 1.0

then the adjustment is :

P(W) *= P(c) + P(d)
P(W) *= Ptail('c')
P(W) *= Ptail(first char that's not a child)

P(W) *= Ptail( num_children(W) )
(I'm zero-indexing, so no +1 here as in the Marlin paper, they 1-base-index)

ADD : I realized there's a simpler way to think about this. When you add a child word, you simply remove that probability from the parent. That is :

let P_init(W) be the initial probability of word W
when it is first added to the dictionary and has no children

track running estimate of P(W)

when you add child 'x' making word "Wx"

The child word probability is initialized from the parent's whole probability :

P_init(Wx) = P_init(W) * P('x')

And remove that from the running P(W) :

P(W) -= P_init(Wx)

That is you just make P(W) the probability of word W, excluding children that exist.
Once you add all children, P(W) will be zero and the word is useless.

Okay, so that does the first issue (probability of words reduced by the presence of longer words). Now the next issue. Consider the same simple example case first :

W,Wa,Wb are in dictionary, Wc,Wd are not
(no longer children of W are either)

Say you reach node "Wa"

there are no children of "Wa" in the dictionary, so all following characters are equally likely

This means that starting the next word, the character probabilities are equal to their original true probabilities

But say you reach node "W" and leave via 'c' or 'd'

In that case the next character must be 'c' or 'd' , it can never be 'a' or 'b'

So the probability of the next character being 'c' goes up by the probability of using word "W" and the
probability of being a 'c' after "W" , that's :

estimate_P('c') +=  P("W") * P('c') / ( P('c') + P('d') )


estimate_P('c') +=  P("W") * P('c') / Ptail( num_children(W) )

now you have to do this for all paths through the dictionary. But all ways to exit with a certain child count are similar, so you can merge those paths to reduce the work. All words with 2 children will be in the same exit probability state ('a' and 'b' can't occur but chars >= 'c' can).

This is the Marlin state S_i. S_i means that character is >= i. It happens because you left the tree with a word that had i children.

When you see character 2 that can happen from state 0 or 1 or 2 but never states >= 3.

for estimating probability of word W

W can only occur in states where the first character W[0] is possible

that is state S_i with i <= W[0]

When character W[0] does occur in state S_i , the probability of that character is effectively higher,
because we know that chars < i can't occur.

Instead of just being P(char W[0]) , it's divided by Ptail(i)

(as in estimate_P('c') +=  P("W") * P('c') / Ptail( num_children(W) ) above)

So :

P(W) = Sum[ i <= W[0] ] P( state S_i ) * P( W | S_i )

the probability of W is the sum of the probability of states it can start from
(recall states = certain terminal character sets)
times the probability of W given that state


P_naive(W) = Product[ chars c in W ] P(char 'c')

be the naive word probability, then :

P(W | S_i) = (1 / Ptail(i)) * P_naive(W) * Ptail( num_children(W) )

is what we need.  This is equation (1) in the Marlin paper.

The first term increases the probability of W for higher chars, because we know the more probable lower chars can't occur in this state (because they found longer words in the dictionary)

The last term decreases the probability of W because it will only be used when the following character doesn't cause a longer word in the dictionary to be used

Now of course there's a problem. This P(W) probability estimate for words requires the probability of starting the word from state S_i, which we don't know. If we had the P(W) then the P of states is just :

P(S_i) = Sum[ words W that have i children ] * P(W)

so to solve this you can just iterate. Initialize the P(S_i) to some guess; the Marlin code just does :

P(state 0) = 1.0
P(all others) = 0.0

(recall state 0 is the state where all chars are possible, no exclusions, so
characters just have their original order-0 probability)

feeds that in to get P(W), feeds that to update P(S_i), and repeats to convergence.

To build the dictionary you simply find the word W with highest P(W) and split it (adding its next most probable child and increasing its child count by 1).

The Marlin code does this :

seed state probabilities


build dictionary greedily using fixed state probabilities

update state probabilities


That is, during the dictionary creation, word probabilities are estimated using state probabilities from the previous iteration. They hard-code this to 3 iterations.

There is an alternative, which is to update the state probabilities as you go. Any time you do a greedy word split, you're changing 3 state probabilities, so that's not terrible. But changing the state probabilities means all your previous word estimate probabilities are now wrong, so you have to go back through them and recompute them. This makes it O(N^2) in the dictionary size, which is bad.

For reference, combining our above equations to make the word probability estimate :

P(W) = Sum[ i <= W[0] ] P( state S_i ) * P( W | S_i )

P(W | S_i) = (1 / Ptail(i)) * P_naive(W) * Ptail( num_children(W) )


P(W) = P_naive(W) * Ptail( num_children(W) ) * Sum[ i <= W[0] ] P( state S_i ) / Ptail(i)

the second half of that can be tabulated between iterations :

P_state_tail(j) = Sum[ i <= j ] P( state S_i ) / Ptail(i)

so :

P(W) = P_naive(W) * Ptail( num_children(W) ) * P_state_tail( W[0] )

you can see the "Marlin" aspect of all this is just in using this P(W) rather than P_naive(W) . How important is it exactly to get this P(W) right? (and is it right?) We'll find out next time...

04-13-17 | Tunstall Context

Looking at Marlin today, some reminders to self/all about context :

Tunstall was originally designed with binary alphabets in mind; variable to fixed on *binary*. In that context, doing full child trees (so dictionaries are full prefix trees and encoding is unique) makes sense. As soon as you do variable-to-fixed (hence VTF) on large alphabets, "plural" trees are obviously better and have been written about much in the past. With plural trees, encoding is not unique ("a" and "ab" are both in the dictionary).

There's a big under-specified distinction between VTF dictionaries that model higher level correlation and those that don't. eg. does P("ab") = P(a)*P(b) or is there order-1 correlation?

I looked at Tunstall codes a while ago (TR "failed experiment : Tunstall Codes" 12/4/2015). I didn't make this clear but in my experiment I was looking at a specific scenario :

symbols are assumed to have only order-0 entropy
(eg. symbol probabilities describe their full statistics)

encoder transmits symbol probabilities (or the dictionary of words)
but there are other possibilities that some of the literature addresses. There are at lot of papers on "improved Tunstall" that use the order-N probabilities (the true N-gram counts for the words rather than multiplying the probability of each character). Whether or not this works in practice depends on context, eg. on LZ literals the characters are non-adjacent in the source so this might not make sense.

There's a fundamental limitation with Tunstall in practice and a very narrow window where it makes sense.

On current chips, 12-bit words is ideal (because 4096 dwords = 16k = fits in L1). 16 bit can sometimes give much better compression, but falling out of L1 is a disaster for speed.

12-bit VTF words works great if the entropy of the source is <= 5 bits or so. As it goes over 5, you have too many bigrams that don't pack well into 12, and the compression ratio starts to suffer badly (and decode speed suffers a bit).

I was investigating Tunstall in the case of normal LZ literals, where entropy is always in the 6-8 bpc range (because any more compressability has been removed by the string-match portion of the LZ). In that case Tunstall just doesn't work.

Tunstall is best when entropy <= 3 bits or so. Not only do you get compression closer to entropy, you also get more decode speed.

Now for context, that's a bit of a weird place to just do entropy coding. Normally in low-entropy scenarios, you would have some kind of coder before just tossing entropy coding at it. eg. take DCT residuals, or any image residual situation. You will have lots of 0's and 1's so it looks like a very low entropy scenario for order-0 entropy, but typically you would remove that by doing RLE or something else so that the alphabet you hand to the entropy coder is higher entropy. (eg. JPEG does RLE of 0's and EOB).

Even if you did just entropy code on a low-entropy source, you might instead use a kind of cascaded coder. Again assuming something like prediction residuals where the 0's and 1's are very common, you might make a two-stage alphabet that's something like :

alphabet 1 : {0,1,2,3+}
alphabet 2 : {3,4,...255}

Then with alphabet 1 you could pack 4 symbols per byte and do normal Huffman. Obviously a Huffman decode is a little slower than Tunstall, but you're getting always 4 symbols per decode so output len is not variable, and compression ratio is better.

Tunstall for LZ literals might be interesting in a very fast LZ with MML 8 or so. (eg. things like ZStd level 1, which is also where multi-symbol-output Huff works well).

Point is - the application window here is pretty narrow, and there are other techniques that also address the same problem.

03-27-17 | If anyone is serious about lossy image compression

If any big player (Google, Facebook, Instagram, etc.) is serious about lossy image compression (and they should be) -

it would be very easy to make huge steps that contribute substatially to this problem.

1. Devise a new set of human perceptual quality rating experiments. Get vision scientists, statisticians, survey experiments, etc. involved to make the experiment well founded. Test lots of images and gather lots of score. Make half of them public and keep half private.

2. Do a public competition Netflix-prize style for a perceptual metric that can match the human scores. Let people submit code to score images and run that on your secret private test set.

Unlike Netflix prize, require that all submissions be open-source BSD/public-domain after the competition is over, with no patent encumbrance. Also set a maximum run time & memory use on the metrics so that they are constrained to be practical. The goal is to get actually usable code out of this.

3. Make a competition to take various lossy image compressor submissions and score the results perceptually, not from algorithmic metrics but by showing them to humans.

What we need is not more random algorithms (I'm look at you, JPEG-XR, webp-lossy, Guetzli, etc.) which are not clearly better. We desperately need more data and solid ways to test "this is better or not".

There are tons of great data compression developers out there in the world (many of whom are not getting paid for their work) that could make great advances in an open competition.

Designing a perceptual test is very hard.

For example when I'm allowed to A-B images (toggle between them) to look for flaws, the flaws that I see that way are very different than I'm just given a compressed image without knowing what the original was.

The way you score things when you can compare to original (side-by-side or slow-fade toggle) is very different than if you're just given the lossy image and asked to make a no-reference score.

I suspect that the "click on worst artifact" in the Guetzli test biases the test in a certain way.

Of course you want to consider different monitors, different viewing conditions, etc.

As I wrote over in the rambles, I spent some time on perceptual metrics myself but aborted it because there's a major problem. With any perceptual test database that we currently have, you can easily beat existing metrics by over-training to the test set. Perceptual metrics all have lots of ceofficiencts for various options (and even if they don't look like numerical coefficients, there are ways to over-train with things like how you do your "pooling"). If you go and "train your metric" what you are actually doing is baking in knowledge about the particular test images, the particular test conditions. That's crap.

03-24-17 | JPEG2

JPEG2 proposal / rough principles :

1. Simple simple simple. The decoder should be implementable in ~5000 lines as a single file stb.h style header. Keep it simple!

2. It should be losslessly transcodable from JPEG , ala packJPG/Lepton. That is, JPEG1 should be contained as a subset. (this just means having 8x8 DCT mode, quantization matrix). You could have other block modes in JPEG2 that simply aren't used when you transcode JPEG. You replace the entropy coded back-end with JPEG2 and should get about 20% file size reduction.

IMO this is crucial for rolling out a new format, nobody should ever be trancoding existing JPEGs and thereby introducing new error.

3. Reasonably fast to decode. Slower than JPEG1 by maybe 2X is okay, but not by 10X. eg. JPEG-ANS is okay, JPEG-Ari is probably not okay. Also think about parallelism and GPU decoding for huge images (100 MP). Keeping decoding local is important (eg. each 32x32 block or so should be independently decodable).

4. Decent quality encoding without crazy optimizing encoders. The straightforward encode without big R-D optimizing searches should still beat JPEG.

5. Support for per-block Q , so that sophisticated encoders can do bit rate allocation.

6. Support alpha, HDR. Make a clean definition of color space and gamma. But *don't* go crazy with supporting ICC profiles and lots of bit depths and so on. Needs to be the smallest set of features here. You don't want to get into the situation that's so common where the format is too complex and nobody actually supports it right in practice, so there becomes a "spec standard" and a "de-facto standard" that don't parse lots of the optional modes correctly.

7. Support larger blocks & non-square blocks; certainly 16x16 , maybe 32x32 ? Things like 16x8 , etc. This is important for increasingly large images.

Most of all keep it simple, keep it close to JPEG, because JPEG actually works and basically everything else in lossy image compression doesn't.

Anything that's not just DCT + quantize + entropy is IMO a big mistake, very suspicious and likely to be vaporware in the sense that you can make it look good on paper but it won't work well in reality.

03-21-17 | MozJPEG Works Well

In my Guetzli test I noticed that mozjpeg was performing impressively well. I ran some more tests to check it out. Here they are :


Key :

jpg_h = IJG encoder + decoder (progressive and -optimize of course)
jpg_m = mozjpeg encoder + IJG baseline decoder
guetzli = guetzi encoder + IJG baseline decoder
jpg_pack = IJG encoder + decoder + packjpg entropy coded file format
jpg_pdec = jpg_pack with my jpeg decoder

Some notes on interpretation :

What I see is MozJPEG does very well on RMSE (it does as well as jpg_pack ! this despite mozjpeg being baseline decoded while jpg_pack gets a custom entropy back end). On the two perceptual metrics, mozjpeg is roughly tied with jpeg-huff, just very slightly better in Combo.

To my eyes (looking at the images myself (take with salt)), MozJPEG is a definite win over jpeg-huff. This is why I show the three different metrics, and no one of them can be trusted on its own, you have to look at the full picture. In this case - tied on two metrics and a big win on the other is pretty strong evidence that it is in fact better.

If we ran at lower bit-rates where the Huffman starts to be a huge disadvantage, packjpg would show a bigger win over mozjpeg. But that's outside of the functional range of JPEG anyway. This test shows quality starting at 40 only.

(BTW yes I know at high bit rate my jpeg decoder (jpeg_pdec) is flawed; it's doing too much deblocking & deringing there, it needs to get weaker at high bit rate. (in the graphs you can see it actually hurts RMSE quite a lot at the highest bit rate, but helps at low bit rate).)

Guetzli is run at quality 85-90-95. Guetzli does consistently poorly, so much so that its poor showing can't be justified merely by saying it targets a different metric.

03-21-17 | Guetzli Context

Some history and context WRST Guetzli.

First practical stuff. If you (you being Google or any of the other big web companies serving images (eg. Instagram, Snap, Tumblr, etc.)) want to improve the quality of JPEGs for consumers, IMO the best place is in the *decoder* not the encoder. Deblocking, deringing, and chroma-from-luma are all pretty straightforward and provide huge quality wins in the low-bit-rate range where JPEG needs the most help.

Decoder-side fixes also work on the huge body of existing JPEGs in the wild, and don't tempt people to do awful things like recompress from an existing JPEG to a new lossy format.

If you want to reduce the size of transmitted JPEGs (assuming baseline decoder), mozjpeg is good.

If you can change the format (eg. if you were willing to push a new format like you did with webp-lossy, and you have control over both the servers and the client, as Google is now in a unique position to do, since they control Chrome, Android, and also many servers) - then Lepton (based on packJPG) is awesome.

The great thing about Lepton/packJPG is that you get big gains in size at the *exact same* quality. You can transcode existing JPEGs - you don't have to find the uncompressed original or transcode from existing JPEG with introduction of new loss. You get a very simple decision - smaller files, same content. It's not ambiguous or questionable or involves any user evaluation or drawbacks.

Links to Lepton :

uncmpJPG packJPG
JPEG Open Source Package packJPG
Lepton image compression saving 22% losslessly from images at 15MBs Dropbox Tech Blog
GitHub - dropboxlepton Lepton is a tool and file format for losslessly compressing JPEGs by an average of 22%.
packjpg (Matthias Stirner) · GitHub
Lepton 1.2 free download - Software reviews, downloads, news, free trials, freeware and full commercial software - Downloadc

A bit of a historical ramble about JPEG optimization.

The Guetzli paper doesn't describe the implementation in much detail, and I haven't looked in the code so I don't know exactly what's in there. The basic ideas of how they optimize JPEGs are ancient (quant matrix optimization and spatial-adaptive quantization by zeroing tails). The ideas go back to 1993 and the very introduction of the JPEG standard. Some of the classic work is Watson's DCTune and "RD-OPT" (Ratnakar and Livny), which optimize quantization matrices per-image. Trellis quantization and block truncation were also common. In fact the idea of being able to optimize the quantization matrix per image is why the matrix is transmitted in the format, rather than just sending a scalar quality (which would be smaller). The designers of the JPEG standard had all this in mind.

There are tons of papers on this stuff, it was a popular area of research for years. Data compression practitioners were excited about it and many big claims were made. But it never caught on, and we mostly stopped working on it, it was a bit of a dead end. The problem is the perceptual metric. These optimizers would go off and fiddle with the image and report they made it better by some metric, and sometimes it would look better, but sometimes it wouldn't.

For any given metric, you can write an optimizer that goes off and optimizes to that metric. And the result is .... ? better ? sometimes ? you hope ?

Back in the long ago, people ran DCTune and RD-OPT and similar coders, and some metric would say they succeeded, but you'd look at the images and not be convinced. But worse than that, perceptual metrics assume certain viewing conditions, certain brightness, certain image size, so maybe it looked good in testing, but then when people actually used it looked worse.

We (data compression researchers) wound up just throwing up our hands and punting, saying "we'll come back to this when there's a better metric". If we had a perceptual metric we could trust, then sure lots of optimization could be done in the encoder.

03-20-17 | Guetzli Test

Quick test of Guetzli. Guetzli is a new perceptually-optimizing JPEG encoder from the Google compression research team. Let's try it!

My "porsche640.bmp" test image. I ran guetzli at quality 85 to set a target size, because :

Guetzli should be called with quality >= 84, otherwise the
output will have noticeable artifacts. If you want to
proceed anyway, please edit the source code.

My normal imdiff run would be at a variety of qualities, but Guetzli doesn't work except in a very small range of qualities, so let's just take the end of that range to stress everything as much as possible.

Then I ran baseline JPEG (IJG cjpeg) and mozjpeg and adjusted their quality to get sizes as close as possible. The sizes are :

guetzli 85 : 62544
jpeg 77    : 61983
jpeg 78    : 63662
mozjpeg 84 : 63046
then I ran them through my imdiff. Imdiff reports "imdiff" as the raw diff score (the scale of this score and higher/lower better depends on the diff type), and "fit_imdiff" is always a 0-10 quality with higher is better.


imDiff Type : 0 : RMSE_RGB
got option : html output to r:\id0.html
recurse on dir : porsche640.bmp_guetzli
loading : porsche640.bmp_guetzli\guetzli_000062544.bmp
compSize : 62544 , bpp :  1.629 , logbpp :  0.704
imdiff     : 8.633
fit_imdiff : 5.837
loading : porsche640.bmp_guetzli\jpeg_000061983.bmp
compSize : 61983 , bpp :  1.614 , logbpp :  0.691
imdiff     : 8.555
fit_imdiff : 5.850
loading : porsche640.bmp_guetzli\jpeg_000063662.bmp
compSize : 63662 , bpp :  1.658 , logbpp :  0.729
imdiff     : 8.433
fit_imdiff : 5.870
loading : porsche640.bmp_guetzli\mozj_000063046.bmp
compSize : 63046 , bpp :  1.642 , logbpp :  0.715
imdiff     : 7.640
fit_imdiff : 6.005

Guetzli has slightly higher RMSE (eg. worse) than baseline JPEG. Mozjpeg does much better. Perhaps this is not surprising if Guetzli is perceptually optimized.


imDiff Type : 4 : MS_SSIM_IW_Y
got option : html output to r:\id4.html
recurse on dir : porsche640.bmp_guetzli
loading : porsche640.bmp_guetzli\guetzli_000062544.bmp
compSize : 62544 , bpp :  1.629 , logbpp :  0.704
imdiff     : 0.997
fit_imdiff : 6.022
loading : porsche640.bmp_guetzli\jpeg_000061983.bmp
compSize : 61983 , bpp :  1.614 , logbpp :  0.691
imdiff     : 0.998
fit_imdiff : 6.237
loading : porsche640.bmp_guetzli\jpeg_000063662.bmp
compSize : 63662 , bpp :  1.658 , logbpp :  0.729
imdiff     : 0.998
fit_imdiff : 6.260
loading : porsche640.bmp_guetzli\mozj_000063046.bmp
compSize : 63046 , bpp :  1.642 , logbpp :  0.715
imdiff     : 0.998
fit_imdiff : 6.287

the raw score is an SSIM so it's like a cosine (1.0 is perfect); my fit to a more perceptually uniform score uses an acos. Mozjpeg is not much better than baseline JPEG by this metric. Guetzli does poorly.

Combo :

imDiff Type : 8 : Combo
got option : html output to r:\id8.html
recurse on dir : porsche640.bmp_guetzli
loading : porsche640.bmp_guetzli\guetzli_000062544.bmp
compSize : 62544 , bpp :  1.629 , logbpp :  0.704
imdiff     : 3.013
fit_imdiff : 6.061
loading : porsche640.bmp_guetzli\jpeg_000061983.bmp
compSize : 61983 , bpp :  1.614 , logbpp :  0.691
imdiff     : 2.812
fit_imdiff : 6.266
loading : porsche640.bmp_guetzli\jpeg_000063662.bmp
compSize : 63662 , bpp :  1.658 , logbpp :  0.729
imdiff     : 2.788
fit_imdiff : 6.290
loading : porsche640.bmp_guetzli\mozj_000063046.bmp
compSize : 63046 , bpp :  1.642 , logbpp :  0.715
imdiff     : 2.731
fit_imdiff : 6.348

By the Combo metric (my perceptual metric, a combination of MS-SSIM-IW-Y, SCIELAB delta, and PSNR-HVS-M), MozJPEG distinguishes itself from baseline JPEG. Guetzli still does poorly.

I assume that Guetzli would win when compared under the Butteraugli metric (I hope?) but it's way behind in my imdiff metrics.

Personally eyeballing the images, I see some places where Guetzli is better than baseline JPEG, and some places where it's worse. (Guetzli is way better on the ringing of the flower over the canoe, but it adds a bunch of distortion on the car that baseline JPEG doesn't have; the worst is on the driver's side rear wheel). To my eyes MozJPEG is clearly vastly superior to either. Well done mozjpeg team!

Get the images :

porsche640_guetzli_compare.zip at tinyupload.com

Links :

[1703.04421] Guetzli Perceptually Guided JPEG Encoder
Performance Calendar » MozJPEG 3.0
GitHub - googleguetzli Perceptual JPEG encoder
Releases · googleguetzli · GitHub
GitHub - mozillamozjpeg Improved JPEG encoder.
mozjpeg codelove
binaries - mozjpeg codelove
Research Blog Announcing Guetzli A New Open Source JPEG Encoder
mozjpeg 3.1 Complied for Windows (.exe) - Thomas Coward

03-08-17 | Kraken Perf with Simultaneous Threaded Decodes

I had a report from a customer of poor Kraken decode performance on PS4 when using 10 simultaneous threads for decoding, and it occurred to me I had never tested that thoroughly. (Their issue turned out to be something else; see end of post).

There is reason to be concerned about running a lot of Kraken (or Mermaid/Selkie) decodes simultaneously. On most modern systems, like the PS4, the many cores share caches, perhaps share memory busses. That means while you have N* the compute performance, you may have cache conflicts, and you could wind up bottlenecking on some of the memory subsystem. (generally we don't run into bandwidth bottlenecks, but there are lots of other limitted resources, like latency stalling ops, queue sizes, etc.)

Anyhoo, onto the testing -

I ran N theaded decodes of the same file. The buffers are copied for each thread so they can't share any cache for input or output buffers. Wiped caches before runs. I then wait on all N decodes being done and time that.

The graphs show total time for all N decodes, and time per decode (total/N).

If you had infinite compute resources, then "total time" (orange) would be a flat line. Any number of threads would take the same total time, it would not change.

Once you hit the limits of the system, the "time per" (blue) should be constant, and total then should go up linearly. (actually not quite, because when you are off the core # modulo, the threads don't all complete at the same time so you get wasted idle time; see the jump on lappy from 4-6 cores then how flat it is from 6-8, same on PS4 from 6-8 cores then flat from 9-12). If you have the threads to spare, then you can maximize throughput by minimizing "time per".

Conclusion :

No problem with lots of simultaneous Kraken decodes. Even when heavily over-subscribed, there's no major perf inversion due to overloading cache or memory subsystems.

Kraken on PS4 has near perfect threading up to 6 threads (total time goes from 0.0099 - 0.0111) ; on lappy it's not as good but still provides benefit to the time per decode up to 4 threads (total time from 0.0060 - 0.0095).

It's a surprise to me that the PS4 scales so well despite sharing cache & memory bus for the first 4 cores. It's also a surprise that lappy scales less well, I thought it would be near perfect on the first 4 cores, but maybe that's just Windows not giving me the whole machine? That was backward from my expectation.

Charts :

Kraken on PS4 (6 cores; 4 cores per 2MB L2) :

lzt24 :


Almost perfect threading from 1-6 cores (total time constant) even with large binary file.


webster is a large text file that uses a lot of long distance matches (offset > 1M). Text files have very different character than binary files like the lzt's. We can see that the large hot memory region used by webster does put some stress on the shared L2, there's falloff in perf from 1-4 cores.

webster Selkie :

Selkie is much faster than Kraken (2.75X faster on webster PS4) so all else being equal it should be affected a lot more by thread contention hurting memory latency. But, Selkie has some unique cleverness that makes it immune to this drawback. Threading even on webster from 1-6 cores is near perfect.

Kraken on my laptop (4 cores) (Core i7 Q820) (4x256 kb L2 , 8 MB L3) (+4 hypercores) no turbo :

lzt24 :

lzt99 :

webster :

Similar to PS4, lappy has almost perfect threading on binary files from 1-4 cores. On webster there is falloff in perf due to the

Kraken on my laptop (4 cores) (Core i7 Q820) (4x256 kb L2 , 8 MB L3) (+4 hypercores) WITH TURBO :

lzt24 :

lzt99 :

I initially mistakenly posted lappy timings with turbo enabled. I usually turn it off for perf testing on my laptop so that timings are more reliable. I think it's interesting actually to look at how the perf falloff is different with turbo.

Without turbo, total time is constant on lzt24 and lzt99 from 1-4 cores, but with turbo it steadily falls off, as adding more cores causes the laptop to reduce its clock rate. Despite that there's still a solid gain to throughput (the blue "time per" is going down despite the clock rate also going down).

raw data : (lzt24)

lappy : no turbo : (*1000)
1,   9.1360,   9.1360
2,   9.5523,   4.7761
3,   9.7850,   3.2617
4,  10.1901,   2.5475
5,  14.6867,   2.9373
6,  16.6759,   2.7793
7,  19.1105,   2.7301
8,  20.1687,   2.5211
9,  23.6391,   2.6266
10,  25.9279,   2.5928
11,  27.7395,   2.5218
12,  27.6459,   2.3038
13,  30.7935,   2.3687
14,  31.8541,   2.2753
15,  33.7883,   2.2526
16,  34.8252,   2.1766

lappy : with turbo :
1,   0.0060,   0.0060
2,   0.0070,   0.0035
3,   0.0087,   0.0029
4,   0.0095,   0.0024 <- 4
5,   0.0133,   0.0027
6,   0.0170,   0.0028
7,   0.0175,   0.0025
8,   0.0193,   0.0024 <- 8
9,   0.0228,   0.0025
10,   0.0252,   0.0025
11,   0.0262,   0.0024
12,   0.0278,   0.0023 <- 12
13,   0.0318,   0.0024
14,   0.0310,   0.0022
15,   0.0325,   0.0022
16,   0.0346,   0.0022 <- 16

PS4 :
1,   0.0099,   0.0099
2,   0.0102,   0.0051
3,   0.0104,   0.0035
4,   0.0106,   0.0027
5,   0.0110,   0.0022
6,   0.0111,   0.0018 <- min
7,   0.0147,   0.0021
8,   0.0180,   0.0022
9,   0.0204,   0.0023
10,   0.0214,   0.0021
11,   0.0217,   0.0020
12,   0.0220,   0.0018 <- same min again
13,   0.0257,   0.0020
14,   0.0297,   0.0021
15,   0.0310,   0.0021
16,   0.0319,   0.0020

comparing just lappy turbo to no-turbo :

lappy : no turbo :
1,   9.1360,   9.1360
2,   9.5523,   4.7761
3,   9.7850,   3.2617
4,  10.1901,   2.5475

lappy : with turbo :
1,   6.0,   6.0
2,   7.0,   3.5
3,   8.7,   2.9
4,   9.5,   2.4

You can see with only 1 core, turbo is 1.5X faster (9.13/6.0) than no turbo
With 4 cores they are getting close to the same speed, (10.2 vs 9.5), the turbo
has almost completely clocked down

The customer's actual issue was decoding into write-combined graphics memory. This is an absolute killer for decoder perf because Kraken (like any LZ decoder) needs to read back the buffers it writes.

On the PS4 I think the best way to decode to graphics memory (garlic) is to allocate the memory as writeback onion, do the decompress, then change it to wb_garlic with sceKernelBatchMap (which will cause a CPU cache flush; several of these changes could be combined together, eg. for level loading you only need to do it once at the end of all the resource decoding, don't do it per resource).

02-24-17 | Oodle Perf with Chunking and Dictionary Size

I get a lot of customers that want to cut their data into small blocks for paging, who ask "what's the benefit of using larger blocks" ?

The larger the block = more compression, and can help throughput (decode speed).

Obviously larger block = longer latency (to load & decode one whole block).

(though you can get data out incrementally, you don't have to wait for the whole decode to get the first byte out; but if you only needed the last byte of the block, it's strictly longer latency).

If you need fine grain paging, you have to trade off the desire to get precise control of your loading with small blocks & the benefits of larger blocks.

(obviously always follow general good paging practice, like amortize disk seeks, combine small resources into paging units, don't load a 256k chunk and just keep 1k of it and throw the rest away, etc.)

As a reference point, here's Kraken on Silesia with various chunk sizes :

Silesia : (Kraken Normal -z4)

 16k : ooKraken    : 211,938,580 ->75,624,641 =  2.855 bpb =  2.803 to 1 
 16k : decode           : 264.190 millis, 4.24 c/b, rate= 802.22 mb/s

 32k : ooKraken    : 211,938,580 ->70,906,686 =  2.676 bpb =  2.989 to 1 
 32k : decode           : 217.339 millis, 3.49 c/b, rate= 975.15 mb/s

 64k : ooKraken    : 211,938,580 ->67,562,203 =  2.550 bpb =  3.137 to 1 
 64k : decode           : 195.793 millis, 3.14 c/b, rate= 1082.46 mb/s

128k : ooKraken    : 211,938,580 ->65,274,250 =  2.464 bpb =  3.247 to 1 
128k : decode           : 183.232 millis, 2.94 c/b, rate= 1156.67 mb/s

256k : ooKraken    : 211,938,580 ->63,548,390 =  2.399 bpb =  3.335 to 1 
256k : decode           : 182.080 millis, 2.92 c/b, rate= 1163.99 mb/s

512k : ooKraken    : 211,938,580 ->61,875,640 =  2.336 bpb =  3.425 to 1 
512k : decode           : 182.018 millis, 2.92 c/b, rate= 1164.38 mb/s

1024k: ooKraken    : 211,938,580 ->60,602,177 =  2.288 bpb =  3.497 to 1 
1024k: decode           : 181.486 millis, 2.91 c/b, rate= 1167.80 mb/s

files: ooKraken    : 211,938,580 ->57,451,361 =  2.169 bpb =  3.689 to 1 
files: decode           : 206.305 millis, 3.31 c/b, rate= 1027.31 mb/s

16k   :  2.80:1 ,   15.7 enc mbps ,  802.2 dec mbps
32k   :  2.99:1 ,   19.7 enc mbps ,  975.2 dec mbps
64k   :  3.14:1 ,   22.8 enc mbps , 1082.5 dec mbps
128k  :  3.25:1 ,   24.6 enc mbps , 1156.7 dec mbps
256k  :  3.34:1 ,   25.5 enc mbps , 1164.0 dec mbps
512k  :  3.43:1 ,   25.4 enc mbps , 1164.4 dec mbps
1024k :  3.50:1 ,   24.6 enc mbps , 1167.8 dec mbps
files :  3.69:1 ,   18.9 enc mbps , 1027.3 dec mbps

(note these are *chunks* not a window size; no carry-over of compressor state or dictionary is allowed across chunks. "files" means compress the individual files of silesia as whole units, but reset compressor between files.)

You may have noticed that the chunked files (once you get past the very small 16k,32k) are somewhat faster to decode. This is due to keeping match references in the CPU cache in the decoder.

Limitting the match window (OodleLZ_CompressOptions::dictionarySize) gives the same speed benefit for staying in cache, but with a smaller compression win.

window 128k : ooKraken    : 211,938,580 ->61,939,885 =  2.338 bpb =  3.422 to 1 
window 128k : decode           : 181.967 millis, 2.92 c/b, rate= 1164.71 mb/s

window 256k : ooKraken    : 211,938,580 ->60,688,467 =  2.291 bpb =  3.492 to 1 
window 256k : decode           : 182.316 millis, 2.93 c/b, rate= 1162.48 mb/s

window 512k : ooKraken    : 211,938,580 ->59,658,759 =  2.252 bpb =  3.553 to 1 
window 512k : decode           : 184.702 millis, 2.97 c/b, rate= 1147.46 mb/s

window 1M : ooKraken    : 211,938,580 ->58,878,065 =  2.222 bpb =  3.600 to 1 
window 1M : decode           : 184.912 millis, 2.97 c/b, rate= 1146.16 mb/s

window 2M :  ooKraken    : 211,938,580 ->58,396,432 =  2.204 bpb =  3.629 to 1 
window 2M :  decode           : 182.231 millis, 2.93 c/b, rate= 1163.02 mb/s

window 4M :  ooKraken    : 211,938,580 ->58,018,936 =  2.190 bpb =  3.653 to 1 
window 4M : decode           : 182.950 millis, 2.94 c/b, rate= 1158.45 mb/s

window 8M : ooKraken    : 211,938,580 ->57,657,484 =  2.176 bpb =  3.676 to 1 
window 8M : decode           : 189.241 millis, 3.04 c/b, rate= 1119.94 mb/s

window 16M: ooKraken    : 211,938,580 ->57,525,174 =  2.171 bpb =  3.684 to 1 
window 16M: decode           : 202.384 millis, 3.25 c/b, rate= 1047.21 mb/s

files     : ooKraken    : 211,938,580 ->57,451,361 =  2.169 bpb =  3.689 to 1 
files     : decode           : 206.305 millis, 3.31 c/b, rate= 1027.31 mb/s

window 128k:  3.42:1 ,   20.1 enc mbps , 1164.7 dec mbps
window 256k:  3.49:1 ,   20.1 enc mbps , 1162.5 dec mbps
window 512k:  3.55:1 ,   20.1 enc mbps , 1147.5 dec mbps
window 1M  :  3.60:1 ,   20.0 enc mbps , 1146.2 dec mbps
window 2M  :  3.63:1 ,   19.7 enc mbps , 1163.0 dec mbps
window 4M  :  3.65:1 ,   19.3 enc mbps , 1158.5 dec mbps
window 8M  :  3.68:1 ,   18.9 enc mbps , 1119.9 dec mbps
window 16M :  3.68:1 ,   18.8 enc mbps , 1047.2 dec mbps
files      :  3.69:1 ,   18.9 enc mbps , 1027.3 dec mbps

WARNING : tuning perf to cache size is obviously very machine dependent; I don't really recommend fiddling with it unless you know the exact hardware you will be decoding on. The test machine here has a 4 MB L3, so speed falls off slightly as window size approaches 4 MB.

If you do need to use tiny chunks with Oodle ("tiny" being 32k or smaller; 128k or above is in the normal intended operating range) here are a few tips to consider :

1. Consider pre-allocating the Decoder object and passing in the memory to the OodleLZ_Decompress calls. This avoids doing a malloc per call, which may or may not be significant overhead.

2. Consider changing OodleConfigValues::m_OodleLZ_Small_Buffer_LZ_Fallback_Size . The default is 2k bytes. Buffers smaller than that will use LZB16 instead of the requested compressor, because many of the new ones don't do well on tiny buffers. If you want to have control of this yourself, you can set this to 0.

3. Consider changing OodleLZ_CompressOptions::spaceSpeedTradeoffBytes . This is the number of bytes that must be saved from the compressed output size before the encoder will choose a slower decode mode. eg. it controls decisions like whether literals are sent raw or with entropy coding. This number is scaled for full size buffers (128k bytes or more). When using tiny buffers, it will choose to avoid entropy coding more often. You may wish to dial down this value to scale to your buffers. The default is 256 ; I recommend trying 128 to see what the effect is.

02-14-17 | Android Needs

We (RAD / perf-conscious developers in general) desperately need on Android :

1. A light weight high res timer or cycle counter.

ADD : okay, yeah there's cntpct_el0. Lots of weird stuff with this though that make it less than ideal. There's access bits so the OS might deny you access (why!?). It seems like on Linux/Android that access to cntpct_el0 is denied but cntvct_el0 is allowed? Getting the frequency seems to not always work; and how does the frequency of the timer relate to the frequency of the cpu? It's all a bit nastier than it should be.

2. A fast query for which core we are on, and a way to map that core id to processor information (eg. is it an A53 or A15 or whatever). This has to be fast enough to do frequently, because tasks get moved around cores so you can't store what core you think you're on.

3. The ability to lock the clock rate and stop the thermal insanity. Even if it was locked at the lowest clock rate, that would be better than nothing (though it would cause other anomalies in timing, like CPU to RAM relative speeds might not be the same as in typical use). Just anything to make measuring perf not so random.

(and while I'm at it : command line args and host filesystem mapping. (you too Durango!))

02-09-17 | Tips for using Oodle as Efficiently as Possible

Tips for using Oodle as efficiently and robustly as possible. (wrst your game runtime loading + decoding only).

1. Use the new compressors (Kraken/Mermaid/Selkie/Hydra). Aside from being great performance, they have the most robust and well-tested fuzz safety.

2. Pass FuzzSafe_Yes to the OodleLZ_Decompress option. The KMS decoders are always internally fuzz safe. What the FuzzSafe_Yes option is add some checks to the initial header decode which will cause the decode to fail if the header byte has been tampered with to change it to a non-KMS compressor.

3. Use Oodle Core lib only, not Ext. Core lib is very light and tight. Core lib makes no threads, requires no init, and will do no allocations to decode (if you pass in the memory).

4. Disable Oodle's callbacks :


5. Because you disabled Oodle's access to an allocator, instead pass in the memory needed. You can ask the data for the compressor if you don't always know it.

    compressor = OodleLZ_GetChunkCompressor(in_comp,NULL);
    decoderMemorySize = OodleLZDecoder_MemorySizeNeeded(compressor,in_raw_length);
    decoderMemory = malloc( decoderMemorySize );

6. If possible keep the Decoder memory around or pull from some shared scratch space rather than allocating & freeing it every time.

7. If you're on a platform where Oodle is in a DLL or .so , sign it with a mechanism like authentisign to ensure it isn't tampered with.

8. If possible do async IO and use double-buffering to incrementally load data and decompress, so that you are maximally using the IO bus and the CPU at the same time. If loading and decoding large buffers, consider running the decoders "ThreadPhased".

As always, feel free to contact me and ask questions.

02-09-17 | strtod

I've been fooling around with strtod for a few days for no good reason. It's been quite interesting.

Some little notes :

strtod in many compilers & standard libraries is broken. (see the excellent pages at exploring binary for details)

(to clarify "broken" : they all round-trip doubles correctly; if you print a double and scan it using the same compiler, you will get the same double; that's quite easy. They're "broken" in the sense of not converting a full-precision string to the closest possible double, and they're "broken" in the sense of not having a single consistent rule that tells you how any given full precision numeral string will be converted)

The default rounding rule for floats is round-nearest (banker). What that means is when a value is exactly at the midpoint of either round-up or round-down (the bits below the bottom bit are 100000..) , then round up or down to make the bottom bit of the result zero. This is sometimes called "round to even" but crucially it's round to even *mantissa* not round to even *number*.

Our goal for strtod should be to take a full numeral string and convert it to the closest possible double using banker rounding.

The marginal rounding value is like this in binary :


^ ^              ^ ^- bits below mantissa are exactly at rounding threshold
| |              |
| |              +- bottom bit of mantissa = "banker bit"
| |
| +- 52 bits of mantissa
+- implicit 1 bit at top of double

in this case the "banker bit" (bottom bit of mantissa bit range) is off, the next bit is on.

If this value was exact, you should round *down*. (if the banker bit was on, you should round up). If this value is not exact by even the tiniest bit (as in, there are more significant bits below the range we have seen, eg. it was 1000....001), it changes to rounding up.

If you think of the infinity of the real numbers being divided into buckets, each bucket corresponds to one of the doubles that covers that range, this value is the boundary of a bucket edge.

In practice the way to do strtod is to work in ints, so if you have the top 64 bits of the (possibly very long) value in an int, this is :

hi = a u64 with first 64 bits
top bit of "hi" is on

(hi>>11) is the 52 bits of mantissa + implicit top bit

hi & 0x400 is the "rounding bit"
hi & 0x800 is the "banker bit"
hi & 0x3ff are the bits under the rounding bit

hi & 0xfff == 0x400 is low boundary that needs more bits
hi & 0xfff == 0xBFF is high boundary that needs more bits

At 0x400 :
"rounding bit" is on, we're right on threshold
"banker bit" is off, so we should round down if this value is exact
but any more bits beyond the first 64 will change us to rounding up
so we need more bits
- just need to see if there are any bits at all that could be on

At 0xBFF :
"banker bit" is on, so if we were at rounding threshold, we should round up
(eg. 0xC00 rounds up, and doesn't need any more bits, we know that exactly)
the bits we have are just below rounding threshold
if the remaining bits are all on (FFFF)
OR if they generate a carry into our bottom bit
then we will round up
- need enough of the remaining value to know that it can't push us up to 0xC00

The standard approach to doing a good strtod is to start by reading the first 19 digits into a U64. You just use *= 10 integer multiplies to do the base-10 to base-2 conversion, and then you have to adjust the place-value of the right hand side of those digits using a table to find a power of 10. (the place-value is obviously adjusted based on where the decimal was and the exponent provided in the input string ; so if you are given "70.23e12" you read "7023" as an int and then adjust pow10 exponent +10).

Once you have the first 19 digits in the U64, you know that the full string must correspond to an interval :

lo = current u64 from first 19 digits

hi = lo + (all remaining digits = 99999)*(place value) + (bias for placevalue mult being too low)

final value is in [lo,hi]

so the difficult cases that need a lot of digits to discriminate are the ones where the first 19 digits put you just below the threshold of rounding, but the hi end of the interval is above it.

Older MSVC only used the first 17 digits so fails sooner. For example :


this is right on a rounding threshold; because the banker bit is off it should round down

the correct closest double is 

but if you bias that up beyond the digits that MSVC reads :


this should round up; the closest double is

but old MSVC gets it wrong


Another example :


is the double threshold


is definitely above the threshold, should round up

but if you only read the first 19 base-10 digits :


you see a value that is below the threshold and would round down

You have to look at the interval of uncertainty -


and see that you straddle and boundary and must get more digits.

There are two things that need refinement : getting more digits & doing your place value scaling to more bits of precision. You can interatively increase the precision of each, which refines your interval smaller and smaller, until you either know which side of the rounding barrier to take, or you have got all the bits of precision.

BTW this needing lots of precision case is exactly the same as the arithmetic coder "underflow" case , where your coding interval looks like, in binary :

hi = 101101010101001 100000000000000.110101010101
lo = 101101010101001 011111111111111.01010101010
     ^               ^               ^- active coding zone, new symbols add at this fixed point position
     |               |
     |               +-- bad underflow zone! can't yet tell if this bit should be a 1 or 0
     +-- hi and lo the same in top bits, these bits have been sent & renormalized out

anyway, just a funny parallel to me.

There are obviously nasty issues to be aware of with the FPU rounding more, control word, precision, or with the optimizer doing funny things to your FPU math (and of course be aware of x86 being on the FPU and x64 being in SSE). The best solution to all that is to just not use floats, use ints and construct the output floats by hand.

(there is an optimization possible if you can trust the FPU ; numbers that fit completely in an int you can just use the FPU's int-to-float to do all the work for you, if the int-to-float rounding mode matches the rounding mode you want from your strtod)

Now, you may think "hey who cares about these boundary cases - I can round-trip doubles perfectly without them". In fact, round-tripping doubles is easy, since they don't ever have any bits on below the (52+1) in the mantissa, you never get this problem of bits beyond the last one! (you only need 17 digits to round-trip doubles).

Personally I think that these kinds of routines should have well-defined behavior for all inputs. There should be a single definite right answer, and a conforming routine should get that right answer. Then nutters can go off and optimize it and fiddle around, and you can run it through a test suite and verify it *if* you have exactly defined right answers. This is particulary true for things like the CRT. (this also comes up in how the compiler converts float and double constants). The fact that so many compilers fucked this up for so long is a bit of a head scratcher (especially since good conversion routines have been around since the Fortran days). (the unwillingess of people to just use existing good code is so bizarre to me, they go off and roll their own and invariably fuck up some of the difficult corner cases).

Anyway, rolling your own is a fun project, but fortunately there's good code to do this :

"dtoa" (which contains a strtod) by David M Gay :

dtoa.c from http://www.netlib.org/fp/

(BTW lots of people seem to have different versions of dtoa with various changes/fixes; for example gcc, mozilla, chromium; I can't find a good link or home page for the best/newest version of dtoa; help?)

dtoa is excellent code in the sense of working right, using good algorithms, and being fast. It's terrible code in the sense of being some apalling spaghetti. This is actual code from dtoa :

    if (k &= 0x1f) {
        k1 = 32 - k;
        z = 0;
        do {
            *x1++ = *x << k | z;
            z = *x++ >> k1;
            while(x < xe);
        if ((*x1 = z))
    if (k &= 0xf) {
        k1 = 16 - k;
        z = 0;
        do {
            *x1++ = *x << k  & 0xffff | z;
            z = *x++ >> k1;

holy order-of-operations reliance batman! Jeebus.

To build dtoa I use :

#define IEEE_8087
#pragma warning(disable : 4244 4127 4018 4706 4701 4334 4146)
#define NO_ERRNO
Note that dtoa can optionally check the FLT_ROUNDS setting but does not round correctly unless it is 1 (nearest). Furthermore, in MSVC the FLT_ROUNDS value in the header is broken in some versions (always returns 1 even if fesetenv has changed it). So, yeah. Don't mess with the float rounding mode please.

dtoa is partly messy because it supports lots of wacky stuff from rare machines (FLT_RADIX != 2 for example). (though apparently a lot of the weird float format modes are broken).

An alternative I looked at is "floatscan" from MUSL. Floatscan produces correct results, but is very slow.

Here's my timing on random large (20-300 decimal digits) strings :

strtod dtoa.c
ticks = 353

strtod mine
ticks = 267

MSVC 2005 CRT atof
ticks = 1921

MUSL floatscan
ticks = 11445

My variant here ("mine") is a little bit faster than dtoa. That basically just comes from using the modern 64-bit CPU. For example I use mulq to do 64x64 to 128 multiply , whereas he uses only 32*32 multiplies and simulates large words by doing the carries manually. I use clz to left-justify binary, whereas he uses a bunch of if's. Stuff like that.

The MUSL floatscan slowness is mmrmm. It seems to be O(N) in the # of digits even when the first 19 digits can unambiguously resolve the correct answer. Basically it just goes straight into bigint (it makes an array of U32's which each hold 9 base10 digits) which is unnecessary most of the time.

01-24-17 | Order 0 estimators for data compression

I thought this might be an interesting simple survey topic to illustrate an introduction to data compression.

Assume that we are writing a compressor with only order-0 modeling, and that we are working on a binary alphabet, so we are just modeling the count of 0's and 1's. Maybe we have some binary data that we believe only has order-0 correlation in it, or maybe this is the back-end of some other stage of a compressor.

If the data is in fact stationary (the probabilites don't change over time) and truly order-0, then the best we can do is to count the # of 0's and 1's in the whole sequence to get the best possible estimate of the true probability of 0's and 1's in the source.

The first option is a static coder : (using the nomenclature of "static huffman" vs "adaptive huffman" ; eg. static means non-streaming, probabilities or counts transmitted at the start of the buffer)

Encoder counts n0 and n1 in the whole sequence
Encoder transmits n0 and n1 exactly

Encoder & Decoder both make
p0 = n0 / (n0+n1)
p1 = n1 / (n0+n1)

Lots of little notes here already. We didn't have to do any +1's to ensure we had non-zero probabilities as you often see, because we have the exact count of the whole stream. eg. if n0 is 0, that's okay because we won't have any 0's to code so it's okay that they're impossible to code.

Now, how do you do your entropy coding? You could feed p0&p1 to arithmetic coding, ANS, to an enumerative coder (since we know n0 and n1, we are just selecting one of the arrangements of those bits, of which there are (n0+n1)!/n0!n1! , and those are all equally likely, so just send an integer that selects one of those), you could group up bits and use huffman. For now we don't care how the back end works, we're just trying to model the probability to feed to the back end.

If n0 and n1 are large, they are probably specifying more precision than the coder can use, which is wasting bits. So maybe you want to send an approximation of just p0 in 14 bits or whatever your back-end can use.

If you do send n0 and n1 exactly, then obviously you don't need to send the file length (it's n0+n1), and furthermore you can gain some efficiency by decrementing n0 or n1 as you go, so that the last symbol you see is known exactly.

Okay, so moving on to adaptive estimators. Instead of transmitting p0 up front, we will start with no a-priori knowledge of the stream (hence p0 = 50%), and as we encounter symbols, we will update p0 to make it the best estimate based on what we've seen so far. The standard solution is :

Encoder & Decoder start with n0 and n1 = 0

Encoder & Decoder form a probability from the n0 and n1 seen so far

p0 = (n0 + B)/(n0+n1 + 2B)

symbols are coded with the current estimate of p0
after which n0 or n1 is incremented and a new p0 is formed

B is a constant bias factor
if B = 1/2 this is a KT estimator (optimal in a specific synthetic case, irrelevant)
if B = 1 this is a laplace estimator

Note that the bias B must be > 0 so that we can encode a novel symbol, eg. coding the first 0 bit when n0 = 0.

There's stuff in the literature about "optimal estimators" but it's all a bit silly, because the optimal estimator depends on the source and what the distribution of possible sources is.

That is, say you actually are getting bits from a stationary source that has a true (unknown) probability of 0 bits, T0. You could see a wide variety of sources with different values of T0, which occur with probability P(T0). After you see some bits, n0 and n1, you wish to compute a p0 which minimizes the expected codelen of the next symbol you see. To do that, you can compute the relative probability of seeing n0 and n1 events from a source of probability T0. But to form the correct final estimate you must have the information about the a-priori likelihood of each source P(T0) which in practice you never have.

So we have these estimators for stationary sources, but in the real world you almost never have a stationary source. So let's start looking at estimators we might actually want to use in the real world.

(it may actually be a pretty stationary source, but it could be stationary only under a more complex model, and any time you are not fully modeling the data, stationary sources appear to be dynamic. This is like flatlanders in 2d watching a 3d object move through their plane - it may actually be a rigid body in a higher dimension, but it looks dynamic when you have an incomplete view of it. For example data that has Order-1 correlation (probability depends on the previous symbol) will appear to have dynamic statitics under only an order-0 model (the probabilities will seem to change after each symbol is coded))

Let's start with the "static" case, transmitting p0 or n0/n1. We can improve it by just breaking the source into chunks and transmitting a model on each chunk, rather than a single count for the whole buffer. These chunks could be fixed size, but there are sometimes large wins by finding the ideal places to put the chunk boundaries. This is an unsolved problem in general, I don't know of any algorithm to do it optimally (other than brute force, which is O(N!) or something evil like that), we use hacky heuristics. Obviously chunks have a cost in that you must spend bits to indicate where the chunk boundaries are, and what the probabilities are in each chunk, so you must count the cost to send the chunk information vs. the bits saved by coding with different probabilities.

(the most extreme case is a buffer that has n0=n1, which would take n0+n1 bits to send as a single chunk, but if in fact all the 0's are at the start, and all the 1's are the end, then you can cut it into two chunks, in the first chunk p0=100% so the bits are sent in zero bits, in the second chunk p0=0% , so the total size is only the overhead of specifying the chunks and probabilities)

A slightly more sophisticated version of this scheme is to have several probability groups and to be able to switch between them from chunk to chunk, that is :

send the # of models, M
send the models
  in the binary case, p0 or n0/n1 for each model

send the # of chunks
for each chunk :
  send its length
  send a model selection m in [0,M)
  send the data in that chunk using model m

In a binary coder this is a bit silly, but in a general alphabet coder, the model might be very large (100 bytes or so), so sending the model selection m is much cheaper than sending the whole model. This method allows you to switch rapidly between models at a lower cost. eg. if your data is like 000000111111111100000001111111000000 - the runs of different-character data are best coded by switching between models. (we're still assuming we can only use order-0 coding). (this is what Brotli does)

Now moving on to adaptive estimators.

The basic approach is that instead of forming an estimate of future probabilities by counting all n0 and n1 events we have seen in the past, we will count based on what we've seen in the recent past, or weight more recent events higher than old ones.

This is rarely done in practice, but you can simply count the # of each symbol in a finite window and update it incrementally :

at position p
code bit[p]

p0 = (n0 + B)/(n0+n1 + 2B)

after coding, increment n0 or n1

if (n0+n1) = T , desired maximum total
  remove the bit b[p - T]
  by subtracting one from n0 or n1

this has the advantage of keeping the sum constant (once the sum reaches T), which you could use to make the sum power of 2. But it requires you actually have the previous T bits, which you usually don't if you are using the adaptive coder as part of a larger model.

This does illustrate a problem we will face with many of these adaptive estimators. There's an initial run-up phase. They start empty with no symbols seen, then count normally up to T, at which point they reach steady state.

A common old-fashioned approach is to renormalize the total to T/2 once it reaches T. This was originally done as a way of limitting the sum T inside the range allowed by the entropy coder (eg. it must fit in 14 bits in old arithmetic coders so that the multiplies fit in 32 bits). It was found that applying limits like this didn't hurt compression, they in fact help in practice, because they make the statistics more adaptive to local changes.

after coding increment n0 or n1

if (n0+n1) = T
    n0 /= 2 , n1 /= 2;

This is actually the same as a piecewise-linear approximation of geometric falloff of counts. A true geometric update is like this :

once steady state is reached :
n0+n1 == T always

after coding
n0 or n1 += 1 
n0+n1 == T+1 now

n0 *= T/(T+1)
n1 *= T/(T+1)

now n0+n1 == T again

this is equivalent to doing :

n0 or n1 += inc
inc *= (T+1)/T

let G = (T+1)/T is the geometric growth factor

events contribute with weights :


now, nobody does a geometric update quite like this because it requires high precision counts (though you can do piecewise linear approximations of this and fixed point versions, which can be interesting). There is a way to do a geometric update in finite precision that's extremely common :

p0 probability is fixed point (12-14 bits is common)

at steady state

after coding a 1 : p0 -= p0 >> updshift
after coding a 0 : p0 += (one - p0) >> updshift

this is equivalent to the "renorm every step to keep n0+n1 = T" with T = 1<<updshift

This gives an efficient way to do a very recency-biased (geometric) estimator. For most of the estimators I'm talking about, the non-binary alphabet extension is obvious, and I'm just doing binary here for simplicitly, but in this case the non-binary alphabet version is non trivial. Fabian works it out here : Mixing discrete probability distributions , and Models for adaptive arithmetic coding .

For people familiar with filtering, it should be obvious that what we're really doing here is running filters over the previous events. The "window" estimator is a simple FIR filter with a box response. The geometric estimator is the simplest IIR filter.

In all our (adaptive) estimators, we have ensured that P0 and P1 are never zero - we need to be able to code either bit even if we've never seen one before.

To do this, we often add on a count to n0 and n1 (+B above), or ensure it's non-zero.

In the binary updshift case, the minimum of p0 is where (p0 >> updshift) is zero, that's

p0min = (1 << updshift) - 1

which in practice is actually quite a large minimum probability of the novel symbol. That turns out to be desirable in very local fast-adaptive estimators. What you want is if the last 4 events were all 1 bits, you want the probability P1 to go very high very fast - but you don't want to be over-confident about that local model matching future bits, so you want P0 to stay at some floor.

Essentially what we are doing here is blending in the unknown or "flat" model (50/50 probability of 0 or 1 bit) with some desired weight. So you might have a very jerky strongly adapting local model, but then you also blend in the flat model as a hedge.

The geometric update be extended to "two speed" :

track two running estimators, p0_a and p0_b

make p0 = (p0_a + p0_b)/2
use p0 for coding

after the event is see update each with different speeds :

after coding a 1 : p0_a -= p0_a >> updshift_a
after coding a 0 : p0_a += (one - p0_a) >> updshift_a

and p0_b with updshift_b

eg. you might use
updshift_a = 4 (a very fast model)
updshift_b = 8 (a slower model)
(with one = 1<<14)

Naively this looks like an interesting blend of two models. Actually since it's all just linear, it's in fact still just an IIR filter. It's simply a slightly more general IIR filter; the previous one was a one-tap filter (previous total and new event), this one is a two-tap filter (two previous totals and new event).

But this leads us to somethat that is interesting, which is more general blending.

You could have something like 3 models : flat (all symbols likely), a very fast estimator that strongly adapts to local statistics, and a slow estimator (perhaps n0/n1 counts for the whole file) that is more accurate if the file is in fact stationary.

Then blend the 3 models based on local performance. The blend weight for a simple log-loss system is simply the multiple of probabilities of that model on the preceding symbols.

Now, a common problem with these IIR type filters is that they assume steady state. You may recall previously we talked about the renormalization-based adaptive coder that has two phases :

track n0,n1

ramp-up phase , while (n0+n1) < T
  initialize n0=n1=0
  n0 or n1 += 1

stready-state :
  when n0+n1 = T , renorm total to T/2
  n0 or n1 += 1

If you're doing whole-file entropy coding (eg. lots of events) then maybe the ramp-up phase is not important to you and you can just ignore it, but if you're doing context modeling (lots of probability estimators in each node of the tree, which might not see very many events), then the ramp-up phase is crucial and can't be ignored.

If you want something efficient (like the updshift geometric model), but that accounts for ramp-up vs steady state, the answer is table lookups. (the key difference in the ramp-up phase is that adaptation early on is much faster than once you reach steady state)

This actually goes back to the ancient days of arithmetic codec, in the work of people like Howard & Vitter, and things like the Q-coder from IBM.

The idea is that you have a compact state variable which is your table index. It starts at an index for no events (n0=0,n1=0), and counts up through the ramp-up phase. Then once you reach steady state the index ticks up and down on a line like the p0 in updshift. Each index has a state transition for "after a 0" and "after a 1" to adapt. Something like :

ramp-up :

0: {0,0} -> 1 or 2
1: {1,0} -> 3 or 4
2: {0,1} -> 3 or 5
3: {1,1} -> 6 or 7
4: {2,0} -> 
5: {0,2} -> 


then say T = 16 is steady state, you have

{0,16} {1,15} {2,14} ... {16,0}

that just transitions up and down

And obviously you don't need to actually store {n0,n1}, you just store p0 in fixed point so you can do divide-free arithmetic coding. So there's like a tree of states for the ramp-up phase, then just a line back and forth at steady state.

And those states are not actually what you want at steady state. Actually finding the ideal probabilities for steady state is complex and in the end can only be solved by iteration. I won't go into the details but just quickly touch on the issues.

You might start with a mid point at p0=0.5 , at simulated T=16 that corresponds to {8,8} , so you consider stepping to {8,9} after seeing a 1 and renormalize to T=16, that gives p0=8/17 = 0.47059 ; that corresponds to a geometric update with scaling factor G = 17/16. If you keep seeing 1's, then p0 keeps going down like that. But if you saw a 0, then p0 -> p0 + (1 - p0) * (1 - 1/G) , so 0.47059 -> 0.50173 , which is not back to where you were.

This should be intuitive because with geometric recency, if you see a 1 bit then a 0 bit, the 0 you just saw counts a bit more than the 1 before, so you don't get back to the midpoint. With geometry recency the p0 estimated for seeing bits 01 is not the same as after seeing 10 - the order matters. This is also good intuition why simple counting estimators like KT are not very useful in data compression - the probability of 0 after seeing "11110000" is most likely the not the same after seeing "00001111" . Now you might argue that we're asking our order-0 estimator to do non-order-0 things, we aren't giving it a memoryless bit, we should have used some higher order statistics or a transform or something first, but in practice that's not helpful.

The short answer is you just need lots of states on the steady-state line, and you have to numerically optimize what the probability in each state is by simulating what the desired probability is when you arive there in various ways and averaging them; a kind of k-means quantization type of thing.

Another issue is how you do the state transition graph on the steady-state line. When you are out at the ends, say very low p0 so a 1 bit is highly predicted - if you see another 1 bit, then p0 does not change very much, but if you see a 0 bit (unexpected), then p0 should change a lot. This is actually information theory in a microcosm - when you see the expected events, they don't jar your model very much, because they are what you expected, they contain little new information, when you see events that had very low probability, that's huge information and jars p0 a lot.

(there's some ancient code for a coder like this and a table in crblib ; "rungae.c" / "ladder.c")

You could store the # of steps to take up or down after seeing a 0 or 1 bit. One of them could be implicit. For example when you see a more probable symbol, always take 1 step, when you see a less probable symbol, take many steps (maybe 3). Another clever way to do it is used in the Q-coder (and QM and MQ). They have a steady state line of states, but only change state when the arithmetic coder outputs a bit. This means you have to see 1/log2(P) events before you change states, which is exactly what you want - when P is very high, log2(P) is tiny and you won't step until you see several. This method cannot be used in modern arithmetic coders that output byte by byte, it requires bitwise renormalization. It's neat because it lets you use a very tiny table (53 states) and you can put the density where you need it (mostly around p0=0.5) but still have states way out at the extreme probabilities to code them efficiently.

The next step in the evolution is secondary statistics.

If you have this {n0,n1} state transition table in the last section, that's a state index. The straightforward way to do it is that each state has a p0 precomputed that corresponds to n0,n1 and you use that for coding.

With secondary statistics, instead of using the p0 that you *expected* to observe for given past counts, you use the p0 that you actually *observed* in that same state in the past.

Say you're in a given state S after seeing bits 0100
(n0 =3, n1 =1 , but order matters too)

You could compute the p0 that should be seen after that sequence with some standard estimator
(geometric or KT or whatever)

Or, screw them.  Instead use S as a lookup to a secondary model.


contains the n0 and n1 actually coded from the state S
previous times that you were in state S

This was the SEE idea from PPMZ (then Shkarin's PPMD (different from Teahan's PPMD) and Mahoney's PAQ (sometimes called APM there)). In the real world there are weird nonlinearities in the actual probabilities of states that can't be expressed well with simple estimators. Furthermore, those change from file to file, so you can't just tabulate them, you need to observe them.

A common hacky thing to do is to use a different estimator if n0=0 or n1=0 ; eg. if one of the possible symbols has never been seen at all, special case it and don't use something like a standard KT estimator that gives it a bias to non-zero probability. This is done because in practice it's been observed that deterministic contexts have very different statistics. Really this is just a special case version of something more general like secondary statistics.

The other big step you could take is mixing. But that's rather going beyond simple order-0 estimators so I think it's time to stop.

02-01-17 | Oodle Hydra

Oodle Hydra - the many headed beast.

Hydra is a meta-compressor which selects Kraken, Mermaid, or Selkie per block. It uses the speed fit model of each compressor to do a lagrangian space-speed optimization decision about which compressor is maximizing the desired lagrange cost (size + lambda*time).

It turns out to be quite interesting.

(this is of course in addition to each of those compressors internally making space-speed decisions; each of them can enable or disable internal processing modes using the same lagrange optimization model. (eg. they can turn on and off entropy coding for various streams). And there are additional per-block implicit decisions such as choosing uncompressed blocks and huff-only blocks.)

Hydra is a single entry point to all the Oodle compressors. You simply choose how much you care about size vs. decode speed, that corresponds to a certain lagrange lambda. In Oodle this is called "spaceSpeedTradeoffBytes". It's the # of bytes that compression must save in order to take up N cycles more of decode time. You then no longer think about "do I want Kraken or Mermaid" , Oodle makes the right decision for you that optimizes the goal.

Hydra can interpolate the performance of Kraken & Mermaid to create a meta-compressor that targets the points in between. That in itself is a somewhat surprising result. Say Kraken is at 1000 mb/s , Mermaid is at 2000 mb/s decode speed, but you really want a compressor that's around 1500 mb/s with compression between the two. We don't know of a Pareto-optimal compressor that is between Kraken and Mermaid, so you're sunk, right? No, you can use Hydra.

I should note that Hydra is very much about *whole corpus* performance. That is, if your target is 1500 mb/s, you may not hit that on any one file - that file could go either all-Kraken or all-Mermaid. The target is hit overall. This is intentional and good, but if for whatever reason you are trying to hit a specific speed for an individual file then Hydra is not the way to do that.

It leads to an idea that I've tried to advocate for before : corpus lagrange optimization for bit rate allocation. If you are dealing with a limited resource that you want to allocate well, such as disk size or download size or time to load - you want to allocate that resource to the data that can make the best use of it. eg. spend your decode time where it makes the biggest size difference. (I encourage this for lossy bit rate allocation as well). So with Hydra some files decode slower and some decode faster, but when they are slower it's because the time was worth it.

And now some reports. We're going to look at 3 copora. On Silesia and gametestset, Hydra interpolates as expected. But then on PD3D, something magic happens ...

(Oodle 2.4.2 , level 7, Core i7-3770 x64)

Silesia :

total                : Kraken     : 4.106 to 1 : 994.036 MB/s
total                : Mermaid    : 3.581 to 1 : 1995.919 MB/s
total                : Hydra200   : 4.096 to 1 : 1007.692 MB/s
total                : Hydra288   : 4.040 to 1 : 1082.211 MB/s
total                : Hydra416   : 3.827 to 1 : 1474.452 MB/s
total                : Hydra601   : 3.685 to 1 : 1780.476 MB/s
total                : Hydra866   : 3.631 to 1 : 1906.823 MB/s
total                : Hydra1250  : 3.572 to 1 : 2002.683 MB/s

gametestset :

total                : Kraken     : 2.593 to 1 : 1309.865 MB/s
total                : Mermaid    : 2.347 to 1 : 2459.442 MB/s
total                : Hydra200   : 2.593 to 1 : 1338.429 MB/s
total                : Hydra288   : 2.581 to 1 : 1397.465 MB/s
total                : Hydra416   : 2.542 to 1 : 1581.959 MB/s
total                : Hydra601   : 2.484 to 1 : 1836.988 MB/s
total                : Hydra866   : 2.431 to 1 : 2078.516 MB/s
total                : Hydra1250  : 2.366 to 1 : 2376.828 MB/s

PD3D :

total                : Kraken     : 3.678 to 1 : 1054.380 MB/s
total                : Mermaid    : 3.403 to 1 : 1814.660 MB/s
total                : Hydra200   : 3.755 to 1 : 1218.745 MB/s
total                : Hydra288   : 3.738 to 1 : 1249.838 MB/s
total                : Hydra416   : 3.649 to 1 : 1381.570 MB/s
total                : Hydra601   : 3.574 to 1 : 1518.151 MB/s
total                : Hydra866   : 3.487 to 1 : 1666.634 MB/s
total                : Hydra1250  : 3.279 to 1 : 1965.039 MB/s

Whoah! Magic!

On PD3D, Hydra finds big free wins - it not only compresses more than Kraken, it decodes significantly faster, repeating the above to point it out :

total                : Kraken     : 3.678 to 1 : 1054.380 MB/s

total                : Hydra288   : 3.738 to 1 : 1249.838 MB/s
 Kraken compression ratio is in between here, around 1300 MB/s
total                : Hydra416   : 3.649 to 1 : 1381.570 MB/s

You can see it visually in the loglog plot; if you draw a line between Kraken & Mermaid, the Hydra data points are above that line (more compression) and to the right (faster).

What's happening is that once in a while there's a block where Mermaid gets the same or more compression than Kraken. While that's rare, when it does happen you just get a big free win from switching to Mermaid on that block. More often, Mermaid only gets a little bit less compression than Kraken but a lot less decode time, so switching is advantageous in the space-speed lagrange cost.

Crucial to Hydra is having a decoder speed fit for every compressor that can simulate decoding a block and count cycles needed to decode on an imaginary machine. You need a model because you don't want to actually measure the time by running the decoder on the current machine - it would take lots of runs to get reliable timing, and it would mean that you are optimizing for the exact machine that you are encoding on. I currently use a single virtual machine that is a blend of various real platforms; in the future I might expose the ability to use virtual machines that simulate specific target machines (because Hydra might make decisions differently if it knows it is targeting PC-x64 vs. Jaguar-x64 vs. Aarch64-on-A57 , etc.).

Hydra is exciting to me as a general framework for the future of Oodle. It provides a way to add in new compression modes and be sure that they are never worse. That is, you always can start with Kraken per block, and then new modes could be picked block by block only when they are known to beat Kraken (in a space-speed sense). It lets you mix in compressors that you specifically don't expect to be good in general on all data, but that might be amazing once in a while on certain data.

(Hydra requires compressors that carry no state across blocks, so you can't naively mix in something like PPM or CM/PAQ. To optimize a switching choice with compressors that carry state requires a trellis-quantization like lattice dynamic programming optimization and is rather more complex to do quickly)

01-23-17 | How I Think about Compression

Casey asked me to talk about compression, the specific prompt was "how do you think about compression?" . I talked with him yesterday, and I thought I would add some more notes.

The video of the conversation is on Youtube

(also see the preceding chat with Fabian & Jeff at Handmade Con on Youtube )

The way I think about compression is the way I approach all technical problems. I come from a math/science background, and I like to understand the theory behind things. So in the background I'm always thinking about basic coding theory, entropy, probabilities, conditional probability, etc.

When I start on a new problem, or am exploring a new data compression space, I usually start by writing a compressor in the most obvious way, not worrying about efficiency, using standard model-coder patterns.

I then start looking at what is going on in the data. One way to do that is by making charts and gathering statistics. Another way is simply to try adding or removing things from the model and checking your compression.

Usually I will keep adding things to the model, trying to find things that are helpful correlations. Does the previous byte help? Does the position help? Does the distance to the last byte with the same value help? Keep tossing them in.

Then I will start to try to make things more efficient. I start cutting things out of the model that only help a little bit. Try to bake it down to the simplest thing that captures most of the structure of the data. eg. if I code the value as log2 + remainder bits does that hurt?

Once I have an idea of which factors make a big difference and which don't, I then throw all that work away and start over. Writing a final efficient implementation may actually be totally different, but starting from a simple model-coder allowed a clean way to get an understanding of the problem space.

Principle : Algorithm options, question everything

This is a principle I follow in data compression, but also in all algorithm implementation. There are lots of places in the algorithm where you have choices. Many of the things are arbitrary or not well justified. Any time I'm reading a paper on data compression and they say "we did X this way" I think "why?" and "is there a better way?" or "what about other options?".

When you increment the count of your statistics after seeing a symbol, why do +1? Why not +2? Why not + (previous_count*0.10)+1 ? Why not a file-specific count?

Unless something is rigorously set in stone that it mathematically must be a certain way, then it's something I will explore. As I go through understanding an algorithm, I keep popping these things on my stack, todo : try other options. Obviously some intuition is required here to guess what is fruitful to test and what is not.

Data compression models are designed to learn the structure of the data. However, the choice of data compression model *type* is also a modeling step. That is, you must know something about the data to choose the model that fits the data. For example, PPM can only learn a byte-oriented finite-context model of the data. Aside from just trying to make the PPM as good as possible, it will only capture that one type of model of the data and could totally miss other things.

The implicit model of LZ77 is that it predicts strings are more likely to occur again, proportionally to how often they have occurred in the past. The exact model in LZ77 is a little subtle (see Langdon), but the variant LZSA is very easy to show an exact model correspondence.

Most compressors are very generic and find their compression from simple assumptions about what data is likely (data that's likely has some bytes that occur more often than others, bytes are likely to repeat in their neighborhood, etc.). If you know something specific about your data you can of course make a better model and get better compression than a generic solution.

One thing I think about a lot is *what* do I want an encoder to optimize. Not how (which is also a big problem), but what is the goal of the optimization. Many data compression encoders are optimizers, or searches in a big space. They are trying to optimize some metric. It's easy to say that you want to minimize error in a lossy codec, or that you want to minimize size in a lossless codec, but that's often wrong. In a lossy codec, what is the right way to quantify distortion? The answer depends partly on how the content will be used. How do approximations of distortion affect the search and result? In lossless codecs, you might want to consider speed or memory use or other factors in the optimization.

Principle : decoder first design.

For performance, we design codecs decoder first. It starts by thinking about how you want to arrange the execution flow for the decoder, and then how can the encoder get data into the form that the decoder wants.

Principle : try the exact solution first.

I almost never just start hacking away with heuristics and approximations. I like to know what is the exact answer to the problem first. If it's something that is solveable in reasonable time, I'll write an exact solver before I go messing around with approximations.

For example in lossy coding, there is usually one place in the codec where you are intentionally introducing loss in a controlled way (usually a quantization step, possibly in DCT domain). But there are also other places where you may be unintentionally introducing loss, perhaps in your colorspace transform, or your downsample-upsample pass, or by approximating the DCT for speed, or in scaling to stay in small integers, possibly in other places you aren't aware of. I like to do a first implementation where those losses are as low as possible, do everything right with zero cost.

This gives a reference to know how good your quality should be, and also how fast the exact answer is. Then when you start making approximations and using heuristics, you can compare and say - exactly how much is this costing me (in quality) and how much speed am I gaining? Is it worth it?

01-20-17 | Oodle on the Nintendo Switch

Oodle is coming soon to the Nintendo Switch (NX), an ARM A57 device.

Initial performance test vs. the software zlib (1.2.8) provided in the Nintendo SDK :

lzt99                : nn_deflate : 1.883 to 1 : 74.750 MB/s
lzt99                : LZNA       : 2.723 to 1 : 24.886 MB/s
lzt99                : Kraken     : 2.549 to 1 : 238.881 MB/s
lzt99                : Hydra      : 2.519 to 1 : 274.433 MB/s
lzt99                : Mermaid    : 2.393 to 1 : 328.930 MB/s
lzt99                : Selkie     : 1.992 to 1 : 660.859 MB/s

total                : nn_deflate : 1.883 to 1 : 74.750 MB/s
total                : LZNA       : 2.723 to 1 : 24.886 MB/s
total                : Kraken     : 2.549 to 1 : 238.881 MB/s
total                : Hydra      : 2.519 to 1 : 274.433 MB/s
total                : Mermaid    : 2.393 to 1 : 328.930 MB/s
total                : Selkie     : 1.992 to 1 : 660.859 MB/s

Kraken is 3.21X faster than zlib, with way more compression (35% more).

All tests single threaded, 64-bit.

Commentary :

Kraken seems to be the sweet spot on the NX. Mermaid is not as much of a speed gain on the ARM A57 as it is on other chips (most x64 chips, for example), which means taking the compression hit of Mermaid vs Kraken is not as attractive. (ADD : these conclusions may be premature, see below)

I've also included Hydra, at a space-speed tradeoff value between Kraken & Mermaid (sstb=300). It's a bit subtle, perhaps you can see it best in the loglog chart, but Hydra here is not just interpolating between Kraken & Mermaid performance, it's actually beating both of them in a Pareto frontier sense.

ADD : the speeds above were from the first port of Oodle to NX ; we've been doing some work since then and they're getting better. Mermaid & Selkie got a lot faster. Kraken will get faster too and we'll have a nice rev in a few months.

Mermaid :
decode           : 66.752 millis, 2.75 c/b, rate= 370.04 mb/s
Selkie :
decode           : 28.258 millis, 1.16 c/b, rate= 874.12 mb/s

11-13-16 | Thinking About Data Compression : Global Feedback

Almost every modern data compression codec has a global feedback problem. There is no tractable rigorous solution to this problem. Here I will describe a few examples of this problem and a few of the heuristics we use to address it.

The global feedback problem is the problem that local decisions in the coder affect future coding, in a way that is too complex to track. Modern coders often have choices of how to code the current event, and evaluate those coding choices by computing a cost for them. What we do is to just pretend that that decision is the last, that we don't care about how it affects the future.

All lossy codecs have this problem, because in lossy codecs you always have coding choices (you can introduce more or less loss; even in codecs that don't seem to have multiple ways to code a block (eg. perhaps a wavelet codec, not MPEG style) you always actually do have choices, you can choose to degrade the current pixel, eg. perhaps zero some small high-frequency wavelet). Lossless codecs that are over-complete (eg. provide multiple ways to send the same data) (such as LZ) also have this problem. Lossless codecs that are strongly constrained (only one way to send a given coding event) do not have this problem.

In some cases we do deal with the global feedback on some limited tractable portion of the coding choice. For example in LZ we do "optimal parsing" ; this accounts only for the very limited feedback issue that the location of the termination of the current codeword affects future coding costs, but in LZ optimal parsing does not account for the way current choices affect the future offset cache, or the future entropy coder state. In lossy DCT codecs we might do "trellis quantization" which is a simple model of a quantizer where each coefficient coding only depends on the one previous (in its simplest form it only depends on whether the previous was zero or not, so only two states). The large benefits of optimal parsing & trellis quantization are demonstrations of how significant this global optimization problem is.

Put another way, the issue is that the current decision is part of the history for future decisions, and many modern codecs have very long histories that are used as part of the coding of current decisions. While it is possible to efficiently evaluate the current decision based on a fixed history, it's not possible to consider how the current decision affects the future by giving them different histories.

Obviously this affect is stronger at the begininng of each coding block, and less important near the end. The very last decision can be made purely locally.

Techniques :

1. Guiding to expectation.

The general technique here is to bias local decisions towards what we expect to be more useful as history in the future. This is generally done using a-priori knowledge of how we expect good coded streams to behave.

This can be done by biasing code costs to favor choices that match the guide. Another way is to seed or limit searches to only explore the area around the neighborhood of the expected good choice.

Sometimes the guidance strength is adaptive; it may start higher at the beginning of coding and decrease (even to zero) once the model is sufficiently strong to act as enough guidance on its own.

Quite often codecs do guidance without being explicit about it (they might not even be aware of what they are doing). For example most LZ codecs have lots of simple heuristics like - if a match is found of length >= 4, then never choose a literal, or if two matches are found with the same offset, always choose the lower offset. These heuristics might be intended as simplifications or for speed, but in fact they strongly guide the coding towards a certain a-priori expectation. (another common example of unintentional guidance is local movec search)

Another common form of guidance is "fudge factors". Many who have experimented in data compression have seen that if they get the cost estimate for local decisions slightly wrong, it makes the result better. The reason is that the wrong cost acts as a fudge factor to bias the local decision to one that is worse if that decision is the last, but that provides a better global solution. For example in LZ it's common to fudge the costs so that rep-matches appear cheaper than they really are (normal matches & literals appear more expensive) or that longer matches appear cheaper. Note that this fudging is also faking a lagranging space-speed optimization cost.

2. Iteration and model pre-conditioning.

One general approach to this problem is iteration. Run the coding once, then save the model (history) that was observed in the first coding, and use it as history in the next coding pass.

The idea here is that once the model is well established, it provides guidance towards coding that works well within that model. The problem is that at the beginning of coding, the model is empty, so all choices seem to cost the same, and there's no particular reason for coding to proceed in any particular direction. By using the model from the end of coding at the beginning of the next iteration, it makes the choices in the beginning direct towards ones that we used last time at the end, so we expect we will want to use those choices again at the end, and by making them at the beginning on the next pass we decrease their cost at the end.

A related variant of this is to use pre-conditioned models, based on expectation or measurement on a corpus. This builds up an expected or average model, which we use to seed the coder, and as long as the data to code is structural similar to the expectation, the pre-conditioned model will provide direction towards a good global solution. Of course pre-conditioning can also reduce the cost of early coding events (relative to starting with a blank model), but here we are not so much concerned as the net savings in coding cost that come from preconditioning as we are concerned with the fact that pre-conditioning makes some decisions relatively cheaper than others and thus acts as guidance.

Examples :

1. LZ

In modern LZ there are many ways to code every stream. At each coding event you might have options for literal, rep-match, or normal-match. There are also parse choices which can make any given point in the stream either be a participating coding event or not. We won't discuss parse here.

Local decisions act as history for future decisions through the rep match cache and through the entropy coder.

We have a-priori ideas about what well-behaved LZ streams look like. rep-matches are the cheapest way to code things, long normal matches are next best, least desirable is short normal matches and literals. We expect low offsets to be more frequent - this has an effect not only on the entropy coder feedback but also on the rep match cache (you want to bias towards offsets that will be useful again in the future; simply prefering lower offsets accomplishes much here).

2. Motion Vectors @@

3. Adaptive VQ Codebooks @@ guiding (fudging) iteration

.. bleh got bored of this post .. guiding (fudging) iteration

08-29-16 | Shrinking Data for Fun & Profit

Dietmar Hauser did a talk at GDCE called "Shrinking Data for Fun & Profit" . It covers a lot of data compression background, and includes some comparison of Oodle to other options :

The slides and talk are available :

gdcvault slides
gdcvault talk

It's a very thorough talk for people in the game industry who want some background on data compression. Thanks to Dietmar for including Oodle!

08-20-16 | PNG without ZLib

If you need to send PNG images in a compressed archive, here's a tip.

PNG's are internally compressed with Zlib. When you run another compressor (such as Oodle) on an already-compressed file like PNG, it won't be able to do much with it. It might get a few bytes out of the headers, but typically the space-speed tradeoff decision in Oodle will not think that gain is worth bothering with, so the PNG will just be sent uncompressed.

There are a few reasons why you might want to use an Oodle compressor rather than the Zlib inside PNG. One is to reduce size; some of the Oodle compressors can make the files smaller than Zlib can. Another is for speed, if you use Kraken or Mermaid the decoder is much faster than the Zlib decompression in PNG.

Now obviously if you want the smallest possible lossless image, you should use an image-specific codec like webp-ll , but we will assume here that that isn't an option.

You could of course just decode the PNG to BMP or TGA or some kind of simple sample format, but that is not desirable. For one thing it changes the format, and your end usage loader might be expecting PNG. Your PNG's might be using PNG-specific features like borders or transparency or whatever that is hard to translate to other formats.

But another is that we want the PNG to keep doing its filtering. Filtered image samples from PNG will usually be more compressible by the back-end compressor than the raw samples in a BMP.

The easy way to do this all is just to take an existing PNG and set its ZLib compression level to 0 (just store). You keep all the PNG headers, and you still get the pixel filtering. But the samples are now uncompressed, so the back-end compressor (Oodle or whatever) gets to work on them instead of passing through already-ZLibbed data.


pngcp is a utility from the official libpng distribution. It reads & writes a png and can change some options.

Usage for what we want is :

pngcp --level=0 --text-level=0 from.png to.png

I have made a Win32 build with static libs of pngcp for your convenience :


I also added a --help option ; run "pngcp --help". The official pngcp seems to have no help or readme at all that explains usage.

I *think* that pngcp preserves headers & options & pixel formats BUT I'M NOT SURE, it's not my code, YMMV, don't go fuck up your pngs without testing it. If it doesn't work - hey you can get pngcp from the official distro and fix it.

I used libpng 1624. The vc7.1 project in libpng worked fine for me. pngcp needed a little bit of de-unixification to build in VC but it was straightforward. You need zlib ; I used 1.2.8 and it worked fine; you need to make a dir named "zlib" at the same level as libpng. I did "mklink /j zlib zlib-1.2.8".

* CAVEAT : this isn't really the way I'd like to do this. pngcp loads the PNG and then saves it out again, which introduces the possibility of losing metadata that was stuffed in the file or just screwing it up somehow. I'd much rather do this conversion without ever actually loading it as an image. That is, take the PNG file as just a binary blob, find the zlib streams and unpack them, store them with a level 0 header, and pass through the PNG headers totally untouched. That would be a much more robust way to ensure you don't lose anything.


cbpngz0 usage :

cbpngz0 from to

cbpngz0 uses the cblib loaders, so it can load bmp,tga,png,jpeg and so on. It writes a PNG at zlib level 0. Unlike pngcp, cbpngz0 does NOT support lots of weird formats; it only writes 8-bit gray, 24-bit RGB, and 32-bit RGBA. This is not a general purpose PNG zlib level changer!! Nevertheless I find it useful because of the wider range of formats it can load.


cbpngz0 is an x64 exe and uses the DLLs included.

Some sample results.

I take an original PNG, then try compressing it with Oodle two ways. First, convert it to a BMP and compress the BMP. Second, convert to a Zlib level 0 PNG (the "_z0.png") and then compress with Oodle. The differene between the two is that the _z0.png gets the PNG filters, and of course stays a PNG if that's what your loader expects. If you give the original PNG to Oodle, it passes it through uncompressed.

porsche640.png             529,821

porsche640.bmp             921,654

porsche640.bmp.ooz         711,273

porsche640_z0.png.ooz      508,091


blinds.png                 328,754

blinds.bmp               1,028,826

blinds.bmp.ooz             193,130

blinds_z0.png.ooz          195,558


xxx.png                    420,149

xxx.bmp                    915,054

xxx.bmp.ooz                521,861

xxx_z0.png.ooz             409,311

The ooz files are made with Oodle LZNA -z6 (level Optimal2).

You can see there are some big gains possible with replacing Zlib (on "blinds"). On normal photographic continuous tone images Zlib does okay so the gains are small. On those images, compressing the BMP without filters is very bad.

Another small note : if your end usage PNG loader supports the optional MNG format LOCO color transform, that usually helps compression.

ADD : Chris Maiwald points out that he gets better PNG filter choice by using "Z_FIXED" (which is the zlib option for fixed huffman tables instead of per-file huffman). A bit weird, but perhaps it biases the filter choice to be more consistent?

I wonder if choosing a single PNG filter for the whole image would be better than letting PNG do its per-row thing? (to try to make the post-filter residuals more consistent for the back end modeling stage). For max compression you would use something like a png optimizer that tried various filter strategies, but instead of rating them using zlib, rate with the back-end of your choice.

08-19-16 | Kraken recommended compressor settings

Some rambling about Kraken compressor setting selection.

OodleLZ_CompressionLevel_Optimal2 - (level 6) this is my default, goto high compress setting.

Most users of Kraken want max compression ratio and max decode speed. This should be your first choice for that. Encode speed and memory usage at encode time can be quite high.

Oodle's Optimal2 is pretty comparable to lzma -mx9 or ZStd max compression or any other optimal parse LZ with a strong string matcher.

For making your distributions I recommend Optimal2.

If Optimal2 is basically what you want, you might also try Optimal1 and Optimal3 which offer certain advantages :

OodleLZ_CompressionLevel_Optimal3 - (level 7) favors small size a bit more. Optimal3 can make measurably smaller files than Optimal2, so if the main thing you care about is size, not encode or decode time, then go with Optimal3.

Optimal3 not only works a little harder at encode time (thus takes a bit more time), it also enables some modes in the decoder which cause decodes to run a little slower. (maybe 10% slower to decode, eg. 950 mb/s instead of 1050 mb/s - still way way faster than anything else).

Because these modes slow down decode they aren't in Optimal2. The goal of Optimal 1 and 2 is to decode just as fast as the lower compress modes and maximize ratio under that constraint of preserving decode speed.

OodleLZ_CompressionLevel_Optimal1 - (level 5) faster to encode high compress mode.

Optimal1 is comparable to lzma's -mx5 mode, in both cases it's the fastest level that does an optimal parse.

Kraken's Optimal1 is a bit of a funny compromise. I don't generally recommend it. But if Optimal2 is too slow for you, then maybe Optimal1 does the trick. One thing you might like about Optimal1 is that it does very few memory allocations and is decent about limiting memory use, whereas Optimal2 is quite heavy on the memory subsystem.

(Optimal2 and higher can of course get very very slow if they run out of memory and start going to swap; if you have less than 8 GB of RAM, stick to Optimal1 and lower on very large files (over 100MB))

OodleLZ_CompressionLevel_Normal - (level 4) the default non-optimal parse mode.

Normal is memory limited and decently fast. Its encode speed is similar to ZLib.

Basically if you tried the Optimal modes and want something faster, your next step is to try Normal.

OodleLZ_CompressionLevel_Fast & OodleLZ_CompressionLevel_VeryFast - (level 3 and 2) ; these are for when you tried _Normal and want something a little faster.

We don't really have super-fast low-compression modes in Kraken yet (nothing comparable to ZStd's super fast low-compress modes, for example). All the Kraken levels, even VeryFast, are pretty high compression.

These modes can be useful for faster turnaround of daily iterative work, like when artists make new content and want to preview it in game or whatever.

The other thing you can play with in Kraken is the "spaceSpeedTradeoffBytes" option in the CompressOptions.

The CompressionLevel is generally a tradeoff of encoder time vs. compressed size - it tries to maintain decode speed (except for the aforementioned exception at Optimal3).

If you are willing to give up some decode speed to get smaller sizes, you do that with spaceSpeedTradeoffBytes.

The default is 256. To make smaller compressed files, make this number lower. Try 200 or 128. I don't think there's much reason to go below 128, you start giving up a lot of time for not much size gain.

I don't recommend making spaceSpeedTradeoffBytes higher than 300 or so with Kraken. The reason is that if you want more speed, you should be at some point switching to Mermaid. In Oodle 2.4 you can do that automatically by using "Hydra" (the many-headed beast) which will automatically select Kraken/Mermaid/Selkie based on your space-speed tradeoff. When you use Hydra, if you set spaceSpeedTradeoffBytes to 512, you might get a little of Kraken and a little of Mermaid).

08-17-16 | Patents

So, the Oodle DLL has been stolen and disassembled to reverse engineer some parts of Kraken.

We try to be very generous with our knowledge here. We write lots of articles about our technology discoveries. We don't patent anything because we believe patents are generally bullshit and other researchers should be able to make the same discovery.

We haven't written much about Kraken because it's mainly "engineering" not "science". It's very careful, sometimes very clever, very hard-fought engineering, but it's mostly implementation details. So when someone can just disassemble and steal those engineering details, it's incredibly disheartening.

The idea of not patenting our inventions is that independent researchers should be able to come up with the same inventions on their own, and we shouldn't have ownership of that idea. But that assumes a kind of honor code that those people are doing their own research, not just taking apart your creation to see how it works.

In the end of course Kraken will be taken apart and the ideas will get out, we can't stop that. There are lots of obvious clues to what it's doing that don't require dissasembly. We always knew that the ideas would get out - just the existance of Kraken and the possibility is in itself a valuable clue for researchers that there's something worth looking at in that space.

I think that we've done some pretty interesting research over the years, and we need to sell software to be able to live and support that research. It's an amazing environment at RAD that has supported us in doing full-time development of various ideas that don't always immediately pay off. It seems there are people who are opposed to the fact that we're trying to sell software, and I think that's fucking ridiculous.


Disassembling the Oodle lib is obviously illegal (*). This is not a legal reverse engineering (which you certainly could do, such as by passing in known buffers and looking at the output bytes from the compressor, or something like that). Without patents, our mechanism to enforce this is the evaluation agreement (which someone clearly violated) and copyright.

The disassembly is obvious enough that we could probably win against that specific copy of the code. But that's not really the problem.

We also don't really care about anyone figuring out the Kraken bitstream and having their own decoders. That was always bound to happen (as modders and hackers will want to get access to Kraken-encoded game data files).

What is disturbing is that there are now sure to be a raft of 2nd-generation codecs based on the stolen Kraken disassembly. They will come from people who have looked at the disassembly and seen the ideas, and then write their "own" version of those ideas from scratch. So in the future we might get a bunch of "new" "original" LZ codecs coming out with Kraken-like performance that are just based on what they stole from Kraken. That sucks.

(* = there appear to be many parts of the world where disassembly for "research purposes" is allowed. In those parts of the world, the law that allows disassembly for research trums the T&C or EULA that forbids disassembly. IANAL but I suspect that even in those places, wholesale disassembly and publishing of that code is still illegal, otherwise we would see it done much more often. In any case, trying to protect an implementation with just copyright is very difficult, which is why most people use patents.)

I find many things about this experience to be incredibly painful.

I think RAD in general has tried about as hard as possible to be one of the "good guys" that gives back to the community. We don't patent anything, we share our ideas, we've written extensively and put lots of great code in the public domain (such as on my blog & Fabian's).

Most of the money that's made off of compression is done in the most disgusting of ways, by getting patents on trivial obvious shit, then getting those patents to apply to an open standard that gets into DVDs or web browsers or whatever, so you get rich with no fucking real contribution to the world. In contrast, we actually invent major algorithms, we don't patent them, we try to make money by charging a one time fee to our clients with no strings attached. It's just about the hardest possible way to make money on compression.

Not only has RAD done about as much as possible to give back to the community, I've personally given huge huge amounts of my life to compression. Starting 20 years ago when I made LZP and PPMZ and order-1-huffman and secondary statistics and etc. etc. and gave it all away. I wrote about it, gave out source code, taught lots of people, answered questions in emails. I've basically never made a penny on any of that. More recently we've written about most of the things we've discovered in modern LZ, like optimal parse strategies, literals-after-match and LZ-sub, rep match cache strategies, ANS coders, etc. etc.

And the thanks we get is that when we invent something pretty special that we want to keep secret for a couple of years so we can sell it, it just gets stolen.

One of the extra disgusting things about the thieves is that they are so self-righteous, so victim-blaming, that somehow some aspect of our behavior makes us deserve it, or that stealing someone's livelihood, stealing someone's hard work and their fucking sweat and years of effort is somehow a benevolent act.

08-11-16 | Hashes

I've seen a bunch of hash comparos and fast hashes recently and I think they're all missing some basic points.

1. You make one consistent hash value. You don't get to have a hash function for 32-bit and one for 64-bit and make different values. Similarly you don't get to make different values in your SIMD hash.

It is very useful to have different code for 32-bit/64-bit/SIMD so that you can run well on different machines. But you have to always make the same value.

At the moment, hashes that rely on 64-bit maths are marginal IMO. There are still quite a bit of 32-bit devices out there (older mobile phones for example) and the hit of running something like 64-bit multiplies on those is too great.

And, crucially, the idea of speeding up the hash by using 64-bit scalar code is just wrong. Every mainstream processor that has 64-bit scalar also has SIMD, and running 32-bit hashes in SIMD is better.

2. I don't understand people who use SIMD to try to speed up linear code, or try to take linear code and just enable the advanced instructions in the compiler and think something magic will happen.

You don't just take some hash code that linearly scans a buffer and is full of dependencies and enable arch:avx2 in the compiler and expect anything magic. That's not how SIMD works. You need independent data flows and execution sequences that are fully parallel.

3. Why are you trying to use the same code on tiny buffers and huge buffers? They're totally different problems. How about

if ( len < 1024 )
    // use short hash
    // use long hash


In the case of hashing it's just so easy and obvious how to do it properly and I don't understand why nobody else seems to get it. (I'm talking about the long length case; for the short len case you just use FNV or something super simple with minimal rollup) (and in short len, small details can dominate, like whether you can inline the call and so on)

You hash with 32-bit registers. You do 4 (or 8) or whatever at a time independently. You always do 8 streams even in scalar mode, so that the value always comes out the same.

Then you have a final combine to mix the independent stream hashes.

There are two ways to do the multiple streams.

A. Interleaved. Each 32-bit value in order goes to a separate stream, like :


For 8-way. In this case the maximum SIMD width must be decided in advance so that the value can be consistent. (I would probably go with 8-wide for the future even though it would usually run 4-wide).

B. Chunked. Chunks of 4k or 16k or whatever bytes each get an independent hash. Like :


With the chunked method you can hash every chunk independently, so the SIMD width can be decided at runtime and still make the same hash value.

That's not to say that the recent hash work isn't awesome, and there are some crazy-fast good (non-cryptographic but highly likely to detect corruption) hashes out there.

07-29-16 | Slow slow compressors

lzma is really too slow to decode.

total                : Kraken     : 2.914 to 1 : 1053.961 MB/s
total                : lzma       : 3.186 to 1 : 52.660 MB/s

(Win64 Core i7-3770 3.4 GHz)

Kraken is around 20X faster than lzma, but lzma compresses better (about 9%). That's already a tip that something is horribly wrong; you have a 2000% speed difference and a 9% size difference.

If we look at the total time to load compressed from disk + decompress, we can make these speedup factor curves :

At very low disk speeds, the higher compression of lzma provides a speedup over Kraken. But how slow does the disk have to be? You can see the intersection of the curves is between 0 and 1 on the log scale, that's 1-2 MB/s !!

For any disk faster than 2 MB/s , load+decomp is *way* faster with Kraken. At a disk speed of 16 MB/s or so (log scale 4) the full load+decomp for Kraken is around 2X faster than with lzma. And that's still a very slow disk (around optical speed).

Now, this is a speedup factor for load *then* decomp. If you are fully overlapping overlapping IO with decompression, then some of the decode time is hidden.

*But* that also assumes that you have a whole core to give to decompression. And it assumes you have no other CPU to work to do after loading.

The idea that you can hide decompressor time in IO time only works if you have enough independent loads so that there's lots to overlap (because if you don't, then the first IO and last decompress will never overlap anything), and it assumes you have no other CPU work to do.

In theory I absolutely love the idea that you just load pre-baked data which is all ready to go, and you just point at it, so there's no CPU work in loading other than decompression, but in practice that is almost never the case. eg. for loading compressed web pages, there's tons of CPU work that needs to be ton to parse the HTML or JS or whatever, so the idea that you can hide the decompressor time in the network latency is a lie - the decompressor time adds on to the later processing time and adds directly onto total load latency.

The other factor that people often ignore is the fact that loading these days is heterogeneous.

What you actually encounter is something like this :

Download from internet ~ 1 MB/s
Load from optimal disc ~ 20 MB/s
Load from slow HDD ~ 80 MB/s
Fast SSD ~ 500 MB/s
NVMe drive on PCIe ~ 1-2 GB/s
Load from cache in RAM ~ 8 GB/s

We have very heterogeneous loading - even for a single file loaded by the same application.

The first time you load it, maybe you download from the internet, and in that case a slow decompressor like lzma might be best. But the next time you load it's from the cache in RAM. And the time after that it's from HDD. In those cases, using lzma is a disaster (in the sense that the loading is now nearly instant, but you spend seconds decoding; or in the sense that just loading uncompressed would have been way faster).

One issue that I think is not considered is that making the right choice in the slow-disk zone is not that big of a deal. On a 1 MB/s disk, the difference in "speedup" between lzma and Kraken is maybe 2% in favor of lzma. But on a 100 MB/s it's something like 400% in favor of Kraken.

Now in theory maybe it would be nice to have different compressors for download & disk storage; like you use something like lzma for downloadable, and then decode and re-encode to ZStd for HDD loading. In practice nobody does that and the advantage over just using ZStd all the time is very marginal.

Also in theory it would be nice if the OS cache would cache the decompressed data rather than caching the compressed data.

TODO : time lzma on PS4. Usually PS4 is 2-4X slower than my PC, so that puts lzma somewhere in the 10-25 mb/s range, which is very borderline for keeping up with the optical disc.

DVD 16x is ~ 20 MB/s (max)
PS4 Blu-Ray is 6x ~ 27 MB/s (max)

PS4 transparently caches Blu-Ray to HDD

Of course because of the transparent caching to HDD, if you actually keep files in lzma on the disc, and they are cached to HDD, loading them from HDD is a huge mismatch and makes lzma the bottleneck.

That is, in practice on the PS4 when you load files from disc, they are sometimes actually coming from the HDD transparent cache, so you sometimes get 20 MB/s speeds, and sometimes 100 MB/s.

Now of course we'd love to have a higher-ratio compressor than Kraken which isn't so slow. Right now, we just don't have it. We have Kraken at 1000 MB/s , LZNA at 120 MB/s , lzma at 50 MB/s - it's too big of a step down in speed, even for LZNA.

In order for the size gain of lzma/LZNA to be worth it, it needs to run a *lot* faster, more like 400 mb/s. There needs to be a new algorithmic step in the high compress domain to get there.

At the moment the only reason to use the slower decoders than Kraken is if you simply must get smaller files and damn the speed; like if you have a downloadable app size hard limit and just have to fit in 100 MB, or if you are running out of room on an optical disc or whatever.

07-29-16 | Scatter Plots

I tweaked my scatter plot generation per Fabian. They're still log-log but now labeled with the non-log axis values so it's easier to read off the actual ratio and speed without doing a pow2 in your head.

Silesia :

Game Test Set :

Seven, total :

Seven, all files :

07-27-16 | Improving the compression of block-compressed textures

I'm often asked how to get more compression on block-compressed textures. (and was asked again today, hence writing this)

If you're working from existing BCn data (not RGB originals), there's not a lot you can do. One small thing you can do is to de-interleave the end points and indexes.

In BC1/DXT1 for example each block is 4 bytes of end points then 4 bytes of index data. You can take each alternating 4 bytes out and instead put all the end points together, then all the index data together. Sometimes this improves compression, sometimes it doesn't, it depends on the compressor and the data. When it does help it's in the 5-10% range.

If you're using mips, then you can convert the BCn endpoint colors into deltas from the parent mip. (that will only be a good idea if your BCn encoder is one that is *not* aggressive about finding endpoints outside of the original image colors)

If you have original RGB data, you can make new BCn data that's designed to be more compressible. This opens up a whole new world of powerful possibilities : R/D decisions in the BCn encoding.

There are some obvious basic ideas, like - instead of aggressive end point searches, only choose end points that occur or are near the colors in the block; try to reuse previous index dwords rather than make new ones; try to use completely flat color blocks with the whole index dword = 0, etc.

See for example Jon Olick's articles on doing this .

But unless you really need to do it manually for some reason you should probably just use Rich Geldreich's cool tool crunch .

Crunch can make its own "crn" compressed texture format, which you would need to load with the crn-lib. crn-lib would decode the crn file back to BC1 at load time. That may be an awesome thing to do, I really can't comment because I haven't looked into it in detail.

Let's assume for the moment that you don't want to use the "crn" custom compressed format. You just want DDS or raw BCn data that you will run through your normal compression pipeline (Oodle or whatever). Crunch can also make BCn data that's more compressible by reducing its complexity, choosing encodings that are lower quality but less complex.

You tell it to make BCn and output DDS and you can specify a "quality". Then when you run it through your back-end compressor you get smaller files :

lena 512x512 RGB (absolutely terrible as a representative game texture)

DXT1 DDS quality 255

 rmse : 7.6352 psnr : 30.5086

Oodle LZNA   :   131,200 ->   102,888 =  6.274 bpb =  1.275 to 1
Oodle Kraken :   131,200 ->   107,960 =  6.583 bpb =  1.215 to 1

DXT1 DDS quality 200

 rmse : 8.2322 psnr : 29.8547

Oodle LZNA   :   131,200 ->    80,264 =  4.894 bpb =  1.635 to 1
Oodle Kraken :   131,200 ->    85,268 =  5.199 bpb =  1.539 to 1

CRN quality 255

 rmse : 8.2699 psnr : 29.8150
   crunched.crn                74,294

DXT1 DDS quality 128

 rmse : 9.0698 psnr : 29.0131

Oodle LZNA   :   131,200 ->    62,960 =  3.839 bpb =  2.084 to 1
Oodle Kraken :   131,200 ->    66,628 =  4.063 bpb =  1.969 to 1

CRN quality 160

rmse : 9.0277 psnr : 29.0535

crunched.crn                53,574

DXT1 DDS quality 80

 rmse : 10.2521 psnr : 27.9488

Oodle LZNA   :   131,200 ->    50,983 =  3.109 bpb =  2.573 to 1
Oodle Kraken :   131,200 ->    54,096 =  3.299 bpb =  2.425 to 1

CRN quality 100

 rmse : 10.1770 psnr : 28.0126

 crunched.crn               41,533

So going from rmse 7.64 to 10.26 we reduced the Oodle-compressed DDS files to about half their size! Pretty cool.

The CRN format files are even smaller at equal error. (unfortunately the -quality setting is not a direct comparison, you have to hunt around to find qualities that give equal rmse to do a comparison).

For my reference :

@echo test.bat [file] [quality]
@echo quality in 1-255 optional 128 default
set file=%1
if "%file%"=="" end.bat 
set q=%2
if "%q%"=="" set q=128
crunch_x64.exe -DXT1 -fileformat dds -file %file% -maxmips 1 -quality %q% -out crunched.dds
@REM -forceprimaryencoding ??

@REM verified same :
@REM radbitmaptest64 copy crunched.dds crunched_dds_un.bmp
crunch_x64.exe -R8G8B8 -file crunched.dds -out crunched_dds_un.bmp -fileformat bmp

crunch_x64.exe -DXT1 -file %file% -maxmips 1 -quality %q% -out crunched.crn

crunch_x64.exe -R8G8B8 -file crunched.crn -out crunched_crn_un.bmp -fileformat bmp

call bmp mse %file% crunched_dds_un.bmp
@echo --------------------------

call ooz crunched.dds -zc7 -zl8
call ooz crunched.dds -zc8 -zl8

call bmp mse %file% crunched_crn_un.bmp
@echo --------------------------

call d crunched.crn

07-26-16 | Compilers and ZStd performance

Add/Update :

After some more months with this I have a better view of it.

ZStd (and to some extent LZ4 as well) are way faster with modern GCC -O3 and vectorizer (that they are with MSVC or older/disabled GCC ; and they benefit a lot more from those things than my compressors, or most code in general). They are written in a simple clean way that really works well with a compiler that turns that code into good implementations for the machine.

Most of the timings I post are of ZStd/LZ4 in non-ideal compilations which is a bit unfair to them.

ZStd in the optimal compression levels has MML 3 and is slower to decode (than ZStd at low compression level).

IMO the sweet spot for ZStd is in the faster compression levels (-2 to -9) particularly if you care about round-trip time. It's quite excellent as a mix of encode & decode speed and is able to get that with surprisingly simple code.

Original :

Yann wrote to ask about a possible anomaly in my measurement of ZStd's performance, so I did a little digging.

I do have a bit of a funny mix of compilers in my Windows tests, which is maybe slightly unfair, though my testing indicates it's not a big factor.

The PS4 report is always one of the best to look at for absolute numbers; everything is built with the same compiler (clang 3.6.1) with the same options, run on standard hardware.

On Windows, I run Oodle from the shipping DLL which is built with MSVC 2012. The non-Oodle codecs that I test are mostly built with MSVC 2005 , which is just because my personal dev machine that I build that test on uses MSVC 2005, while the build machine that makes Oodle is on 2012. In my tests this difference is less than 5%.

For example when I post results like :

silesia              : Kraken     : 4.082 to 1 : 1004.014 MB/s
silesia              : Mermaid    : 3.571 to 1 : 2002.079 MB/s
silesia              : Selkie     : 3.053 to 1 : 2889.536 MB/s
silesia              : lz4hc      : 2.723 to 1 : 2269.788 MB/s
silesia              : zlib9      : 3.128 to 1 : 358.593 MB/s
silesia              : lzma       : 4.369 to 1 : 78.655 MB/s

K,M,S are from the Oodle DLL with MSVC 2012
lz4 and lzma and built from source with MSVC 2005
zlib on Windows I run from zlib1x64.dll that somebody else built long ago

when I post results on non-Windows platforms, everything is built from source with the same compiler as Oodle.

First let's look at the effect of the MSVC version on Windows :

MSVC 2005 :

(actually zlib1x64.dll , not my build)
zlib9 : 24,700,820 ->13,115,250 =  4.248 bpb =  1.883 to 1
decode           : 79.907 millis, 11.01 c/b, rate= 309.12 mb/s

lz4hc : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
decode           : 9.499 millis, 1.31 c/b, rate= 2600.32 mb/s

zstdmax : 24,700,820 ->10,401,235 =  3.369 bpb =  2.375 to 1
decode           : 58.505 millis, 8.06 c/b, rate= 422.20 mb/s

Win64 MSVC 2012 :

miniz      : 24,700,820 ->13,120,668 =  4.249 bpb =  1.883 to 1
miniz_decompress_time : 77.631 millis, 10.70 c/b, rate= 318.18 mb/s
(miniz != zlib but the times are quite comparable anyway)

zstd       : 24,700,820 ->10,403,228 =  3.369 bpb =  2.374 to 1
zstd_decompress_time : 57.932 millis, 7.98 c/b, rate= 426.37 mb/s

Zstd : 422.20 -> 426.37 mb/s

lz4hc      : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
LZ4_decompress_safe_time : 9.214 millis, 1.27 c/b, rate= 2680.92 mb/s

LZ4 : 2600.32 -> 2680.92 mb/s

Oodle MSVC 2012  :

ooKraken    :  2.48:1 ,    2.4 enc mbps , 1178.4 dec mbps
ooMermaid   :  2.31:1 ,    2.1 enc mbps , 2166.4 dec mbps
ooSelkie    :  1.94:1 ,    2.6 enc mbps , 3838.2 dec mbps

so VC 2012 (vs 2005) is a small speed gain for the competition but it's not a huge factor.

Let's try another platform entirely, with a standardized compiler :

Mac x64 :
Intel(R) Core(TM) i7-3720QM CPU @ 2.60GHz
Apple LLVM version 7.3.0 (clang-703.0.29)

Kraken  : 24,700,820 -> 9,970,882 =  3.229 bpb =  2.477 to 1
decode only      : 21.248 millis, 2.23 c/b, rate= 1162.51 mb/s

Mermaid : 24,700,820 ->10,838,455 =  3.510 bpb =  2.279 to 1
decode only      : 10.957 millis, 1.15 c/b, rate= 2254.29 mb/s

Selkie  : 24,700,820 ->12,752,506 =  4.130 bpb =  1.937 to 1
decode only      : 6.517 millis, 0.68 c/b, rate= 3790.49 mb/s

miniz      : 24,700,820 ->13,120,668 =  4.249 bpb =  1.883 to 1
miniz_decompress_time : 90.072 millis, 9.46 c/b, rate= 274.23 mb/s

zstd       : 24,700,820 ->10,403,228 =  3.369 bpb =  2.374 to 1
zstd_decompress_time : 54.176 millis, 5.69 c/b, rate= 455.94 mb/s

brotli-9   : 24,700,820 ->10,473,560 =  3.392 bpb =  2.358 to 1
brotli_decompress_time : 99.937 millis, 10.50 c/b, rate= 247.16 mb/s

brotli-11  : 24,700,820 -> 9,848,721 =  3.190 bpb =  2.508 to 1
brotli_decompress_time : 133.675 millis, 14.04 c/b, rate= 184.78 mb/s

lz4hc      : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
LZ4_decompress_safe_time : 8.662 millis, 0.91 c/b, rate= 2851.75 mb/s

And another compiler, everyone built the same way, but on the same hardware as my Windows tests :

Linux x64 :
Core i7-3770 3.4 GHz
gcc-4.7.2 -O2 (*)

Kraken  : 24,700,820 -> 9,970,882 =  3.229 bpb =  2.477 to 1
decode only      : 23.059 millis, 3.64 c/b, rate= 1071.20 mb/s

Mermaid : 24,700,820 ->10,838,455 =  3.510 bpb =  2.279 to 1
decode only      : 11.565 millis, 1.83 c/b, rate= 2135.83 mb/s

Selkie  : 24,700,820 ->12,752,506 =  4.130 bpb =  1.937 to 1
decode only      : 7.178 millis, 1.13 c/b, rate= 3441.18 mb/s

miniz      : 24,700,820 ->13,120,668 =  4.249 bpb =  1.883 to 1
miniz_decompress_time : 85.327 millis, 13.47 c/b, rate= 289.48 mb/s

zstd       : 24,700,820 ->10,403,228 =  3.369 bpb =  2.374 to 1
zstd_decompress_time : 66.987 millis, 10.58 c/b, rate= 368.74 mb/s

brotli-9   : 24,700,820 ->10,473,560 =  3.392 bpb =  2.358 to 1
brotli_decompress_time : 93.457 millis, 14.76 c/b, rate= 264.30 mb/s

brotli-11  : 24,700,820 -> 9,828,093 =  3.183 bpb =  2.513 to 1
brotli_decompress_time : 134.560 millis, 21.25 c/b, rate= 183.57 mb/s

lz4hc      : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
LZ4_decompress_safe_time : 14.070 millis, 2.22 c/b, rate= 1755.57 mb/s

(* = I have to use a bad old GCC on Linux because of the nightmare of Linux binary lib compatibility; I use the oldest GCC possible to have maximum compatibility. This GCC also has a code gen bug in -O3 that creates crashing code due to the vectorizer F'ing up, so I have to use -O2. These factors seem to hurt ZStd and LZ4 a *lot*.)

               Win     Linux    Mac
ooKraken    :  1178.4  1071.20  1162.51
ooMermaid   :  2166.4  2135.83  2254.29
ooSelkie    :  3838.2  3441.18  3790.49

miniz       :  318.18  289.48   274.23
zstdmax     :  426.37  368.74   455.94
lz4hc       :  2680.9  1755.57  2851.75

Win = MSVC 2012  Core i7-3770 3.4 GHz
Linux = gcc-4.7.2 -O2 Core i7-3770 3.4 GHz
Mac = Apple LLVM version 7.3.0 , Intel(R) Core(TM) i7-3720QM CPU @ 2.60GHz

The Oodle timings are pretty consistent (Selkie takes a hit on the bad old Linux GCC) even though the Mac is a different CPU. ZStd and LZ4 vary a lot!

There's another reference point I have for Windows performance. I can run the tasty "lzbench" which has lots of compressors.

lzbench runs are not directly comparable to mine. The biggest differences are that lzbench sets the process to "realtime" priority, and it doesn't invalidate the cache between runs. These two factors should mean that lzbench measures speeds slightly faster than I do in general. But that shouldn't be a huge factor.

Win64 :
Core i7-3770 3.4 GHz
lzbench (realtime prio, no cache invalidate)
GCC 5.3.0
lzbench 1.2 (64-bit Windows)   Assembled by P.Skibinski

r:\z>lzbench.exe -ebrotli,9 -j40 r:\testsets\big\lzt99
r:\z>lzbench.exe -ezstd,99 -j40 r:\testsets\big\lzt99
r:\z>lzbench.exe -ezlib,9 -j40 r:\testsets\big\lzt99
r:\z>lzbench.exe -elz4hc,99 -j40 r:\testsets\big\lzt99

Compressor name         Compress. Decompress. Compr. size  Ratio Filename
brotli 0.4.0 -9          4.25 MB/s   262 MB/s    10481262  42.43 lzt99
zstd 0.7.1 -99           3.62 MB/s   560 MB/s    10401235  42.11 lzt99
zlib 1.2.8 -9            5.89 MB/s   271 MB/s    13063244  52.89 lzt99
lz4hc r131 -99             10 MB/s  2801 MB/s    14801510  59.92 lzt99

(note that this zlib is != my zlib dll, and != miniz , but is nonetheless similar speed)

What you should notice is that the zlib and brotli & lz4 times are about the same in lzbench, but ZStd got way faster.

My conclusion is that ZStd speed is very strongly affected by compiler & options. On Windows, with GCC -O3 it looks like ZStd can be around 25% faster than I've been reporting.

On the same hardware : (Core i7-3770 3.4 GHz)

zlib dll         : 309.12 mb/s
zstdmax MSVC 2005: 422.20 mb/s
lz4hc MSVC 2005  : 2600.32 mb/s

miniz MSVC 2012 : 318.18 mb/s
zstd  MSVC 2012 : 426.37 mb/s
lz4hc MSVC 2012 : 2680.92 mb/s

miniz  gcc-4.7.2 -O2  : 289.48 mb/s
zstd   gcc-4.7.2 -O2  : 368.74 mb/s
brotli9 gcc-4.7.2 -O2 : 264.30 mb/s
lz4hc   gcc-4.7.2 -O2 : 1755.57 mb/s

brotli 0.4.0 GCC 5.3.0 :   262 MB/s
zstd 0.7.1 -99 GCC 5.3.0 : 560 MB/s
zlib 1.2.8 -9  GCC 5.3.0 : 271 MB/s
lz4hc r131 -99 GCC 5.3.0 : 2801 MB/s

Another note of fairness to ZStd :

I've run all the compressors at max / optimal encode setting, just to remove that variable so I don't have to track another axis of encoder and try to make it as apples-to-apples as possible. These tests have all been looking at decode speed and max compression ratio.

But ZStd gets quite a lot faster to decode at lower encode settings. The Oodle compressors are much more constant in decode speed (we work hard to make our optimal parsers not produce files that are slower to decode; if you want slower decodes you have the "spaceSpeedTradeoff" setting; in fact this has been a concerted focus in my last few revs is to try to separate that axis of variation, so that increasing the encoder Level in Oodle should just improve compression ratio without hurting decode speed).

For example at level 9 ZStd gets a lot faster :


lzbench :

zstd 0.7.1 -9              34 MB/s   737 MB/s    11344386  45.93 lzt99

MSVC 2005 :

zstd9 : 24,700,820 ->11,344,386 =  3.674 bpb =  2.177 to 1
decode           : 43.955 millis, 6.06 c/b, rate= 561.95 mb/s

If you just look at that 737 MB/s , it's getting closer to Kraken. Though of course at level 9, ZStd's compression ratio is way down, so it's not really comparable any more. In fact it's compressing worse than Mermaid at that point.

ooMermaid   :  2.31:1 ,    2.1 enc mbps , 2166.4 dec mbps

So anyway.

ADD : of course this is why we (RAD) ship compiled libs, and it's the kind of thing we spend a lot of time on. Like, oh crap I updated my compiler and all of a sudden my speed is down by 20%. So go look at the disasm and see WTF the compiler is doing differently and try to poke it to make it generate the right code again, etc.

07-26-16 | Oodle 2.3.0 Thread-Phased Performance

Thread-Phased (two threads) decoding can be used with Mermaid just as it was with Kraken.

It's not as big a benefit on Mermaid as it is for Kraken. (Kraken gets around 1.5X, Mermaid much less).

There is a little neat thing about thread-phased Mermaid though, and that's the ability to run Mermaid+ at almost the exact same speed as Mermaid.

Mermaid+ is a hybrid option that's hidden in Oodle 2.3.0 and will be exposed in the next release. It gets compression between Mermaid & Kraken, with a small speed hit vs Mermaid.

Seven :

ooSelkie    :  2.19:1 ,    3.0 enc mbps , 3668.0 dec mbps
ootp2Mermaid:  2.46:1 ,    2.3 enc mbps , 3046.1 dec mbps
lz4hc       :  2.00:1 ,   12.8 enc mbps , 2532.4 dec mbps
ooMermaid   :  2.46:1 ,    2.3 enc mbps , 2364.4 dec mbps
ootp2Kraken :  2.91:1 ,    2.6 enc mbps , 1660.9 dec mbps
ooKraken    :  2.91:1 ,    2.6 enc mbps , 1049.6 dec mbps
zlib9       :  2.33:1 ,    7.9 enc mbps ,  315.1 dec mbps

ootp2Merm+  :  2.64:1 ,    2.3 enc mbps , 3042.4 dec mbps
ooMermaid+  :  2.64:1 ,    2.3 enc mbps , 2044.5 dec mbps

Silesia :

ooSelkie    :  3.05:1 ,    1.3 enc mbps , 2878.4 dec mbps
ootp2Mermaid:  3.57:1 ,    1.1 enc mbps , 2600.8 dec mbps
lz4hc       :  2.72:1 ,   13.6 enc mbps , 2273.5 dec mbps
ooMermaid   :  3.57:1 ,    1.1 enc mbps , 1994.2 dec mbps
ootp2Kraken :  4.08:1 ,    1.2 enc mbps , 1434.4 dec mbps
ooKraken    :  4.08:1 ,    1.2 enc mbps , 1000.5 dec mbps
zlib9       :  3.13:1 ,    8.3 enc mbps ,  358.4 dec mbps

ootp2Merm+  :  3.58:1 ,    1.1 enc mbps , 2583.9 dec mbps
ooMermaid+  :  3.58:1 ,    1.1 enc mbps , 1986.8 dec mbps

Game Test Set :

ooSelkie    :  2.03:1 ,    3.3 enc mbps , 4548.0 dec mbps
lz4hc       :  1.78:1 ,   14.0 enc mbps , 3171.1 dec mbps
ootp2Mermaid:  2.28:1 ,    2.7 enc mbps , 3099.4 dec mbps
ooMermaid   :  2.28:1 ,    2.7 enc mbps , 2622.8 dec mbps
ootp2Kraken :  2.57:1 ,    2.9 enc mbps , 1812.7 dec mbps
ooKraken    :  2.57:1 ,    2.9 enc mbps , 1335.9 dec mbps
zlib9       :  1.99:1 ,    8.3 enc mbps ,  337.2 dec mbps

ootp2Merm+  :  2.35:1 ,    2.7 enc mbps , 3034.9 dec mbps
ooMermaid+  :  2.35:1 ,    2.7 enc mbps , 2409.0 dec mbps

Pulling out just the relevant numbers on Seven, you can see Mermaid+ is between Mermaid and Kraken, but thread-phased it runs at full Mermaid speed :

Seven :

ooMermaid   :  2.46:1 ,    2.3 enc mbps , 2364.4 dec mbps
ooMermaid+  :  2.64:1 ,    2.3 enc mbps , 2044.5 dec mbps
ooKraken    :  2.91:1 ,    2.6 enc mbps , 1049.6 dec mbps

ootp2Mermaid:  2.46:1 ,    2.3 enc mbps , 3046.1 dec mbps
ootp2Merm+  :  2.64:1 ,    2.3 enc mbps , 3042.4 dec mbps
ootp2Kraken :  2.91:1 ,    2.6 enc mbps , 1660.9 dec mbps

07-18-16 | Oodle 2.3.0 All Test Sets

Putting the total performance on various testsets together in one place. Tests on Win64 Core i7-3770 3.4 GHz as usual.

Showing speed & ratio here, higher is better.

As usual the total on a test set is total size of all individually compressed files, and total time.

I think the scatter plot most clearly shows the way Kraken, Mermaid & Selkie are just on a whole new Pareto Frontier than the older compressors. You can connect the dots of K-M-S performance for each test set and they form a very consistent space-speed tradeoff curve that's way above the previous best.

The raw numbers :

gametestset          : Kraken     : 2.566 to 1 : 1363.283 MB/s
gametestset          : Mermaid    : 2.284 to 1 : 2711.458 MB/s
gametestset          : Selkie     : 2.030 to 1 : 4870.413 MB/s
gametestset          : lz4hc      : 1.776 to 1 : 3223.279 MB/s
gametestset          : zlib9      : 1.992 to 1 : 338.063 MB/s
gametestset          : lzma       : 2.756 to 1 : 43.782 MB/s

pd3d                 : Kraken     : 3.647 to 1 : 1072.833 MB/s
pd3d                 : Mermaid    : 2.875 to 1 : 2299.860 MB/s
pd3d                 : Selkie     : 2.379 to 1 : 3784.850 MB/s
pd3d                 : lz4hc      : 2.238 to 1 : 2370.193 MB/s
pd3d                 : zlib9      : 2.886 to 1 : 382.226 MB/s
pd3d                 : lzma       : 4.044 to 1 : 63.878 MB/s

seven                : Kraken     : 2.914 to 1 : 1053.961 MB/s
seven                : Mermaid    : 2.462 to 1 : 2374.796 MB/s
seven                : Selkie     : 2.194 to 1 : 3717.074 MB/s
seven                : lz4hc      : 2.000 to 1 : 2522.824 MB/s
seven                : zlib9      : 2.329 to 1 : 315.344 MB/s
seven                : lzma       : 3.186 to 1 : 52.660 MB/s

silesia              : Kraken     : 4.082 to 1 : 1004.014 MB/s
silesia              : Mermaid    : 3.571 to 1 : 2002.079 MB/s
silesia              : Selkie     : 3.053 to 1 : 2889.536 MB/s
silesia              : lz4hc      : 2.723 to 1 : 2269.788 MB/s
silesia              : zlib9      : 3.128 to 1 : 358.593 MB/s
silesia              : lzma       : 4.369 to 1 : 78.655 MB/s

See the index of this series of posts for more information : Introducing Oodle Mermaid and Selkie .
For more about Oodle visit RAD Game Tools

07-18-16 | Oodle 2.3.0 ARM Report

I prepared a detailed report of Oodle's performance on ARM mobile devices (Android and iOS).

The full report is here :

oodle_arm_report on cbloom.com

It's a thorough test on many devices and several corpora. See the full details there.

Cliff notes is : Oodle's great on ARM.

For example on the iPadAir2 64-bit , on Silesia :

We found that the iOS devices are generally very good and easy to program for. They're more like desktop Intel chips; they don't have any terrible performance cliffs. The Android ARM devices we tested on were rather more difficult. For one thing they have horrible thermal saturation problems that makes testing on them very difficult. They also have some odd performance quirks.

I'm sure we could get a lot more speed on ARM, but it's rather nasty to optimize for. For one thing the thermal problems mean that iterating and getting good numbers is a huge pain. It's hard to tell if a change helped or not. For another, there's a wide variety of devices and it's hard to tell which to optimize for, and they have different performance shortfalls. So there's definitely a lot left on the table here.

Mermaid & Selkie are quite special on ARM. Many of these devices have small caches (as small as 512k L2) and very slow main memory (slow wrst latency; they often have huge bandwidth, but latency is what I need). Mermaid & Selkie are able to use unbounded windows for LZ without suffering a huge speed hit, due to the unique way they are structured. Kraken doesn't have the same magic trick so it benefits from a limited window, as demonstrated in the report.

See the index of this series of posts for more information : Introducing Oodle Mermaid and Selkie .
For more about Oodle visit RAD Game Tools

07-18-16 | Oodle Selkie

Selkie is the faster cousin of Mermaid, distant relative of Kraken.

Selkie is all about decode speed, it aims to be the fastest mainstream decompressor in the world, and still gets more compression than anything in the high-speed domain.

Selkie does not currently have a super fast encoder. It's got good optimal parse encoders that produce carefully tuned encoded file which offer excellent space-speed tradeoff.

The closest compressors to Selkie are the fast byte-wise small-window coders like LZ4 and LZSSE (and Oodle's LZB16). These are all just obsolete now (in terms of ratio vs decode speed), Selkie gets a lot more compression (sometimes close to Zlib compression levels!) and is also much faster.

Selkie will not compress tiny buffers, or files that only compress a little bit. For example if you give Selkie something like an mp3, it might be able to compress it to 95% of its original size, saving a few bytes. Selkie will refuse to do that and just give you the original uncompressed file. If you wanted that compression, that means you wanted to save only a few bytes at a large time cost, which means you don't actually want a fast compressor like Selkie. You in fact wanted a compressor that was more willing to trade time for bytes, such as Mermaid or Kraken. Selkie will not abide logical inconsistency.

Selkie generally beats LZ4 compression even on small files (under 64k) but really gets ahead on files larger than 64k where the unbounded match distances can find big wins.

As usual, I'm not picking on LZ4 here because it's bad; I'm comparing to it because it's the best of the rest, and it's widely known. Both decompressors are run fuzz-safe.

Tests on Win64 (Core i7-3770 3.4 GHz) : 
(for reference, this machine runs memcpy at roughly 8 GB/s)
(total of time & size on each test set)

gametestset : ooSelkie    : 143,579,361 ->70,716,380 =  3.940 bpb =  2.030 to 1 
gametestset : decode      : 29.239 millis, 0.69 c/b, rate= 4910.61 mb/s

gametestset : lz4hc       : 143,579,361 ->80,835,018 =  4.504 bpb =  1.776 to 1 
gametestset : decode      : 44.495 millis, 1.05 c/b, rate= 3226.89 mb/s

pd3d : ooSelkie    : 31,941,800 ->13,428,298 =  3.363 bpb =  2.379 to 1 
pd3d : decode      : 8.381 millis, 0.89 c/b, rate= 3811.29 mb/s

pd3d : lz4hc       : 31,941,800 ->14,273,195 =  3.575 bpb =  2.238 to 1 
pd3d : decode      : 13.479 millis, 1.44 c/b, rate= 2369.67 mb/s

seven : ooSelkie    : 80,000,000 ->36,460,084 =  3.646 bpb =  2.194 to 1 
seven : decode      : 21.458 millis, 0.91 c/b, rate= 3728.26 mb/s

seven : lz4hc       : 80,000,000 ->39,990,656 =  3.999 bpb =  2.000 to 1 
seven : decode      : 31.730 millis, 1.35 c/b, rate= 2521.30 mb/s

silesia : ooSelkie    : 211,938,580 ->69,430,966 =  2.621 bpb =  3.053 to 1 
silesia : decode      : 72.340 millis, 1.16 c/b, rate= 2929.77 mb/s

silesia : lz4hc       : 211,938,580 ->77,841,566 =  2.938 bpb =  2.723 to 1 
silesia : decode      : 93.488 millis, 1.50 c/b, rate= 2267.02 mb/s

The edge that Selkie has over LZ4 is even greater on more difficult platforms like the PS4.

To get a better idea of the magic of Selkie it's useful to look at the other Oodle compressors that are similar to Selkie.

LZB16 is Oodle's LZ4 variant; it gets slightly more compression and slightly more decode speed, but they're roughly equal. It's included here for comparison to LZBLW.

Oodle's LZBLW is perhaps the most similar compressor to Selkie. It's like LZB16 (LZ4) but adds large-window matches. That ability to do long-distance matches hurts speed a tiny bit (2873 mb/s -> 2596 mb/s), but helps compression a lot.

Oodle's LZNIB is nibble-wise, with unbounded offsets and a rep match. It gets good compression, generally better than Zlib, with speed much higher than any LZ-Huff. LZNIB is in a pretty unique space speed tradeoff zone without much competition outside of Oodle.

lz4hc     : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1 
decode    : 9.481 millis, 1.31 c/b, rate= 2605.37 mb/s

ooLZB16   : 24,700,820 ->14,754,643 =  4.779 bpb =  1.674 to 1
decode    : 8.597 millis, 1.18 c/b, rate= 2873.17 mb/s

ooLZNIB   : 24,700,820 ->12,014,368 =  3.891 bpb =  2.056 to 1
decode    : 17.420 millis, 2.40 c/b, rate= 1417.93 mb/s

ooLZBLW   : 24,700,820 ->13,349,800 =  4.324 bpb =  1.850 to 1
decode    : 9.512 millis, 1.31 c/b, rate= 2596.80 mb/s

ooSelkie  : 24,700,820 ->12,752,506 =  4.130 bpb =  1.937 to 1 
decode    : 6.410 millis, 0.88 c/b, rate= 3853.57 mb/s

LZNIB and LZBLW were both pretty cool before Selkie, but now they're just obsolete.

LZBLW gets a nice compression gain over LZB16, but Selkie gets even more, and is way faster!

LZNIB beats Selkie compression, but is way slower, around 3X slower, in fact it's slower than Mermaid (2283.28 mb/s and compresses to 10,838,455 = 3.510 bpb = 2.279 to 1).

You can see from the curves that Selkie just completely covers the curves of LZB16,LZBLW, and LZ4. When a curve is completely covered like that, it means that it was beaten for both space and speed, so there is no domain where that compressor is ever better. LZNIB just peeks out of the Selkie curve because it gets higher compression (albeit at lower speed), so there is a domain where it is the better choice - but in that domain Mermaid just completely dominates LZNIB, so it too is obsolete.

See the index of this series of posts for more information : Introducing Oodle Mermaid and Selkie .
For more about Oodle visit RAD Game Tools

07-18-16 | Oodle Mermaid

Mermaid is a new compressor with a unique balance of space and speed. Mermaid is very close to LZ4 decode speeds, while usually beating Zlib compression ratios.

There's really nothing even close. It's way beyond what was previously thought possible.

Mermaid supports unbounded distance match references. This is part of how it gets such high compression. It does so in a new way which reduces the speed penalty normally incurred by large-window LZ's.

Mermaid almost always compresses better than ZLib. The only exception is on small files, less than 32k or so. The whole Oceanic Bestiary family is best suited to files over 64k. They work fine on smaller files, but they lose their huge advantage. It's always best to combine small files into larger units for compression, particularly so with these compressors.

There's not really any single compressor to compare Mermaid to. What we can do is compare vs. Zlib's compression ratio and LZ4's speed. A kind of mythological hybrid like a Chimera, the head of a Zlib and the legs of an LZ4.

Tests on Win64 (Core i7-3770 3.4 GHz) :

Silesia :

On Silesia, Mermaid is just slightly slower than LZ4 but compresses much more than Zlib !!

PD3D :

On PD3D, Mermaid gets almost exactly the compression level of ZLib but the decode speed of LZ4. Magic! It turns out you *can* have your cake and eat it too.

Game Test Set :

lzt99 :

Mermaid really compresses well on lzt99 ; not only does it kill Zlib, it gets close to high compression LZ-Huffs like RAR. (RAR gets 10826108 , Mermaid 10838455 bytes).

Seven :

Because of the space-speed optimizing nature of Mermaid, it will make decisions to be slower than LZ4 when it can find big compression gains. For example if you look at the individual files of the "Seven" test set below - Mermaid is typically right around the same speed as LZ4 or even faster (baby7,dds7,exe7,game7,wad7 - all same speed or faster than LZ4). On a few files it decides to take an encoding slower to decode than LZ4 - model7,enwik7, and records7. The biggest differences are enwik7 and records7, but if you look at the compression ratios - those are all the files where it found huge size differences over LZ4. It has an internal exchange rate for time vs. bytes that it must meet in order to take that encoding, trying to optimize for its space-speed target usage.

Seven files :

Silesia              : Mermaid    : 3.571 to 1 : 2022.038 MB/s
Silesia              : lz4hc      : 2.723 to 1 : 2267.021 MB/s
Silesia              : zlib9      : 3.128 to 1 : 358.681 MB/s

GameTestSet          : Mermaid    : 2.284 to 1 : 2718.095 MB/s
GameTestSet          : lz4hc      : 1.776 to 1 : 3226.887 MB/s
GameTestSet          : zlib9      : 1.992 to 1 : 337.986 MB/s

lzt99                : Mermaid    : 2.279 to 1 : 2283.278 MB/s
lzt99                : lz4hc      : 1.669 to 1 : 2605.366 MB/s
lzt99                : zlib9      : 1.883 to 1 : 309.304 MB/s

PD3D                 : Mermaid    : 2.875 to 1 : 2308.830 MB/s
PD3D                 : lz4hc      : 2.238 to 1 : 2369.666 MB/s
PD3D                 : zlib9      : 2.886 to 1 : 382.349 MB/s

Seven                : Mermaid    : 2.462 to 1 : 2374.212 MB/s
Seven                : lz4hc      : 2.000 to 1 : 2521.296 MB/s
Seven                : zlib9      : 2.329 to 1 : 315.370 MB/s

See the index of this series of posts for more information : Introducing Oodle Mermaid and Selkie .
For more about Oodle visit RAD Game Tools

07-18-16 | Oodle Mermaid and Selkie on PS4

The PS4 is a lovely platform to benchmark on because it's standard. It's also very easy to run tests on. Performance of these compressors on the Xbox One is extremely similar, small variatation due to clock rate (1.75 vs 1.6 GHz) and compiler (MSVC vs clang/llvm).

Everything is slow on the PS4 in absolute terms (it's a slow chip and difficult to optimize for). The Oodle compressors do very well, even better in relative terms on PS4 than on typical PC's.

Kraken is usually around ~2X faster than ZStd on PC's, but is 3X faster on PS4. Mermaid is usually just slightly slower than LZ4 on PC's, but is solidly faster than LZ4 on PS4.

lzt99 :

Kraken     : 2.477 to 1 : 390.582 MB/s
Mermaid    : 2.279 to 1 : 749.896 MB/s
Selkie     : 1.937 to 1 : 1159.064 MB/s

zstd       : 2.374 to 1 : 133.498 MB/s
miniz      : 1.883 to 1 : 85.654 MB/s
lz4hc-safe : 1.669 to 1 : 673.616 MB/s
LZSSE8     : 1.626 to 1 : 767.106 MB/s

Mermaid is faster than LZ4 on PS4 !! Wow! And the compression level is in a totally different domain than other super-fast decompressors like LZ4 or LZSSE.

lzt99 is a good case for Selkie & Mermaid. Selkie beats zlib compression ratio while being 75% faster than LZ4.

All compressors here are fuzz-safe, and run in safe mode if they have optional safe/unsafe modes.

Charts : (showing time and size - lower is better!)

lzt99 :

the raw data :

PS4 : Oodle 230 : (-z6)

inName : lzt:/lzt99

reference :

miniz      : 24,700,820 ->13,120,668 =  4.249 bpb =  1.883 to 1
miniz_decompress_time : 288.379 millis, 18.61 c/b, rate= 85.65 mb/s

zstd       : 24,700,820 ->10,403,228 =  3.369 bpb =  2.374 to 1
zstd_decompress_time : 185.028 millis, 11.94 c/b, rate= 133.50 mb/s

lz4hc      : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
LZ4_decompress_safe_time : 36.669 millis, 2.37 c/b, rate= 673.62 mb/s

LZSSE8     : 24,700,820 ->15,190,395 =  4.920 bpb =  1.626 to 1
decode_time      : 32.200 millis, 2.08 c/b, rate= 767.11 mb/s

Oodle :

Kraken     : 24,700,820 -> 9,970,882 =  3.229 bpb =  2.477 to 1
decode           : 63.241 millis, 4.08 c/b, rate= 390.58 mb/s

Mermaid    : 24,700,820 ->10,838,455 =  3.510 bpb =  2.279 to 1
decode           : 32.939 millis, 2.13 c/b, rate= 749.90 mb/s

Selkie : 24,700,820 ->12,752,506 =  4.130 bpb =  1.937 to 1
decode           : 21.311 millis, 1.38 c/b, rate= 1159.06 mb/s

BTW for reference, the previous best compressor in Mermaid's domain was LZNIB. Before these new compressors, LZNIB was quite unique in that it got good decode speeds, much faster than the LZ-Huffs of the time (eg. 3X faster than ZStd) but with compression usually better than ZLib. Well, LZNIB is still quite good compared to other competition, but it's just clobbered by the new Oceanic Bestiary compressors. The new compressor in this domain is Mermaid and it creams LZNIB for both size and speed :

LZNIB -z6  : 24,700,820 ->12,015,591 =  3.892 bpb =  2.056 to 1 
decode           : 58.710 millis, 3.79 c/b, rate= 420.73 mb/s

Mermaid    : 24,700,820 ->10,838,455 =  3.510 bpb =  2.279 to 1
decode           : 32.939 millis, 2.13 c/b, rate= 749.90 mb/s

See the index of this series of posts for more information : Introducing Oodle Mermaid and Selkie .
For more about Oodle visit RAD Game Tools

07-18-16 | Introducing Oodle Mermaid and Selkie

I'm pleased to announce the release of two new compressors in Oodle 2.3.0 : Mermaid and Selkie.

Mermaid and Selkie are the super-fast-to-decode distant relatives of Kraken. They use some of the same ideas and technology as Kraken, but are independent compressors targetted at even higher speed and lower compression. Mermaid & Selkie make huge strides in what's possible in compression in the high-speed domain, the same way that Kraken did in the high-compression domain.

Mermaid is about twice as fast as Kraken, but with compression around Zlib levels.

Selkie is one of the fastest decompressors in the world, and also gets much more compression than other very-high-speed compressors.

( Oodle is my data compression library that we sell at RAD Game Tools , read more about it there )

Kraken, Mermaid, and Selkie all use an architecture that makes space-speed decisions in the encoder to give the best tradeoff of compressed size vs decoding speed. The three compressors have different performance targets and make decisions suited for each one's usage domain (Kraken favors more compression and will give up some speed, Selkie strongly favors speed, Mermaid is in between).

For detailed information about the new Mermaid and Selkie I've written a series of posts :

cbloom rants Introducing Oodle Mermaid and Selkie
cbloom rants Oodle 2.3.0 All Test Sets
cbloom rants Oodle 2.3.0 ARM Report
cbloom rants Oodle Mermaid and Selkie on PS4
cbloom rants Oodle Mermaid
cbloom rants Oodle Selkie
RAD Game Tools - Oodle Network and Data Compression

Here are some representative numbers on the Silesia test set : (sum of time and size on individual files)

Oodle 2.3.0 Silesia -z6

Kraken     : 4.082 to 1 : 999.389 MB/s
Mermaid    : 3.571 to 1 : 2022.038 MB/s
Selkie     : 3.053 to 1 : 2929.770 MB/s

zstdmax    : 4.013 to 1 : 468.497 MB/s
zlib9      : 3.128 to 1 : 358.681 MB/s
lz4hc      : 2.723 to 1 : 2267.021 MB/s

on Win64 (Core i7-3770 3.4 GHz)

On Silesia, Mermaid is 5.65X faster to decode than zlib, and gets 14% more compression. Selkie is 1.3X faster to decode than LZ4 and gets 12% more compression.

Charts on Silesia total : (charts show time and size - lower is better!)

And the speedup chart on Silesia, which demonstrates the space-speed efficiency of a compressor in different usage domains.

Kraken was a huge step in the Pareto frontier that pushed the achievable speedup factor way up beyond what other compressers were doing. There's a pre-Kraken curve where we thought the best possible tradeoff existed, that most other compressors in the world roughly lie on (or under). Kraken set a new frontier way up on its own with nobody to join it; Mermaid & Selkie are the partners on that new curve that have their peaks at higher speeds than Kraken.

You can also see this big jump of the new family very easily in scatter plots, which we'll see in later posts .

07-14-16 | Oodle 2.3.0 : Kraken Improvement

Oodle 2.3.0 includes some pretty solid improvements to Kraken. The result is around a 10% gain in decode speed.

There were two major factors in the gains. One was just some more time optimizing some inner loops (including some new super-tight pathways from Fabian).

The other was more rigorous analysis of the space-speed tradeoff decisions inside Kraken. One of the fundamental things that makes Kraken work is the fact that it consider space-speed when making its internal decisions, but before 230 those decisions were made in a rather ad-hoc way. Making those decisions better means that even with the same decoder, the new encoder is able to create files that are the same size but decode faster.

The tradeoff point (technically, the lagrange lambda, or the exchange rate from time to bytes) that's used by Oodle to make space-speed decisions is exposed to the client in the OodleLZ_CompressOptions so you can adjust it to bias for compression or decode speed. Each compressor sets what I believe to be a reasonable default for its usage domain, so adjustments to this value should typically be small (you can't massively change behavior with it; Kraken won't start arithmetic coding things if you set the tradeoff really small, for example, there's a small window where the compressor works well and you can just bias sightly within that window).

Some dry numbers for reference :

On PS4 :

Oodle 230 Kraken -zl4 : 24,700,820 ->10,377,556 =  3.361 bpb =  2.380 to 1
decode only      : 65.547 millis, 4.23 c/b, rate= 376.84 mb/s

Oodle 230 Kraken -zl6 : 24,700,820 -> 9,970,882 =  3.229 bpb =  2.477 to 1
decode           : 63.453 millis, 4.09 c/b, rate= 389.28 mb/s

Oodle 230 Kraken -zl7 : 24,700,820 -> 9,734,771 =  3.153 bpb =  2.537 to 1
decode           : 67.915 millis, 4.38 c/b, rate= 363.70 mb/s

Oodle 220 Kraken -zl4 : 24,700,820 ->10,326,584 =  3.345 bpb =  2.392 to 1
decode only      : 0.073 seconds, 211.30 b/kc, rate= 336.76 mb/s

Oodle 220 Kraken -zl6 : 24,700,820 ->10,011,486 =  3.242 bpb =  2.467 to 1
decode           : 0.074 seconds, 208.83 b/kc, rate= 332.82 mb/s

Oodle 220 Kraken -zl7 : 24,700,820 -> 9,773,112 =  3.165 bpb =  2.527 to 1
decode           : 0.079 seconds, 196.70 b/kc, rate= 313.49 mb/s

On Win64 (Core i7-3770 3.4 GHz) :

Oodle 2.3.0 :

Silesia Kraken -z6

total   : 211,938,580 ->51,918,269 =  1.960 bpb =  4.082 to 1
decode           : 210.685 millis, 3.38 c/b, rate= 1005.95 mb/s
Weissman 1-256 : [8.575]

mozilla : 51,220,480 ->14,410,181 =  2.251 bpb =  3.554 to 1
decode only      : 51.280 millis, 3.41 c/b, rate= 998.83 mb/s

lzt99 : 24,700,820 -> 9,970,882 =  3.229 bpb =  2.477 to 1
decode only      : 20.943 millis, 2.89 c/b, rate= 1179.44 mb/s

win81 : 104,857,600 ->38,222,311 =  2.916 bpb =  2.743 to 1
decode only      : 108.344 millis, 3.52 c/b, rate= 967.82 mb/s

Oodle 2.2.0 :

Silesia Kraken -z6

total : 211,938,580 ->51,857,427 =  1.957 bpb =  4.087 to 1
decode   : 0.232 seconds, 268.43 b/kc, rate= 913.46 M/s
Weissman 1-256 : [8.431]


Kraken 230  :  3.55:1 ,   998.8 dec mb/s
Kraken 220  :  3.60:1 ,   896.5 dec mb/s
Kraken 215  :  3.51:1 ,   928.0 dec mb/s


Kraken 230  :  2.48:1 ,   998.8 dec mb/s
Kraken 220  :  2.53:1 ,   912.0 dec mb/s
Kraken 215  :  2.46:1 ,   957.1 dec mb/s


Kraken 230  :  2.74:1 ,   967.8 dec mb/s
Kraken 220  :  2.77:1 ,   818.0 dec mb/s
Kraken 215  :  2.70:1 ,   877.0 dec mb/s

NOTE : Oodle 2.3.0 Kraken data cannot be read by Oodle 2.2.0 or earlier. Oodle 230 can load all old Oodle data (new versions of Oodle can always load all data created by older versions). If you need to make data that be loaded with an older version using Oodle 230, then you can set the minimum decoder version to something lower (by default it's the current version). Contact Oodle support for details.

Some of the biggest gains were found on ARM, which I'll post about more in the future.

06-09-16 | Fundamentals of Modern LZ : Two-Step Parse

For some reason I feel like writing a note on this today.

A two-step parse is an enhancement to a forward-arrivals parse.

(background : forward-arrivals parse stores the minimum cost from head at each position, along with information on the path taken to get there. At each pos P, it takes the best incoming arrival and considers all ways to go further into the parse (literal/match/rep/etc.). At each destination point it stores arrival_cost[P] + step cost. In simple cases (no carried state, no entropy coding, like LZSS) the forward-arrivals parse is a perfect parse just like the backward dynamic-programming parse. In modern LZ with carried state such as a rep set or markov state, the forward parse is preferable.)

A two-step parse extends the standard forward-arrivals parse by being able to store an arrival from a single coding step, or from two coding steps. The standard usage (as in LZMA/7zip) is to be able to store a two-step arrival from the sequence { normal match, some literals, rep match }. This multi-step arrival is stored with the cost of the whole sequence at the end point of the sequence.

If you stored *all* arrivals (not just the cheapest), you would not need two-step parse. You could just store the first step, and then when your parse origin point advanced to the end of the first step, it would find the second step and be able to choose it as an option.

But obviously you don't store all arrivals at each position, since the number would massively explode, even with reduction by symmetries. (see, eg. previous articles on A* parse)

The problem arrises when you have a cheap multi-step sequence, but the first step is expensive. Then the first step might be replaced (or never filled in the first place) and the parse will not be able to find the second step cheap option.

Let's consider a concrete example for clarity.

Parser is at pos P consider all ways to continue

At pos P there's a length 4 normal match available at offset O

It stores an arrival at [P+4] that's rather expensive

(because it has to send offset O).

At pos P+1 the parser finds a length 3 rep match

The exit from (P+1) length 3 also lands at [P+4]

This is a cheaper way to arrive at [P+4] , so the previous arrival from P via O is replaced

When the parser reaches P+4 it sees the incoming arrival as
begin a rep match match from P+1

But we missed something !

At pos P+5 (one step after the arrival) there are 2 bytes that match at offset O

if we had chosen the normal match to arrive at P+4 , we could now code a rep match

but we lost it, so we don't see the rep as an option.

Two-step to the rescue!

Back at pos P , we consider the one-step arrival :

{match len 4, offset O} to arrive at P+4

We also look after the end of that for cheap rep matches and find one.

So we store a two-step arrival :

{match len4, offset O, 1 literal, rep len 2} to arrive at P+7

Now at pos P+1 the arrival at P+4 is stomped

but the arrival at P+7 remains!  So we are able to find that in the future.

The options look like :

   P   P+4
   V   V

Option 2 is cheaper at P+4
but Option 1 is cheaper at P+7

This is the primary application of two-step parse.

It's a (very limited) way of finding non-local minima in the parse search space.

The other option is "multi-parse" that stores multiple arrivals at each position (something like 4 is typical). Multi-parse and two-step provide diminishing returns when used together, so they usually aren't. Two-step is generally a faster way and provides more win per CPU time, multi-parse is able to find longer-range non-local-minimum moves and so provides more compression.

All good modern LZ's need some kind of non-local-minimum parse, because to get into a good state for the future (typically by getting the right offset into the rep offset cache) you may need to make a more expensive initial step.

05-17-16 | The Weissman Score

Wikipedia suggests the Weissman score should be

which ignoring constants is just W = r/logT

That's just wrong. You don't take a logarithm of something with units. But there are aspects of it that are correct. W should be proportional to r (compression ratio), and a logarithm of time should be involved. Just not like that.

I present a formula which I call the correct Weissman Score :

W = comp_ratio * log10( 1 + speed/(disk_speed_lo *comp_ratio) )  -
    comp_ratio * log10( 1 + speed/(disk_speed_hi *comp_ratio) )


W = comp_ratio * log10( ( comp_ratio + speed/disk_speed_lo ) / ( comp_ratio + speed/disk_speed_hi ) )

You can have a Weissman score for encode speed or decode speed. It's a measure of space-speed tradeoff success.

I suggest the range should be 1-256. disk_speed_lo = 1 MB/s (to evaluate performance on very slow channels, favoring small files), disk_speed_hi = 256 MB/s (to evalue performance on very fast disks, favoring speed). And because 1 and 256 are amongst programmers' favorite numbers.

You could also just let the hi range go to infinity. Then you don't need a hi disk speed parameter and you get :

Weissman-infinity = comp_ratio * log10( 1 + speed/(disk_speed_lo *comp_ratio) )

with disk_speed_lo = 1 MB/s ; which is neater, though this favors fast compressors more than you might like. While it's a cleaner formula, I think it's less useful for practical purposes, where the bounded hi range focuses the score more on the area that most people care about.

I came up with this formula because I started thinking about summarizing a score from the Pareto charts I've made . What if you took the speedup value at several (log-scale) disk speeds; like you could take the speedup at 1 MB/s,2 MB/s,4 MB/s, and just average them? speedup is a good way to measure a compressor even if you don't actually care about speed. Well, rather than just average a bunch of points, what if I average *all* points? eg. integrate to get the area under the curve? Note that we're integrating in log-scale of disk speed.

Turns out you can just do that integral :

    speedup = (time to load uncompressed) / (time to load compressed + decompress)
    speedup = (raw_size/disk_speed) / (comp_size/disk_speed + raw_size/ decompress_speed)
    speedup = (1/disk_speed) / (1/(disk_speed*compression_ratio) + 1 / decompress_speed)
    speedup = 1 / (1/compression_ratio + disk_speed / decompress_speed)
    speedup = 1 / (1/compression_ratio + exp( log_disk_speed ) / decompress_speed)
    speedup = compression_ratio / (1 + exp( log_disk_speed ) * compression_ratio/decompress_speed)
    speedup = compression_ratio * 1 / (1 + exp( log_disk_speed + log(compression_ratio/decompress_speed)))

speedup is a sigmoid :

    y = 1 / (1 + e^-x ) 
    Integral{y} = ln( 1 + e^x )

    x = - ( log_disk_speed + log(compression_ratio/decompress_speed) )

so substitute some variables and you get the above formula for the Weissman score.

In the final formula, I changed from natural log to log-base-10, which is just a constant scaling factor.

The Weissman (decode Core i7-3770 3.4 GHz; 1-256 range) scores on Silesia are :

lz4hc    : 6.243931
zstdmax  : 7.520236
lzham    : 6.924379
lzma     : 5.460073
zlib9    : 5.198510
Kraken   : 8.431461

Weissman-infinity scores are :

lz4hc    : 7.983104
zstdmax  : 8.168544
lzham    : 7.277707
lzma     : 5.589155
zlib9    : 5.630476
Kraken   : 9.551152

Goal : beat 10.0 !

ADD : this post was a not-sure-if-joking. But I actually think it's useful. I find it useful anyway.

When you're trying to tweak out some space-speed tradeoff decisions, you get different sizes and speeds, and it can be hard to tell if that tradeoff was good. You can do things like plot all your options on a space-speed graph and try to guess the pareto frontier and take those. But when iterating an optimization of a parameter you want just a simple score.

This corrected Weissman score is a nice way to do that. You have to choose what domain you're optimizing for, size-dominant slower compressors should use Weissman 1-256 , for balance of space and super speed use Weissman 1-inf (or 40-800), for the fast domain (LZ4-ish) use a range like 100-inf. Then you can just iterate to maximize that number!

For whatever space-speed tradeoff domain you're interested in, there exists a Weissman score range (lo-hi disk speed paramaters) such that maximizing the Weissman score in that range gives you the best space-speed tradeoff in the domain you wanted. The trick is choosing what that lo-hi range is (it doesn't necessarily directly correspond to actual disk or channel speeds; there are other factors to consider like latency, storage usage, etc. that might cause you to bias the lo-hi away from the actual channel speeds in some way; for example high speed decoders should always set the upper speed to infinity, which corresponds to the use case that the compressed data might be already resident in RAM so it has zero time to load).

05-15-16 | PS4 Battle : LZ4 vs LZSSE vs Oodle

PS4 is the arena. Three compressors enter. (revised 05-16)

Advantages of the PS4 : consistent well-defined hardware for reproducible testing. Slow platform that game developers care about being fast on. Builds with clang which is the target of choice for some compression libraries that don't build so easily on MSVC.

After the initial version of this post, I went and fuzz-safed LZB16, so they're all directly comparable. To compare apples, look at LZ4_decompress_safe. I also include LZ4_decompress_fast for reference.

LZ4_decompress_safe : fuzz safe (*)
LZ4_decompress_fast : NOT fuzz safe
LZSSE8_Decode : fuzz safe
Oodle LZB16 : fuzz safe
LZSSE and Oodle both use multiple copies of the core loop to minimize the pain of fuzz safing. LZ4's code is much simpler, it doesn't do a ton of macro or .inl nastiness. (* = this is the only one that I would actually trust to put in a satellite or a bank or something critical, it's just so simple, it's way easier to be sure that it's correct)

Conclusion :

Comparing the two Safe open-source options, LZ4_safe vs. LZSSE8 : LZSSE8 is pretty consistently faster than LZ4_Safe on PS4 (though the difference is small). PS4 is a better platform for LZSSE than x64 (PS4 is actually a pretty bad platform for LZ4; there're a variety of issues; see GDC "Taming the Jaguar" slides ; but particular issues for LZ4 are the front-end bottleneck and cache latency). When I tested on x64 before, it was much more mixed, sometimes LZ4 was faster.

I was surprised to find that Oodle LZB16 is quite a lot faster than LZ4 on PS4. (for example, that's not the case on Windows/x64, it's much closer there). I've never run third party codecs on PS4 before. I suppose this reflects the per-platform tweaking that we spend so much time on, and I'm sure LZ4 would catch up with some time spent fiddling with the PS4 codegen.

The compression ratios are mostly close enough to not care, though LZSSE8 does a bit worse on some of the DXTC/BCn files (lightmap.bc3 and d.dds).

On some files I include Oodle LZBLW numbers (LZB-bytewise-large-window). Sometimes Oodle LZBLW is a pretty big free compression win at about the same speed. Sometimes it gets worse ratio, sometimes much worse speed. If I was a client using this, I might try LZBLW and drop down to LZB16 any time it's not a good tradeoff.

Full data :

REMINDER : LZ4_decompress_fast is not directly comparable to the others, it's not fuzz safe, the others are!

PS4 clang-3.6.1


lzt99 :

lz4hc : 24,700,820 ->14,801,510 =  4.794 bpb =  1.669 to 1
LZ4_decompress_safe_time : 0.035 seconds, 440.51 b/kc, rate= 702.09 mb/s
LZ4_decompress_fast_time : 0.032 seconds, 483.55 b/kc, rate= 770.67 mb/s

LZSSE8  : 24,700,820 ->15,190,395 =  4.920 bpb =  1.626 to 1
LZSSE8_Decode_Time : 0.033 seconds, 467.32 b/kc, rate= 744.81 mb/s

Oodle LZB16 : lzt99 : 24,700,820 ->14,754,643 =  4.779 bpb =  1.674 to 1 
decode           : 0.027 seconds, 564.72 b/kc, rate= 900.08 mb/s

Oodle LZBLW : lzt99 : 24,700,820 ->13,349,800 =  4.324 bpb =  1.850 to 1
decode           : 0.033 seconds, 470.39 b/kc, rate= 749.74 mb/s



lz4hc : 2,188,524 -> 2,068,268 =  7.560 bpb =  1.058 to 1
LZ4_decompress_safe_time : 0.004 seconds, 322.97 b/kc, rate= 514.95 mb/s
LZ4_decompress_fast_time : 0.004 seconds, 353.08 b/kc, rate= 562.89 mb/s

LZSSE8 : 2,188,524 -> 2,111,182 =  7.717 bpb =  1.037 to 1
LZSSE8_Decode_Time : 0.004 seconds, 360.21 b/kc, rate= 574.42 mb/s

Oodle LZB16 : texture.bc1 :  2,188,524 -> 2,068,823 =  7.562 bpb =  1.058 to 1 
decode           : 0.004 seconds, 368.67 b/kc, rate= 587.84 mb/s



lz4hc : 4,194,332 ->   632,974 =  1.207 bpb =  6.626 to 1
LZ4_decompress_safe_time : 0.005 seconds, 521.54 b/kc, rate= 831.38 mb/s
LZ4_decompress_fast_time : 0.005 seconds, 564.63 b/kc, rate= 900.46 mb/s

LZSSE8 encode    :  4,194,332 ->   684,062 =  1.305 bpb =  6.132 to 1
LZSSE8_Decode_Time : 0.005 seconds, 551.85 b/kc, rate= 879.87 mb/s

Oodle LZB16 : lightmap.bc3 :  4,194,332 ->   630,794 =  1.203 bpb =  6.649 to 1 
decode           : 0.005 seconds, 525.10 b/kc, rate= 837.19 mb/s



lz4hc : 51,220,480 ->22,062,995 =  3.446 bpb =  2.322 to 1
LZ4_decompress_safe_time : 0.083 seconds, 385.47 b/kc, rate= 614.35 mb/s
LZ4_decompress_fast_time : 0.075 seconds, 427.14 b/kc, rate= 680.75 mb/s

LZSSE8 : 51,220,480 ->22,148,366 =  3.459 bpb =  2.313 to 1
LZSSE8_Decode_Time : 0.070 seconds, 461.53 b/kc, rate= 735.59 mb/s

Oodle LZB16 : silesia_mozilla : 51,220,480 ->22,022,002 =  3.440 bpb =  2.326 to 1 
decode           : 0.065 seconds, 492.03 b/kc, rate= 784.19 mb/s

Oodle LZBLW : silesia_mozilla : 51,220,480 ->20,881,772 =  3.261 bpb =  2.453 to 1
decode           : 0.112 seconds, 285.68 b/kc, rate= 455.30 mb/s



lz4hc :   589,952 ->   116,447 =  1.579 bpb =  5.066 to 1
LZ4_decompress_safe_time : 0.001 seconds, 568.65 b/kc, rate= 906.22 mb/s
LZ4_decompress_fast_time : 0.001 seconds, 624.81 b/kc, rate= 996.54 mb/s

LZSSE8 encode    :  589,952 ->   119,659 =  1.623 bpb =  4.930 to 1
LZSSE8_Decode_Time : 0.001 seconds, 604.14 b/kc, rate= 962.40 mb/s

Oodle LZB16 : breton.dds :    589,952 ->   113,578 =  1.540 bpb =  5.194 to 1 
decode           : 0.001 seconds, 627.56 b/kc, rate= 1001.62 mb/s

Oodle LZBLW : breton.dds :    589,952 ->   132,934 =  1.803 bpb =  4.438 to 1
decode           : 0.001 seconds, 396.04 b/kc, rate= 630.96 mb/s



lz4hc encode     :  1,048,704 ->   656,706 =  5.010 bpb =  1.597 to 1
LZ4_decompress_safe_time : 0.001 seconds, 554.69 b/kc, rate= 884.24 mb/s
LZ4_decompress_fast_time : 0.001 seconds, 587.20 b/kc, rate= 936.34 mb/s

LZSSE8 encode    :  1,048,704 ->   695,583 =  5.306 bpb =  1.508 to 1
LZSSE8_Decode_Time : 0.001 seconds, 551.13 b/kc, rate= 879.05 mb/s

Oodle LZB16 : d.dds :  d.dds :  1,048,704 ->   654,014 =  4.989 bpb =  1.603 to 1 
decode           : 0.001 seconds, 537.78 b/kc, rate= 857.48 mb/s



lz4hc : 79,993,099 ->47,848,680 =  4.785 bpb =  1.672 to 1
LZ4_decompress_safe_time : 0.158 seconds, 316.67 b/kc, rate= 504.70 mb/s
LZ4_decompress_fast_time : 0.143 seconds, 350.66 b/kc, rate= 558.87 mb/s

LZSSE8 : 79,993,099 ->47,807,041 =  4.781 bpb =  1.673 to 1
LZSSE8_Decode_Time : 0.140 seconds, 358.61 b/kc, rate= 571.54 mb/s

Oodle LZB16 : all_dds : 79,993,099 ->47,683,003 =  4.769 bpb =  1.678 to 1 
decode           : 0.113 seconds, 444.38 b/kc, rate= 708.24 mb/s



lz4hc : 58,788,904 ->32,998,567 =  4.490 bpb =  1.782 to 1
LZ4_decompress_safe_time : 0.090 seconds, 412.04 b/kc, rate= 656.71 mb/s
LZ4_decompress_fast_time : 0.080 seconds, 460.55 b/kc, rate= 734.01 mb/s

LZSSE8 : 58,788,904 ->33,201,406 =  4.518 bpb =  1.771 to 1
LZSSE8_Decode_Time : 0.076 seconds, 485.14 b/kc, rate= 773.20 mb/s

Oodle LZB16 : baby_robot_shell.gr2 : 58,788,904 ->32,862,033 =  4.472 bpb =  1.789 to 1
decode           : 0.070 seconds, 530.45 b/kc, rate= 845.42 mb/s

Oodle LZBLW : baby_robot_shell.gr2 : 58,788,904 ->30,207,635 =  4.111 bpb =  1.946 to 1
decode           : 0.090 seconds, 409.88 b/kc, rate= 653.26 mb/s

After posting the original version with non-fuzz-safe LZB16, I decided to just go and do the fuzz-safing for LZB16.

LZB16, PS4 clang-3.6.1

post-fuzz-safing :

    lzt99 : 24,700,820 ->14,754,643 =  4.779 bpb =  1.674 to 1 
    decode           : 0.027 seconds, 564.72 b/kc, rate= 900.08 mb/s
    texture.bc1 :  2,188,524 -> 2,068,823 =  7.562 bpb =  1.058 to 1 
    decode           : 0.004 seconds, 368.67 b/kc, rate= 587.84 mb/s
    lightmap.bc3 :  4,194,332 ->   630,794 =  1.203 bpb =  6.649 to 1 
    decode           : 0.005 seconds, 525.10 b/kc, rate= 837.19 mb/s
    silesia_mozilla : 51,220,480 ->22,022,002 =  3.440 bpb =  2.326 to 1 
    decode           : 0.065 seconds, 492.03 b/kc, rate= 784.19 mb/s
    breton.dds :    589,952 ->   113,578 =  1.540 bpb =  5.194 to 1 
    decode           : 0.001 seconds, 627.56 b/kc, rate= 1001.62 mb/s
    d.dds :  1,048,704 ->   654,014 =  4.989 bpb =  1.603 to 1 
    decode           : 0.001 seconds, 537.78 b/kc, rate= 857.48 mb/s
    all_dds : 79,993,099 ->47,683,003 =  4.769 bpb =  1.678 to 1 
    decode           : 0.113 seconds, 444.38 b/kc, rate= 708.24 mb/s
    baby_robot_shell.gr2 : 58,788,904 ->32,862,033 =  4.472 bpb =  1.789 to 1
    decode           : 0.070 seconds, 530.45 b/kc, rate= 845.42 mb/s

pre-fuzz-safing reference :

    lzt99 912.92 mb/s
    texture.bc1 598.61 mb/s
    lightmap.bc3 876.19 mb/s
    silezia_mozilla 794.72 mb/s
    breton.dds 1078.52 mb/s
    d.dds 888.73 mb/s
    all_dds 701.45 mb/s
    baby_robot_shell.gr2 877.81 mb/s

Mild speed penalty on most files.

05-15-16 | PS4 Battle : MiniZ vs Zlib-NG vs ZStd vs Brotli vs Oodle

What a sucky way I've spent my work day today. Running other people's code. Yeurg. I have a headache and tunnel vision.

Everything run at max compression options, level 99, max dict size. All libs are the latest on github, downloaded today. Zlib-NG has the arch/x86 stuff enabled. PS4 is AMD Jaguar , x64.

I'm going to omit encode speeds on the per-file results for simplicity, these are pretty representative :

aow3_skin_giants.clb :
zlib-ng encode   : 2.699 seconds, 1.65 b/kc, rate= 2.63 mb/s
miniz encode     : 2.950 seconds, 1.51 b/kc, rate= 2.41 mb/s
zstd encode      : 5.464 seconds, 0.82 b/kc, rate= 1.30 mb/s
brotli-9  encode    : 23.110 seconds, 0.19 b/kc, rate= 307.44 kb/s
brotli-10 encode    : 68.072 seconds, 0.07 b/kc, rate= 104.38 kb/s
brotli-11 encode    : 79.844 seconds, 0.06 b/kc, rate= 88.99 kb/s

Results :

PS4 clang-3.5.0


lzt99 :

MiniZ : 24,700,820 ->13,120,668 =  4.249 bpb =  1.883 to 1
miniz_decompress_time : 0.292 seconds, 53.15 b/kc, rate= 84.71 mb/s

zlib-ng : 24,700,820 ->13,158,385 =  4.262 bpb =  1.877 to 1
miniz_decompress_time : 0.226 seconds, 68.58 b/kc, rate= 109.30 mb/s

ZStd : 24,700,820 ->10,403,228 =  3.369 bpb =  2.374 to 1
zstd_decompress_time : 0.184 seconds, 84.12 b/kc, rate= 134.07 mb/s

Brotli-9 : 24,700,820 ->10,473,560 =  3.392 bpb =  2.358 to 1
brotli_decompress_time : 0.259 seconds, 59.83 b/kc, rate= 95.36 mb/s

Brotli-10 : 24,700,820 -> 9,949,740 =  3.222 bpb =  2.483 to 1
brotli_decompress_time : 0.319 seconds, 48.54 b/kc, rate= 77.36 mb/s

Brotli-11 : 24,700,820 -> 9,833,023 =  3.185 bpb =  2.512 to 1
brotli_decompress_time : 0.317 seconds, 48.84 b/kc, rate= 77.84 mb/s

Oodle Kraken -zl4 : 24,700,820 ->10,326,584 =  3.345 bpb =  2.392 to 1
encode only      : 4.139 seconds, 3.74 b/kc, rate= 5.97 mb/s
decode only      : 0.073 seconds, 211.30 b/kc, rate= 336.76 mb/s

Oodle Kraken -zl6 : 24,700,820 ->10,011,486 =  3.242 bpb =  2.467 to 1
decode           : 0.074 seconds, 208.83 b/kc, rate= 332.82 mb/s

Oodle Kraken -zl7 : 24,700,820 -> 9,773,112 =  3.165 bpb =  2.527 to 1
decode           : 0.079 seconds, 196.70 b/kc, rate= 313.49 mb/s

Oodle LZNA : lzt99 : 24,700,820 -> 9,068,880 =  2.937 bpb =  2.724 to 1
decode           : 0.643 seconds, 24.12 b/kc, rate= 38.44 mb/s


normals.bc1 :

miniz :   524,316 ->   291,697 =  4.451 bpb =  1.797 to 1
miniz_decompress_time : 0.008 seconds, 39.86 b/kc, rate= 63.53 mb/s

zlib-ng :   524,316 ->   292,541 =  4.464 bpb =  1.792 to 1
zlib_ng_decompress_time : 0.007 seconds, 47.32 b/kc, rate= 75.41 mb/s

zstd :   524,316 ->   273,642 =  4.175 bpb =  1.916 to 1
zstd_decompress_time : 0.007 seconds, 49.64 b/kc, rate= 79.13 mb/s

brotli-9 :   524,316 ->   289,778 =  4.421 bpb =  1.809 to 1
brotli_decompress_time : 0.010 seconds, 31.70 b/kc, rate= 50.52 mb/s

brotli-10 :   524,316 ->   259,772 =  3.964 bpb =  2.018 to 1
brotli_decompress_time : 0.011 seconds, 28.65 b/kc, rate= 45.66 mb/s

brotli-11 :   524,316 ->   253,625 =  3.870 bpb =  2.067 to 1
brotli_decompress_time : 0.011 seconds, 29.74 b/kc, rate= 47.41 mb/s

Oodle Kraken -zl6 :    524,316 ->   247,217 =  3.772 bpb =  2.121 to 1
decode           : 0.002 seconds, 135.52 b/kc, rate= 215.95 mb/s

Oodle Kraken -zl7 :    524,316 ->   238,844 =  3.644 bpb =  2.195 to 1
decode           : 0.003 seconds, 123.96 b/kc, rate= 197.56 mb/s

Oodle BitKnit :    524,316 ->   225,884 =  3.447 bpb =  2.321 to 1
decode only      : 0.010 seconds, 31.67 b/kc, rate= 50.47 mb/s


lightmap.bc3 :

miniz :  4,194,332 ->   590,448 =  1.126 bpb =  7.104 to 1 
miniz_decompress_time : 0.025 seconds, 105.14 b/kc, rate= 167.57 mb/s

zlib-ng : 4,194,332 ->   584,107 =  1.114 bpb =  7.181 to 1
zlib_ng_decompress_time : 0.019 seconds, 137.77 b/kc, rate= 219.56 mb/s

zstd :  4,194,332 ->   417,672 =  0.797 bpb = 10.042 to 1 
zstd_decompress_time : 0.014 seconds, 182.53 b/kc, rate= 290.91 mb/s

brotli-9 : 4,194,332 ->   499,120 =  0.952 bpb =  8.403 to 1 
brotli_decompress_time : 0.022 seconds, 118.64 b/kc, rate= 189.09 mb/s

brotli-10 : 4,194,332 ->   409,907 =  0.782 bpb = 10.232 to 1 
brotli_decompress_time : 0.021 seconds, 125.20 b/kc, rate= 199.54 mb/s

brotli-11 : 4,194,332 ->   391,576 =  0.747 bpb = 10.711 to 1 
brotli_decompress_time : 0.021 seconds, 127.12 b/kc, rate= 202.61 mb/s

Oodle Kraken -zl6 :   4,194,332 ->   428,737 =  0.818 bpb =  9.783 to 1 
decode           : 0.009 seconds, 308.45 b/kc, rate= 491.60 mb/s

Oodle BitKnit :   4,194,332 ->   416,208 =  0.794 bpb = 10.077 to 1
decode only      : 0.021 seconds, 122.59 b/kc, rate= 195.39 mb/s

Oodle LZNA :  4,194,332 ->   356,313 =  0.680 bpb = 11.771 to 1 
decode           : 0.033 seconds, 79.51 b/kc, rate= 126.71 mb/s



Miniz : 7,105,158 -> 3,231,469 =  3.638 bpb =  2.199 to 1
miniz_decompress_time : 0.070 seconds, 63.80 b/kc, rate= 101.69 mb/s

zlib-ng : 7,105,158 -> 3,220,291 =  3.626 bpb =  2.206 to 1
zlib_ng_decompress_time : 0.056 seconds, 80.14 b/kc, rate= 127.71 mb/s

Zstd : 7,105,158 -> 2,700,034 =  3.040 bpb =  2.632 to 1
zstd_decompress_time : 0.050 seconds, 88.69 b/kc, rate= 141.35 mb/s

brotli-9 :  7,105,158 -> 2,671,237 =  3.008 bpb =  2.660 to 1
brotli_decompress_time : 0.080 seconds, 55.84 b/kc, rate= 89.00 mb/s

brotli-10 : 7,105,158 -> 2,518,315 =  2.835 bpb =  2.821 to 1
brotli_decompress_time : 0.098 seconds, 45.54 b/kc, rate= 72.58 mb/s

brotli-11 : 7,105,158 -> 2,482,511 =  2.795 bpb =  2.862 to 1
brotli_decompress_time : 0.097 seconds, 45.84 b/kc, rate= 73.05 mb/s

Oodle Kraken -zl6 : aow3_skin_giants.clb :  7,105,158 -> 2,638,490 =  2.971 bpb =  2.693 to 1
decode           : 0.023 seconds, 195.25 b/kc, rate= 311.19 mb/s

Oodle BitKnit : 7,105,158 -> 2,623,466 =  2.954 bpb =  2.708 to 1
decode only      : 0.095 seconds, 47.11 b/kc, rate= 75.08 mb/s

Oodle LZNA : aow3_skin_giants.clb :  7,105,158 -> 2,394,871 =  2.696 bpb =  2.967 to 1
decode           : 0.170 seconds, 26.26 b/kc, rate= 41.85 mb/s



MiniZ : 51,220,480 ->19,141,389 =  2.990 bpb =  2.676 to 1
miniz_decompress_time : 0.571 seconds, 56.24 b/kc, rate= 89.63 mb/s

zlib-ng : 51,220,480 ->19,242,520 =  3.005 bpb =  2.662 to 1
zlib_ng_decompress_time : 0.457 seconds, 70.31 b/kc, rate= 112.05 mb/s

zstd : malloc failed

brotli-9 : 51,220,480 ->15,829,463 =  2.472 bpb =  3.236 to 1
brotli_decompress_time : 0.516 seconds, 62.27 b/kc, rate= 99.24 mb/s

brotli-10 : 51,220,480 ->14,434,253 =  2.254 bpb =  3.549 to 1
brotli_decompress_time : 0.618 seconds, 52.00 b/kc, rate= 82.88 mb/s

brotli-11 : 51,220,480 ->14,225,511 =  2.222 bpb =  3.601 to 1
brotli_decompress_time : 0.610 seconds, 52.72 b/kc, rate= 84.02 mb/s

Oodle Kraken -zl6 : 51,220,480 ->14,330,298 =  2.238 bpb =  3.574 to 1
decode           : 0.200 seconds, 160.51 b/kc, rate= 255.82 mb/s

Oodle Kraken -zl7 : 51,220,480 ->14,222,802 =  2.221 bpb =  3.601 to 1
decode           : 0.201 seconds, 160.04 b/kc, rate= 255.07 mb/s

Oodle LZNA : silesia_mozilla : 51,220,480 ->13,294,622 =  2.076 bpb =  3.853 to 1
decode           : 1.022 seconds, 31.44 b/kc, rate= 50.11 mb/s

I tossed in tests of BitKnit & LZNA in some cases after I realized that the Brotli decode speeds are more comparable to BitKnit than Kraken, and even LZNA isn't that far off (usually less than a factor of 2). eg. you could do half your files in LZNA and half in Kraken and that would be about the same total time as doing them all in Brotli.

Here are charts of the above data :

(silesia_mozilla omitted due to lack of zstd results)

(I'm trying an experiment and showing inverted scales, which are more proportional to what you care about. I'm showing seconds per gigabyte, and percent out of output size, which are proportional to *time* not speed, and *size* not ratio. So, lower is better.)

log-log speed & ratio :

Time and size are just way better scales. Looking at "speed" and "ratio" can be very misleading, because big differences in speed at the high end (eg. 2000 mb/s vs 2200 mb/s) don't translate into a very big time difference, and *time* is what you care about. On the other hand, small differences in speed at the low end *are* important - (eg. 30 mb/s vs 40 mb/s) because those mean a big difference in time.

I've been doing mostly "speed" and "ratio" because it reads better to the novice (higher is better! I want the one with the biggest bar!), but it's so misleading that I think going to time & size is worth it.

05-13-16 | When you don't want Oodle Kraken

For the vast majority of data compression problems, the answer is Oodle Kraken. What should I use to pack my distribution? -> Kraken. What should I use for streaming/paging -> Kraken? What should I use for text? for binary? -> Kraken, Kraken, Kraken.

There are some cases where it's not the answer. Those are easier to enumerate, so I'll do that, mainly with the Oodle compressors you might want instead.

*. If you want the smallest possible files and don't care much about decode speed or decode-time CPU usage, then you might prefer Oodle LZNA.

*. If you want maximum decode speed and don't care much about compression ratio, you might prefer Oodle's LZB16, LZBLW, or LZNIB. (or maybe you don't want compression at all)

*. If you want to compress tiny files independently, Kraken is probably not the best choice. Typically for loading or unpacking, tiny files should be stuck together in a larger loading unit, so that you read and decompress several of them per unit. But if for some reason you need independent tiny files, Kraken won't do great under 16k or so. The best alternatives in Oodle that work well on tiny files are LZNA (high compression) and LZNIB (high speed).

One common case that's equivalent to "tiny files" is communication buffers like network packets; Oodle has special LZ modes for this problem and the best compressors for it are LZNA and LZNIB. Of course you could also use the specialized Oodle Network for packets; contact oodle support for more information on special uses like this.

Similarly, Kraken doesn't do "streaming" or incremental encoding or decoding. It needs large chunks or whole buffers. 90% of the time when people are using streaming, they just shouldn't. For the example if you're trying to persist a save game, and you are streaming out bytes from your objects, you shouldn't be passing them one by one to the encoding layer, you should just be doing *ptr++ to fill a buffer, and then encode that buffer all at once when you're done. Most of the time when you think "I need streaming", you don't. The exception is when you actually need to flush out small independent atoms, like the network packet case above, and then Kraken is not suitable.

*. If you're extremely memory-use constrained, you might not want Kraken. Kraken needs around 256k of memory in addition to the output buffer. This is the largest decoder memory requirement in Oodle, so if for some reason that's too much, there are much smaller overhead decoders available, such as LZNA (around 12k) and LZNIB (zero, or around 1k of stack usage).

*. If you have a lot of specialized data types, and care mainly about compression ratio, you probably want something data-type specific. This might be just some kind of preprocessor, or a whole specialized compressor, but with specialized data (lots of text, or DNA, or whatever) you can always do better with a customized compressor than a generic one.

And some other junk.

05-11-16 | RAR Filters

I had a poke around the RAR unpack code to have a look at filters. This is what I found :

From the unpack code I can't see anything about how filters are chosen, obviously.
(which is the interesting part)

RAR filters have a start & length, so they can apply to fine-grained portions of the file.

There can be N filters per file, and they can overlap, so there could be multiple filters
on any given byte.  They're applied in a defined order.

There's a standard E8E9/BCJ filter.

These are the others :



is just byte delta
it can have N channels
delta is at channel stride (from byte -N)
and it de-interleaves the channels

so eg. if you used it on RGB
it would be channels=3
and it would produce output like RRRRGGGGBBB

The older versions of RAR (30 ?) had much more complex filters :


could send arbitrary filters in theory using the VM script
I have no idea if this was actually done in normal use

The VM filters also have special hard-coded modes in C :


same as v50 DELTA


special image filter
transmits the Width of scan lines
hard-coded to 24-bit RGB
  (odd because it does for i to Channels, but Channels is just a const int = 3)
  (they never heard of 8-bit or 32-bit image data?)
uses a Paeth predictor to make a residual
  (N,W,NW depending on which is closest to grad = N+W-NW)


special audio/WAV filter
sends # of channels
does de-interleaving
crazy complicated adaptive weight linear predictor
does just delta from neighbor
but biases that delta by three different slopes
adjusts the weight of the slope by which was the best predictor over recent data
(or something like that)

The important one is just DELTA which is very simple.

The trick bit is not the filter, but finding ranges to apply it on (without just brute-force trying lots of options and seeing which produces the best result - which RAR obviously doesn't do because they sometimes get it so wrong, as demonstrated in the earlier post).

05-11-16 | Oodle Kraken Thread-Phased Decoding

Oodle Kraken is already by far the fastest-to-decode high-compression compressor in the world (that's a mouthful!). But it's got a magic trick that makes it even faster :

Oodle Kraken can decode its normal compressed data on multiple threads.

This is different than what a lot of compressors do (and what Oodle has done in the past), which is to split the data into independent chunks so that each chunk can be decompressed on its own thread. All compressors can do that in theory, Oodle makes it easy in practice with the "seek chunk" decodes. But that requires special encoding that does the chunking, and it hurts compression ratio by breaking up where matches can be found.

The Oodle Kraken threaded decode is different. To distinguish it I call it "Thread-Phased" decode. It runs on normal compressed data - no special encoding flags are needed. It has no compressed size penalty because it's the same normal single-thread compressed data.

The Oodle Kraken Thread-Phased decode gets most of its benefit with just 2 threads (if you like, the calling thread + 1 more). The exact speedup varies by file, usually in the 1.4X - 1.9X range. The results here are all for 2-thread decode.

For example on win81, 2-thread Oodle Kraken is 1.7X faster than 1-thread : (with some other compressors for reference)

win81 :

Kraken 2-thread  : 104,857,600 ->37,898,868 =  2.891 bpb =  2.767 to 1 
decode           : 0.075 seconds, 410.98 b/kc, rate= 1398.55 M/s

Kraken           : 104,857,600 ->37,898,868 =  2.891 bpb =  2.767 to 1 
decode           : 0.127 seconds, 243.06 b/kc, rate= 827.13 M/s

zstdmax          : 104,857,600 ->39,768,086 =  3.034 bpb =  2.637 to 1 
decode           : 0.251 seconds, 122.80 b/kc, rate= 417.88 M/s

lzham            : 104,857,600 ->37,856,839 =  2.888 bpb =  2.770 to 1 
decode           : 0.595 seconds, 51.80 b/kc, rate= 176.27 M/s

lzma             : 104,857,600 ->35,556,039 =  2.713 bpb =  2.949 to 1 
decode           : 2.026 seconds, 15.21 b/kc, rate= 51.76 M/s

Charts on a few files :

Oodle 2.2.0 includes helper functions that will just run a Thread-Phased decode for you on Oodle's own thread system, as well as example code that runs the entire Thread-Phased decode client-side so you can do it on your own threads however you like.

Performance on the Silesia set for reference :

Silesia total :

Oodle Kraken -z6 : 211,938,580 ->51,857,427 =  1.957 bpb =  4.087 to 1

single threaded decode   : 0.232 seconds, 268.43 b/kc, rate= 913.46 M/s

two threaded decode      : 0.158 seconds, 394.55 b/kc, rate= 1342.64 M/s

Note that because the Kraken Thread-Phased decode is a true threaded decode of individual compressed buffers that means it is a *latency* reduction for decoding individual blocks, not just a *throughput* reduction. For example, if you were really decoding the whole Silesia set, you might just run the decompression of each file on its own thread. That is a good thing to do, and it would give you a near 2X speedup (with two threads). But that's a different kind of threading - that gives you a throughput improvement of 2X but the latency to decode any individual file is not improved at all. Kraken Thread-Phased decode reduces the latency of each independent decode, and of course it can also be used with chunking or multiple-file decoding to get further speedups.

05-10-16 | Oodle 2.2.0 Kraken Optimal Parse improvements

Oodle 2.2.0 is about to ship, with some improvements to the Kraken optimal parse compression ratios. Compressed size is improved by around 1%. Speed is approximately the same at -z6 (previous max level for Kraken) but there's a new -z7 mode that's slightly slower and even higher compression.

I think we'll continue to find improvements in the optimal parsers over the coming months (optimal parsing is hard!) which should lead to some more tiny gains in the compression ratio in the slow encoder modes.

Silesia , sum of all files

uncompressed : 211,938,580

Kraken 2.1.5 -z6 : 52,366,897
Kraken 2.2.0 -z6 : 51,857,427
Kraken 2.2.0 -z7 : 51,625,488

Oodle Kraken 2.1.5 topped out at -z6 (Optimal2). There's a new -z7 (Optimal3) mode which gets a bit more compression at the cost of a bit of speed, which is why it's on a separate option instead of just part of -z6.

Results on some individual files (Kraken 220 is -z7) :


by ratio:
lzma        :  3.88:1 ,    2.0 enc mb/s ,   63.7 dec mb/s
Kraken 220  :  3.60:1 ,    1.1 enc mb/s ,  896.5 dec mb/s
lzham       :  3.56:1 ,    1.5 enc mb/s ,  186.4 dec mb/s
Kraken 215  :  3.51:1 ,    1.2 enc mb/s ,  928.0 dec mb/s
zstdmax     :  3.24:1 ,    2.8 enc mb/s ,  401.0 dec mb/s
zlib9       :  2.51:1 ,   12.4 enc mb/s ,  291.5 dec mb/s
lz4hc       :  2.32:1 ,   36.4 enc mb/s , 2351.6 dec mb/s


by ratio:
lzma        :  2.65:1 ,    3.1 enc mb/s ,   42.3 dec mb/s
Kraken 220  :  2.53:1 ,    2.0 enc mb/s ,  912.0 dec mb/s
Kraken 215  :  2.46:1 ,    2.3 enc mb/s ,  957.1 dec mb/s
lzham       :  2.44:1 ,    1.9 enc mb/s ,  166.0 dec mb/s
zstdmax     :  2.27:1 ,    3.8 enc mb/s ,  482.3 dec mb/s
zlib9       :  1.77:1 ,   13.3 enc mb/s ,  286.2 dec mb/s
lz4hc       :  1.67:1 ,   30.3 enc mb/s , 2737.4 dec mb/s


by ratio:
lzma        :  2.37:1 ,    2.1 enc mb/s ,   40.8 dec mb/s
Kraken 220  :  2.23:1 ,    1.0 enc mb/s ,  650.6 dec mb/s
Kraken 215  :  2.18:1 ,    1.0 enc mb/s ,  684.6 dec mb/s
lzham       :  2.17:1 ,    1.3 enc mb/s ,  127.7 dec mb/s
zstdmax     :  2.02:1 ,    3.3 enc mb/s ,  289.4 dec mb/s
zlib9       :  1.83:1 ,   13.3 enc mb/s ,  242.9 dec mb/s
lz4hc       :  1.67:1 ,   20.4 enc mb/s , 2226.9 dec mb/s


by ratio:
lzma        :  4.35:1 ,    3.1 enc mb/s ,   59.3 dec mb/s
Kraken 220  :  3.82:1 ,    1.4 enc mb/s ,  837.2 dec mb/s
Kraken 215  :  3.77:1 ,    1.5 enc mb/s ,  878.3 dec mb/s
lzham       :  3.77:1 ,    1.6 enc mb/s ,  162.5 dec mb/s
zstdmax     :  2.77:1 ,    5.7 enc mb/s ,  405.7 dec mb/s
zlib9       :  2.19:1 ,   13.9 enc mb/s ,  332.9 dec mb/s
lz4hc       :  1.78:1 ,   40.1 enc mb/s , 2364.4 dec mb


by ratio:
lzma        :  2.95:1 ,    2.5 enc mb/s ,   51.9 dec mb/s
lzham       :  2.77:1 ,    1.6 enc mb/s ,  177.6 dec mb/s
Kraken 220  :  2.77:1 ,    1.0 enc mb/s ,  818.0 dec mb/s
Kraken 215  :  2.70:1 ,    1.0 enc mb/s ,  877.0 dec mb/s
zstdmax     :  2.64:1 ,    3.5 enc mb/s ,  417.8 dec mb/s
zlib9       :  2.07:1 ,   16.8 enc mb/s ,  269.6 dec mb/s
lz4hc       :  1.91:1 ,   28.8 enc mb/s , 2297.6 dec mb/s


by ratio:
lzma        :  3.64:1 ,    1.8 enc mb/s ,   79.5 dec mb/s
lzham       :  3.60:1 ,    1.4 enc mb/s ,  196.5 dec mb/s
zstdmax     :  3.56:1 ,    2.2 enc mb/s ,  394.6 dec mb/s
Kraken 220  :  3.51:1 ,    1.4 enc mb/s ,  702.8 dec mb/s
Kraken 215  :  3.49:1 ,    1.5 enc mb/s ,  789.7 dec mb/s
zlib9       :  2.38:1 ,   22.2 enc mb/s ,  234.3 dec mb/s
lz4hc       :  2.35:1 ,   27.5 enc mb/s , 2059.6 dec mb/s

You can see that encode & decode speed is slightly worse at level -z7 , and compression ratio si improved. (most of the other compression levels have roughly the same decode speed; -z7 enables some special options that can hurt decode speed a bit). Of course even at -z7 Kraken is way faster than anything else comparable!

05-10-16 | Tips for benchmarking a compressor

You're about to evaluate Oodle (thanks for having a look!) or some other compressor. Before you start, consider these tips :

1. Time only the compressor.

Place your time measurements only around the compressor. Not IO, not your parsing, not mallocs, just the compress or decompress calls. I understand that in the end what you care about is total time to load, but there can be a lot of issues there that need fixing, and they can cloud the comparison of just the compression part. eg. if your parsing is really slow, that will dominate the CPU time and hide the differences between the compressors.

A common problem is that your app-loading takes a large amount of CPU independent of decompression. In that case, you care about how much CPU the decompressor uses, regardless of total load latency, because it runs into the CPU usage of your post-decompress loading code. Another problem is that accurately timing the disk load time is very difficult; it strongly depends on the exact hardware, disk cache usage, file layout and packaging for seek times; etc. It's usually better to simulate disk load times rather than measure it, because good quality measurements require a wide variety of systems to get a spectrum of results. (it's a bit like doing a medical trial on one person otherwise)

There are lots of reasons why you shouldn't just put your timing around your IO to get a "total load time". IO speeds differ massively these days, from network loads at less than 1 MB/s to persistent flash that's getting ever closer to RAM speed (1 GB/s !). You would need to time across a massive range of devices. Even if you fix an average HD speed, are you timing first load (not in cache) or second load (in cache, disk speed = RAM speed). You might decide that LZMA/7zip is appropriate for network loads, but then it's massively inappropriate on a fast SSD and totally catastrophic when the files are in disk cache. Is your IO async and overlapping with CPU work, or are you needlessly stalling threads on IO? Is your data loaded with just a big binary splat and point at it, or are you crazily parsing byte by byte? etc. too many variables for this to be considered reasonably.

2. Time what you actually care about.

If you care about decode time, time the decompression. If you care about encode time, time compression. If you care about round-trip time, add the two times. Compressors are not just "fast" or "slow" at both ends, you can't time encoding and decide that it's a fast or slow compressor if what you care about is decoding.

3. Choose the right options.

Most compressors have the ability to target slightly different use cases. The most common option is the ability to trade off encode time vs. compression ratio. So, if what you care about is smallest size, then run the compressor at its highest encode effort level. It can be tricky to get the options right in most compression libraries; we are woefully non-standardized and not well documented. Aside from the simple "level" parameter, there may be other options that are relevant to your goals, perhaps trading off decompressor memory usage, or decompression speed. With Oodle the best option is always to email us and ask what options will best suit your goals.

4. Run apples-to-apples (threads-to-threads) comparisons.

It can be tricky to compare compressors fairly. As much as possible they should be run in the same way, and they should be run in the way that you will actually use them in your final application. Don't profile them with threads if you will not use them threaded in your shipping application.

Threads are a common problem. Compressors should either be tested all threaded (if you will use threads in your final application), or all non-threaded. Unfortunately the defaults are not the same. "lzma" (7z) and LZHAM create threads by default. You have to change their options to tell them to *not* create threads. The normal Oodle_Compress calls will not use threads by default, you have to specifically call one of the _Async threaded routines. (my personal preference is to benchmark everything without threads to compare single-threaded performance, and you can always add threads for production use)

5. Take the MIN of N run times.

To get reliable timing, you need to run the loop many times, and take the MIN of all times. The min will give you the time it takes when the OS isn't interrupting you with task switches, the CPU isn't clocking-down for speedstep, etc. I usually do 30 *per core* but you can probably get a way with a bit less.

6. Wipe the cache.

Assuming you are now doing N loops, you need to invalidate the cache between iterations. If you don't, you will be running the compressor in a "hot cache" scenario, with some buffers already in cache.

7. Don't pack a bunch of files together in a tar if that's not how you load.

It may seem like a good way to test to grab your bunch of test files and pack them together in a tar (or zip -0 or similar package) and run the compression tests on that tar. That's a fine option if that's really how you load data in your final application - as one big contiguous chunk that must be loaded in one big blob. But most people don't. You need to test the compressors in the same way they will be used in the final application. If you load whole file at a time, test the compressors on whole file units. Many people do loading on some kind of paging unit, like perhaps 1 MB chunks. If you do that, then test the compressor on the same thing.

8. Choose your test set.

If you could test on the entire set of buffers that your final application will load, that would be an accurate test. (though actually, even that is a bit subtle, since some buffers are more latency sensitive than others, so for example you might care more about the first few things you load to get into a running application as quickly as possible). That's probably not practical, so you want to choose a set that is representative of what you will actually load. Don't exclude things like already-compressed files (JPEGs and so on) *if* you will be running them through the compressor. (though consider *not* running them your compressed-file loading path, in which case you should exclude them from testing). It's pretty hard to get an accurate representative sample, so it's generally best to just get a variety of files and look at individual per-file results.

9. Look at the spectrum of results, not the sum.

After you run on your test set, don't just add up the compressed sizes and times to make a "total" result. Sums can be misleading. One issue is there are some large incompressible files, they can hide the differences on the more compressible files. But a bigger and more subtle trap is the way that sums weight the combination of results. A sum is a weighting by the size of each file in the test set. That's fine if your test set is all of your data, or is a perfectly proportionally representative sampling of all of your data (a subset which acts like the whole). But most likely it's not. It's best to keep the results per file separate and just have a look at individual cases to see what's going on, how the results differ, and try not to simplify to just looking at the sum.

10. If you do sum, sum *time* not speed, sum *size* not ratio.

Speed (like mb/s) and ratio (raw size/comp size) are inverted measures and shouldn't be summed. What you actually care about is total compressed size, and total time to decode. So if you run over a set of files, don't look at "average speed" or "average ratio" , because those are inverted meaures that will oddly weight the accumulation. Instead accumulate total time to decode, total raw size, and total compressed size, and then if you like you can make "overall speed" and "overall ratio" from those total.

11. Try not to malloc in the timing loop.

Your malloc might be fast, it might be slow, it's best to not have that as a variable in the timing. In general try to allocate the memory for the compressor or decompressor outside of the timing loop. (In Oodle this is done by passing in your own pointer for the "decoderMemory" argument of OodleLZ_Decompress). That would be an unfair test if you didn't also do that in the final application - so do it in the final application too! (similarly, make sure there's no logging inside the timing loop).

12. Consider excluding almost-incompressible files.

This is something you should consider for final shipping application, and if you do it in your shipping application, then you should do it for the benchmark too. The most common case is already-compressed files like JPEG images and MP3 audio. These files can usually be compressed slightly, maybe saving 1% of their size, but the time to decode them is not worth it overall - you can get more total size savings by running a more powerful compressor on other files. So it's most efficient to just send them uncompressed.

13. Tiny files should either be excluded or packed together.

There's almost never a use case where you really want to compress tiny files (< 16k bytes or so) as independent units. There's too much per-unit overhead in the compressor, and more importantly there's too much per-unit overhead in IO - you don't want to eat a disk seek to just to get one tiny file. So in a real application tiny files should always be grouped into paging units that are 256k or more, a size where loading them won't just be a total waste of disk seek time. So, when benchmarking compressors you also shouldn't run them on tiny independent files, because you will never do that in a shipping application (I hope). And of course don't just do this for the benchmark, do it in the final app too.

05-08-16 | Order-1 Huffman

This is a simple idea that's rarely written down, so I thought I'd do a quick summary.

To my knowledge I was the first person to write about it (in "New Techniques in Context Modeling and Arithmetic Encoding" (PDF) ) but it's one of those simple ideas that probably a lot of people had and didn't write about (like Deferred Summation). It's also one of those ideas that keeps being forgotten and rediscovered over the years.

(I don't know much about the details of how Brotli does this, it may differ. I'll be talking about how I did it).

(also by "Huffman" I pretty much always mean "static Huffman" where you measure the histogram of a block and transmit the code lengths, not "adaptive Huffman" (modifying codelens per symbol (bleck)) or "deferred summation Huffman" (codelens computed from histogram of previous data with no explicit codelen transmission))

Let's start with just the case of order-1 8 bit literals. So you're coding a current 8-bit symbol with an 8-bit previous symbol as context. You can do this naively by just have 256 arrays, one for each 8-bit context. The decoder looks like this :

256 times :
read codelens from file
build huffman decode table

per symbol :

o1 = ptr[-1];
ptr[0] = huff_decode( bitstream , huff_table[o1] );

and on a very large file (*) that might be okay.

(* actually it's only okay on a very large file with completely stable statistics, which never happens in practice. In the real world "very large files" don't usually exist; instead they act like a sequence of small/medium files tacked together. That is, you want a decoder that works well on small files, and you want to be able to reset it periodically (re-transmit huffman codelens in this case) so that it can adapt to local statistics).

On small files, it's disastrous. You're sending 256 sets of codelens, which can be a lot of wasted data. Worst of all it's a huge decode time overhead to parse out the codelens and build the decode tables if you're only going to get a few symbols in that context.

So you want to reduce the count of huffman tables. A rough guideline is to make the number of tables proportional to the number of bytes. Maybe 1 table per 1024 bytes is tolerable to you, it depends.

(another goal for reduction might be to get all the huff tables to fit in L2 cache)

So we want to merge the Huffman tables. You want to find pairs of contexts that have the most similar statistics and merge those. If you don't mind the poor encoder-time speed, a good solution is a best-first merge :

for each pair {i,j} (i<j)
merge_cost(i,j) = Huffman_Cost( symbols_i + symbols_j ) - Huffman_Cost( symbols_i ) - Huffman_Cost( symbols_j )

Huffman_Cost( symbols ) = bits to send codelens + bits to encode symbols using those codelens

while # of contexts > target , and/or merge cost < target
pop lowest merge_cost
merge context j onto i
delete all merge costs involving j
recompute all merge costs involving i

if the cost was just entropy (H) instead of Huffman_Cost , then a merge_cost would always be strictly >= 0 (separate statistics are always cheaper than combining). But since the Huffman codelen transmission is not free, the first merges will actually reduce encoded size. So you should always do merges that are free or beneficial, even if huffman table count is low enough.

So contexts with similar statistics will get merged together, since coding them with a combined set of codelens either doesn't hurt or hurts only a little (or helps, with the cost of codelen transmission counted). In this way contexts where it wasn't really helping to differentiate them will get reduced.

Once this is done, the decoder becomes :

get n = number of huffman tables

n times :
read codelens from file
build huffman decode table

256 times :
read tableindex from file
merged_huff_table_ptr[i] = huff_table[ tableindex ]

per symbol :

o1 = ptr[-1];
ptr[0] = huff_decode( bitstream , merged_huff_table_ptr[o1] );

So merged_huff_table_ptr[] is still a [256] array, but it points at only [n] unique Huffman tables.

That's order-1 Huffman!

In the modern world, we know that o1 = the previous literal is not usually the best use of an 8-bit context. You might do something like top 3 bits of ptr[-1], top 2 bits of [ptr-2], 2 bits of position, to make a 7-bit context.

One of the cool things order-1 Huffman can do is to adaptively figure out the context for you.

For example with LZMA you have the option of the # of literal context bits (lc) and literal pos bits (lp). You want them to be as low as possible for better statistics, and there's no good way to choose them per file. (usually lc=2 or lp=2 , usually just one or the other, not both)

With order-1 Huffman, you just make a context with 3 bits of lc and 3 bits of lp, so you have a [64] 6-bit context. Then you let the merger throw away states that don't help. For example if it's a file where pos-bits are irrelevant (like text), they will just get merged out, all the lc contexts that have different lp values will merge together.

05-03-16 | Brotli signed int mode

Brotli signed int context mode. Looks like a good idea. My guess is this is what's helping Brotli10 on the binary files I wrote about in the previous post (horse.vipm and so on)

Signed int takes the previous two bytes and forms a 6-bit context from them thusly :

  Context = (Lut2[b2]<<3) | Lut2[b1];

      Lut2 :=
         0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
         2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
         2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
         2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
         3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
         4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
         4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
         4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
         4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
         5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
         5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
         5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
         6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7

So, it's roughly categorizing the two values into ranges, which means it can act as a kind of linear predictor (if that fits the data), eg. two preceding values in group 4 = my value probably is too, or if b2 is a "3" and b1 is a "4" then I'm likely a "5". Or not, if the data isn't linear like that. Or maybe there's only correlation to b1 and b2 gets ignored, which the order-1-huff can also model.

One thing I like is holding out values 00 and FF and special cases that get a unique bucket. This lets you detect the special cases of last two bytes = 0000,FFFF,FF00,00FF , which can be pretty important on binary.

I think that for the type of data we get in games that often has floats, it might be worth it to single out 7F and 80 as well, something like :

but who knows, would have to test to see.

05-03-16 | Underappreciated Compressors

1. LZX. LZX is crazy good. It was such a huge step at the time, and nobody really recognized it. (I sure didn't) (I guess someone at MS did because they bought it).

It's a shame it never got a good mainstream implementation. It could/should have been the LZ we all used for the past 10 years.

One of the little mistakes in LZX was the 21 bit offset limit. This must have seemed enormous back on the Amiga in 1995, but very quickly became a major handicap against LZs with unlimited windows.

LZX with unlimited window (eg. on files less than 2 MB) is competitive with any modern LZ, especially on binary structured data where it really shines. In hindsight, LZX is the clear ancestor to LZMA and it was way ahead of its time. We're only clearly beating it in the past year or two (!!).

2. RAR. The primary LZ in RAR is a pretty straightforward LZ-Huff (I believe). It's fine, it's nothing bad or special.

What makes RAR special is the filters. It still has the best filters of any compressor I know.

RAR+filters often *beats* LZMA and other very slow high ratio compressors.

The special thing about the RAR filters is that they aren't like most of the "precomp" solutions that just try to recognize WAV headers and things like that - RAR may do some of that (I have no idea) - but it also definitely finds filters that work on headerless data. Like, you can take a BMP or WAV and strip off the header and RAR will still figure out that there's data to filter in there; it must have some analysis heuristics, and they're better than anything else I've seen.

As an example of when RAR filters do magic, here's a 24-bit RGB BMP with the first 100k stripped, so it's headerless and not easily recognized by file-type-detection filters :

PDI_1200_bmp_no_header.BitKnit,1268120  // <- wow BitKnit !
PDI_1200_bmp_no_header.rar,1312621  // <- RAR filters!
PDI_1200_bmp_no_header.mc-.rar,1631419 // <- RAR unfiltered

That said, it does make mistakes. Sometimes filters can make things way worse if they make a wrong decision. They don't have a "filters must help" safety check. This is easy to prevent, you just run also with no filter and make sure it helped, but they seem to not do that (presumably to save the encode time) and the results can be disastrous :

lightmap.bc3.mc-.rar,457893  // <- RAR with disabled filters
lightmap.bc3.rar,778363  // <- RAR with filters huge fuckup !!
RAR filters fucking up on DXTC (BCn) is pretty consistent :
c.dds.mc-.rar,408363 // <- unfiltered is okay
c.dds.rar,438070     // <- oops!
Sometimes it does magic :
horse.vipm.brotli10,955363 // <- brotli10 big step
horse.vipm.rar,971716 // <- RAR with filters does magic
horse.vipm.mc-.rar,1066205 // <- RAR with disabled filters
Here's an XRGB dds where the RAR filters do magic :
d.dds.BitKnit,360220  // (at zl6 BitKnit beats LZNA ! crushes 7z! wow)
d.dds.rar,382282  // <- RAR filter crushes 7z
d.dds.mc-.rar,534913 // <- RAR unfiltered is poor
happy.mc-.rar,1177426 // <- RAR unfiltered is okay
happy.rar,1354649 // <- RAR filters fucks up
Not about RAR, but for historical comparison, lzt24 is another mesh (the "struct72" file here )
Found another weird one where RAR filters do magic; lzt25 is super-structured 13-byte structs :
lzt25.rar,40024  // <- WOW RAR filters!
lzt25.zl8.LZNA,61582  // <- zl8 LZNA worse than zl6 - weird file
lzt25.zstd060,64550  // <- ZStd does surprisingly well here, I thought you needed more reps on this file
lzt25.brotli10,68472 // <- brotli10 worse than brotli9 !
lzt25.BitKnit,92940  // <- BitKnit oddly struggling
lzt25.mc-.rar,106423 // <- unfiltered RAR is the worst of the LZ's

A lot of interesting things to pick out in those reports. (just saying, I'm not gonna address them all)

One just general thing is that the performance of these LZ's is in no way consistent. You can't just say that "X LZ is 5% better than Y", there's no really consistent pattern, they have wildly variable relative performance.

There's a family of sort of normal LZ's - LZX, Brotli9, ZStd, & unfiltered RAR. Then there's the family of the high-compress LZ's, LZNA, 7z, nz. Those are pretty consistently together, and form two end-points.

But then there are the floaters. BitKnit, Kraken, Filtered RAR, and Brotli10 can jump around between the "normal LZ" and "high-compress LZ" region. BitKnit and Brotli10 are the most variable - they both can jump right up to the high-compress LZ's like 7z, but on other files they drop right down into the pack of normal LZ's (LZX, etc.).

I have a guess about what's happening with Brotli. I haven't looked at the code at all, but my guess is that between level 9 and 10 the order-1 context optimization is turned on. In particular, there's this "signed int" context mode which I believe is what does the magic for brotli on things like horse.vipm (for example it has contexts for the case of last two bytes = 0x0000 , or last two bytes = 0xFFFF , which are pretty common on horse). My guess is that this mode is just not even tried at all at level 9, and at level 10 it turns on the code to pick the best context mode, and finds the signed int mode which is great on these files. Not sure.

04-30-16 | Oodle Kraken Pareto Frontier

The whole idea of Kraken is to excel in the size-decodespeed tradeoff. From the beginning of its design, every decision was considered in terms of the size vs decodespeed.

So how does it do?

To visualize the size-decodespeed Pareto frontier, I like to use an imaginary loading problem. You want to load compressed data and then decompress it. One option is the null compressor (or "memcpy") that just loads uncompressed data and then memcpys it. Or you can use compressors that give smaller file sizes, thus quicker loads, but take more time to decompress. By dialing the virtual disk speed, you can see which compressor is best at different tradeoffs of space vs. speed.

Of course you may not actually be just trying to optimize load time, but you can still use this imaginary loading problem as a way to study the space-speed tradeoff. If you care more about size, you look at lower imaginary disk speeds, if you core more about CPU use, you look at higher imaginary disk speeds.

I like to show "speedup" which is the factor of increase in speed using a certain compressor to do load+decomp vs. the baseline (memcpy). So the left hand y-intercepts (disk speed -> 0) show the compression ratio, and the right hand y-intercepts side show the decompression speed (disk speed -> inf), and in between shows the tradeoff. (By "show" I mean "is linearly proportional to, so you can actually look at the ratio of Y-intercepts in the Pareto curve and it tells you compression ratio on the left and decompression speed on the right).

03-02-15 - Oodle LZ Pareto Frontier and 05-13-15 - Skewed Pareto Chart

The chart showing "millis" shows time, so obviously lower is better. I show a few ways to combine load & decomp. Sum is the time to load then decomp sequentially. Max is the larger of the two, which is the time if they were perfectly overlapped (not usually possible). Personally I think "l2 sum" is most useful. This is the sqrt of sum of squares, which is a kind of sum that biases towards the larger; it's kind of like a mix of "sum" and "max", it means you want the sum to be small, but you also want them to similar times.

Kraken tops the Pareto curve for decodespeed vs size for a huge range of virtual disk speed; from around 2 mb/s up to around 300 mb/s.

Of course the Pareto curve doesn't tell the whole picture. For one thing I don't have encode speed in the equation here at all (and sometimes you need to look at the memory use tradeoff too, so it's really a size-decodespeed-encodespeed-memoryuse surface). For another you sometimes have strict requirements, like I must hit a certain file size, and then you just pick the fastest decoder that meets that requirement. One thing the curves do clearly tell you is when a curve just completely covers another (that is, is greater in Y for all values of X), then that compressor is just never needed (in space & decodespeed).

Silesia :

Game Test Set :

(BTW for anyone trying to compare new charts to old ones on my blog - "Game Test Set" is not a static set. It changes all the time as I get more customer data and try to make it match the most representative data I have for games.)

Just for comparison to earlier posts on my Blog about the other Oodle compressors, here's a run of lzt99 with the full Oodle compressor set.

I've included ZStd for reference here just to show that Kraken jumping way up is not because the previous Oodle compressors were bad - far from it, they were already Pareto optimal. (I like to compare against ZStd not because it's bad, but because it's excellent; it's the only other compressor in the world I know of that's even close to Oodle in terms of good compression ratio and high speed (ZStd also has nice super-fast encode speeds, and it's targetted slightly differently, it's better on text and Oodle is better on binary, it's not a direct apples comparison)).

You can see that LZHLW is just completely covered by Kraken, and so is now deprecated in Oodle. Even LZNIB and BitKnit are barely peeking out of the curve, so the range where they are the right answer is greatly reduced to more specialized needs. (for example BitKnit still romps on strongly structured data, and is useful if you just need a size smaller than Kraken)

04-28-16 | Performance of Oodle Kraken

A continuing series reporting on the performance of recently released Oodle Kraken

First some general notes about Oodle before the big dump of numbers. (skip to the bottom for charts)

Oodle is not intended to solve every problem in data compression. Oodle Data Compression is mainly designed for compress-once load-many usage patterns, where the compressed size and decode speed is important, but encode speed is not as important. Things like distribution, packaging, when you bake content into a compressed archive and then serve it to many people. I do consider it a requirement to keep the encoders faster than 1 MB/s on my ancient laptop, because less than that is just too slow even for content baking.

Like most data compressors, Oodle has various compression level options that trade off encoder speed for compressed size. So there are faster and slower encoders; some of the fast modes are good tradeoffs for space-speed. Kraken turns out to be pretty good at getting high compression even in the fast modes. I'll do a post that goes into this in the future.

Oodle is mainly intended for packing binary data. Because Oodle is built for games, we focus on the types of data that games ship, such as textures, models, animations, levels, and other binary structured data that often contains various types of packed numeric data. Oodle is good on text but is not really built for text. In general if you are focusing on a specific type of data (eg. text/html/xml) you will get the best results with domain-specific preprocessors, such as xwrt or wbpe. Oodle+wbpe is an excellent text compressor.

Oodle Kraken is intended for high compression use cases, where you care about size. There's a whole family of compressors now that live in the "just below lzma (7zip)" compression ratio domain, such LZHAM, Brotli, Oodle BitKnit, and ZStd. In general the goal of these is to get as close to lzma compression ratio as possible while providing much better speed. This is where Kraken achieves far more than anyone has before, far more than we thought possible.

Today I will be focusing on high compression modes, looking at decode speed vs. compression ratio. All compressors will generally be run in their max compression mode, without going into the "ridiculously slow" below 1 MB/s range. (for Oodle this means running -zl6 Optimal2 but not -zl7 or higher).

Okay, on to lots of numbers.

Rather than post an average on a test set, which can be misleading due to the selection of the test set or the way the results are averaged (total compressed size or average ratio?), I'll post results on a selection of individual files :


by ratio:
lzma        :  3.88:1 ,    2.0 enc mb/s ,   63.7 dec mb/s
lzham       :  3.56:1 ,    1.5 enc mb/s ,  186.4 dec mb/s
Oodle Kraken:  3.51:1 ,    1.2 enc mb/s ,  928.0 dec mb/s
zstdmax     :  3.24:1 ,    2.8 enc mb/s ,  401.0 dec mb/s
zlib9       :  2.51:1 ,   12.4 enc mb/s ,  291.5 dec mb/s
lz4hc       :  2.32:1 ,   36.4 enc mb/s , 2351.6 dec mb/s

by encode speed:
lz4hc       :  2.32:1 ,   36.4 enc mb/s , 2351.6 dec mb/s
zlib9       :  2.51:1 ,   12.4 enc mb/s ,  291.5 dec mb/s
zstdmax     :  3.24:1 ,    2.8 enc mb/s ,  401.0 dec mb/s
lzma        :  3.88:1 ,    2.0 enc mb/s ,   63.7 dec mb/s
lzham       :  3.56:1 ,    1.5 enc mb/s ,  186.4 dec mb/s
Oodle Kraken:  3.51:1 ,    1.2 enc mb/s ,  928.0 dec mb/s

by decode speed:
lz4hc       :  2.32:1 ,   36.4 enc mb/s , 2351.6 dec mb/s
Oodle Kraken:  3.51:1 ,    1.2 enc mb/s ,  928.0 dec mb/s
zstdmax     :  3.24:1 ,    2.8 enc mb/s ,  401.0 dec mb/s
zlib9       :  2.51:1 ,   12.4 enc mb/s ,  291.5 dec mb/s
lzham       :  3.56:1 ,    1.5 enc mb/s ,  186.4 dec mb/s
lzma        :  3.88:1 ,    2.0 enc mb/s ,   63.7 dec mb/s

by ratio:
lzma        :  2.65:1 ,    3.1 enc mb/s ,   42.3 dec mb/s
Oodle Kraken:  2.46:1 ,    2.3 enc mb/s ,  957.1 dec mb/s
lzham       :  2.44:1 ,    1.9 enc mb/s ,  166.0 dec mb/s
zstdmax     :  2.27:1 ,    3.8 enc mb/s ,  482.3 dec mb/s
zlib9       :  1.77:1 ,   13.3 enc mb/s ,  286.2 dec mb/s
lz4hc       :  1.67:1 ,   30.3 enc mb/s , 2737.4 dec mb/s

by encode speed:
lz4hc       :  1.67:1 ,   30.3 enc mb/s , 2737.4 dec mb/s
zlib9       :  1.77:1 ,   13.3 enc mb/s ,  286.2 dec mb/s
zstdmax     :  2.27:1 ,    3.8 enc mb/s ,  482.3 dec mb/s
lzma        :  2.65:1 ,    3.1 enc mb/s ,   42.3 dec mb/s
Oodle Kraken:  2.46:1 ,    2.3 enc mb/s ,  957.1 dec mb/s
lzham       :  2.44:1 ,    1.9 enc mb/s ,  166.0 dec mb/s

by decode speed:
lz4hc       :  1.67:1 ,   30.3 enc mb/s , 2737.4 dec mb/s
Oodle Kraken:  2.46:1 ,    2.3 enc mb/s ,  957.1 dec mb/s
zstdmax     :  2.27:1 ,    3.8 enc mb/s ,  482.3 dec mb/s
zlib9       :  1.77:1 ,   13.3 enc mb/s ,  286.2 dec mb/s
lzham       :  2.44:1 ,    1.9 enc mb/s ,  166.0 dec mb/s
lzma        :  2.65:1 ,    3.1 enc mb/s ,   42.3 dec mb/s

by ratio:
lzma        :  2.37:1 ,    2.1 enc mb/s ,   40.8 dec mb/s
Oodle Kraken:  2.18:1 ,    1.0 enc mb/s ,  684.6 dec mb/s
lzham       :  2.17:1 ,    1.3 enc mb/s ,  127.7 dec mb/s
zstdmax     :  2.02:1 ,    3.3 enc mb/s ,  289.4 dec mb/s
zlib9       :  1.83:1 ,   13.3 enc mb/s ,  242.9 dec mb/s
lz4hc       :  1.67:1 ,   20.4 enc mb/s , 2226.9 dec mb/s

by encode speed:
lz4hc       :  1.67:1 ,   20.4 enc mb/s , 2226.9 dec mb/s
zlib9       :  1.83:1 ,   13.3 enc mb/s ,  242.9 dec mb/s
zstdmax     :  2.02:1 ,    3.3 enc mb/s ,  289.4 dec mb/s
lzma        :  2.37:1 ,    2.1 enc mb/s ,   40.8 dec mb/s
lzham       :  2.17:1 ,    1.3 enc mb/s ,  127.7 dec mb/s
Oodle Kraken:  2.18:1 ,    1.0 enc mb/s ,  684.6 dec mb/s

by decode speed:
lz4hc       :  1.67:1 ,   20.4 enc mb/s , 2226.9 dec mb/s
Oodle Kraken:  2.18:1 ,    1.0 enc mb/s ,  684.6 dec mb/s
zstdmax     :  2.02:1 ,    3.3 enc mb/s ,  289.4 dec mb/s
zlib9       :  1.83:1 ,   13.3 enc mb/s ,  242.9 dec mb/s
lzham       :  2.17:1 ,    1.3 enc mb/s ,  127.7 dec mb/s
lzma        :  2.37:1 ,    2.1 enc mb/s ,   40.8 dec mb/s

by ratio:
lzma        :  4.35:1 ,    3.1 enc mb/s ,   59.3 dec mb/s
Oodle Kraken:  3.77:1 ,    1.5 enc mb/s ,  878.3 dec mb/s
lzham       :  3.77:1 ,    1.6 enc mb/s ,  162.5 dec mb/s
zstdmax     :  2.77:1 ,    5.7 enc mb/s ,  405.7 dec mb/s
zlib9       :  2.19:1 ,   13.9 enc mb/s ,  332.9 dec mb/s
lz4hc       :  1.78:1 ,   40.1 enc mb/s , 2364.4 dec mb/s

by encode speed:
lz4hc       :  1.78:1 ,   40.1 enc mb/s , 2364.4 dec mb/s
zlib9       :  2.19:1 ,   13.9 enc mb/s ,  332.9 dec mb/s
zstdmax     :  2.77:1 ,    5.7 enc mb/s ,  405.7 dec mb/s
lzma        :  4.35:1 ,    3.1 enc mb/s ,   59.3 dec mb/s
lzham       :  3.77:1 ,    1.6 enc mb/s ,  162.5 dec mb/s
Oodle Kraken:  3.77:1 ,    1.5 enc mb/s ,  878.3 dec mb/s

by decode speed:
lz4hc       :  1.78:1 ,   40.1 enc mb/s , 2364.4 dec mb/s
Oodle Kraken:  3.77:1 ,    1.5 enc mb/s ,  878.3 dec mb/s
zstdmax     :  2.77:1 ,    5.7 enc mb/s ,  405.7 dec mb/s
zlib9       :  2.19:1 ,   13.9 enc mb/s ,  332.9 dec mb/s
lzham       :  3.77:1 ,    1.6 enc mb/s ,  162.5 dec mb/s
lzma        :  4.35:1 ,    3.1 enc mb/s ,   59.3 dec mb/s

by ratio:
lzma        :  2.95:1 ,    2.5 enc mb/s ,   51.9 dec mb/s
lzham       :  2.77:1 ,    1.6 enc mb/s ,  177.6 dec mb/s
Oodle Kraken:  2.70:1 ,    1.0 enc mb/s ,  877.0 dec mb/s
zstdmax     :  2.64:1 ,    3.5 enc mb/s ,  417.8 dec mb/s
zlib9       :  2.07:1 ,   16.8 enc mb/s ,  269.6 dec mb/s
lz4hc       :  1.91:1 ,   28.8 enc mb/s , 2297.6 dec mb/s

by encode speed:
lz4hc       :  1.91:1 ,   28.8 enc mb/s , 2297.6 dec mb/s
zlib9       :  2.07:1 ,   16.8 enc mb/s ,  269.6 dec mb/s
zstdmax     :  2.64:1 ,    3.5 enc mb/s ,  417.8 dec mb/s
lzma        :  2.95:1 ,    2.5 enc mb/s ,   51.9 dec mb/s
lzham       :  2.77:1 ,    1.6 enc mb/s ,  177.6 dec mb/s
Oodle Kraken:  2.70:1 ,    1.0 enc mb/s ,  877.0 dec mb/s

by decode speed:
lz4hc       :  1.91:1 ,   28.8 enc mb/s , 2297.6 dec mb/s
Oodle Kraken:  2.70:1 ,    1.0 enc mb/s ,  877.0 dec mb/s
zstdmax     :  2.64:1 ,    3.5 enc mb/s ,  417.8 dec mb/s
zlib9       :  2.07:1 ,   16.8 enc mb/s ,  269.6 dec mb/s
lzham       :  2.77:1 ,    1.6 enc mb/s ,  177.6 dec mb/s
lzma        :  2.95:1 ,    2.5 enc mb/s ,   51.9 dec mb/s

by ratio:
lzma        :  3.64:1 ,    1.8 enc mb/s ,   79.5 dec mb/s
lzham       :  3.60:1 ,    1.4 enc mb/s ,  196.5 dec mb/s
zstdmax     :  3.56:1 ,    2.2 enc mb/s ,  394.6 dec mb/s
Oodle Kraken:  3.49:1 ,    1.5 enc mb/s ,  789.7 dec mb/s
zlib9       :  2.38:1 ,   22.2 enc mb/s ,  234.3 dec mb/s
lz4hc       :  2.35:1 ,   27.5 enc mb/s , 2059.6 dec mb/s

by encode speed:
lz4hc       :  2.35:1 ,   27.5 enc mb/s , 2059.6 dec mb/s
zlib9       :  2.38:1 ,   22.2 enc mb/s ,  234.3 dec mb/s
zstdmax     :  3.56:1 ,    2.2 enc mb/s ,  394.6 dec mb/s
lzma        :  3.64:1 ,    1.8 enc mb/s ,   79.5 dec mb/s
Oodle Kraken:  3.49:1 ,    1.5 enc mb/s ,  789.7 dec mb/s
lzham       :  3.60:1 ,    1.4 enc mb/s ,  196.5 dec mb/s

by decode speed:
lz4hc       :  2.35:1 ,   27.5 enc mb/s , 2059.6 dec mb/s
Oodle Kraken:  3.49:1 ,    1.5 enc mb/s ,  789.7 dec mb/s
zstdmax     :  3.56:1 ,    2.2 enc mb/s ,  394.6 dec mb/s
zlib9       :  2.38:1 ,   22.2 enc mb/s ,  234.3 dec mb/s
lzham       :  3.60:1 ,    1.4 enc mb/s ,  196.5 dec mb/s
lzma        :  3.64:1 ,    1.8 enc mb/s ,   79.5 dec mb/s

In chart form :

(lz4 decode speed is off the top of the chart)

I'm not including the other Oodle compressors here just to keep things as simple as possible. If you do want more compression than Kraken, and care about decode speed, then Oodle LZNA or BitKnit are much faster to decode than lzma (7zip) at comparable or better compression ratios.

Visit radgametools.com to learn more about Kraken and Oodle.

04-27-16 | Introducing Kraken

Kraken is out. Release notice on my blogger blog :

Release the Kraken!

I'll be doing some more expert-oriented techy followup posts here at rants.html

04-25-16 | Data Compression History : Finnish

Finnish was perhaps the fastest (non-nop) compressor in the world around 1995 (? not sure on the exact year. Definitely before P-Pro and CMOV and branch penalties and such; this is a pre-Pentium-era optimized compressor; it definitely existed before LZP1 (1996) since it was one of the things I benchmarked against). (heck it might be a 286-era compressor, seeing as it's all 16-bit!)

Finnish was by some guys that I assume were from Finland. If anybody knows the correct attribution please let me know.

I was thinking about it the other day because we talked about the old segment register trick that we used to do, and I always thought this was such a neat little bit of code. It also uses the byte-regs as part of word-reg tricks.

Finnish :

; es = CharTable
; bx = hash index
; dl = control bits
; ds[si] = input
; ds[di] = output
; ax/al/ah = input char
; bp = control ptr

ProcessByte     macro SourceReg,BitVal
                        cmp     SourceReg, es:[bx]
                        je      ProcessByte_done
                        or      dl, BitVal
                        mov     es:[bx], SourceReg
                        mov     ds:[di], SourceReg
                        inc     di
ProcessByte_done:       mov     bh, bl
                        mov     bl, SourceReg

                        mov bp, di           ; ControlPtr = CompPtr++;
                        inc di
                        xor dl, dl           ; Control = 0;

                        lodsw                ; AX = ds[si] , si += 2
                        ProcessByte al, 80h
                        ProcessByte ah, 40h
                        ProcessByte al, 20h
                        ProcessByte ah, 10h
                        ProcessByte al, 08h
                        ProcessByte ah, 04h
                        ProcessByte al, 02h
                        ProcessByte ah, 01h

                        mov     ds:[bp], dl  ; *ControlPtr = Control

04-25-16 | Huffman Correction

A reader pointed out an error in my blog post - 08-12-10 - The Lost Huffman Paper

I had :

if ( bits >= huff_branchCodeLeftAligned[TABLE_N_BITS] )
    U32 peek = bits >> (WORD_SIZE - TABLE_N_BITS);
    Consume( table[peek].codeLen );
    return table[peek].symbol;

it should have been :

if ( bits < huff_branchCodeLeftAligned[TABLE_N_BITS] )
    U32 peek = bits >> (WORD_SIZE - TABLE_N_BITS);
    Consume( table[peek].codeLen );
    return table[peek].symbol;

it's corrected now.

In my convention, branchCodeLeftAligned is the left-aligned bitbuff value that means you must go to a higher codelen.

I thought for clarity I'd go ahead and post the example I did with him :

You have this alphabet :

symbol_id, codeLen, code:
0 ; 2 ; 00
1 ; 3 ; 010
2 ; 3 ; 011
3 ; 3 ; 100
4 ; 4 ; 1010
5 ; 4 ; 1011
6 ; 4 ; 1100
7 ; 4 ; 1101
8 ; 4 ; 1110
9 ; 5 ; 11110
10; 5 ; 11111

baseCode[n] = first code of len n - # of codes of lower len

    [2]     0
    [3]     1       = 010 - 1
    [4]     6       = 1010 - 4
    [5]     21      = 11110 - 9

    [2]   0x4000000000000000      010000...
    [3]   0xa000000000000000      101000...
    [4]   0xf000000000000000      111100...
    [5]   0xffffffffffffffff      111111...

My decode loop is :

for(int codeLen=1;;codeLen++) // actually unrolled, not a loop

if ( bitbuff < huff_branchCodeLeftAligned[codeLen] ) return symbolUnsort[ getbits(codeLen) - baseCode[codeLen] ];



int codeLen = minCodeLen;
while ( bitbuff >= huff_branchCodeLeftAligned[codeLen] ) codeLen++;
sym = symbolUnsort[ getbits(codeLen) - baseCode[codeLen] ];

so if bitbuff is


codeLen starts at 2
we check

if ( 11010000.. < 0x4000... ) - false
if ( 11010000.. < 0xa000... ) - false
if ( 11010000.. < 0xf000... ) - true
  return ( 1101 - baseCode[4] ); = 13 - 6 = 7

And a full table-accelerated decoder for this code might be :

// 3-bit acceleration table :
#define TABLE_N_BITS 3
if ( bits < huff_branchCodeLeftAligned[TABLE_N_BITS] )
    U32 peek = bits >> (WORD_SIZE - TABLE_N_BITS);
    Consume( table[peek].codeLen );
    return table[peek].symbol;

if ( bitbuff < huff_branchCodeLeftAligned[4] ) return symbolUnsort[ getbits(4) - baseCode[4] ];

// 5 is max codelen
// this compare is not always true (because of the bitbuff=~0 problem), but we take it anyway
//if ( bitbuff < huff_branchCodeLeftAligned[5] )

return symbolUnsort[ getbits(5) - baseCode[5] ];

And there you go. MSB-first Huffman that supports long code lengths that exceed the acceleration table size.

04-22-16 | Understanding Brotli

I got curious just now and went and had a read of the Brotli spec to see what's going on in there. My cliff notes on how Brotli works.

(In particular I was curious if the slow encode speeds for level 10 & 11 were inherent. My conclusion is basically they are. Brotli gets its high compression from the crazy flexibility of Huffman context assignment and table switching, which is an inherently slow thing to encode. It's a very asymmetric format.)

Shout out for order-1 Huffman with merge tables. I'm not sure I've seen that used in production since my paper - "New Techniques in Context Modeling and Arithmetic Encoding" (PDF) (twenty years ago, ZOMG).

Highlighting the things I think are significant or interesting :

Brotli is LZ+Huff Mostly it's LZX (reps, bottom bits, huff resets) plus order-1-huff plus some details The main stream is {packet (LRL+ML) , literals , offset} Brotli has 16 rep codes : 0: last distance 1: second-to-last distance 2: third-to-last distance 3: fourth-to-last distance 4: last distance - 1 5: last distance + 1 6: last distance - 2 7: last distance + 2 8: last distance - 3 9: last distance + 3 10: second-to-last distance - 1 11: second-to-last distance + 1 12: second-to-last distance - 2 13: second-to-last distance + 2 14: second-to-last distance - 3 15: second-to-last distance + 3 (? I'm curious how much this helps; how would Brotli do with just the normal 4 reps?) Brotli does "bottom bits" for offsets, and sends the # of bottom bits in a header (NPOSTFIX) so it's variable per file. Brotli uses an {LRL,ML} , but instead of linear up to excess flag (like LZ4) it uses a Zlib style log2ish + extrabits encoding. This packet has a rather large alphabet (704 codes) Brotli has very flexible capability for Huffman resets. It can send Huff resets anywhere, for each Huffman category. It can also switch *back* which is kind of interesting. At any byte, for each type of entropy coding, it can send a Huffman code index ("block type") and the number of bytes to code in that type. So it could do for literals Huff type i ; use Huff table 0 for the next 200 bytes then use Huff table 1 for 100 bytes, then back to table 0 for 100 bytes etc. Packets are sent order-0 Literals and offsets are sent with order-1 Huffman The order-1 Huffman can have separate tables per context, or they can be shared. So the encoder combines context buckets with similar statistics. This is sent as a "context map". Crazily, there is a separate "context map" per block type! So "block type" is actually selecting a possibly different context map assignment of the prefix code tables. The context for offsets is a 2-bit context from the match length of the current match. {ML=2,3,4,5+} (models the ML-offset correlation) Literals are context-coded using the previous 2 literals. It's not really order-2 in that there's no escape down. It just takes the 2 literals and forms a single context value, which is always 6 bits. There are four methods, called context modes, to compute the Context ID: * LSB6, where the Context ID is the value of six least-significant bits of p1, * MSB6, where the Context ID is the value of six most-significant bits of p1, * UTF8, where the Context ID is a complex function of p1, p2, optimized for text compression, and * Signed, where Context ID is a complex function of p1, p2, optimized for compressing sequences of signed integers. (note that order1 huff bin merging can effectively reduce the bit count; eg. MSB6 can become MSB2 if the lower bits are not very helpful, by sending them all as the same huffman code index)

03-14-16 | XRGB Bitmap Test

This is obvious and I think it's been done before, but hey.

I was remembering how modern LZ's like LZMA (BitKnit, etc.) that (can) do pos&3 for literals might like bitmaps in XRGB rather than 24-bit RGB.

In XRGB, each color channel gets its own entropy coding. Also offset bottom bits works if the offsets are whole pixel steps (the off&3 will be zero). In 24-bit RGB that stuff is all mod-3 which we don't do.

(in general LZMA-class compressors fall apart a bit if the structure is not the typical 4/8/pow2)

In compressors it's generally terrible to stick extra bytes in and give the compressor more work to do. In this case we're injecting a 0 in every 4th byte, and the compressor has to figure out those are all redundant just to get back to its original size.

Anyway, this is an old idea, but I don't think I ever actually tried it. So :



24-bit RGB : LZNA : 2,760,054 -> 1,376,781
32-bit XRGB: LZNA : 3,676,818 -> 1,311,502

24-bit  RGB with DPCM filter : LZNA : 2,760,054 -> 1,022,066
32-bit XRGB with DPCM filter : LZNA : 3,676,818 -> 1,015,379  (MML8 : 1,012,988)

webpll : 961,356
paq8o8 : 1,096,342


24-bit RGB : LZNA : 6,580,854 -> 3,274,757
32-bit XRGB: LZNA : 8,769,618 -> 3,022,320

24-bit  RGB with DPCM filter : LZNA : 6,580,854 -> 2,433,246
32-bit XRGB with DPCM filter : LZNA : 8,769,618 -> 2,372,921

webpll : 2,204,444
gralic111d : 1,822,108

other compressors :

32-bit XRGB with DPCM filter : LZA  : 8,769,618 -> 2,365,661 (MML8 : 2,354,434)

24-bit  RGB no filter : BitKnit : 6,580,854 -> 3,462,455
32-bit XRGB no filter : BitKnit : 8,769,618 -> 3,070,141
32-bit XRGB with DPCM filter : BitKnit : 8,769,618 -> 2,601,463

32-bit XRGB: LZNA : 8,769,618 -> 3,022,320
32-bit XRGB: LZA  : 8,769,618 -> 3,009,417

24-bit  RGB: LZMA : 6,580,854 -> 3,488,546 (LZMA lc=0,lp=2,pb=2)
32-bit XRGB: LZMA : 8,769,618 -> 3,141,455 (LZMA lc=0,lp=2,pb=2)


bmp copy moses.bmp moses.tga 32
radbitmaptest64 rrz -z0 r:\moses.tga moses.tga.rrz -f8 -l1

Key observations :

1. On "moses" unfiltered : padding to XRGB does help a solid amount (3,274,757 to 3,022,320 for LZNA) , despite the source being 4/3 bigger. I think that proves the concept. (BitKnit & LZMA even bigger difference)

2. On filtered data, padding to XRGB still helps, but much (much) less. Presumably this is because post-filter data is just a bunch of low values, so the 24-bit RGB data is not so multiple-of-three structured (it's a lot of 0's, +1's, and -1's, less coherent, less difference between the color channels, etc.)

3. On un-filtered data, "sub" literals might be helping BitKnit (it beats LZMA on 32-bit unfiltered, and hangs with LZNA). On filtered data, the sub-literals don't help (might even hurt) and BK falls behind. We like the way sub literals sometimes act as an automatic structure stride and delta filter, but they can't compete with a real image-specific DPCM.

Now, XRGB padding is an ugly way to do this. You'd much rather stick with 24-bit RGB and have an LZ that works inherently on 3-byte items.

The first step is :

LZ that works on "items"

(eg. item = a pixel)

LZ matches (offsets and lens) are in whole items

(the more analogous to bottom-bits style would be to allow whole-items and "remainders";
that's /item and %item, and let the entropy coder handle it if remainder==0 always;
but probably best to just force remainders=0)

When you don't match (literal item)
each byte in the item gets it own entropy stats
(eg. color channels of pixels)

which maybe is useful on things other than just images.

The other step is something like :

Offset is an x,y delta instead of linear
(this replaces offset bottom bits)

could be generically useful in any kind of row/column structured data

Filtering for values with x-y neighbors

(do you do the LZ on un-filtered data, and only filter the literals?)
(or do you filter everything and do the LZ on filter residuals?)

and a lot of this is just webp-ll

03-11-16 | Seven Test Space-Speeds

Showing decompress time space-speed tradeoff on the different files of "seven test" :








Note on the test :

This is running the non-Oodle compressors via my build of their lib (*). Brotli not included because it's too hard to build in MSVC (before 2010). "oohc" here is "Optimal2" level (originally posted with Optimal1 level, changed to Optimal2 for consistency with previous post).

The sorting of the labels on the right is by compressed size.

Report on total of all files :

by ratio:
oohcLZNA    :  2.37:1 ,    2.9 enc mb/s ,  125.5 dec mb/s
lzma        :  2.35:1 ,    2.7 enc mb/s ,   37.3 dec mb/s
oohcBitKnit :  2.27:1 ,    4.9 enc mb/s ,  258.0 dec mb/s
lzham       :  2.23:1 ,    1.9 enc mb/s ,  156.0 dec mb/s
oohcLZHLW   :  2.16:1 ,    3.4 enc mb/s ,  431.9 dec mb/s
zstdmax     :  1.99:1 ,    4.6 enc mb/s ,  457.5 dec mb/s
oohcLZNIB   :  1.84:1 ,    7.2 enc mb/s , 1271.4 dec mb/s

by encode speed:
oohcLZNIB   :  1.84:1 ,    7.2 enc mb/s , 1271.4 dec mb/s
oohcBitKnit :  2.27:1 ,    4.9 enc mb/s ,  258.0 dec mb/s
zstdmax     :  1.99:1 ,    4.6 enc mb/s ,  457.5 dec mb/s
oohcLZHLW   :  2.16:1 ,    3.4 enc mb/s ,  431.9 dec mb/s
oohcLZNA    :  2.37:1 ,    2.9 enc mb/s ,  125.5 dec mb/s
lzma        :  2.35:1 ,    2.7 enc mb/s ,   37.3 dec mb/s
lzham       :  2.23:1 ,    1.9 enc mb/s ,  156.0 dec mb/s

by decode speed:
oohcLZNIB   :  1.84:1 ,    7.2 enc mb/s , 1271.4 dec mb/s
zstdmax     :  1.99:1 ,    4.6 enc mb/s ,  457.5 dec mb/s
oohcLZHLW   :  2.16:1 ,    3.4 enc mb/s ,  431.9 dec mb/s
oohcBitKnit :  2.27:1 ,    4.9 enc mb/s ,  258.0 dec mb/s
lzham       :  2.23:1 ,    1.9 enc mb/s ,  156.0 dec mb/s
oohcLZNA    :  2.37:1 ,    2.9 enc mb/s ,  125.5 dec mb/s
lzma        :  2.35:1 ,    2.7 enc mb/s ,   37.3 dec mb/s

How to for my reference :

type test_slowies_seven.bat
@REM test each one individially :
spawnm -n external_compressors_test.exe -e2 -d10 -noohc -nlzma -nlzham -nzstdmax r:\testsets\seven\* -cr:\seven_csvs\@f.csv
@REM test as a set :
external_compressors_test.exe -e2 -d10 -noohc -nlzma -nlzham -nzstdmax r:\testsets\seven

dele r:\compressorspeeds.*
@REM testproj compressorspeedchart
spawnm c:\src\testproj\x64\debug\TestProj.exe r:\seven_csvs\*.csv
ed r:\compressorspeeds.*

(* = I use code or libs to test speeds, never exes; I always measure speed memory->memory, single threaded, with cold caches)

03-11-16 | Seven Test

I made a new test set called "sevens", taking the lead from enwik7, the size of each file is 10 MB (10^7).

The goal here is not to show the total or who does best overall (that relies on how you weight each type of file and whether you think this selection is representative of the occurance ratios in your data), rather to show how each compressor does on different types of data, to highlight their different strengths.

Showing compression factor (eg. N:1 , higher is better) :

run details :

ZStd is 0.5.1 at level 21 (optimal)
LZMA is 7z -mx9 -m0=lzma:d24
Brotli is bro.exe by Sportman --quality 9 --window 24 (*)
Oodle is v2.13 at -z6 (Optimal2)

All competitors run via their provided exe

Some takeaways :

Binary structured data is really where the other compressors leave a lot of room to beat them. ("granny" and "records"). The difference in sizes on all the other files is pretty meh.

BitKnit does its special thang on granny - close to LZNA but 2X faster to decode (and ~ 6X faster than LZMA). Really super space-speed. BitKnit drops down to more like LZHLW levels on the non-record files (LZNA/LZMA has a small edge on them).

I was really surprised by ZStd vs Brotli. I actually went back and double checked by CSV to make sure I hadn't switched the columns by accident. In particular - Brotli does poorly on enwik7 (huh!?) but it does pretty well on "granny", and surprisingly ZStd does quite poorly on "granny" & "records". Not what I expected at all. Brotli is surprising poor on text/web and surprisingly good on binary record data.

LZHLW is still an excellent choice after all these years.

(* = Brotli quality 10 takes an order of magnitude longer than any of the others. I got fed up with waiting for it. Oodle also has "super" modes at -z8 that aren't used here. (**))

(for concreteness : Brotli 11 does pretty well on granny7 ; (6.148:1 vs 4.634:1 at q9) but it runs at 68 kb/s (!!) (and still not LZMA-level compression))

(** = I used to show results in benchmarks that required really slow encoders (for example the old LZNIB optimal "super parse" was hella slow); that can result in very small sizes and great decode speed, but it's a form of cheating. Encoders slower than 1 mb/s just won't be used, they're too slow, so it's reporting a result that real users won't actually see, and that's BS. I'm trying to be more legit about this now for my own stuff. Slow encoders are still interesting for research purposes because they show what should be possible, so you can try to get that result back in a faster way. (this in fact happened with LZNIB and is a Big Deal))

02-29-16 | Bit Input Notes

1. The big win of U64 branchless bit input is having >= 56 bits (or 57) after refill. The basic refill operation itself is not faster than branchy 32-at-a-time refills, but that only has >= 32 (or 33) bits after refill. The advantage comes if you can unconditionally consume bits knowing that count. eg. if you have a 12-bit limitted Huffman, you can consume 4 symbols without needing to refill.

2. The best case for bit input is when the length that you consume is not very variable. eg. in the Huffman case, 1-12 bits, has a reasonably low limit. The worst case is when it has a high max and is quite random. Then you can't avoid refill checks, and they're quite unpredictable (if you do the branchy case)

3. If your refills have a large maximum, but the average is low, branchy can be faster than branchless. Because the maximum is high (eg. maybe a max of 32 bits consumed), you can only do one decode op before checking refill. Branchless will then always refill. Branchy can skip the refill if the average is low - particularly if it's predictably low.

4. If using branchy refills, try to make it predictable. An interesting idea is to use multiple bit buffers so that each consumption spot gets its own buffer, and then can create a pattern. A very specific case is consuming a fixed number of bits. something like :


if ( random )
  consume 4 bits from bitbuffer
  if bitbuffer out -> refill
  consume 6 bits from bitbuffer
  if bitbuffer out -> refill

these branches (for bitbuffer refill) will be very random because of the two different sites that consume different amounts. However, this :

bitbuffer1, bitbuffer2

if ( random )
  consume 4 bits from bitbuffer1
  if bitbuffer1 out -> refill
  consume 6 bits from bitbuffer2
  if bitbuffer2 out -> refill

these branches for refill are now perfectly predictable in a pattern (they are taken every Nth time exactly).

5. Bit buffer work is slow, but it's "mathy". On modern processors that are typically math-starved, it can be cheap *if* you have enough ILP to fully use all the execution units. The problem is a single bit buffer on its own is super serial work, so you need multiple bit buffers running simultaneously, or enough other work.

For example, it can actually be *faster* than byte-aligned input (using something like "EncodeMod") if the byte-input does a branch, and that branch is unpredictable (in the bad 25-75% randomly taken range).

02-29-16 | LZSSE Notes

There are a few things that I think are interesting in LZSSE. And really very little of it is about the SIMD-ness.

1. SIMD processing of control words.

All LZ-Bytewises do a little bit of shifts and masks to pull out fields and flags from the control word. Stuff like lrl = (control>>4) and numbytesout = lrl+ml;

This work is pretty trivial, and it's fast already in scalar. But if you can do it N at a time, why not.

A particular advantage here is that SSE instruction sets are somewhat better at branchless code than scalar, it's a bit easier to make masks from conditions and such-like, so that can be a win. Also helps if you're front-end-bound, since decoding one instruction to do an 8-wide shift is less work than 8 instructions. (it's almost impossible for a data compressor to be back-end bound on simple integer math ops, there are just so many execution units; that's rare, it's much possible to hit instruction decode limits)

2. Using SSE in scalar code to splat out match or LRL.

LZSSE parses the control words SIMD (wide) but the actual literal or match copy is scalar, in the sense that only one is done at a time. It still uses SSE to fetch those bytes, but in a scalar way. Most LZ's can do this (many may do it already without being aware of it; eg. if you use memcpy(,16) you might be doing an SSE splat).

3. Limitted LRL and ML in control word with no excess. Outer looping on control words only, no looping on LRL/ML.

To output long LRL's, you have to output a series of control words, each with short LRL. To output long ML's, you have to output a series of control words.

This I think is the biggest difference in LZSSE vs. something like LZ4. You can make an LZ4 variant that works like this, and in fact it's an interesting thing to do, and is sometimes fast. In an LZ4 that does strictly alternating LRL-ML, to do this you need to be able to send ML==0 so that long literal runs can be continued as a sequence of control words.

Traditional LZ4 decoder :

lrl = control>>4;
ml = (control&0xF)+4;
off = get 2 bytes;  comp += 2;

// get excess if flagged with 0xF in control :
if ( lrl == 0xF ) lrl += *comp++; // and maybe more
if ( ml == 19 ) ml += *comp++; // and maybe more

copy(out,comp,lrl); // <- may loop on lrl
out += lrl; comp += lrl;

copy(out,out-off,ml); // <- may loop on ml
out += ml;

non-looping LZ4 decoder : (LZSSE style)

lrl = control>>4;
ml = control&0xF; // <- no +4 , 0 possible
off = get 2 bytes;  comp += 2;  // <- * see below

// no excess

copy(out,comp,16); // <- unconditional 16 byte copy, no loop
out += lrl; comp += lrl;

copy(out,out-off,16); // <- unconditional 16 byte copy, no loop
out += ml;

(* = the big complication in LZSSE comes from trying to avoid sending the offset again when you're continuing a match; something like if previous control word ml == 0xF that means a continuation so don't get offset)

(ignoring the issue of overlapping matches for now)

This non-looping decoder is much less branchy, no branches for excess lens, no branches for looping copies. It's much faster than LZ4 *if* the data doesn't have long LRL's or ML's in it.

4. Flagged match/LRL instead of strictly alternating LRL-ML. This is probably a win on data with lots of short matches, where matches often follow matches with no LRL in between, like text.

If you have to branch for that flag, it's a pretty huge speed hit (see, eg. LZNIB). So it's only viable in a fast LZ-Bytewise if you can do it branchless like LZSSE.

02-29-16 | LZSSE Results

Quick report of my results on LZSSE. (updated 03/06/2016)

(LZSSE Latest commit c22a696 ; fetched 03/06/2016 ; test machine Core i7-3770 3.4 GHz ; built MSVC 2012 x64 ; LZSSE2 and 8 optimal parse level 16)

Basically LZSSE is in fact great on text, faster than LZ4 and much better compression.

On binary, LZSSE2 is quite bad, but LZSSE8 is roughly on par with LZ4. It looks like LZ4 is maybe slightly better on binary than LZSSE8, but it's close.

In general, LZ4 is does well on files that tend to have long LRL's and long ML's. Files with lots of short (or zero) LRL's and short ML's are bad for LZ4 (eg. text) and not bad for LZSSE.

(LZB16 is Oodle's LZ4 variant; 64k window like LZSSE; LZNIB and LZBLW have large windows)

Some results :

enwik8 LZSSE2 : 100,000,000 ->38,068,528 : 2866.17 mb/s
enwik8 LZSSE8 : 100,000,000 ->38,721,328 : 2906.29 mb/s
enwik8 LZB16  : 100,000,000 ->43,054,201 : 2115.25 mb/s

(LZSSE kills on text)

lzt99  LZSSE2 : 24,700,820 ->15,793,708  : 1751.36 mb/s
lzt99  LZSSE8 : 24,700,820 ->15,190,395  : 2971.34 mb/s
lzt99  LZB16  : 24,700,820 ->14,754,643  : 3104.96 mb/s

(LZSSE2 really slows down on heterogenous binary file lzt99)
(LZSSE8 does okay, but slightly worse than LZ4/LZB16 in size & speed)

mozilla LZSSE2: 51,220,480 ->22,474,508 : 2424.21 mb/s
mozilla LZSSE8: 51,220,480 ->22,148,366 : 3008.33 mb/s
mozilla LZB16 : 51,220,480 ->22,337,815 : 2433.78 mb/s

(all about the same size on silesia mozilla)
(LZSSE8 definitely fastest)

lzt24  LZB16  : 3,471,552 -> 2,379,133 : 4435.98 mb/s
lzt24  LZSSE8 : 3,471,552 -> 2,444,527 : 4006.24 mb/s
lzt24  LZSSE2 : 3,471,552 -> 2,742,546 : 1605.62 mb/s
lzt24  LZNIB  : 3,471,552 -> 1,673,034 : 1540.25 mb/s

(lzt24 (a granny file) really terrible for LZSSE2; it's as slow as LZNIB)
(LZSSE8 fixes it though, almost catches LZB16, but not quite)


Some more binary files.  LZSSE2 is not good on any of these, so omitted.

win81  LZB16  : 104,857,600 ->54,459,677 : 2463.37 mb/s
win81  LZSSE8 : 104,857,600 ->54,911,633 : 3182.21 mb/s

all_dds LZB16 : 79,993,099 ->47,683,003 : 2577.24 mb/s
all_dds LZSSE8: 79,993,099 ->47,807,041 : 2607.63 mb/s

LZB16  :  7,105,158 -> 3,498,306 : 3350.06 mb/s
LZSSE8 :  7,105,158 -> 3,612,433 : 3548.39 mb/s

LZB16  : 58,788,904 ->32,862,033 : 2968.36 mb/s
LZSSE8 : 58,788,904 ->33,201,406 : 2642.94 mb/s

LZSSE8 vs LZB16 is pretty close.

LZSSE8 is maybe more consistently fast; its decode speed has less variation than LZ4. Slowest LZSSE8 was all_dds at 2607 mb/s ; LZ4 went down to 2115 mb/s on enwik8. Even excluding text, it was down to 2433 mb/s on mozilla. LZB16/LZ4 had a slightly higher max speed (on lzt24).

Conclusion :

On binary-like data, LZ4 and LZSSE8 are pretty close. On text-like data, LZSSE8 is definitely better. So for general data, it looks like LZSSE8 is a definite win.

02-17-16 | LZSSE

An LZ Codec Designed for SSE Decompression

LZSSE code

Some good stuff.

Basically this is a nibble control word LZ (like LZNIB). The nibble has a threshold value T, < T is an LRL (literal run len), >= T is a match length. LZSSET are various threshold variants. As Conor noted, ideally T would be variable, optimized per file (or even better - per quantum) to adapt to different data better.

LZSSE has a 64k window (like LZ4/LZB16) but unlike them supports MML (minimum match length) of 3. MML 3 typically helps compression a little, but in scalar decoders it really hurts speed.

I think the main interesting idea (other than implementation details) is that by limitting the LRL and ML, with no excess/overflow support (ML overflow is handled with continue-match nibbles), it means that you can do a non-looping output of 8/16 bytes. You get long matches or LRL's by reading more control nibbles.

That is, a normal LZ actually has a nested looping structure :

loop on controls from packed stream
 control specifies lrl/ml

 loop on lrl/ml
   output bytes

LZSSE only has *one* outer loop on controls.

There are some implementation problems at the moment. The LZSSE2 optimal parse encoder is just broken. It's unusably slow and must have some bad N^2 degeneracy. This can be fixed, it's not a problem with the format.

Another problem is that LZSSE2 expands incompressible data too much. Real world data (particularly in games) often has incompressible data mixed with compressible. The ideal fix would be to have the generalized LZSSET and choose T per quantum. A simpler fix would be to do something like cut files into 16k or 64k quanta, and to select the best of LZSSE2/4/8 per-quantum and also support uncompressed quanta to prevent expansion.

I will take this moment to complain that the test sets everyone is using are really shit. Not Conors fault, but enwiks and Silesia are grossly not at all representative of data that we see in the real world. Silesia is mostly text and weird highly-compressible data; the file I like best in there for my own testing is "mozilla" (though BTW mozilla also contains a bunch of internal zlib streams; it benefits enormously from precomp). We need a better test corpus!!!

02-11-16 | String Match Stress Test Files

A gift. My string match stress test set :

string_match_stress_tests.7z (60,832 bytes)

Consists of :


An optimal parse matcher (matching at every position in each file against all previous bytes within that file) should get these average match lengths : (min match length of 4, and no matches searched for in the last 8 bytes of each file)

paper1_twice : 13294.229727
stress_all_as : 21119.499148
stress_many_matches : 32.757760
stress_search_limit : 823.341331
stress_sliding_follow : 199.576550
stress_suffix_forward : 5199.164464

total ml : 2896554306
total bytes : 483870

Previous post on the same test set : 09-27-11 - String Match Stress Test

And these were used in the String Match Test post series , though there I used "twobooks" instead of "paper1_twice".

These stress tests are designed to make imperfect string matchers show their flaws. Correct implementations of Suffix Array or Suffix Tree searchers should find this total match length without ever going into bad N^2 slowdowns (their speed should be roughly constant). Other matchers like hash-link, LzFind (hash-btree) and MMC will either find lower total match length (due to an "amortize" step limit) or will fall into bad N^2 (or worse!) slowdowns.

01-29-16 | Oodle Network Usage Notes

Two things I thought to write down.

1. Oodle Network speed is very cache sensitive.

Oodle Network uses a shared trained model. This is typically 4 - 8 MB. As it compresses or decompresses, it needs to access random bits of that memory.

If you compress/decompress a packet when that model is cold (not in cache), every access will be a cache miss and performance can be quite poor.

In synthetic test, coding packets over and over, the model is as hot as possible (in caches). So performance can seem better in synthetic test loops than in the real world.

In real use, it's best to batch up all encoding/decoding operations as much as possible. Rather than do :

decode one packet
apply packet to world
do some other stuff

decode one packet
apply packet to world
do some other stuff


try to group all the Oodle Network encoding & decoding together :

gather up all my packets to send

receive all packets from network stack

encode all my outbound packets
decode all my inbound packets

now act on inbound packets

this puts all the usage of the shared model together as close as possible to try to maximize the amount that the model is found in cache.

2. Oodle Network should not be used on already compressed data. Oodle Network should not be used on large packets.

Most games send pre-compressed data of various forms. Some send media files such as JPEGs that are already compressed. Some send big blobs that have been packed with zlib. Some send audio data that's already been compressed.

This data should be excluded from the Oodle Network path and send without going through the compressor. It won't get any compression on them and will just take CPU time. (you could send them as a packet with complen == rawlen, which is a flag for "raw data" in Oodle Network).

More importantly, these packets should NOT be included in the training set for building the model. They are essentially random bytes and will just crud up the model. It's a bit like if you're trying to memorize the digits of Pi and someone keeps yelling random numbers in your ear. (Well, actually it's not like that at all, but those kind of totally bullshit analogies seem very popular, so there you are.)

On large packets that are not precompressed, Oodle Network will work, but it's just not the best choice. It's almost always better to use an Oodle LZ data compressor (BitKnit, LZNIB, whatever, depending on your space-speed tradeoff desired).

The vast majority of games have a kind of bipolar packet distribution :

A. normal frame update packets < 1024 bytes

B. occasional very large packets > 4096 bytes

it will work better to only use Oodle Network on the type A packets (smaller, standard updates) and to use Oodle LZ on the type B packets (rarer, large data transfers).

For example some games send the entire state of the level in the first few packets, and then afterward send only deltas from that state. In that style, the initial big level dump should be sent through Oodle LZ, and then only the smaller deltas go through Oodle Network.

Not only will Oodle LZ do better on the big packets, but by excluding them from the training set for Oodle Network, the smaller packets will be compressed better because the data will all have similar structure.

01-16-16 | Oodle 2.1.2

Oodle 2.1.2 is out. Oodle - now with more BitKnit!

Oodle 2.1.2 example_lz_chart [file] [repeats]
got arg : input=r:\testsets\big\lzt99
got arg : num_repeats=5
lz test loading: r:\testsets\big\lzt99
uncompressed size : 24700820
chart cell contains : raw/comp ratio : encode mb/s : decode mb/s
LZB16: LZ-bytewise: super fast to encode & decode, least compression
LZNIB: LZ-nibbled : still fast, but more compression; between LZB & LZH
LZHLW: LZ-Huffman : like zip/zlib, but much more compression & faster
LZNA : LZ-nib-ANS : very high compression with faster decodes than LZMA
All compressors can be run at different encoder effort levels
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |
LZB16  |1.51:517:2988|1.57:236:2971|1.62:109:2964|1.65: 37:3003|
LZBLW  |1.64:249:2732|1.74: 80:2682|1.77: 24:2679|1.85:1.6:2708|
LZNIB  |1.80:264:1627|1.92: 70:1557|1.94: 23:1504|2.04: 12:1401|
LZHLW  |2.16: 67: 424|2.30: 20: 447|2.33:7.2: 445|2.35:5.4: 445|
BitKnit|2.43: 28: 243|2.47: 20: 245|2.50: 13: 249|2.54:6.4: 249|
LZNA   |2.36: 24: 115|2.54: 18: 119|2.58: 13: 120|2.69:4.9: 120|
compression ratio:
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |
LZB16  |    1.510    |    1.569    |    1.615    |    1.654    |
LZBLW  |    1.636    |    1.739    |    1.775    |    1.850    |
LZNIB  |    1.802    |    1.921    |    1.941    |    2.044    |
LZHLW  |    2.161    |    2.299    |    2.330    |    2.355    |
BitKnit|    2.431    |    2.471    |    2.499    |    2.536    |
LZNA   |    2.363    |    2.542    |    2.584    |    2.686    |
encode speed (mb/s):
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |
LZB16  |    517.317  |    236.094  |    108.555  |     36.578  |
LZBLW  |    248.537  |     80.299  |     23.663  |      1.610  |
LZNIB  |    263.950  |     69.930  |     22.617  |     11.735  |
LZHLW  |     67.154  |     20.019  |      7.200  |      5.425  |
BitKnit|     28.203  |     20.223  |     12.672  |      6.371  |
LZNA   |     24.192  |     18.423  |     12.883  |      4.907  |
decode speed (mb/s):
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |
LZB16  |   2988.429  |   2971.339  |   2963.616  |   3003.187  |
LZBLW  |   2731.951  |   2681.796  |   2678.558  |   2707.534  |
LZNIB  |   1626.806  |   1557.309  |   1504.097  |   1400.654  |
LZHLW  |    423.936  |    446.990  |    444.832  |    445.040  |
BitKnit|    242.916  |    245.409  |    248.812  |    248.972  |
LZNA   |    114.791  |    119.369  |    119.994  |    120.362  |

Another test :

Oodle 2.1.2 example_lz_chart [file] [repeats]
got arg : input=r:\game_testset_m0.7z
got arg : num_repeats=5
lz test loading: r:\game_testset_m0.7z
uncompressed size : 79290970
chart cell contains : raw/comp ratio : encode mb/s : decode mb/s
LZB16: LZ-bytewise: super fast to encode & decode, least compression
LZNIB: LZ-nibbled : still fast, but more compression; between LZB & LZH
LZHLW: LZ-Huffman : like zip/zlib, but much more compression & faster
LZNA : LZ-nib-ANS : very high compression with faster decodes than LZMA
All compressors can be run at different encoder effort levels
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |   Optimal2  |
LZB16  |1.4:1039:4304|1.41:438:4176|1.42:184:4202|1.44: 52:4293|1.44:4.5:4407|
LZBLW  |1.51:380:3855|1.55:124:3778|1.56: 26:3774|1.62:1.0:3862|1.62:1.0:3862|
LZNIB  |1.56:346:2406|1.59: 84:2398|1.62: 24:2054|1.67: 15:2048|1.67: 10:2053|
LZHLW  |1.67: 85: 647|1.74: 25: 679|1.75:6.5: 635|1.77:3.3: 613|1.79:1.5: 618|
BitKnit|1.83: 24: 395|1.90: 18: 409|1.90: 12: 408|1.91:7.1: 402|1.91:6.5: 401|
LZNA   |1.78: 22: 171|1.84: 18: 178|1.88: 12: 185|1.93:5.6: 167|1.93:1.5: 167|
compression ratio:
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |   Optimal2  |
LZB16  |    1.390    |    1.408    |    1.424    |    1.436    |    1.442    |
LZBLW  |    1.509    |    1.548    |    1.558    |    1.615    |    1.615    |
LZNIB  |    1.557    |    1.593    |    1.622    |    1.669    |    1.668    |
LZHLW  |    1.669    |    1.745    |    1.754    |    1.767    |    1.790    |
BitKnit|    1.825    |    1.897    |    1.905    |    1.913    |    1.915    |
LZNA   |    1.781    |    1.838    |    1.878    |    1.927    |    1.932    |
encode speed (mb/s):
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |   Optimal2  |
LZB16  |   1038.910  |    437.928  |    184.457  |     52.008  |      4.465  |
LZBLW  |    380.030  |    123.621  |     26.028  |      0.973  |      0.973  |
LZNIB  |    345.905  |     83.577  |     24.299  |     14.544  |     10.444  |
LZHLW  |     84.519  |     25.218  |      6.542  |      3.256  |      1.547  |
BitKnit|     24.116  |     17.944  |     12.476  |      7.052  |      6.464  |
LZNA   |     21.859  |     18.034  |     11.767  |      5.602  |      1.465  |
decode speed (mb/s):
       |   VeryFast  |   Fast      |   Normal    |   Optimal1  |   Optimal2  |
LZB16  |   4304.144  |   4175.854  |   4202.491  |   4292.925  |   4406.853  |
LZBLW  |   3855.255  |   3777.826  |   3774.093  |   3861.922  |   3861.582  |
LZNIB  |   2406.379  |   2397.753  |   2054.429  |   2048.329  |   2053.340  |
LZHLW  |    646.796  |    679.173  |    635.035  |    613.051  |    617.994  |
BitKnit|    394.599  |    408.539  |    408.044  |    402.239  |    401.352  |
LZNA   |    171.111  |    177.565  |    184.677  |    167.439  |    166.904  |

vs LZMA :
ratio: 1.901
enc  : 2.70 mb/s
dec  : 30.27 mb/s

On this file, BitKnit is 13X faster to decode than LZMA, and gets more compression. (or at "Normal" level, the ratio is similar and BitKnit is 4.6X faster to encode).

12-24-15 | RANS in practice

RANS in practice

Usage points for me :

0. My god, adaptive coding is sweet. I've been doing static Huffman and TANS for a while, so I sort of got used to them, and I forgot how nice it is to not have to deal with that shit. (optimal parsing with static entropy coders has the horrible feedback loop and iterations required, you have to find optimal chunking/transmission points, you have to tweak out your codelen/probability transmission to send them compactly and quickly, blah blah). In comparison, adaptive coding is just so simple. It's literally 10X fewer lines of codes.

1. For binary coding, RANS is no win over arithmetic. (Jarek calls "binary ANS" "ABS" but I see no need for another acronym; let's just say "binary ANS"). (and given the option, you'd rather have the FIFO arithmetic coding)

2. For multi-symbol, power-of-2 cumulative probability sum, adaptive RANS is really good.

3. If your model is really complex, like an N-ary Fenwick tree or anything crazy, or if you have to do binary search in cumprobs to do decoding, the difference between RANS and arithmetic can be hidden.

To make adaptive RANS really shine, you need a model specialized for power-of-2 totals, such as the classic "deferred summation" or the new nibble model (cumprob blending), or other. It's only for models that are quite fast that the speed difference between RANS and arithmetic becomes dramatic.

What I'm trying to get at is if you just take an existing compressor based on arithmetic coding, which probably uses binary arithmetic coding, or a rather complex N-ary coder, and just replace the arithmetic part with ANS - you might not see much benefit at all. There are three big stalls - divides, cache misses, branches - and they can hide each other, so if you just eliminate one of the three stalls, it doesn't help much.

ADD : 4. A lot of the recent work (TANS, Yann's Huff work, some of the RANS encoders, etc.) that are very fast also use rather a lot of memory. They make use of tables to speed up coding. That's fine for order-0 coding, or if you have very few contexts (perhaps 2 pos bits), but for order-1 coding or larger contexts, it becomes a problem. Of course your memory use becomes high, but the bigger problem is that your tables no longer fit in cache. Fast table-based coding doesn't make any sense if accessing the tables is a cache miss.

12-23-15 | Oodle Results Update

Major improvements coming in Oodle 2.1.2

Fabian's BitKnit is coming to Oodle. BitKnit is a pretty unique LZ; it makes clever use of the properties of RANS to hit a space-speed tradeoff point that nothing else does. It gets close to LZMA compression levels (sometimes more, sometimes less) while being more like zlib speed.

LZNA and LZNIB are also much improved. The bit streams are the same, but we found some little tweaks in the encoders & decoders that make significant difference. (5-10%, but that's a lot in compression, and they were already world-beating, so the margin is just bigger now). The biggest improvement came from some subtle issues in the parsers.

As usual, I'm trying to be as fair as possible to the competition. Everything is run single threaded. LZMA and LZHAM are run at max compression with context bits at their best setting. Compressors like zlib that are just not even worth considering are not included, I've tried to include the strongest competition that I know of now. This is my test of "slowies" , that is, all compressors set at high (not max) compression levels. ("oohc" is Oodle Optimal1 , my compression actually goes up quite a bit at higher levels, but I consider anything below 2 mb/s to encode to be just too slow to even consider).

The raw data : ("game test set")

by ratio:
oohcLZNA    :  2.88:1 ,    5.3 enc mb/s ,  135.0 dec mb/s
lzma        :  2.82:1 ,    2.9 enc mb/s ,   43.0 dec mb/s
oohcBitKnit :  2.76:1 ,    6.4 enc mb/s ,  273.3 dec mb/s
lzham       :  2.59:1 ,    1.8 enc mb/s ,  162.9 dec mb/s
oohcLZHLW   :  2.38:1 ,    4.2 enc mb/s ,  456.3 dec mb/s
zstdhc9     :  2.11:1 ,   29.5 enc mb/s ,  558.0 dec mb/s
oohcLZNIB   :  2.04:1 ,   11.5 enc mb/s , 1316.4 dec mb/s

by encode speed:
zstdhc9     :  2.11:1 ,   29.5 enc mb/s ,  558.0 dec mb/s
oohcLZNIB   :  2.04:1 ,   11.5 enc mb/s , 1316.4 dec mb/s
oohcBitKnit :  2.76:1 ,    6.4 enc mb/s ,  273.3 dec mb/s
oohcLZNA    :  2.88:1 ,    5.3 enc mb/s ,  135.0 dec mb/s
oohcLZHLW   :  2.38:1 ,    4.2 enc mb/s ,  456.3 dec mb/s
lzma        :  2.82:1 ,    2.9 enc mb/s ,   43.0 dec mb/s
lzham       :  2.59:1 ,    1.8 enc mb/s ,  162.9 dec mb/s

by decode speed:
oohcLZNIB   :  2.04:1 ,   11.5 enc mb/s , 1316.4 dec mb/s
zstdhc9     :  2.11:1 ,   29.5 enc mb/s ,  558.0 dec mb/s
oohcLZHLW   :  2.38:1 ,    4.2 enc mb/s ,  456.3 dec mb/s
oohcBitKnit :  2.76:1 ,    6.4 enc mb/s ,  273.3 dec mb/s
lzham       :  2.59:1 ,    1.8 enc mb/s ,  162.9 dec mb/s
oohcLZNA    :  2.88:1 ,    5.3 enc mb/s ,  135.0 dec mb/s
lzma        :  2.82:1 ,    2.9 enc mb/s ,   43.0 dec mb/s

Log opened : Fri Dec 18 17:56:44 2015

total : oohcLZNIB   : 167,495,105 ->81,928,287 =  3.913 bpb =  2.044 to 1 
total : encode           : 14.521 seconds, 3.39 b/kc, rate= 11.53 M/s
total : decode           : 0.127 seconds, 386.85 b/kc, rate= 1316.44 M/s
total : encode+decode    : 14.648 seconds, 3.36 b/kc, rate= 11.43 M/s
total : oohcLZHLW   : 167,495,105 ->70,449,624 =  3.365 bpb =  2.378 to 1 
total : encode           : 40.294 seconds, 1.22 b/kc, rate= 4.16 M/s
total : decode           : 0.367 seconds, 134.10 b/kc, rate= 456.33 M/s
total : encode+decode    : 40.661 seconds, 1.21 b/kc, rate= 4.12 M/s
total : oohcLZNA    : 167,495,105 ->58,242,995 =  2.782 bpb =  2.876 to 1 
total : encode           : 31.867 seconds, 1.54 b/kc, rate= 5.26 M/s
total : decode           : 1.240 seconds, 39.68 b/kc, rate= 135.04 M/s
total : encode+decode    : 33.107 seconds, 1.49 b/kc, rate= 5.06 M/s
total : oohcBitKnit : 167,495,105 ->60,763,350 =  2.902 bpb =  2.757 to 1 
total : encode           : 26.102 seconds, 1.89 b/kc, rate= 6.42 M/s
total : decode           : 0.613 seconds, 80.33 b/kc, rate= 273.35 M/s
total : encode+decode    : 26.714 seconds, 1.84 b/kc, rate= 6.27 M/s
total : zstdhc9     : 167,495,105 ->79,540,333 =  3.799 bpb =  2.106 to 1 
total : encode           : 5.671 seconds, 8.68 b/kc, rate= 29.53 M/s
total : decode           : 0.300 seconds, 163.98 b/kc, rate= 558.04 M/s
total : encode+decode    : 5.971 seconds, 8.24 b/kc, rate= 28.05 M/s
total : lzham       : 167,495,105 ->64,682,721 =  3.089 bpb =  2.589 to 1 
total : encode           : 93.182 seconds, 0.53 b/kc, rate= 1.80 M/s
total : decode           : 1.028 seconds, 47.86 b/kc, rate= 162.86 M/s
total : encode+decode    : 94.211 seconds, 0.52 b/kc, rate= 1.78 M/s
total : lzma        : 167,495,105 ->59,300,023 =  2.832 bpb =  2.825 to 1 
total : encode           : 57.712 seconds, 0.85 b/kc, rate= 2.90 M/s
total : decode           : 3.898 seconds, 12.63 b/kc, rate= 42.97 M/s
total : encode+decode    : 61.610 seconds, 0.80 b/kc, rate= 2.72 M/s

11-13-15 | Flipped encodemod

A while ago I wrote a series on Encoding Values in Bytes in which I talk about the "EncodeMod" varint encoding.

EncodeMod is just the idea that you send each token (byte, word, nibble, whatever) with two ranges; in one range the values are terminal (no more tokens), while in the other range it means "this is part of the value" but more tokens follow. You can then optimize the division point for a wide range of applications.

In my original pseudo-code I was writing the ranges with the "more tokens" follow at the bottom, and terminal values at the top. That is :

Specifically for the case of byte tokens and pow2 mod

mod = 1<<bits

in each token we send "bits" of values that don't currently fit

upper = 256 - mod

"upper" is the number of terminal values we can send in the current token

I was writing

[0,mod) = bits of value + more tokens follow
[mod,256) = terminal value

Ryg spotted that the code is slightly simpler if you switch the ranges. Use the low range [0,upper) for terminal values and [upper,256) for non-terminal values. The ranges are the same, so you get the same encoded lengths.

(BTW it also occurred to me when learning about ANS that EncodeMod is a form of ANS. You're trying to send a bit - "do more bytes follow". You're putting that bit in a token, and you have some extra information you can send with that bit - so just put some of your value in there. The number of slots for bit=0 and 1 should correspond to the probability of each event.)

The switched encodemod is :

U8 *encmod(U8 *to, int val, int bits)
    const int upper = 256 - (1<<bits); // binary, this is 1110000 or similar (8-bits ones, bits zeros)
    while (val >= upper)
        *to++ = (U8) (upper | val);
        val = (val - upper) >> bits;

    *to++ = (U8) val;
    return to;

const U8 *decmod(int *outval, const U8 *from, int bits)
    const int upper = 256 - (1<<bits);
    int shift = 0;
    int val = 0;

    for (;;)
        int byte = *from++;
        val += byte << shift;
        if (byte < upper)
        shift += bits;

    *outval = val;
    return from;

The simplification of the encoder here :

    *to++ = (U8) (upper | val);
    val = (val - upper) >> bits;

written in long-hand is :

    low = val & ((1<<bits)-1);
    *to++ = upper + low;  // (same as upper | low, same as upper | val)
    val -= upper;
    val >>= bits;


    val -= upper;
    low = val & ((1<<bits)-1);
    *to++ = upper + low;  // (same as upper | low, same as upper | val)
    val >>= bits;

and the val -= upper can be done early or late because val >= upper it doesn't touch "low"

Basically by using "upper" like this, the mask of low bits and add of upper is done in one op.

10-17-15 | Huffman Performance

I'm following Yann Collet's nice blog series on Huffman. I thought I'd have my own look.

Background : 64-bit mode. 12-bit lookahead table, and 12-bit codelen limit, so there's no out-of-table case to handle.

Here's conditional bit buffer refill, 32-bits refilled at a time, aligned refill. Always >= 32 bits in buffer so you can do two decode ops per refill :

            uint64 peek; int cl,sym;
            peek = decode_bits >> (64 - CODELEN_LIMIT);
            cl = codelens[peek];
            sym = symbols[peek];
            decode_bits <<= cl; thirtytwo_minus_decode_bitcount += cl;
            *decodeptr++ = (uint8)sym;
            peek = decode_bits >> (64 - CODELEN_LIMIT);
            cl = codelens[peek];
            sym = symbols[peek];
            decode_bits <<= cl; thirtytwo_minus_decode_bitcount += cl;
            *decodeptr++ = (uint8)sym;
            if ( thirtytwo_minus_decode_bitcount > 0 )
                uint64 next = _byteswap_ulong(*decode_in++);
                decode_bits |= next << thirtytwo_minus_decode_bitcount;
                thirtytwo_minus_decode_bitcount -= 32;

325 mb/s.

(note that removing the bswap to have a little-endian u32 stream does almost nothing for performance, less than 1 mb/s)

The next option is : branchless refill, unaligned 64-bit refill. You always have >= 56 bits in buffer, now you can do 4 decode ops per refill :

            // refill :
            uint64 next = _byteswap_uint64(*((uint64 *)decode_in));
            bits |= next >> bitcount;
            int bytes_consumed = (64 - bitcount)>>3;
            decode_in += bytes_consumed;
            bitcount += bytes_consumed<<3;
            uint64 peek; int cl; int sym;
            #define DECONE() \
            peek = bits >> (64 - CODELEN_LIMIT); \
            cl = codelens[peek]; sym = symbols[peek]; \
            bits <<= cl; bitcount -= cl; \
            *decodeptr++ = (uint8) sym;
            #undef DECONE
373 mb/s

These so far have both been "traditional Huffman" decoders. That is, they use the next 12 bits from the bit buffer to look up the Huffman decode table, and they stream bits into that bit buffer.

There's another option, which is "ANS style" decoding. To do "ANS style" you keep the 12-bit "peek" as a separate variable, and you stream bits from the bit buffer into the peek variable. Then you don't need to do any masking or shifting to extract the peek.

The naive "ANS style" decode looks like this :

            // refill bits :
            uint64 next = _byteswap_uint64(*((uint64 *)decode_in));
            bits |= next >> bitcount;
            int bytes_consumed = (64 - bitcount)>>3;
            decode_in += bytes_consumed;
            bitcount += bytes_consumed<<3;
            int cl; int sym;
            #define DECONE() \
            cl = codelens[state]; sym = symbols[state]; \
            state = ((state << cl) | (bits >> (64 - cl))) & ((1 << CODELEN_LIMIT)-1); \
            bits <<= cl; bitcount -= cl; \
            *decodeptr++ = (uint8) sym;
            #undef DECONE

332 mb/s

But we can use an analogy to the "next_state" of ANS. In ANS, the next_state is a complex thing with certain rules (as we covered in the past). With Huffman it's just this bit of math :

    next_state[state] = (state << cl) & ((1 << CODELEN_LIMIT)-1);

So we can build that table, and use a "fully ANS" decoder :

            // refill bits :
            uint64 next = _byteswap_uint64(*((uint64 *)decode_in));
            bits |= next >> bitcount;
            int bytes_consumed = (64 - bitcount)>>3;
            decode_in += bytes_consumed;
            bitcount += bytes_consumed<<3;
            int cl; int sym;
            #define DECONE() \
            cl = codelens[state]; sym = symbols[state]; \
            state = next_state_table[state] | (bits >> (64 - cl)); \
            bits <<= cl; bitcount -= cl; \
            *decodeptr++ = (uint8) sym;
            #undef DECONE

415 mb/s

Fastest! It seems the fastest Huffman decoder is a TANS decoder. (*1)

(*1 = well, on this machine anyway; these are all so close that architecture and exact usage matters massively; in particular we're relying heavily on fast unaligned reads, and doing four unrolled decodes in a row isn't always useful)

Note that this is a complete TANS decoder save one small detail - in TANS the "codelen" (previously called "numbits" in my TANS code) can be 0. The part where you do :

(bits >> (64 - cl))

can't be used if cl can be 0. In TANS you either have to check for zero, or you have to use the method of

((bits >> 1) >> (63 - cl))

which makes TANS a tiny bit slower - 370 mb/s for TANS on the same file on my machine.

(all times reported are non-interleaved, and without table build time; Huffman is definitely faster to build tables, and faster to decode packed/transmitted codelens as well)

NOTE : earlier version of this post had a mistake in bitcount update and worse timings.

Some tiny caveats :

1. The TANS way means you can't (easily) mix different peek amounts. Say you're doing an LZ, you might want an 11-bit peek for literals, but for the 4 bottom bits you only need an 8-bit peek. The TANS state has the # of bits to peek baked in, so you can't just use that. With the normal bit-buffer style Huffman decoders you can peek any # of bits you want. (though you could just do the multi-state interleave thing here, keeping with the TANS style).

2. Doing Huffman decodes without a strict codelen limit the TANS way is much uglier. With the bits-at-top bitbuffer method there are nice ways to do that.

3. Getting raw bits the TANS way is a bit uglier. Say you want to grab 16 raw bits; you could get 12 from the "state" and then 4 more from the bit buffer. Or just get 16 directly from the bit buffer which means they need to be sent after the next 12 bits of Huffman in a weird TANS interleave style. This is solvable but ugly.

4. For the rare special case of an 8 or 16-bit peek-ahead, you can do even faster than the TANS style by using a normal bit buffer with the next bits at bottom. (either little endian or big-endian but rotated around). This lets you grab the peek just by using "al" on x86.

09-19-15 | Library Writing Realizations

Some learnings about library writing, N years on.

X. People will just copy-paste your example code.

This is obvious but is something to keep in mind. Example code should never be sketches. It should be production ready. People will not read the comments. I had lots of spots in example code where I would write comments like "this is just a sketch and not ready for production; production code needs to check error returns and handle failures and be endian-independent" etc.. and of course people just copy-pasted it and didn't change it. That's not their fault, that's my fault. Example code is one of the main ways people get into your library.

X. People will not read the docs.

Docs are almost useless. Nobody reads them. They'll read a one page quick start, and then they want to just start digging in writing code. Keep the intros very minimal and very focused on getting things working.

Also be aware that if you feel you need to write a lot of docs about something, that's a sign that maybe things are too complicated.

X. Peripheral helper features should be cut.

Cut cut cut. People don't need them. I don't care how nice they are, how proud of them you are. Pare down mercilessly. More features just confuse and crud things up. This is like what a good writer should do. Figure out what your one core function really is and cut down to that.

If you feel that you really need to include your cute helpers, put them off on the side, or put them in example code. Or even just keep them in your pocket at home so that when someone asks about "how I do this" you can email them out that code.

But really just cut them. Being broad is not good. You want to be very narrow. Solve one clearly defined problem and solve it well. Nobody wants a kitchen sink library.

X. Simplicity is better.

Make everything as simple as possible. Fewer arguments on your functions. Remove extra functions. Cut everywhere. If you sacrifice a tiny bit of possible efficiency, or lose some rare functionality, that's fine. Cut cut cut.

For example, to plug in an allocator for Oodle used to require 7 function pointers : { Malloc, Free, MallocAligned, FreeSized, MallocPage, FreePage, PageSize }. (FreeSized for efficiency, and the Page stuff because async IO needs page alignment). It's now down just 2 : { MallocAligned, Free }. Yes it's a tiny bit slower but who cares. (and the runtime can work without any provided allocators)

X. Micro-efficiency is not important.

Yes, being fast and lean is good, but not when it makes things too complex or difficult to use. There's a danger of a kind of mental-masturbation that us RAD-type guys can get caught in. Yes, your big stream processing stuff needs to be competitive (eg. Oodle's LZ decompress, or Bink's frame decode time). But making your Init() call take 100 clocks instead of 10,000 clocks is irrelevant to everyone but you. And if it requires funny crap from the user, then it's actually making things worse, not better. Having things just work reliably and safely and easily is more important than micro-efficiency.

For example, one mistake I made in Oodle is that the compressed streams are headerless; they don't contain the compressed or decompressed size. The reason I did that is because often the game already has that information from its own headers, so if I store it again it's redundant and costs a few bytes. But that was foolish - to save a few bytes of compressed size I sacrifice error checking, robustness, and convenience for people who don't want to write their own header. It's micro-efficiency that costs too much.

Another one I realized is a mistake : to do actual async writes on Windows, you need to call SetFileValidData on the newly enlarged file region. That requires admin privileges. It's too much trouble, and nobody really cares. It's no worth the mess. So in Oodle2 I just don't do that, and writes are no longer async. (everyone else who thinks they're doing async writes isn't actually, and nobody else actually checks on their threading the way I do, so it just makes me more like everyone else).

X. It should just work.

Fragile is bad. Any API's that have to go in some complicated sequence, do this, then this, then this. That's bad. (eg. JPEGlib and PNGlib). Things should just work as simply as possible without requirements. Operations should be single function calls when possible. Like if you take pointers in and out, don't require them to be aligned in a certain way or padded or allocated with your own allocators. Make it work with any buffer the user provides. If you have options, make things work reasonably with just default options so the user can ignore all the option setup if they want. Don't require Inits before your operations.

In Oodle2 , you just call Decompress(pointer,size,pointer) and it should Just Work. Things like error handling and allocators now just fall back to reasonable light weight defaults if you don't set up anything explicitly.

X. Special case stuff should be external (and callbacks are bad).

Anything that's unique to a few users, or that people will want to be different should be out of the library. Make it possible to do that stuff through client-side code. As much as possible, avoid callbacks to make this work, try to do it through imperative sequential code.

eg. if they want to do some incremental post-processing of data in place, it should be possible via : { decode a bit, process some, decode a bit , process some } on the client side. Don't do it with a callback that does decode_it_all( process_per_bit_callback ).

Don't crud up the library feature set trying to please everyone. Some of these things can go in example code, or in your "back pocket code" that you send out as needed.

X. You are writing the library for evaluators and new users.

When you're designing the library, the main person to think about is evaluators and new users. Things need to be easy and clear and just work for them.

People who actually license or become long-term users are not a problem. I don't mean this in a cruel way, we don't devalue them and just care about sales. What I mean is, once you have a relationship with them as a client, then you can talk to them, help them figure out how to use things, show them solutions. You can send them sample code or even modify the library for them.

But evaluators won't talk to you. If things don't just work for them, they will be frustrated. If things are not performant or have problems, they will think the library sucks. So the library needs to work well for them with no help from you. And they often won't read the docs or even use your examples. So it needs to go well if they just start blindly calling your APIs.

(this is a general principle for all software; also all GUI design, and hell just design in general. Interfaces should be designed for the novice to get into it easy, not for the expert to be efficient once they master it. People can learn to use almost any interface well (*) once they are used to it, so you don't have to worry about them.)

(* = as long as it's low latency, stateless, race free, reliable, predictable, which nobody in the fucking world seems to understand any more. A certain sequence of physical actions that you develop muscle memory for should always produce the same result, regardless of timing, without looking at the device or screen to make sure it's keeping up. Everyone who fails this (eg. everyone) should be fucking fired and then shot. But this is a bit off topic.)

X. Make the default log & check errors. But make the default reasonably fast.

This is sort of related to the evaluator issue. The defaults of the library need to be targetted at evaluators and new users. Advanced users can change the defaults if they want; eg. to ship they will turn off logging & error checking. But that should not be how you ship, or evaluators will trigger lots of errors and get failures with no messages. So you need to do some amount of error checking & logging so that evaluators can figure things out. *But* they will also measure performance without changing the settings, so your default settings must also be fast.

X. Make easy stuff easy. It's okay if complicated stuff is hard.

Kind of self explanatory. The API should be designed so that very simple uses require tiny bits of code. It's okay if something complicated and rare is a pain in the ass, you don't need to design for that; just make it possible somehow, and if you have to help out the rare person who wants to do a weird thing, that's fine. Specifically, don't try to make very flexible general APIs that can do everything & the kitchen sink. It's okay to have a super simple API that covers 99% of users, and then a more complex path for the rare cases.

07-26-15 | The Wait on Workers Problem

I'd like to open source my Oodle threading stuff. There's some cool stuff. Some day. Sigh.

This is an internal email I sent on 05-13-2015 :

Cliff notes : there's a good reason why OS'es use thread pools and fibers to solve this problem.

There's this problem that I call the "wait on workers problem". You have some worker threads. Worker threads pop pending work from a queue, do it, then post a completion event. You can't ever call Wait (Wait checks a condition, and if not set, puts the thread to sleep pending that condition) on them, because it could possibly deadlock you (no progress possible) since they could all go to sleep in waits, with work still pending and noone to do it. The most obvious example is just to imagine you only have 1 worker thread. Your worker thread does something like : { stuff spawn work2 Wait(work2); more stuff } Oh crap, work2 never runs because the Wait put me to sleep and there's no worker to do it. In Oodle the solution I use is that you should never do a real Wait on a worker, instead you have to "Yield". What Yield does is change your current work item back to Pending, but with the specified handle as a condition to being run. Then it returns back to the work dispatcher loop. So the above example becomes : [worker thread dispatch loop pops Work1] Work1: { stuff spawnm work2 Yield(work2); } [Work1 is put back on the pending list, with work2 as a condition] [worker thread dispatch loop pops Work2] Work2 Work2 posts completion [worker thread dispatch loop pops Work1] { more stuff } So. The Yield solution works to an extent, but it runs into problems. 1. I only have "shallow yield" (non-stack-saving yield), so the worker must manually save its state or stack variables to be able to resume. I don't have "deep yield" that can yield from deep within a series of calls, that would save the execution location and stack. This can be a major problem in practice. It means you can only yield from the top level, you can't ever be down inside some function calls and logic and decide you need to yield. It means all your threading branching has to be very linear and mapped out at the top level of the work function. It works great for simple linear processing like do an IO then yield on it, then process the results of the IO. It doesn't work great for more complicated general parallelism. 2. Because Yield is different from Wait, you can't share code, and you can still easily accidentally break the system by calling Wait. For example if you have a function like DoStuffInParallel , if you run that on a non-worker thread, it can launch some work items then Wait on them. You can't do that from a worker. You must rewrite it for being run from a worker to launch items then return a handle to yield on them (don't yield internally). It creates an ugly and difficult heterogeneity between worker threads and non-worker threads. So, we'd like to fix this. What we'd like is essentially "deep yield" and we want it to just be like an OS Wait, so that functions can be used on worker threads or non-worker threads without changing them. So my first naive idea was : "Wait on Workers" can be solved by making Wait a dispatch. Any time you call Wait, the system checks - am I a worker thread, and if so, instead of actually going into an OS wait, it pops and runs any runnable work. After completing each work item, it rechecks the wait condition and if it's set, stops dispatching and returns to the Wait-caller. If there is no runnable work, you go into an OS wait on either the original wait condition OR runnable work available. So the original example becomes : { stuff spawn work2 Wait(work2); [Wait sees we're a worker and runs the work dispatcher] [work dispatcher pops work2] { Work2 } [work dispatcher return sees work1 now runnable and returns] more stuff } Essentially this is using the actual stack to do stack-saving. Rather than trying to save the stack and instruction pointer, you just use the fact that they are saved by a normal function call & return. This method has minor disadvantages in that it can require a very large amount of stack if you go very deep. But the real problem is it can easily deadlock. It only works for tree-structured work, and Waits that are only on work items. If you have non-tree wait cycles, or waits on non-work-items, it can deadlock. Here's one example : Work1 : { stuff1 Wait on IO stuff2 } Work2 : { stuff1 Wait on Work1 stuff2 } with current Oodle system, you can make work like this, and it will complete. (*) In any system, if Work1 and Work2 get separate threads, they will complete. But in a Dispatch-on-Wait system, if the Wait on IO in Work1 runs Work2, it will deadlock. (* = the Oodle system ensures completability by only giving you a waitable handle to a work item when that work is enqueued to run. So it's impossible to make loops. But you can make something like the above by doing h1 = Run(Work1) Work2.handle = h1; Run(Work2); *) Once you're started Work2 on your thread, you're hosed, you can't recover from that, because you already have Work1 in progress. Dispatch-on-Wait really only works for a very limited work pattern : you only Wait on work that you made yourself. None of the work you make yourself can Wait on anything but work they make themselves. Really it only allows you to run tree-structured child work, not general threading. So, one option is use Dispatch-on-Wait but with a rule that if you're on a worker you can only use it for tree-strcutured-child-work. If you need to do more general waits, you still do the coroutine Yield. Or you can try to solve the general problem. In hindsight the solution is obvious, since it's what the serious OS people do : thread pools. You want to have 4 workers running on a 4 core system. You actually have a thread pool of 32 worker threads (or whatever) and try to keep at least 4 running at all times. Any time you Wait on a worker, you first Wake a thread from the pool, then put your thread to sleep. Any time a worker completes a work item it checks how many worker threads are awake, and if it's too many it goes to sleep. This is just a way of using the thread system to do the stack-saving and instruction-pointer saving that you need for "deep yield". The Wait() is essentially doing that deep return back up to the Worker dispatch loop, but it does it by sleeping the current thread and waking another that can start from the dispatch loop. This just magically fixes all the problems. You can wait on arbitrary things, you can deep-wait anywhere, you don't get deadlocks. The only disadvantage is the overhead of the thread switch. If you really want the micro-efficiency, you could still provide a "WaitOnChildWork" that runs the work dispatch loop, which is to be used only for the tree-structured work case. This lets you avoid the thread pool work and is a reasonably common case.

06-04-15 | Goodbye and Hello

Well, fuck me. Google has broken the older GData API for posting to blogger.

I understand progress has to happen and so on, and older APIs have to get retired sometimes. Well, no not really; that's not actually what happens in the modern world. I'm sick of the slap-dash upgrading and deprecating that has nothing to do with necessity and is just random chaos. You all can fuck around with it if you want. Not me. I love algorithms. I love programming when the problems are inherent, mathematical problems. Not problems like this fucking API doesn't do what it says it does, or this shit does different things in different versions so I have to detect that and hack it and, oh crap my platform sdk updated and nothing works any more and fuck me.

I think this blog (on Blogger) is probably dead. I can't be bothered to fix my poster (working in C# is a nightmare). Goodbye.

You can read the raw text blog at http://www.cbloom.com/rants.html

also Hello!

For a little while I've been writing a new blog.

It was inspired by el trastero | de Iñigo Quilez which is a fabulous blog. el trastero has some little technical thoughts some times, but also personal stuff, and lots of humanity. I love it. It's how my blog started, and somewhere along the way I lost the point. So I started writing a new blog, inspired by my old blog.

It's called "rambles", and it's here : http://www.cbloom.com/rambles.html

It's personal and inappropriate and you probably shouldn't read it.

Goodbye and hello.

06-04-15 | LZNA encode speed addendum

Filling in a gap in the previous post : cbloom rants 05-09-15 - Oodle LZNA

The encode speeds on lzt99 :

single-threaded :



-z5 (Optimal1) :
24,700,820 -> 9,207,584 =  2.982 bpb =  2.683 to 1
encode           : 10.809 seconds, 1.32 b/kc, rate= 2.29 mb/s
decode           : 0.318 seconds, 44.87 b/kc, rate= 77.58 mb/s

-z6 (Optimal2) :
24,700,820 -> 9,154,343 =  2.965 bpb =  2.698 to 1
encode           : 14.727 seconds, 0.97 b/kc, rate= 1.68 mb/s
decode           : 0.313 seconds, 45.68 b/kc, rate= 78.99 mb/s

-z7 (Optimal3) :
24,700,820 -> 9,069,473 =  2.937 bpb =  2.724 to 1
encode           : 20.473 seconds, 0.70 b/kc, rate= 1.21 mb/s
decode           : 0.317 seconds, 45.06 b/kc, rate= 77.92 mb/s



lzmahigh : 24,700,820 -> 9,329,982 =  3.022 bpb =  2.647 to 1
encode           : 11.373 seconds, 1.26 b/kc, rate= 2.17 M/s
decode           : 0.767 seconds, 18.62 b/kc, rate= 32.19 M/s



lzham : 24,700,820 ->10,140,761 =  3.284 bpb =  2.436 to 1
encode           : 16.732 seconds, 0.85 b/kc, rate= 1.48 M/s
decode           : 0.242 seconds, 59.09 b/kc, rate= 102.17 M/s


lzham : 24,700,820 ->10,097,341 =  3.270 bpb =  2.446 to 1
encode           : 18.877 seconds, 0.76 b/kc, rate= 1.31 M/s
decode           : 0.239 seconds, 59.73 b/kc, rate= 103.27 M/s


lzham : 24,700,820 -> 9,938,002 =  3.219 bpb =  2.485 to 1
encode           : 185.204 seconds, 0.08 b/kc, rate= 133.37 k/s
decode           : 0.245 seconds, 58.28 b/kc, rate= 100.77 M/s


LZNA -z5 threaded :
24,700,820 -> 9,211,090 =  2.983 bpb =  2.682 to 1
encode only      : 8.523 seconds, 1.68 b/kc, rate= 2.90 mb/s
decode only      : 0.325 seconds, 43.96 b/kc, rate= 76.01 mb/s

LZMA threaded :

lzmahigh : 24,700,820 -> 9,329,925 =  3.022 bpb =  2.647 to 1
encode           : 7.991 seconds, 1.79 b/kc, rate= 3.09 M/s
decode           : 0.775 seconds, 18.42 b/kc, rate= 31.85 M/s

LZHAM BETTER threaded :

lzham : 24,700,820 ->10,198,307 =  3.303 bpb =  2.422 to 1
encode           : 7.678 seconds, 1.86 b/kc, rate= 3.22 M/s
decode           : 0.242 seconds, 58.96 b/kc, rate= 101.94 M/s

I incorrectly said in the original version of the LZNA post (now corrected) that "LZHAM UBER is too slow". It's actually the "EXTREME" option that's too slow.

Also, as I noted last time, LZHAM is the best threaded of the three, so even though BETTER is slower than LZNA -z5 or LZMA in single-threaded encode speed, it's faster threaded. (Oodle's encoder threading is very simplistic (chunking) and really needs a larger file to get full parallelism; it doesn't use all cores here; LZHAM is much more micro-threaded so can get good parallelism even on small files).

06-03-15 | Computers Are Evil

Click "close tab".

Nothing happens. Wait.

Click "close tab" again on the same tab.

Two tabs close.


On Android it's even worse. Maybe the worst sin of Android UI design (hard to choose) is that the back/home/panes bar at the bottom is not always there. Some apps make it roll out of the way and put other buttons there. So depending on timing and input races you can be just trying to get back to the home screen and instead hit some other shite.

Fucking basic GUI design principles :

User should get *immediate* acknolwedgement of their action. I mean, for fucks sake you should be able to actually just DO it immediately, computers are fast. But if you can't you still need to acknowledge it.

Buttons should not move! They should not roll in and out. The more important the button, the more it should just stay in the same place all the time.

A sequence of input actions should always lead to the same outcome. There should be no "input races" that make outcome dependent on processing time.

A power user should be able to use the application without looking at it. You should be able to develop muscle memory of sequences that do what you want, and shouldn't have to be tracking "is the app responding" to each of the actions in the sequence.

As much as possible buttons should be *stateless*. The same click gives the same action all the time. Modal UI is a necessary evil.

I have a kitchen timer that has these buttons :

Stop/Start : toggles running or not

Reset : resets timer to 0.

Reset only does anything if the timer is not running. So. How do you make the timer be in the "running from zero" state?

You have to look at it. There is no reliable key sequence to make it be running. If it's already running, you have to hit stop, then reset, then start.

The problem is that the action of the buttons is stateful. Dumb. A better design is something like :

Stop/Start : toggle running

Stop&Reset : stop and reset timer to 0

So you can press "Stop&Reset" + "Stop/Start" to always get into the "running from zero" state without looking at it. There are other options. The point is that people just don't understand fucking usability and good UI design.

A tool should become an extension of yourself, that you can use without thinking about it. That you can use without checking in on it. Oops, I hit a bunch of nails while my hammer was in un-nail mode and now my house is falling down.

Of course this is even more crucial in cars. There needs to be a law that every function in a car can be used by a blind person. There should never be a button/shuttle/touch-screen that you have to look at to use. It should all be possible to do without looking, by sense of location and touch. This is just good UI design in general, but even more important when safety is involved. (and the answer is not a million fucking buttons like an airplane cockpit, it's less fucking unnecessary functions)

Today I woke up and tried to start working, and my VC plugin NiftyPerforce is crashing. It's worked for years and I haven't touched anything and all of a sudden it's crashing. So.. try to debug it.. OMG it's fucking Managed C# I forgot about this nonsense. Hmm, some exception. Turn on exception breaks. OMG fucking C# throws exceptions all the damn time that are benign and you have to ignore. OMG the problem is down in some app pref XML persistence thing, why the fuck is this crashing now and how the fuck do I figure out what's going on. ARG ARG ARG.

Give me a fucking "main()". I want only my code. Nothing happens before main starts. No threads, no fucking binding. No automatically downloading packages!? WTF are you doing? Arg.

I wish I'd written my own text/code editor. It sucks having my primary daily interface with the machine be someone else's code that sucks.

05-25-15 | The Anti-Patent Patent Pool

The idea of the Anti-Patent Patent Pool is to destroy the system using the system.

The Anti-Patent Patent Pool is an independent patent licensing organization. (Hence APPP)

One option would be to just allow anyone to use those patents free of charge.

A more aggressive option would be a viral licensing model. (like the GPL, which has completely failed, so hey, maybe not). The idea of the viral licensing model is like this :

Anyone who owns no patents may use any patent in the APPP for free (if you currently own patents, you may donate them to the APPP).

If you wish to own patents, then you must pay a fee to license from the APPP. That fee is used to fund the APPP's activities, the most expensive being legal defense of its own patents, and legal attacks on other patents that it deems to be illegal or too broad.

(* = we'd have to be aggressive about going after companies that make a subsidiary to use APPP patents while still owning patents in the parent corporation)

The tipping point for the APPP would be to get a few patents that are important enough that major players need to either join the APPP (donate all their patents) or pay a large license.

The APPP provides a way for people who want their work to be free to ensure that it is free. In the current system this is hard to do without owning a patent, and owning a patent and enforcing it is hard to do without money.

The APPP pro-actively watches all patent submissions and objects to ones that cover prior art, are obvious and trivial, or excessively broad. It greatly reduces the issuance of junk patents, and fights ones that are mistakenly issued. (the APPP maintains a public list of patents that it believes to be junk, which it will help you fight if you choose to use the covered algorithms). (Obviously some of these activities have to be phased in over time as the APPP gets more money).

The APPP provides a way for small companies and individuals that cannot afford the lawyers to defend their work to be protected. When some evil behemoth tries to stop you from using algorithms that you believe you have a legal right to, rather than fight it yourself, you simply donate your work to the APPP and they fight for you.

Anyone who simply wants to ensure that they can use their own inventions could use the APPP.

Once the APPP has enough money, we would employ a staff of patent writers. They would take idea donations from the groundswell of developers, open-source coders, hobbyists. Describe your idea, the patent writer would make it all formal and go through the whole process. This would let us tap into where the ideas are really happening, all the millions of coders that don't have the time or money to pursue getting patents on their own.

In the current system, if you just want to keep your idea free, you have to constantly keep an eye on all patent submissions to make sure noone is slipping in and patenting it. It's ridiculous. Really the only safe thing to do is to go ahead and patent it yourself and then donate it to the APPP. (the problem is if you let them get the patent, even if it's bogus it may be expensive to fight, and what's worse is it creates a situation where your idea has a nasty asterisk on it - oh, there's this patent that covers this idea, but we believe that patent to be invalid so we claim this idea is still public domain. That's a nasty situation that will scare off lots of users.)

Some previous posts :

cbloom rants 02-10-09 - How to fight patents
cbloom rants 12-07-10 - Patents
cbloom rants 04-27-11 - Things we need
cbloom rants 05-19-11 - Nathan Myhrvold

Some notes :

1. I am not interested in debating whether patents are good or not. I am interested in providing a mechanism for those of us who hate patents to pursue our software and algorithm development in a reasonable way.

2. If you are thinking about the patent or not argument, I encourage you to think not of some ideal theoretical argument, but rather the realities of the situation. I see this on both sides of the fence; those who are pro-patent because it "protects inventors" but choose to ignore the reality of the ridiculous patent system, and those on the anti-patent side who believe patents are evil and they won't touch them, even though that may be the best way to keep free ideas free.

3. I believe part of the problem with the anti-patent movement is that we are all too fixated on details of our idealism. Everybody has slightly different ideas of how it should be, so the movement fractures and can't agree on a unified thrust. We need to compromise. We need to coordinate. We need to just settle on something that is a reasonable solution; perhaps not the ideal that you would want, but some change is better than no change. (of course the other part of the problem is we are mostly selfish and lazy)

4. Basically I think that something like the "defensive patent license" is a good idea as a way to make sure your own inventions stay free. It's the safest way (as opposed to not patenting), and in the long run it's the least work and maintenance. Instead of constantly fighting and keeping aware of attempts to patent your idea, you just patent it yourself, do the work up front and then know it's safe long term. But it doesn't go far enough. Once you have that patent you can use it as a wedge to open up more ideas that should be free. That patent is leverage, against all the other evil. That's where the APPP comes in. Just making your one idea free is not enough, because on the other side there is massive machinery that's constantly trying to patent every trivial idea they can think of.

5. What we need is for the APPP to get enough money so that it can be stuffing a deluge of trivial patents down the patent office's throat, to head off all the crap coming from "Intellectual Ventures" and its many brothers. We need to be getting at least as many patents as them and making them all free under the APPP.

Some links :

en.swpat.org - The Software Patents Wiki
Patent Absurdity — How software patents broke the system
Home defensivepatentlicense
FOSS Patents U.S. patent reform movement lacks strategic leadership, fails to leverage the Internet

05-21-15 | LZ-Sub

LZ-Sub decoder :

delta_literal = get_sub_literal();

if ( delta_literal != 0 )
    *ptr++ = delta_literal + ptr[-lastOffset];
else // delta_literal == 0
    if ( ! get_offset_flag() )
        *ptr++ = ptr[-lastOffset];
    else if ( get_lastoffset_flag() )
        int lo_index = get_lo_index();
        lastOffset = last_offsets[lo_index];
        // do MTF or whatever using lo_index
        *ptr++ = ptr[-lastOffset];
        // extra 0 delta literal implied :
        *ptr++ = ptr[-lastOffset];
        lastOffset = get_offset();
        // put offset in last_offsets set
        *ptr++ = ptr[-lastOffset];
        *ptr++ = ptr[-lastOffset];
        // some automatic zero deltas follow for larger offsets
        if ( lastOffset > 128 )
            *ptr++ = ptr[-lastOffset];
            if ( lastOffset > 16384 )
                *ptr++ = ptr[-lastOffset];

    // each single zero is followed by a zero runlen
    //  (this is just a speed optimization)
    int zrl = get_zero_runlen();
        *ptr++ = ptr[-lastOffset];

This is basically LZMA. (sub literals instead of bitwise-LAM, but structurally the same) (also I've reversed the implied structure here; zero delta -> offset flag here, whereas in normal LZ you do offset flag -> zero delta)

This is what a modern LZ is. You're sending deltas from the prediction. The prediction is the source of the match. In the "match" range, the delta is zero.

The thing about modern LZ's (LZMA, etc.) is that the literals-after-match (LAMs) are very important too. These are the deltas after the zero run range. You can't really think of the match as just applying to the zero-run range. It applies until you send the next offset.

You can also of course do a simpler & more general variant :

Generalized-LZ-Sub decoder :

if ( get_offset_flag() )
    // also lastoffset LRU and so on not shown here
    lastOffset = get_offset();

delta_literal = get_sub_literal();

*ptr++ = delta_literal + ptr[-lastOffset];

Generalized-LZ-Sub just sends deltas from prediction. Matches are a bunch of zeros. I've removed the acceleration of sending zero's as a runlen for simplicity, but you could still do that.

The main difference is that you can send offsets anywhere, not just at certain spots where there are a bunch of zero deltas generated (aka "min match lengths").

This could be useful. For example when coding images/video/sound , there is often not an exact match that gives you a bunch of exact zero deltas, but there might be a very good match that gives you a bunch of small deltas. It would be worth sending that offset to get the small deltas, but normal LZ can't do it.

Generalized-LZ-Sub could also give you literal-before-match. That is, instead of sending the offset at the run of zero deltas, you could send it slightly *before* that, where the deltas are not zero but are small.

(when compressing text, "sub" should be replaced with some kind of smart lexicographical distance; for each character precompute a list of its most likely substitution character in order of probability.)

LZ is a bit like a BWT, but instead of the contexts being inferred by the prefix sort, you transmit them explicitly by sending offsets to prior strings. Weird.

05-21-15 | Umm

I sent a lawyer an email yesterday.

Today they sent me back an email saying :

"I need your email address so I can send you the documents you need to sign"

Umm... you are not inspiring great confidence in your abilities.

Also, pursuant to my last post about spam - pretty much all my correspondence with lawyers over the past few months, Google decides to put in the spam folder. I keep thinking "WTF why didn't this lawyer get back to me - oh crap, go check the spam". Now, I'm totally down with the comic social commentary that Google is making ("ha ha, all email from lawyers is spam, amirite? lol"). But WTF your algorithms are insanely broken. I mean, fucking seriously you suck so bad.

05-21-15 | Software Patents are Fucking Awesome

Awesome. Spotted on encode.ru. It was inevitable I suppose :

"System and method for compressing data using asymmetric numeral systems with probability distributions"

By these tards :


Someone in the UK go over and punch them in the balls.

For those not aware of the background, ANS is probably the biggest invention in data compression in the last 20 years. Its inventor (Jarek Duda) has explicitly tried to publish it openly and make it patent-free, because he's awesome.

In the next 10 years I'm sure we will get patents for "using ANS with string-matching data compression", "using ANS with block mocomp data compression", "using ANS as a replacement for Huffman coding", "deferred summation with ANS", etc. etc. Lots of brilliant inventions like that. Really stimulating for innovation.

(as has happened over and over in data compression, and software in general in the past; hey let's take two obvious previously existing things; LZ string matching + Huffman = patent. LZ + hash table = patent. JPEG + arithmetic = patent. Mocomp + Huffman = patent. etc. etc.)

(often glossed over in the famous Stac-Microsoft suit story is the question of WHAT THE FUCK the LZS patent was supposed to be for? What was the invention there exactly? Doing LZ with a certain fixed bit encoding? Umm, yeah, like everyone does?)

Our patent system is working great. It obviously protects and motivates the real inventors, and doesn't just act as a way for the richest companies to lock in semi-monopolies of technologies they didn't even invent. Nope.

Recently at RAD we've made a few innovations related to ANS that are mostly in the vein of small improvements or clever usages, things that I wouldn't even imagine to patent, but of course that's wrong.

I've also noticed in general a lot of these vaporware companies in the UK. We saw one at RAD a few years ago that claimed to use "multi-dimensional curve interpolation for data compression" or some crackpot nonsense. There was another one that used alternate numeral systems (not ANS, but p-adic or some such) for god knows what. A few years ago there were lots of fractal-image-compression and other fractal-nonsense startups that did ... nothing. (this was before the VC "pivot" ; hey we have a bunch of fractal image patents, let's make a text messaging app)

They generally get some PhD's from Cambridge or whatever to be founders. They bring a bunch of "industry luminaries" on the board. They patent a bunch of nonsense. And then ...

... profit? There's a step missing where they actually ever make anything that works. But I guess sometimes they get bought for their vapor, or they manage to get a bullshit patent that's overly-general on something they didn't actually invent, and then they're golden.

I wonder if these places are getting college-backed "incubation" incentives? Pretty fucking gross up and down and all around. Everyone involved is scum.

(In general, universities getting patents and incubating startups is fucking disgusting. You take public funding and student's tuition, and you use that to lock up ideas for private profit. Fucking rotten, you scum.)

On a more practical note, if anyone knows the process for objecting to a patent in the UK, chime in.

Also, shame on us all for not doing more to fight the system. All our work should be going in the Anti-Patent Patent Pool.

Under the current first-to-file systems, apparently we are supposed to sit around all day reading every patent that's been filed to see if it covers something that we have already invented or is "well known" / public domain / prior art.

It's really a system that's designed around patents. It assumes that all inventions are patented. It doesn't really work well with a prior invention that's just not patented.

Which makes something like the APPP even more important. We need a way to patent all the free ideas just as a way to keep them legally free and not have to worry about all the fuckers who will rush in and try to patent our inventions as soon as we stop looking.

05-17-15 | The Google Spam Filter is Intentionally Bad

I'm convinced at this point that Google intentionally filters spam wrong.

Not in a nefarious way, like haha we're going to send your good mails to "spam" and let the crap through! Take that!

But actually in a sort of more deeply evil way. A capitalist way. They specifically *want* to allow through mass-mailings from corporations that are they do not consider spam.

In my opinion, those are all spam. There is not a single corporate mass-mailing that I ever intentionally subscribed to.

Basically there's a very very easy spam filtering problem :

Easy 1. Reject all mass-mailings. Reject all mailings about sales, products, offers. Reject all mailings about porn or penises or nigerian princes.

Easy 2. Allow through all mail that's hand-written by a human to me. Particularly to one that I have written to in the past.

That would be fine with me. That would get 99.99% of it right for me.

They don't want to solve that problem. Instead they try to solve the much-harder problem of allowing through viagra offers that are for some reason not spam. For the email user who *wants* to get mass-mail offers of 50% off your next order.

I just don't understand how "yeah, let's go out to dinner" from my friend, who is responding with quote to a fucking mail that I sent goes in the in the Spam box, but "get direct email mass-marketing secrets to double your business!" goes in my inbox. How can it be so bad, I just really don't understand it. Fucking the most basic keyword include/exclude type of filter could do better.

I should have just written my own, because it's the kind of problem that you want to be constantly tweaking on. Every time a mail is misclassified, I want to run it through my system and see why that happened and then try to fix it.

It would be SOOO fucking easy for them. Being in a position as a central mail processor, they can tell which mails are unique and which are mass-sent, and just FUCKING BLOCK ALL THE MASS-SENT MAIL. God dammit. You are fucking me up and I know you're doing it intentionally. I hate you.

I mean, fuck. It's ridiculous.

They are responding to a mail I sent. The mail I sent is fucking quoted right there. I sent the fucking mail from gmail so you can confirm it's for real. I sent to their address with gmail. AND YOU PUT THEIR REPLY IN SPAM. WTF WTF WTF

But this is not spam :

Report: creative teamwork is easier with cloud-based apps

Businesses Increase Screening of Facebook, Twitter Before Hiring

Trying to solve the Prospecting Paradox?

I'd like to add you to my professional network on LinkedIn

Maybe I'm being a bit overly simplistic and harsh. Maybe there are mass-mailings that look spammish, but you actually want to get? Like, your credit card bill is due?

I'm not sure. I'm not sure that I ever need to get any of that. I don't need those "shipping confirmation" emails from Amazon. If they just all got filed to the "mass mail" folder, I could go look for them when I need them.

I want to make my own private internet. And then not allow anyone else to use it because you'd all just fuck it up.

05-16-15 | Threading Primitive : monitored semaphore

A monitored semaphore allows two-sided waiting :

The consumer side decs the semaphore, and waits on the count being positive.

The producer side incs the semaphore, and can wait on the count being a certain negative value (some number of waiting consumers).

Monitored semaphore solves a specific common problem :

In a worker thread system, you may need to wait on all work being done. This is hard to do in a race-free way using normal primitives. Typical ad-hoc solutions may miss work that is pushed during the wait-for-all-done phase. This is hard to enforce, ugly, and makes bugs. (it's particularly bad when work items may spawn new work items).

I've heard of many ad-hoc hacky ways of dealing with this. There's no need to muck around with that, because there's a simple and efficient way to just get it right.

The monitored semaphore also provides a race-free way to snapshot the state of the work system - how many work items are available, how many workers are sleeping. This allows you to wait on the joint condition - all workers are sleeping AND there is no work available. Any check of those two using separate primitives is likely a race.

The implementation is similar to the fastsemaphore I posted before.

"fastsemaphore" wraps some kind of underlying semaphore which actually provides the OS waits. The underlying semaphore is only used when the count goes negative. When count is positive, pops are done with simple atomic ops to avoid OS calls. eg. we only do an OS call when there's a possibility it will put our thread to sleep or wake a thread.

"fastsemaphore_monitored" uses the same kind atomic variable wrapping an underlying semaphore, but adds an eventcount for the waiter side to be triggered when enough workers are waiting. (see who ordered event count? )

Usage is like this :

To push a work item :

push item on your queue (MPMC FIFO or whatever)

To pop a work item :

pop item from queue

To flush all work :


NOTE : in my implementation, post & wait can be called from any thread, but wait_for_waiters must be called from only one thread. This assumes you either have a "main thread" that does that wait, or that you wrap that call with a mutex.

template <typename t_base_sem>
class fastsemaphore_monitored
    atomic<S32> m_state;
    eventcount m_waiters_ec;
    t_base_sem m_sem;

    enum { FSM_COUNT_SHIFT = 8 };
    enum { FSM_COUNT_MASK = 0xFFFFFF00UL };
    enum { FSM_WAIT_FOR_SHIFT = 0 };
    enum { FSM_WAIT_FOR_MASK = 0xFF };

    fastsemaphore_monitored(S32 count = 0)
    :   m_state(count<<FSM_COUNT_SHIFT)
        RL_ASSERT(count >= 0);



    inline S32 state_fetch_add_count(S32 inc)
        S32 prev = m_state($).fetch_add(inc<<FSM_COUNT_SHIFT,mo_acq_rel);
        S32 count = ( prev >> FSM_COUNT_SHIFT );
        RR_ASSERT( count < 0 || ( (U32)count < (FSM_COUNT_MAX-2) ) );
        return count;

    // warning : wait_for_waiters can only be called from one thread!
    void wait_for_waiters(S32 wait_for_count)
        RL_ASSERT( wait_for_count > 0 && wait_for_count < FSM_WAIT_FOR_MAX );
        S32 state = m_state($).load(mo_acquire);
            S32 cur_count = state >> FSM_COUNT_SHIFT;

            if ( (-cur_count) == wait_for_count )
                break; // got it
            S32 new_state = (cur_count<<FSM_COUNT_SHIFT) | (wait_for_count << FSM_WAIT_FOR_SHIFT);
            S32 ec = m_waiters_ec.prepare_wait();
            // double check and signal what we're waiting for :
            if ( ! m_state.compare_exchange_strong(state,new_state,mo_acq_rel) )
                continue; // retry ; state was reloaded
            state = m_state($).load(mo_acquire);
        // now turn off the mask :
            S32 new_state = state & FSM_COUNT_MASK;
            if ( state == new_state ) return;
            if ( m_state.compare_exchange_strong(state,new_state,mo_acq_rel) )
            // retry ; state was reloaded

    void post()
        if ( state_fetch_add_count(1) < 0 )

    void wait_no_spin()
        S32 prev_state = m_state($).fetch_add((-1)<<FSM_COUNT_SHIFT,mo_acq_rel);
        S32 prev_count = prev_state>>FSM_COUNT_SHIFT;
        if ( prev_count <= 0 )
            S32 waiters = (-prev_count) + 1;
            RR_ASSERT( waiters >= 1 );
            S32 wait_for = prev_state & FSM_WAIT_FOR_MASK;
            if ( waiters == wait_for )
                RR_ASSERT( wait_for >= 1 );
    void post(S32 n)
        RR_ASSERT( n > 0 );
        for(S32 i=0;i<n;i++)
    bool try_wait()
        // see if we can dec count before preparing the wait
        S32 state = m_state($).load(mo_acquire);
            if ( state < (1<<FSM_COUNT_SHIFT) ) return false;
            // dec count and leave the rest the same :
            //S32 new_state = ((c-1)<<FSM_COUNT_SHIFT) | (state & FSM_WAIT_FOR_MASK);
            S32 new_state = state - (1<<FSM_COUNT_SHIFT);
            RR_ASSERT( (new_state>>FSM_COUNT_SHIFT) >= 0 );
            if ( m_state($).compare_exchange_strong(state,new_state,mo_acq_rel) )
                return true;
            // state was reloaded
            // loop
            // backoff here optional
    S32 try_wait_all()
        // see if we can dec count before preparing the wait
        S32 state = m_state($).load(mo_acquire);
            S32 count = state >> FSM_COUNT_SHIFT;
            if ( count <= 0 ) return 0;
            // swap count to zero and leave the rest the same :
            S32 new_state = state & FSM_WAIT_FOR_MASK;
            if ( m_state($).compare_exchange_strong(state,new_state,mo_acq_rel) )
                return count;
            // state was reloaded
            // loop
            // backoff here optional
    void wait()
        int spin_count = rrGetSpinCount();
            if ( try_wait() ) 


05-16-15 | LZ literals after match

Some vague rambling about LAMs.

LAMs are weird.

LAM0 , the first literal after a match, has the strong exclusion property (assuming maximum match lengths). LAM0 is strictly != lolit. (lolit = literal at last offset).

LAM1, the next literal after end of match, has the exact opposite - VERY strong prediction of LAM1 == lolit. This prediction continues but weakens as you go to LAM2, LAM3, etc.

In Oodle LZNA (and in many other coders), I send a flag for (LAM == lolit) as a separate event. That means in the actual literal coding path you still have LAM1 != lolit. (the LAM == lolit flag should be context-coded using the distance from the end of the match).

In all cases, even though you know LAM != lolit, lolit is still a very strong predictor for LAM. Most likely LAM is *similar* to lolit.

LAM is both an exclude AND a predictor!

What similar means depends on the file type. In text it means something like vowels stay vowels, punctuation stays punctuation. lolit -> LAM is sort of like substituting one character change. In binary, it often means that they are numerically close. This means that the delta |LAM - lolit| is never zero, but is often small.

One of the interesting things about the delta is that it gives you a data-adaptive stride for a delta filter.

On some files, you can get huge compression wins by running the right delta filter. But the ideal delta distance is data-dependent (*). The sort of magic thing that works out is that the LZ match offsets will naturally pick up the structure & word sizes. In a file of 32-byte structs made of DWORDs, you'll get offsets of 4,8,12,32,etc. So you then take that offset and forming the LAM sub is just a way of doing a delta with that deduced stride. On DWORD or F32 data, you tend to get a lot of offset=4, so LAM tends to just be doing delta from the previous word (note of course this bytewise delta, not a proper dword delta).

(* = this is a huge thing that someone needs to work on; automatic detection of delta filters for arbitrary data; deltas could be byte,word,dword, other, from immediate neighbors or from struct/row strides, etc. In a compression world where we are fighting over 1% gains, this can be a 10-20% jump.)

Experimentally we have observed that LAMs are very rapidly changing. They benefit greatly from very quickly adapting models. They like geometric adaptation rates (more recent events are much more important). They cannot be modeled with large contexts (without very sophisticated handling of sparsity and fast adaptation), they need small contexts to get lots of events and statistical density. They seem to benefit greatly from modeling in groups (eg. bitwise or nibblewise or other), so that events on one symbol also affect other probabilities for faster group learning. Many of these observations are similar for post-BWT data. LAM sub literals does seem to behave like post-BWT data to some extent, and similar principles of modeling apply.

So, for example, just coding an 8-bit symbol using the 8-bit lolit as context is a no-go. In theory this would give you full modeling of the effects of lolit on the current symbol. In practice it dilutes your statistics way too much. (in theory you could do some kind of one-count boosts other counts thing (or a secondary coding table ala PPMZ SEE), but in practice that's a mess). Also as noted previously, if you have the full 8-bit context, then whether you code symbol raw or xor or sub is irrelevant, but if you do not have the full context then it does change things.

Related posts :

cbloom rants 08-20-10 - Deobfuscating LZMA
cbloom rants 09-14-10 - A small note on structured data
cbloom rants 03-10-13 - Two LZ Notes
cbloom rants 06-12-14 - Some LZMA Notes
cbloom rants 06-16-14 - Rep0 Exclusion in LZMA-like coders
cbloom rants 03-15-15 - LZ Literal Correlation Images

05-13-15 | Skewed Pareto Chart

It's hard to see just the decomp speed in the normal Pareto Chart. It gets squished down over at the far-right Y-intercept.

The obvious fix is just to magnify the right side. This is a linear scaling of the data; *1 on the far left, *10 on the far right :

The far-left is still proportional to the compression ratio, the far right is proportional to the decompression speed. The compressor lines are still speedups vs. memcpy, but the memcpy baseline is now sloped.

I'm not really sure how I feel about the warped chart vs unwarped.

The Pareto curves are in fact sigmoids (tanh's).

speedup = 1 / (1/compression_ratio + disk_speed / decompress_speed)

speedup = 1 / (1/compression_ratio + exp( log_disk_speed ) / decompress_speed)

(here they're warped sigmoids because of the magnification; the ones back here in the LZNA post are true sigmoids)

I believe (but have not proven) that a principle of the Pareto Frontier is that the maximum of all compressors should also be a sigmoid.

max_speedup(disk_speed) = MAX{c}( speedup[compressor c](disk_speed) );

One of the nice things about these charts is it makes it easy to see where some compressors are not as good as possible. If we fit a sigmoid over the top of all the curves :

We can easily see that LZHLW and LZNIB are not touching the curve. They're not as good as they should be in space/speed. Even thought nothing beats them at the moment (that I know of), they are algorithmically short of what's possible.

There are two things that constrain compressors from being better in a space/speed way. There's 1. what is our current best known algorithm. And then there's 2. what is possible given knowledge of all possible algorithms. #2 is the absolute limit and eventually it runs into a thermodynamic limit. In a certain amount of cpu time (cpu bit flips, which increase entropy), how much entropy can you take out of a a given data stream. You can't beat that limit no matter how good your algorithm is. So our goal in compression is always to just find improvements in the algorithms to edge closer to that eventual limit.

Anyway. I think I know how to fix them, and hopefully they'll be up at the gray line soon.

05-11-15 | ANS Minimal Flush

A detail for the record :

ANS (TANS or RANS) in the straightforward implementation writes a large minimum number of bytes.

To be concrete I'll consider a particular extremely bad case : 64-bit RANS with 32-bit renormalization.

The standard coder is :

initialize encoder (at end of stream) :

x = 1<<31

renormalize so x stays in the range x >= (1<<31) and x < (1<<63)

flush encoder (at the beginning of the stream) :

output all 8 bytes of x

decoder initializes by reading 8 bytes of x

decoder renormalizes via :

if ( x < (1<<31) )
  x <<= 32;  x |= get32(ptr); ptr += 4;

decoder terminates and can assert that x == 1<<31

this coder outputs a minimum of 8 bytes, which means it wastes up to 7 bytes on low-entropy data (assuming 1 byte minimum output and that the 1 byte required to byte-align output is not "waste").

In contrast, it's well known how to do minimal flush of arithmetic coders. When the arithmetic coder reaches the end, it has a "low" and "range" specifying an interval. "low" might be 64-bits, but you don't need to output them all, you only need to output enough such that the decoder will get something in the correct interval between "low" and "low+range".

Historically people often did arithmetic coder minimum flush assuming that the decoder would read zero-valued bytes after EOF. I no longer do that. I prefer to do a minimum flush such that decoder will get something in the correct interval no matter what byte follows EOF. This allows the decoder to just read past the end of your buffer with no extra work. (the arithmetic coder reads some # of bytes past EOF because it reads enough to fill "low" with bits, even though the top bits are all that are needed at the end of the stream).

The arithmetic coder minimum flush outputs a number of bytes proportional to log2(1/range) , which is the number of bits of information that are currently held pending in the arithmetic coder state, which is good. The excess is at most 1 byte.

So, to make ANS as clean as arithmetic coding we need a minimal flush. There are two sources of the waste in the normal ANS procedure outlined above.

One is the initial value of x (at the end of the stream). By setting x to (1<<31) , the low end of the renormalization interval, we have essentually filled it with bits it has to flush. (the pending bits in x is log2(x)). But those bits don't contain anything useful (except a value we can check at the end of decoding). One way to remove that waste is to stuff some other value in the initial state which contains bits you care about. Any value you initialize x with, you get back at the end of decoding, so then those bits aren't "wasted". But this can be annoying to find something useful to put in there, since you don't get that value out until the end of decoding.

The other source of waste is the final flush of x (at the beginning of the stream). This one is obvious - the # of pending bits stored in x at any time is log2(x). Clearly we should be flushing the final value of x in a # of bits proportional to log2(x).

So to do ANS minimal flush, here's one way :

initialize encoder (at end of stream) :

x = 0

renormalize so x stays in the range x < (1<<63)

flush encoder (at the beginning of the stream) :

output # of bytes with bits set in x, and those bytes

decoder initializes by reading variable # of bytes of x

decoder renormalizes via :

if ( x < (1<<31) )
  if ( ptr < ptrend )
    x <<= 32;  x |= get32(ptr); ptr += 4;

decoder terminates and can assert that x == 0

This ANS variant will output only 1 byte on very-low-entropy data.

There are now two phases of the coder. In the beginning of encoding (at the ending of the stream), x is allowed to be way below the renormalization range. During this phase, encoding just puts information into x, and the value of x grows. (note that x can actually stay 0 and never hold any bits if your consists of entirely the bottom symbol in RANS). Once x grows up into the renormalization interval, you enter the next phase where bits of x are pushed to the output to keep x in the renormalization interval. Decoding, in the first phase you read bytes from the stread to fill x with bits and keep it in the renormalization interval. Once the decoder read pointer hits the end, you switch to the second phase, and now x is allowed to shrink below the renormalization minimum and you can continue to decode the remaining information held in it.

This appears to add an extra branch to the decoder renormalization, but that can be removed by duplicating your decoder into "not near the end" and "near the end" variants.

The #sigbit output of x at the head is just the right thing and should always be done in all variants of ANS.

The checking ptr vs. ptrend and starting x = 0 is the variant that I call "minimal ANS".

Unfortunately "minimal ANS" doesn't play well with the ILP multi-state interleaved ANS. To do interleaved ANS like this you would need an EOF marker for each state. That's possible in theory (and could be done compactly in theory) but is a pain in the butt in practice.

05-10-15 | Did I ever mention that I fucking hate the fucking web?

(I might be a bit cranky today. Too much work and not enough sex. I should probably just go to a bar and talk about how I love Obama and taxes so I can get in a fight. Instead I'll rage about the fucking web.)

I'm trying to get together the photos of my baby to share with my mom. What a fucking nightmare. They're mostly on my phone, and auto-backed up to Google Photos. Should be easy, right?

The Google Photos web interface is fucking wrist-slashing insanity. It's SO FUCKING SLOW. It should not take so long to show me a few little thumbnails. Fucking quit all the fucking AJAX fancy bullshit whatever the fuck you're fucking doing oh my god.

It always only wants to show me "highlights". Who told you to fucking do that? I have never highlighted anything so I'm not sure how you decided what was a highlight and what wasn't. You fucking dicks.

Simple shit like making an album and trying to put the correct photos in the album just has no decent workflow. FUCK.

So I'm going to just download them and do it on my computer. Fine.

There's no download all. I'm supposed to what, click each fucking one and download? (which is a frustrating nightmare because the click is some super slow awful web popup).

Okay, I can use Google Takeouts to just get the whole thing. Hmm. Why are my photos fucking 8 GB? Oh, because it's giving me all my videos too. FUCK FUCK FUCK. I just want the photos not the videos. Nope, Takeouts gives you everything.

Okay, I'll just download the 8 GB. Oh awesome the download the failed. Oh awesome it failed again.

Okay, I'll get the download URL and give it to DownloadThemAll which is good and can do resumes and so on and the main reason I cling to Firefox.

NOPE the fucking download link is not an actual file it's some fucking redirect login bullshit that DTA can't handle. ARG ARG ARG.

And now fuck my fucking baby photos and fuck my mom (sorry mom) I'm not fucking dealing with this shit and I fucking hate the fucking web god dammit.

For some time I've been using Google Classic Maps ("https://maps.google.com/maps?output=classic&dg=opt"). And now it's been killed. Maybe I'll switch to Bing? Or fuck that. Maybe I should just buy a good set of paper maps. I'm not sure that even exists any more. Ever since the Thomas Guide switched to computer-generated maps they really suck, they're ugly and the layout is no good and hard to read.

The reason I saw on the web for killing it (Google Classic Maps) was that too many people were opting out of new maps. You killed it because people liked it. I don't know if that's true, but it is awesomely in character.

For a while I was on the Google Forums complaining about Blogger. Just about everyone who runs a blog at some point gets a troll and realizes that they need the ability to just ban an individual. Can't do it. So they go on the Google product forum and say hey can we get black listing and white listing? The Google response was "we know you want that, and fuck you".

REMINDER TO SELF : always download all the images made by Google Charts because that service will die at some point. (this would be good practice even if Google didn't randomly chop off its own limbs on a regular basis)

I don't keep any cookies or browse history. With everyone going to fucking two-phase login this is starting to get annoying. To login I now have to get a text code to my phone and enter that. It's tedious.

But the thing that really kills me is this stupid detail :

I get the numeric code sent to me. I go to Google Voice on my computer (because actually ever touching the phone is to be avoided at all cost). I double-click the number to copy it. I paste it in the two-phase entry.

It fails. Wrong code.

I try again. It fails.

The fucking double-click is selecting the space after the number, and the fucking login doesn't ignore the trailing space. It's lazy bad programmer shit like that which makes me furious.

Another one I hit often is using online payment thingies. I'll copy-paste the amount from my bill, something like "$1,234" and hit okay and I get

"invalid entry, please enter a numeric value"

IT's A FUCKING PAYMENT ENTRY BOX. You can fucking strip the leading $ and commas you piece of shit mother fucking asshole terrible programmers.

I'm trying to login to Skype on my phone.

(side note: summary of every Skype sessions I've ever had : "I can see you, can you see me? I can't hear you. Oh, you're upside down. Let me log off and disconnect. Now you're black. Try again. It's real glitchy, let's restart it. Hey, it's working! Hi! Hi! Okay, gotta go now.")

It says login with your skype account or your microsoft account.

So I tediously enter my microsoft account login which has a password like fucking @#$ASD@!#$<:22 and is fucking awful to type (and is starred out you fucking fucks the fucking fuck).

Skype says "oh, it looks like you entered a microsoft account, redirecting..."


I'm so fucking sick of loading web pages and seeing "connecting to blah.. connecting to blah.." and seeing shit popping in slowly and reflowing and the focus popping and all this fucking shit.

Hey, fucking remedial loading school. You put all the content needed for the page in one package. Send me the one package. BOOM it loads.

Incremental is bullshit.

Back in the 90's some time, I worked for Eclipse on streaming 3d for the web. One of the things I did was a progressive wavelet image compressor so we could do things like send the first 5k of each image, then the next 10k, and because of the truncation property of bitplane-coded wavelets those were good low quality versions of the image that could just be tacked together.

So we tried to test it and demo it.

Everything just instantly loaded and you couldn't see the progressive wavelet load at all.

Because if you're not a fucking moron and you package together your content and just have a single download bundle to get your content, hey the internet is actually really fucking fast (even back in the 90's !!).

To show it off I put in a bunch of fake delays on the downloader to simulate slow hosts, so that you could see the wavelets gradually getting better, and that's what we showed to VC's or whatever.

I guess I could have just taken all the files and scattered them on different hosts around the world, THE WAY FUCKING NORMAL WEB PAGES DO. It's like they have very carefully gone through this process of intentionally slowing down the internet for no reason.

Sometimes I wish that I was like an air-cooled Porsche mechanic or something very stable and non-computer related, so I could just work away in my shop and not have to ever touch this fucking demon box.

05-09-15 | Oodle LZNA

Oodle 1.45 has a new compressor called LZNA. (LZ-nibbled-ANS)

LZNA is a high compression LZ (usually a bit more than 7z/LZMA) with better decode speed. Around 2.5X faster to decode than LZMA.

Anyone who needs LZMA-level compression and higher decode speeds should consider LZNA. Currently LZNA requires SSE2 to be fast, so it only runs full speed on modern platforms with x86 chips.

LZNA gets its speed from two primary changes. 1. It uses RANS instead of arithmetic coding. 2. It uses nibble-wise coding instead of bit-wise coding, so it can do 4x fewer coding operations in some cases. The magic sauce that makes these possible is Ryg's realization about mixing cumulative probability distributions . That lets you do the bitwise-style shift update of probabilities (keeping a power of two total), but on larger alphabets.

LZNA usually beats LZMA compression on binary, slightly worse on text. LZNA is closer to LZHAM decompress speeds.

Some results :


LZNA -z6 : 24,700,820 -> 9,154,248 =  2.965 bpb =  2.698 to 1
decode only      : 0.327 seconds, 43.75 b/kc, rate= 75.65 mb/s

LZMA : 24,700,820 -> 9,329,925 =  3.021 bpb =  2.647 to 1
decode           : 0.838 seconds, 58.67 clocks, rate= 29.47 M/s

LZHAM : 24,700,820 ->10,140,761 =  3.284 bpb =  2.435 to 1
decode           : 0.264 seconds, 18.44 clocks, rate= 93.74 M/s

(note on settings : LZHAM is run at BETTER because UBER is too slow. LZHAM BETTER is comparable to Oodle's -z6 ; UBER is similar to my -z7. (not quite right; see later post "LZNA encode speed addendum"). LZMA is run at the best compression setting I can find; -m9 and lc=0,lp=2,pb=2 for binary data; with LZHAM I don't see a way to set the context bits. This is the new LZHAM 1.0, slightly different than my previous tests of LZHAM. All 64-bit, big dictionaries.).


LZNA -z6 : 58,788,904 ->12,933,907 =  1.760 bpb =  4.545 to 1
decode only      : 0.677 seconds, 50.22 b/kc, rate= 86.84 mb/s

LZMA : 58,788,904 ->13,525,659 =  1.840 bpb =  4.346 to 1
decode           : 1.384 seconds, 40.70 clocks, rate= 42.49 M/s

LZHAM : 58,788,904 ->15,594,877 =  2.122 bpb =  3.769 to 1
decode           : 0.582 seconds, 17.12 clocks, rate= 100.97 M/s

I'm not showing encode speeds because they're all running different amounts of threading. It would be complicated to show fairly. LZHAM is the most aggressively threaded, and also the slowest without threading.

My "game testset" total sizes, from most compression to least :

Oodle LZNA -z8 :            57,176,229
Oodle LZNA -z5 :            58,318,469

LZMA -mx9 d26:lc0:lp2:pb3 : 58,884,562
LZMA -mx9 :                 59,987,629

LZHAM -mx9 :                62,621,098

Oodle LZHLW -z6 :           68,199,739

zip -9 :                    88,436,013

raw :                       167,495,105

Here's the new Pareto chart for Oodle. See previous post on these charts

This is load+decomp speedup relative to memcpy : (lzt99)

The left-side Y-intercept is the compression ratio. The right-side Y-intercept is the decompression speed. In between you can see the zones where each compressor is the best tradeoff.

With LZMA and LZHAM : (changed colors)

lzt99 is bad for LZHAM, perhaps because it's heterogeneous and LZHAM assumes pretty stable data. (LZHAM usually beats LZHLW for compression ratio). Here's a different example :

load+decomp speedup relative to memcpy : (baby_robot_shell)

05-08-15 | Bernie Sanders For President

I just watched the Daily Show where Jon just makes fun of Bernie for being unknown and looking/sounding a bit like an older Larry David, without mentioning anything about the fact that Bernie is fucking awesome. Bernie's announcement of "okay let's keep this short, I have to get back to work" is fucking awesome typical Bernie and it's what our politicians should be saying. They should be doing fucking work instead of making elaborate announcement pageants. They should actually be reading and writing laws instead of letting lobbyists and aides do it all for them.

Bernie Sanders is fucking amazing. If you haven't had the great pleasure of hearing him talk at length, go do it now. He is the best politician since I don't even know fucking who (*). I have never in my lifetime heard a single politician that actually speaks honestly and intelligently about the issues. Not talking points. Not just a bunch of bullshit promises. Not just verbal gymnastics to avoid the point. Actually directly talks about the issue in a realistic and pragmatic way.

(* = I have seen video of things like the Nixon-Kennedy debates in which politicians actually talk about issues and try to pin each other down on points of policy, rather than scoring "gotchas" and "applause points". I understand that back in the olden days, pandering to cheap emotional vagaries would get you pilloried in the press as "evasive" or "not serious". I've never seen it in my life.)

Even if you're conservative and don't agree with his views, it should be a fucking breath of fresh air for anyone with any fucking scrap of humanity and decency and intelligence to see a politician that refuses to play the games, refuses to pander to the shitty mass-applause points and the special-interest hate groups and most of all corporate money.

Even though Bernie won't win, I want every single debate to be just Bernie. I don't want to hear a single fucking vapid scripted garbage word from any of the other shit-heads. Just let Bernie talk the whole time.

I disagree with Bernie on some points. He tends to be rather more traditional liberal pro-union pro-manufacturing than I necessarily think is wise. But it's easy to get distracted by the disagreement and miss the point - here is a politician that's actually talking about issues and facts. Even if he gets them wrong sometimes at least he's trying to address real solutions. (this is one of the tricks of most other politicians - don't ever actually propose anything concrete, because then it can be attacked, instead just talk about "hope" or "liberty" or say "America fuck yeah!")

It's classic Bernie that he chose to run as a democrat so that he wouldn't be a spoiler ala Nader. It's just totally realistic, pragmatic, to the point. I fucking love Bernie Sanders.

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05-03-15 | Waterproof

I have 3 rain jackets. They all let rain through.

Granted, the first one is actually labelled "water resistant" or "water repellant" or some such nonsense which actually means "fucking useless". But the other two are actually described as "waterproof". And they just aren't.

They seem waterproof at first. Water beads up and runs off and nothing goes through. But over time in a rain they start to get saturated, and eventually they soak through and then they just wick water straight through.

The problem is they're all some fancy waterproof/breathable technical fabric.


Ooo we have this new fancy fabric. NO! No you don't. You have bullshit that doesn't fucking work.

Job #1 : Actually be waterproof.

But it's lighter!, you say. Nope! Zip it! But it's breathable. Zip! Shush. But it's recycled, and rip-stop. Zip. Nope. Is it waterproof? Is it actually fucking waterproof? Like if I stand out in a rain. No, it isn't. Throw it out. It doesn't work. You're fired. Back to the drawing board.

If you want to get fancy, you could use your breathable/not-actually-waterproof material in areas that don't get very wet, such as the inside of the upper arm and the sides of the torso.

At the very least the tops of the shoulders and the upper chest need to be just plastic. Just fucking plastic like a slicker from the 50's. (it could be a separate overhanging shelf of plastic, like a duster type of thing)

Any time I'm browsing REI or whatever these days and see a jacket labelled waterproof, I think "like hell it is".

04-28-15 | Guitar and Teaching

I'm sort of vaguely trying to learn guitar again as a late night alternative to TV.

I'm at the point I always hit where I lose steam. I can play some basic stuff, but not anything too difficult. The problem is I have trouble finding fun songs to play that aren't too hard, or finding songbooks or teach-yourself books that are both fun and not too hard.

What I really want, and what I think is the right way to teach guitar to a dabbler like me is :

A book songs, in progression of difficulty

The songs need to be modern (post-60's), fun, familiar
(classic rock is pretty safe)

The songs need to be the *actual* songs.  Not simplified versions.  Not transposed versions.
Not just the chords when the real song is much more complex.

When I play it, it needs to sound like the actual recording.

No funny tunings.  I can't be bothered with that.

and so far as I know nothing like that exists.

I've got a bunch of "easy rock guitar songbooks" and they all fucking suck.

There are lots of good tabs on the internet, and I've found some good stuff to learn that way, but fuck that. The last thing I want to be doing in my relaxing time is browsing the internet trying to decide which of the 400 fucking versions of the "Heartbreaker" tab is the right one I should try to learn.

(in the past I taught myself some classical guitar, and in contrast there are lots of great classical, and even finger-picking folk guitar song books and instructional progressions that give you nice songs to learn that are actually fun to play and sound like something)

I've tried taking lessons a few times in the past and the teachers always sucked. Maybe they were good in terms of getting you to be a better player, but they were awful at making it fun.

I had a teacher who wanted me to sit with a metronome and just pick the same note over and over to the metronome to work on my meter. WTF. You're fired. All teachers want you to play scales. Nope. And then for the "fun" part they want to teach some basic rock rhythm, A-A-E-E,A-A-E-E. Nope, I'm bored. You're fired. Then I get to learn a song and it's like some basic blues I've never heard of or some fucking John Denver or something. (*)

They seem to completely fail to understand that it has to keep the student interested. That's part of your job being a teacher. I'm not trying to become a professional musician. I don't have some great passionate motivation that's going to keep me going through the boring shit and drudgery of your lessons. You have to make it fun all the time.

(* = there is some kind of weird thing where people who play music generally have horrible taste in music. It's like they pay too much attention to either the notes/chord/key or to the technical playing, neither of which actually matter much. It's the feeling, man.)

It was interesting for me to see this in ceramics. I was lucky to find a really great teacher (Bill Wilcox) who understood that it had to be fun, and that this was a bit of a lark for most of us, and some were more serious than others. Maybe he wasn't the most efficient teacher in terms of conveying maximum learning in a set time period - but he kept you coming back. We occasionally had different guest teachers, and they were way more regimented and methodical and wanted you to do drills (pull a cylinder 20 times and check the walls for evenness), and you could see half the class thinking "fuck this"

I suppose this is true of all learning for some kids. Some kids are inherently motivated, I'm going to learn because I'm supposed to, or to get into a good college, or "for my future", or to be smarter than everyone else, or whatever. But other kids see a cosine and think "wtf is that for, who cares".

I've always thought the right way to teach anything is with a goal in mind. Not just "hey learn this because you're supposed to". But "we want to build a catapult and fire it and hit a target. Okay, we're going to need to learn about angles and triangles and such...". The best/easiest/deepest learning is what you learn because you need to learn it to accomplish something that you want to do.

What I need in guitar is a series of mini goals & accomplishments. Hey here's this new song, and it's a little bit too hard for me, but it's a fucking cool song so I actually want to play it. So I practice for a while and get better, and then I can play it, yay! Then I move on to the next one. Just like good game design. And WTF it just doesn't seem to exist.

04-24-15 | Typical Email Experience

I write very careful emails with clear points and specific questions, something like :

Hello, yes blah blah some stuff.  I need to know these points :

1. What about A?

2. There is also b?

3. and finally C?

and I usually get a response like :

Yep, great!

Umm. WTF. You are fucking fired from your job, from life, from the planet, go away.

Yep to what? There were THREE questions in there. And none of them was really a yes/no question anyway. WTF.

So I'll try to be polite and send back something like -

Thanks for the response; yes, to what exactly?  Did you mean yes to A?

Also I still need to know about B & C.

and then I'll get a response like :

Ok, on B we do this and that.

Umm. Okay, that's better. We got one answer, but THERE WERE THREE FUCKING QUESTIONS. I fucking numbered them so you could count them. That means I need three answers.

Sometimes I'll get a response like :

Ramble ramble, some unrelated stuff, sort of answer maybe A and C but not exactly, some
other rambling.

Okay. Thanks for writing a lot of words, but I HAD SPECIFIC FUCKING QUESTIONS.

This is basic fucking professionalism.

Jesus christ.

04-20-15 | Vitamin D

This post is a month or two too late, since we're now into the sun-times (I hope, fingers crossed), but anyway.

Everybody knows when you move to Seattle and get SAD you have to take vitamin D. So all these years I've been taking a few Vit D pills every day in the winter.

Recently my hair has been falling out, which has never happened to me before. I was pretty sure it was just stress, but I thought hey WTF may as well get a blood test and see if anything is wrong. So I get a blood test. Everything is normal, except -

My vit D levels were way way below normal. There's a normal range (3-7) and I was like a 1.

I was like, WTF? I take 1-2 vit D pills every day.

Turns out those pills are 1000 IU each, so I was taking 1-2000 IU. I thought that was a hell of a lot (it's ten million percent of the US RDA). Nope, not a lot. My doc said I could take 8000-10,000 IU to get my levels back up to normal, then maintenance was more like 5000 IU.

So, I started taking big doses, and BOOM instant happiness. More energy, less depression.

I still fucking hate the gray and the wet. (I recently got some foot fungus from hiking on a rainy day. I hate the fucking wet. I'd like to live on Arrakis and never see a single drop of rain again in my life.) But hey with proper vit D dosing I don't want to kill myself every day. Yay.

Pound that D, yo!

04-14-15 | Bend Oregon

Bend in a nutshell :

Restaurants here write "sando" on the menu when describing sandwiches.

I'm not talking about casual order-at-the-counter places with "crazy" graphics. I mean fancier places with good food. Not conversation, written word. "House-made roast beef sando with blue cheese and carmelized onions". Sando.

Bend has two primary demographics :

The rednecks, which unfortunately still infest so much of Oregon (including, surprisingly, even quite a lot of Portland, mainly on the outside, like a nasty fiery red infection around the anus of liberal Portland). The rednecks wear flannel and baseball caps, drive big trucks, they like off-roading, beer and dogs.

The snowboarders. They wear flannel, baseball caps, drive big trucks, like snowboarding, beer and dogs.

They're actually easy to tell apart. The snowboarders wear $100 designer Helly Hansen flannel, the rednecks wear cheap Walmart flannel.

No, actually you can tell them apart because the rednecks are all so damn ugly. They're constantly angry, they don't smile at you, they stomp around and have bad posture. The contrast is severe, which brings us to the next point :

Bend is the happiest place I have ever seen in my life. It's fucking ridiculous.

For Oddworlders, it's like a town full of Bonnies. For Tash, it's a town full of Bagleys.

Everyone is clear-eyed, that bright clear eye sweetness you get from lots of exercise and being outdoors, that gives you inner peace and patience and just fixes everything. Everyone is so sweet and friendly in a real way, not in that syrupy phoney Southern way.

Kids just walk down the street. There were sweet little kids playing everywhere. People ride their bikes to the corner restaurant and just leave it on the rack unlocked.

It's a fucking utopia.

It's horrible being around those positive, sweet, wholesome people who have great life priorities and friends and seem to have fun doing anything. It makes me sick. You are everything I should be in life and am not. They're the kind of people who buy their friends presents because they actually want to. The kind of people who stand up and dance in a bar when noone else is, and just don't even think about it and laugh and have a great time. I hate you so much. It must be the way ugly girls feel when they visit LA.

Everyone in Bend is a massive alcoholic. When you order your coffee in the morning, they ask if you want a craft brewed IPA with that. There's a brewery per person.

On the down side, there is no road biking around Bend. It's supposed to be this biking mecca, but I guess just for mountain bikes. I think road biking in Oregon is probably shit everywhere. There are no nice dis-used windy roads. God I miss the California biking. I can name like 20 truly epic rides on the west coast of the US and every single one of them is in CA. (roads with lots of traffic and/or no shoulder and/or bad pavement are all disqualified; morons who put things like Hwy 1 on the "good rides" list are morons).

So many fucking stinky trucks. I love to drive around and get that fresh piney mountain air, but every fucking place you go there's some damn F350 enormous monster belching soot in your face. It seems like maybe people in Oregon like diesel more than most of the US? I dunno, I've never noticed so many damn stinky trucks in my life. I guess in Texas I wouldn't even try to open my window.

Pros :



Cheap housing (relative to Seattle & Portland and of course CA)

Gorgeous (I love that dry piney stuff; better than the swampy crap west of the Cascades)

Ski all winter!

Sweet for kids (up until high school age or so, then toxic)

Great mountain biking

Cons :


No road biking

Nice people


Low population = less people to choose from

03-25-15 | My Chameleon

I did my own implementation of the Chameleon compression algorithm. (the original distribution is via the density project)

This is the core of Chameleon's encoder :

    cur = *fm32++; h = CHAMELEON_HASH(cur); flags <<= 1;
    if ( c->hash[h] == cur ) { flags ++; *to16++ = (uint16) h; }
    else { c->hash[h] = cur; *((uint32 *)to16) = cur; to16 += 2; }

This is the decoder :

    if ( (int16)flags < 0 ) { cur = c->hash[ *fm16++ ]; }
    else { cur = *((const uint32 *)fm16); fm16 += 2; c->hash[ CHAMELEON_HASH(cur) ] = cur; }
    flags <<= 1; *to32++ = cur;

I thought it deserved a super-simple STB-style header-only dashfuly-described implementation :


My Chameleon.h is not portable or safe or any of that jizzle. Maybe it will be someday. (Update : now builds on GCC & clang. Tested on PS4. Still not Endian-invariant.)

// Usage :

#include "Chameleon.h"

Chameleon c;


size_t comp_buf_size = CHAMELEON_MAXIMUM_OUTPUT_SIZE(in_size);

void * comp_buf = malloc(comp_buf_size);

size_t comp_len = Chameleon_Encode(&c, comp_buf, in_buf, in_size );


Chameleon_Decode(&c, out_buf, in_size, comp_buf );

int cmp = memcmp(in_buf,out_buf,in_size);
assert( comp == 0 );

ADD : Chameleon2 SIMD prototype now posted : (NOTE : this is not good, do not use)

Chameleon2.h - experimental SIMD wide Chameleon
both Chameleons in a zip

The SIMD encoder is not fast. Even on SSE4 it only barely beats scalar Chameleon. So this is a dead end. Maybe some day when we get fast hardware scatter/gather it will be good (*).

(* = though use of hardware scatter here is always going to be treacherous, because hashes may be repeated, and the order in which collisions resolve must be consistent)

03-25-15 | Density - Chameleon

Casey pointed me at Density .

Density contains 3 algorithms, from super fast to slower : Chameleon, Cheetah, Lion.

They all attain speed primarily by working on U32 quanta of input, rather than bytes. They're sort of LZPish type things that work on U32's, which is a reasonable way to get speed in this modern world. (Cheetah and Lion are really similar to the old LZP1/LZP2 with bit flags for different predictors, or to some of the LZRW's that output forward hashes; the main difference is working on U32 quanta and no match lengths)

The compression ratio is very poor. The highest compression option (Lion) is around LZ4-fast territory, not as good as LZ4-hc. But, are they Pareto? Is it a good space-speed tradeoff?

Well, I can't build Density (I use MSVC) so I can't test their implementation for space-speed.

Compressed sizes :

lzt99 :
uncompressed       24,700,820

density :
c0 Chameleon       19,530,262
c1 Cheetah         17,482,048
c2 Lion            16,627,513

lz4 -1             16,193,125
lz4 -9             14,825,016

Oodle -1 (LZB)     16,944,829
Oodle -2 (LZB)     16,409,913

Oodle LZNIB        12,375,347

(lz4 -9 is not competitive for encode time, it's just to show the level of compression you could get at very fast decode speeds if you don't care about encode time ; LZNIB is an even more extreme case of the same thing - slow to encode, but decode time comparable to Chameleon).

To check speed I did my own implementation of Chameleon (which I believe to be faster than Density's, so it's a fair test). See the next post to get my implementation.

The results are :

comp_len = 19492042
Chameleon_Encode_Time : seconds:0.0274 ticks per: 1.919 mb/s : 901.12
Chameleon_Decode_Time : seconds:0.0293 ticks per: 2.050 mb/s : 843.31

round trip time = 0.05670
I get a somewhat smaller file size than Density's version for unknown reason.

Let's compare to Oodle's LZB (an LZ4ish) :

Oodle -1 :

24,700,820 ->16,944,829 =  5.488 bpb =  1.458 to 1
encode           : 0.061 seconds, 232.40 b/kc, rate= 401.85 mb/s
decode           : 0.013 seconds, 1071.15 b/kc, rate= 1852.17 mb/s

round trip time = 0.074

Oodle -2 :

24,700,820 ->16,409,913 =  5.315 bpb =  1.505 to 1 
encode           : 0.070 seconds, 203.89 b/kc, rate= 352.55 mb/s
decode           : 0.014 seconds, 1008.76 b/kc, rate= 1744.34 mb/s

round trip time = 0.084

lzt99 is a collection of typical game data files.

We can test on enwik8 (text/html) too :

Chameleon :

enwik8 :
Chameleon_Encode_Time : seconds:0.1077 ticks per: 1.862 mb/s : 928.36
Chameleon_Decode_Time : seconds:0.0676 ticks per: 1.169 mb/s : 1479.08
comp_len = 61524068

Oodle -1 :

enwik8 : 
100,000,000 ->57,267,299 =  4.581 bpb =  1.746 to 1 
encode           : 0.481 seconds, 120.17 b/kc, rate= 207.79 mb/s
decode           : 0.083 seconds, 697.58 b/kc, rate= 1206.19 mb/s

here Chameleon is much more compelling. It's competitive for size & decode speed, not just encode speed.

Commentary :

Any time you're storing files on disk, this is not the right algorithm. You want something more asymmetric (slow compress, fast decompress).

I'm not sure if Cheetah and Lion are Pareto for round trip time. I'd have to test speed on a wider set of sample data.

When do you actually want a compressor that's this fast and gets so little compression? I'm not sure.

03-15-15 | LZ Literal Correlation Images

I made some pictures.

I'm showing literal correlation by making an image of the histogram. That is, given an 8-bit predictor, you tally of each event :

int histo[256][256]

histo[predicted][value] ++

then I scale the histo so the max is at 255 and make it into an image.

Most of the images that I show are in log scale, otherwise all the detail is too dark, dominated by a few peaks. I also sometimes remove the predicted=value line, so that the off axis detail is more visible.

Let's stop a moment and look t what we can see in these images.

This is a literal histo of "lzt99" , using predicted = lolit (last offset literal; the rep0len1 literal). This is in log scale, with the diagonal removed :

In my images y = prediction and x = current value. x=0, y=0 is in the upper left instead of the lower left where it should be because fucking bitmaps are retarded (everyone is fired, left handed coordinate systems my ass).

The order-0 probability is the vertical line sum for each x. So any vertical lines indicate just strong order-0 correlations.

Most files are a mix of different probability sources, which makes these images look a sum of different contibuting factors.

The most obvious factor here is the diagonal line at x=y. That's just a strong value=predicted generator.

The red blob is a cluster of events around x and y = 0. This indicates a probability event that's related to |x+y| being small. That is, the sum, or length, or something tends to be small.

The green shows a square of probabilities. A square indicates that for a certain range of y's, all x's are equally likely. In this case the range is 48-58. So if y is in 48-58, then any x in 48-58 is equally likely.

There are similar weaker squarish patterns all along the diagonal. Surprisingly these are *not* actually at the binary 8/16 points you might expect. They're actually in steps of 6 & 10.

The blue blobs are at x/y = 64/192. There's a funny very specific strong asymmetric pattern in these. When y = 191 , it predicts x=63,62,61,60 - but NOT 64,65,66. Then at y=192, predict x=64,65,66, but not 63.

In addition to the blue blobs, there are weak dots at all the 32 multiples. This indicates that when y= any multiple of 32, there's a generating event for x = any multiple of 32. (Note that in log scale, these dots look more important than they really are.). There are also some weak order-0 generators at x=32 and so on.

There's some just general light gray background - that's just uncompressible random data (as seen by this model anyway).

Here's a bunch of images : (click for hi res)

rawrawraw subsubsub xorxorxor
loglogNDlinND loglogNDlinND loglogNDlinND
Fez LO
Fez O1
lzt24 LO
lzt24 O1
lzt99 LO
lzt99 O1
enwik7 LO
enwik7 O1

details :

LO means y axis (predictor) is last-offset-literal , in an LZ match parse. Only the literals coded by the LZ are shown.

O1 means y axis is order1 (previous byte). I didn't generate the O1 from the LZ match parse, so it's showing *all* bytes in the file, not just the literals from the LZ parse.

"log" is just log-scale of the histo. An octave (halving of probability) is 16 pixel levels.

"logND" is log without the x=y diagonal. An octave is 32 pixel levels.

"linND" is linear, without the x=y diagonal.

"raw" means the x axis is just the value. "xor" means the x axis is value^predicted. "sub" means the x axis is (value-predicted+127).

Note that raw/xor/sub are just permutations of the values along a horizontal axis, they don't change the values.


Discussion :

The goal of a de-correlating transform is to create vertical lines. Vertical lines are order-0 probability peaks and can be coded without using the predictor as context at all.

If you use an order-0 coder, then any detail which is not in a vertical line is an opportunity for compression that you are passing up.

"Fez" is obvious pure delta data. "sub" is almost a perfect model for it.

"lzt24" has two (three?) primary probability sources. One is almost pure "sub" x is near y data.

The other sources, however, do not do very well under sub. They are pure order-0 peaks at x=64 and 192 (vertical lines in the "raw" image), and also those strange blobs of correlation at (x/y = 64 and 192). The problem is "sub" turns those vertical lines into diagonal lines, effectively smearing them all over the probability spectrum.

A compact but full model for the lzt24 literals would be like this : <FONT COLOR=GREEN><PRE> is y (predictor) near 64 or 192 ? if so -> strongly predict x = 64 or 192 else -> predict x = y or x = 64 or 192 (weaker)

lzt99, being more heterogenous, has various sources.

"xor" takes squares to squares. This works pretty well on text.

In general, the LO correlation is easier to model than O1.

The lzt99 O1 histo in particular has lots of funny stuff. There are bunch of non-diagonal lines, indicating things like x=y/4 patterns, which is odd.

03-04-15 | LZ Match Finding Redux

Some time ago I did a study of LZ match finders. Since then I've somewhat changed my view. This will be a bit hand wavey. Previous posts :

cbloom rants 09-30-11 - String Match Results Part 5 + Conclusion
cbloom rants 11-02-11 - StringMatchTest Release
cbloom rants 09-24-12 - LZ String Matcher Decision Tree

From fast to slow :

All my fast matchers now use "cache tables". In fact I now use cache tables all the way up to my "Normal" level (default level; something like zip -7).

With cache tables you have a few primary parameters :

hash bits
hash ways
2nd hash

very fastest :
0 :
hash ways =1
2nd hash = off

1 :
hash ways = 2
2nd hash = off

2 :
hash ways = 2
2nd hash = on


hash ways = 16
2nd hash = on

The good thing about cache tables is the cpu cache coherency. You look up by the hash, and then all your possible matches are right there in one cache line. (there's an option of whether you store the first U32 of each match right there in the cache table to avoid a pointer chase to check the beginning of the match).

Cache tables are superb space-speed tradeoff up until ways hits around 16, and then they start to lose to hash-link.

Hash-link :

Hash link is still good, but can be annoying to make fast (*) and does have bad degenerate case behavior (when you have a bad hash collision, the links on that chain get overloaded with crap).

(* = you have to do dynamic amortization and shite like that which is not a big deal, but ugly; this is to handle the incompressible-but-lots-of-hash-collisions case, and to handle the super-compressible-lots-of- redundant-matches case).

The good thing about hash-link is that you are strictly walking matches in increasing offset order. This means you only need to consider longer lengths, which helps break the O(N^2) problem in practice (though not in theory). It also gives you a very easy way to use a heuristic to decide if a match is better or not. You're always doing a simple compare :

previous best match vs.
new match with
higher offset
longer length
which is a lot simpler than something like the cache table case where you see your matches in random order.

Being rather redundant : the nice thing about hash-link is that any time you find a match length, you know absolutely that you have the lowest offset occurance of that match length.

I'm not so high on Suffix Tries any more.

*if* your LZ just needs the longest length at each position, they're superb. If you actually need the best match at every position (traditional optimal parse), they're superb. eg. if you were doing LZSS with large fixed-size offsets, you just want to find the longest match all the time - boom Suffix Trie is the answer. They have no bad degenerate case, that's great.

But in practice on a modern LZ they have problems.

The main problem is that a Suffix Trie is actually quite bad at finding the lowest offset occurance of a short match. And that's a very important thing to be good at for LZ. The problem is that a proper ST with follows is doing its updates way out deep in the leaves of the tree, but the short matches are up at the root, and they are pointing at the *first* occurance of that substring. If you update all parents to the most recent pointer, you lose your O(N) completely.

(I wrote about this problem before : cbloom rants 08-22-13 - Sketch of Suffix Trie for Last Occurance )

You can do something ugly like use a suffix trie to find long matches and a hash->link with a low walk limit to find the most recent occurance of short matches. But bleh.

And my negativity about Suffix Tries also comes from another point :

Match finding is not that important. Well, there are a lot of caveats on that. On structured data (not text), with a pos-state-lastoffset coder like LZMA - match finding is not that important. Or rather, parsing is more important. Or rather, parsing is a better space-speed tradeoff.

It's way way way better to run an optimal parse with a crap match finder (even cache table with low ways) than to run a heuristic parse with great match finder. The parse is just way more important, and per CPU cost gives you way more win.

And there's another issue :

With a forward optimal parse, you can actually avoid finding matches at every position.

There are a variety of ways to get to skip ahead in a forward optimal parse :

Any time you find a very long match -
 just take it and skip ahead
 (eg. fast bytes in LZMA)

 this can reduce the N^2 penalty of a bad match finder

When you are not finding any matches -
 start taking multi-literal steps
 using something like (failedMatches>>6) heuristic

When you find a long enough rep match -
 just take it
 and this "long enough" can be much less than "fast bytes"
 eg. fb=128 for skipping normal matches
 but you can just take a rep match at length >= 8
 which occurs much more often

the net result is lots of opportunity for more of a "greedy" type of match finding in your optimal parser, where you don't need every match.

This means that good greedy-parse match finders like hash-link and Yann's MMC ( my MMC note ) become interesting again (even for optimal parsing).

03-02-15 | Oodle LZ Pareto Frontier

I made a chart.

I'm showing the "total time to load" (time to load off disk at a simulated disk speed + time to decompress). You always want lower total time to load - smaller files make the simulated load time less, faster decompression make the decompress time less.

total_time_to_load = compressed_size / disk_speed + decompress_time

It looks neatest in the form of "speedup". "speedup" is the ratio of the effective speed vs. the speed of the disk :

effective_speed = raw_size / total_time_to_load

speedup = effective_speed / disk_speed

By varying disk speed you can see the tradeoff of compression ratio vs. cpu usage that makes different compressors better in different application domains.

If we write out what speedup is :

speedup = raw_size / (compressed_size + decompress_time * disk_speed)

speedup = 1 / (1/compression_ratio + disk_speed / decompress_speed)

speedup ~= harmonic_mean( compression_ratio , decompress_speed / disk_speed )

we can see that it's a "harmonic lerp" between compression ratio on one end and decompress speed on the other end, with the simulated disk speed as lerp factor.

These charts show "speedup" vs. log of disk_speed :

(the log is log2, so 13 is a disk speed of 8192 mb/s).

On the left side, the curves go flat. At the far left (x -> -infinity, disk speed -> 0) the height of each curve is proportional to the compression ratio. So just looking at how they stack up on the far left tells you the compression ratio performance of each compressor. As you go right more, decompression speed becomes more and more important and compressed size less so.

With ham-fisted-shading of the regions where each compressor is best :

The thing I thought was interesting is that there's a very obvious Pareto frontier. If I draw a tangent across the best compressors :

Note that at the high end (right), the tangent goes from LZB to "memcpy" - not to "raw". (raw is just the time to load the raw file from disk, and we really have to compare to memcpy because all the compressors fill a buffer that's different from the IO buffer). (actually the gray line I drew on the right is not great, it should be going tangent to memcpy; it should be shaped just like each of the compressors' curves, flat on the left (compressed size dominant) and flat on the right (compress time dominant))

You can see there are gaps where these compressors don't make a complete Pareto set; the biggest gap is between LZA and LZH which is something I will address soon. (something like LZHAM goes there) And you can predict what the performance of the missing compressor should be.

It's also a neat way to test that all the compressors are good tradeoffs. If the gray line didn't make a nice smooth curve, it would mean that some compressor was not doing a good job of hitting the maximum speed for its compression level. (of course I could still have a systematic inefficiency; like quite possibly they're all 10% worse than they should be)


If instead of doing speedup vs. loading raw you do speedup vs. loading raw + memcpy, you get this :

The nice thing is the right-hand asymptotes are now constants, instead of decaying like 1/disk_speed.

So the left hand y-intercepts (disk speed -> 0) show the compression ratio, and the right hand y-intercepts side show the decompression speed (disk speed -> inf), and in between shows the tradeoff.

03-02-15 | LZ Rep-Match after Match Strategies

Tiny duh note.

When I did the Oodle LZH I made a mistake. I used a zip-style combined codeword. Values 0-255 are a literal, and 256+ contain the log2ish of length and offset. The advantage of this is that you only have one Huff table and just do one decode, then if it's a match you also fetch some raw bits. It also models length-offset correlation by putting them in the codeword together. (this scheme is missing a lot of things that you would want in a more modern high compression LZ, like pos-state patterns and so on).

Then I added "rep matches" and just stuck them in the combined codeword as special offset values. So the codeword was :

256 : literal
4*L : 4 rep matches * L length slots (L=8 or whatever = 32 codes)
O*L : O offset slots * L length slots (O=14 and L = 6 = 84 codes or whatevs)
= 256+32+84 = 372

The problem is that rep-match-0 can never occur after a match. (assuming you write matches of maximum length). Rep-match-0 is quite important, on binary/structured files it can have very high probability. By using a single codeword which contains rep-match-0 for all coding events, you are incorrectly mixing the statistics of the after match state (where rep-match-0 has zero probability) and after literal state (where rep-match-0 has high probability).

A quick look at the strategies for fixing this :

1. Just use separate statistics. Keep the same combined codeword structure, but have two entropy tables, one for after-match and one for after-literal. This would also let you code the literal-after-match as an xor literal with separate statistics for that.

Whether you do xor-lit or not, there will be a lot of shared probability information between the two entropy tables, so if you do static Huffman or ANS probability transmission, you may need to use the cross-two-tables-similary in that transmission.

In a static Huffman or ANS entropy scheme if rep-match-0 never occurs in the after-match code table, it will be given a codelen of 0 (or impossible) and won't take any code space at all. (I guess it does take a little code space unless you also explicitly special case the knowledge that it must have codelen 0 in your codelen transmitter)

This is the simplest version of the more general case :

2. Context-code the rep-match event using match history. As noted just using "after match" or "after literal" as the context is the simplest version of this, but more detailed history will also affect the rep match event. This is the natural way to fix it in an adaptive arithmetic/ANS coder which uses context coding anyway. eg. this is what LZMA does.

Here we aren't forbidding rep-match after match, we're just using the fact that it never occur to make its probability go to 0 (adaptively) and thus it winds up taking nearly zero code space. In LZMA you actually can have a rep match after match because the matches have a max length of 273, so longer matches will be written as rep matches. Ryg pointed out that after a match that's been limitted by max-length, LZMA should really consider the context for the rep-match coding to be like after-literal , not after-match.

In Oodle's LZA I write infinite match lengths, so this is simplified. I also preload the probability of rep-match in the after-match contexts to be near zero. (I actually can't preload exactly zero because I do sometimes write a rep-match after match due to annoying end-of-buffer and circular-window edge cases). Preconditioning the probability saves the cost of learning that it's near zero, which saves 10-100 bytes.

3. Use different code words.

Rather than relying on statistics, you can explicitly use different code words for the after-match and after-literal case. For example in something like an LZHuf as described above, just use a codeword in the after-match case that omits the rep0 codes, and thus has a smaller alphabet.

This is most clear in something like LZNib. LZNib has three events :

Rep Match
So naively it looks like you need to write a trinary decision at each coding (L,M,R). But in fact only two of them are ever possible :

After L - M or R
  cannot write another L because we would've just made LRL longer

After M or R - L or M
  cannot write an R because we wouldn't just made match longer

So LZNib writes the binary choices (M/R) after L and (L/M) after M or R. Because they're always binary choices, this allows LZNib to use the simple single-divider method of encoding values in bytes .

4. Use a combined code word that includes the conditioning state.

Instead of context modeling, you can always take previous events that you need context from and make a combined codeword. (eg. if you do Huffman on the 16-bit bigram literals, you get order-1 context coding on half the literals).

So we can make a combined codeword like :

(LRL 0,1,2,3+) * (rep matches , normal matches) * (lengths slots)
= 4 * (4 + 14) * 8 = 576

Which is a pretty big alphabet, but also combined length slots so you get lrl-offset-length correlation modeling as well.

In a combined codeword like this you are always writing a match, and any literals that precede it are written with an LRL (may be 0). The forbidden codes are LRL=0 and match =rep0 , so you can either just let those get zero probabilities, or explicitly remove them from the codeword to reduce the alphabet. (there are also other forbidden codes in normal LZ parses, such as low-length high-offset codes, so you would similarly remove or adjust those)

A more minimal codeword is just

(LRL 0,1+) * (rep-match-0, any other match)
= 2 * 2 = 4

which is enough to get the rep-match-0 can't occur after LRL 0 modeling. Or you can do anything between those two extremes to choose an alphabet size.

More :

04/2012 to 02/2015
06/2011 to 04/2012
01/2011 to 06/2011
10/2010 to 01/2011
01/2010 to 10/2010
01/2009 to 12/2009
10/2008 to 01/2009
08/2008 to 10/2008
03/2008 to 08/2008
11/2007 to 03/2008
07/2006 to 11/2007
12/2005 to 07/2006
06/2005 to 12/2005
01/1999 to 06/2005

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