08-28-13 - How to Crunch

Baby is like the worst crunch ever. Anyway it's got me thinking about things I've learned about how to cope with crunch.

1. There is no end date. Never push yourself at an unsustainable level, assuming it's going to be over soon. Oh, the milestone is in two weeks, I'll just go really hard and then recover after. No no no, the end date is always moving, there's always another crunch looming, never rely on that. The proper way to crunch is to find a way to lift your output to the maximum level that you can hold for an indeterminate amount of time. Never listen to anyone telling you "it will be over on day X, let's just go all-out for that", just smile and nod and quietly know that you will have the energy to keep going if necessary.

2. Don't stop taking care of yourself. Whatever you need to do to feel okay, you need to keep doing. Don't cut it because of crunch. It really doesn't take that much time, you do have 1-2 hours to spare. I think a lot of people impose a kind of martyrdom on themselves as part of the crunch. It's not just "let's work a lot" it's "let's feel really bad". If you need to go to the gym, have a swim, have sex, do yoga, whatever it is, keep doing it. Your producers and coworkers who are all fucking stupid assholes will give you shit about it with passive aggressive digs; "ooh I'm glad our crunch hasn't cut into your workout time, none of the rest of us are doing that". Don't let them peer pressure you into being stupid.

3. Resist the peer pressure. Just decided this is worth it's own point. There's a lot of negative peer pressure in crunches. Because others are suffering, you have to also. Because others are putting in stupid long hours at very low productivity, you have to also. A classic stupid one is the next point -

4. Go home. One of the stupidest ideas that teams get in crunches is "if someone on the team is working, we should all stay for moral support". Don't be an idiot. You're going to burn out your whole team because one person was browsing the internet a month ago when they should have been working and is therefore way behind schedule? No. Everyone else GO HOME. If you aren't on the critical path, go sleep, you might be critical tomorrow. Yes the moral support is nice, and in rare cases I do advocate it (perhaps for the final push of the game if the people on the critical path are really hitting the wall), but almost never. Unfortunately as a lead you do often need to stick around if anyone on your team is there, that's the curse of the lead.

5. Sleep. As crunch goes on, lack of sleep will become a critical issue. You've got to anticipate this and start actively working on it from the beginning. That doesn't just mean making the time to lie in bed, it means preparing and thinking about how you're going to ensure you are able to get the sleep you need. Make rules for yourself and then be really diligent about it. For me a major issue is always that the stress of crunch leads to insomnia and the inability to fall asleep. For me the important rules are things like - always stop working by 10 PM in order to sleep by 12 (that means no computer at all, no emails, no nothing), no coffee after 4 PM, get some exercise in the afternoon, take a hot shower or bath at night, no watching TV in bed, etc. Really be strict about it; your sleep rules are part of your todo list, they are tasks that have to be done every day and are not something to be cut. I have occasionally fallen into the habit of using alcohol to help me fall asleep in these insomnia periods; that's a very bad idea, don't do that.

6. Be smart about what you cut out of your life. In order to make time for the work crunch you will have to sacrifice other things you do with your life. But it's easy to cut the wrong things. I already noted don't cut self care. (also don't cut showering and teeth brushing, for the love of god, you still have time for those). Do cut non-productive computer and other electronics time. Do cut anything that's similar to work but not work, anything where you are sitting inside, thinking hard, on a computer, not exercising. Do cut "todos" that are not work or urgent; stuff like house maintenace or balancing your checkbook, all that kind of stuff you just keep piling up until crunch is over. Do cut ways that you waste time that aren't really rewarding in any way (TV, shopping, whatever). Try not to cut really rewarding pleasure time, like hanging out with friends or lovers, you need to keep doing that a little bit (for me that is almost impossible in practice because I get so stressed I can't stop thinking about working for a minute, but in theory it sounds like a good idea).

7. Be healthy. A lot of people in crunch fall into the trap of loading up on sugar and caffeine, stopping exercising, generally eating badly. This might work for a few days or even weeks, but as we noted before crunch is always indeterminate, and this will fuck you badly long term. In fact crunch is the most critical time to be careful with your body. You need it to be healthy so you can push hard, in fact you should be *more* careful about healthy living than you were before crunch. It's a great time to cut out all sugary snacks, fast food, and alcohol.

08-22-13 - Sketch of Suffix Trie for Last Occurance

I don't usually like to write about algorithms that I haven't actually implemented yet, but it seems in my old age that I will not actually get around to doing lots of things that I think about, so here goes one.

I use a Suffix Trie for string matching for my LZ compressors when optimal parsing.

reminder: Suffix Tries are really the super-awesome solution, but only for the case that you are optimal parsing not greedy parsing, so you are visiting every byte, and for large windows (sliding window Suffix Tries are not awesome). see : LZ String Matcher Decision Tree (w/ links to Suffix Trie posts)

Something has always bothered me about it. Almost the entire algorithm is this sweet gem of computer science perfection with no hackiness and a perfect O(N) running time. But there's one problem.

A Suffix Trie really just gives you the longest matching substring in the window. It's not really about the *location* of that substring. In particular, the standard construction using pointers to the string that was inserted will give you the *first* occurance of each substring. For LZ compression what you want is the *last* occurance of each substring.

(I'm assuming throughout that you use path compression and your nodes have pointers into the original window. This means that each step along the original window adds one node, and that node has the pointer to the insertion location.)

In order to get the right answer, whenever you do a suffix query and find the deepest node that you match, you should then visit all children and see if any of them have a more recent pointer. Say you're at depth D, all children at depth > D are also substring matches of the same first D bytes, so those pointers are equally valid string matches, and for LZ you want the latest one.

An equivalent alternative is instead of searching all children on query, you update all parents on insertion. Any time you insert a new node, go back to all your parents and change their pointers to your current pointer, because your pointer must match them all up to their depth, and it's a larger value.

Of course this ruins the speed of the suffix trie so you can't do that.

In Oodle I use limitted parent updates to address this issue. Every time I do a query/insert (they always go together in an optimal parse, and the insert is always directly under the deepest match found), I take the current pointer and update N steps up the parent links. I tested various values of N against doing full updates and found that N=32 gave me indistinguishable compression ratios and very little speed hit.

(any fixed value of N preserves the O(N) of the suffix trie, it's just a constant multiplier). (you need to walk up to parents anyway if you want to find shorter matches at lower offsets; the normal suffix lookup just gives you the single longest match).

So anyway, that heuristic seems to work okay, but it just bothers me because everything else about the Suffix Trie is so pure with no tweak constants in it, and then there's this one hack. So, can we solve this problem exactly?

I believe so, but I don't quite see the details yet. The idea goes like this :

I want to use the "push pointer up to parents method". But I don't actually want to update all parents for each insertion. The key to being fast is that many of the nodes of the suffix trie will never be touched again, so we want to kind of virtually mark those nodes as dirty, and they can update themselves if they are ever visited, but we don't do any work if they aren't visited. (BTW by "fast" here I mean the entire parse should still be O(N) or O(NlogN) but not fall to O(N^2) which is what you get if you do full updates).

In particular in the degenerate match cases, you spend all your time way out at the leaves of the suffix trie chasing the "follows" pointer, you never go back to the root, and many of the updates overwrite each other in a trivial way. That is, you might do substring "xxaaaa" at "ptr", and then "xxaaaaa" at "ptr+1" ; the update of "ptr" back up the tree will be entirely overwrittten by the update from "ptr+1" (since it also serves as an "xxaa" match and is later), so if you just delay the update it doesn't need to be done at all.

(in the end this whole problem boils down to a very simple tree question : how do you mark a walk from a leaf back to the root with some value, such that any query along that walk will get the value, but without actually doing O(depth) work if those nodes are not touched? Though it's not really that question in general, because in order to be fast you need to use the special properties of the Suffix Trie traversal.)

My idea is to use "sentries". (this is a bit like skip-lists or something). In addition to the "parent" pointer, each node has a pointer to the preceding "sentry". Sentry steps take you >= 1 step toward root, and the step distance increases. So stepping up the sentry links might take you 1,1,2,4,.. steps towards root. eg. you reach root in log(depth) steps.

When you insert a new node, instead of walking all parents and changing them to your pointer, you walk all sentries and store your pointer as a pending update.

When you query a node, you walk to all sentries and see if any of them has a lower pointer. This effectively finds if any of your children did an update that you need to know about.

The pointer that you place in the sentry is really a "pending update" marker. It means that update needs to be applied from that node up the tree to the next sentry (ADD: I think you also need to store the range that it applies to, since a large-step range can get broken down to smaller ranges by updates). You know what branch of the tree it applies to because the pointer is the string and the string tells you what branch of the tree to follow.

The tricky bit happens when you set the pointer in the sentry node, there may be another pointer there from a previous insertion that is still pending update. You need to apply the previous pending update before you store your new pointer in the pending update slot.

Say a node contains a pending update with the pointer "a", and you come in and want to mark it with "b". You need to push the "a" update into the range that it applies to, so that you can set that node to be pending with a "b".

The key to speed is that you only need to push the "a" update where it diverges from "b". For example if the substring of "a" and "b" is the same up to a deeper sentry that contains "b" then you can just throw away the "a" pending update, the "b" update completely replaces it for that range.

Saying it all again :

You have one pointer update "a" that goes down a branch of the tree. You don't want to actually touch all those nodes, so you store it as applying to the whole range. You do a later pointer update "b" that goes down a branch that partially overlaps with the "a" branch. The part that is "a" only you want to leave as a whole range marking, and you do a range-marking for "b". You have to find the intersection of the two branches, and then the area where they overlap is again range-marked with "b" because it's newer and replaces "a". The key to speed is that you're marking big ranges of nodes, not individual nodes. My proposal for marking the ranges quickly is to use power-of-2 sentries, to mark a range of length 21 you would mark spans of length 16+4+1 kind of a thing.

Maybe some drawings are clearer. Here we insert pointer "a", and then later do a query with pointer "b" that shares some prefix with "a", and then insert "b".

The "b" update to the first sentry has to push the "a" update that was there up until the substrings diverge. The update back to the root sees that "a" and "b" are the same substring for that entire span and so simply replaces the pending update of "a" with a pending update of "b".

Let's see, finishing up.

One thing that is maybe not clear is that within the larger sentry steps the smaller steps are also there. That is, if you're at a deep leaf you walk back to the root with steps that go 1,1,2,4,8,16,32. But in that last big 32 step, that doesn't mean that's one region of 32 nodes with no other sentries. Within there are still 1,2,4 type steps. If you have to disambiguate an update within that range, it doesn't mean you have to push up all 32 nodes one by one. You look and see hey I have a divergence in this 32-long gap, so can I just step up 16 with "a" and "b" being the same? etc.

I have no idea what the actual O() of this scheme is. It feels like O(NlogN) but I certainly don't claim that it is without doing the analysis.

I haven't actually implemented this so there may be some major error in it, or it might be no speed win at all vs. always doing full updates.

Maybe there's a better way to mark tree branches lazily? Some kind of hashing of the node id? Probabilistic methods?

08-19-13 - Sketch of multi-Huffman Encoder

Simple way to do small-packet network packet compression.

Train N different huffman code sets. Encoder and decoder must have a copy of the static N code sets.

For each packet, take a histogram. Use the histogram to measure the transmitted length with each code set, and choose the smallest. Transmit the selection and then the encoding under that selection.

All the effort is in the offline training. Sketch of training :

Given a large number of training packets, do this :

for - many trials - 

select 1000 or so seed packets at random
(you want a number 4X N or so)

each of the seeds is a current hypothesis of a huffman code set
each seed has a current total histogram and codelens

for each packet in the training set -
add it to one of the seeds
the one which has the most similar histogram
one way to measure that is by counting the huffman code length

after all packets have been accumulated onto all the seeds,
start merging seeds

each seed has a cost to transmit; the size of the huffman tree
plus the data in the seed, huffman coded

merge seeds with the lowest cost to merge
(it can be negative when merging makes the total cost go down)

keep merging the best pairs until you are down to N seeds

once you have the N seeds, reclassify all the packets by lowest-cost-to-code
and rebuild the histograms for the N trees using only the new classification

those are your N huffman trees

measure the score of this trial by encoding some other training data with those N trees.

It's just k-means with random seeds and bottom-up cluster merging. Very heuristic and non-optimal but provides a starting point anyway.

The compression ratio will not be great on most data. The advantage of this scheme is that there is zero memory use per channel. The huffman trees are const and shared by all channels. For N reasonable (4-16 would be my suggestion) the total shared memory use is quite small as well (less than 64k or so).

Obviously there are many possible ways to get more compresion at the cost of more complexity and more memory use. For packets that have dword-aligned data, you might do a huffman per mod-4 byte position. For text-like stationary sources you can do order-1 huffman (that is, 256 static huffman trees, select by the previous byte), but this takes rather more const shared memory. Of course you can do multi-symbol huffman, and there are lots of ways to do that. If your data tends to be runny, an RLE transform would help. etc. I don't think any of those are worth pursuing in general, if you want more compression then just use a totally different scheme.

---

Oh yeah this also reminds me of something -

Any static huffman encoder in the vernacular style (eg. does periodic retransmission of the table, more or less optimized in the encoder (like Zip)) can be improved by keeping the last N huffman tables. That is, rather than just throwing away the history when you send a new one, keep them. Then when you do retransmission of a new table, you can just send "select table 3" or "send new table as delta from table 5".

This lets you use locally specialized tables far more often, because the cost to send a table is drastically reduced. That is, in the standard vernacular style it costs something like 150 bytes to send the new table. That means you can only get a win from sending new tables every 4k or 16k or whatever, not too often because there's big overhead. But there might be little chunks of very different data within those ranges.

For example you might have one Huffman table that only has {00,FF,7F,80} as literals (or whatever, specific to your data). Any time you encounter a run where those are the only characters, you send a "select table X" for that range, then when that range is over you go back to using the previous table for the wider range.

08-12-13 - Cuckoo Cache Tables - Failure Report

This is a report on a dead end, which I wish people would do more often.

Ever since I read about Cuckoo Hashing I thought, hmm even if it's not the win for hash tables, maybe it's a win for "cache tables" ?

(A cache table is like a hash table, but it never changes size, and inserts might overwrite previous entries (or not insert the new entry, though that's unusual). There may be only a single probe or multiple).

Let me introduce it as a progression :

1. Single hash cache table with no hash check :

This is the simplest. You hash a key and just look it up in a table to get the data. There is no check to ensure that you get the right data for your key - if you have collisions you may just get the wrong data back from lookup, and you will just stomp other people's data when you write.

Data table[HASH_SIZE];

lookup :

hash = hash_func(key);
Data & found = table[hash];

insert :

table[hash] = data;

This variant was used in LZP1 ; it's a good choice in very memory-limited situations where collisions are either unlikely or not that big a deal (eg. in data compression, a collision just means you code from the wrong statistics, it doesn't break your algorithm).

2. Single hash cache table with check :

We add some kind of hash-check value to our hash table to try to ensure that the entry we get actually was from our key :

Data table[HASH_SIZE];
int table_check[HASH_SIZE]; // obviously not actually a separate array in practice

lookup :

hash = hash_func(key);
check = alt_hash_func(key);
if ( table_check[hash] == check )
{
  Data & found = table[hash];
}

insert :

table_check[hash] = check;
table[hash] = data;

In practice, hash_func and alt_hash_func are usually actually the same hash function, and you just grab different bit ranges from it. eg. you might do a 64-bit hash func and grab the top and bottom 32 bits.

In data compression, the check hash value can be quite small (8 bits is common), because as noted above collisions are not catastrophic, so just reducing the probability of an undetected collision to 1/256 is good enough.

3. Double hash cache table with check :

Of course since you are now making two hashes, you could look up two spots in your table. We're basically running the primary hash and alt_hash above, but instead of unconditionally using only one of them as the lookup hash and one as the check, we can use either one.

Data table[HASH_SIZE];
int table_check[HASH_SIZE]; // obviously not actually a separate array in practice

lookup :

hash1 = hash_func(key);
hash2 = alt_hash_func(key);
if ( table_check[hash1] == hash2 )
{
  Data & found = table[hash1];
}
else if ( table_check[hash2] == hash1 )
{
  Data & found = table[hash2];
}

insert :

if ( quality(table[hash1]) <= quality(table[hash2]) )
{
    table_check[hash1] = hash2;
    table[hash1] = data;
}
else
{
    table_check[hash2] = hash1;
    table[hash2] = data;
}

Where we now need some kind of quality function to decide which of our two possible insertion locations to use. The simplest form of "quality" just checks if one of the slots is unused. More complex would be some kind of recency measure, or whatever is appropriate for your data. Without any quality rating you could still just use a random bool there or a round-robin, and you essentially have a hash with two ways, but where the ways are overlapping in a single table.

Note that here I'm showing the check as using the same number of bits as the primary hash, but it's not required for this type of usage, it could be fewer bits.

(also note that it's probably better just to use hash1 and hash1+1 as your two hash check locations, since it's so much better for speed, but we'll use hash1 and hash2 here as it leads more directly to the next -)

4. Double hash cache table with Cuckoo :

Once you get to #3 the possibility of running a Cuckoo is obvious.

That is, every entry has two possible hash table indices. You can move an entry to its alternate index and it will still be found. So when you go to insert a new entry, instead of overwriting, you can push what's already there to its alternate location. Lookup is as above, but insert is something like :

insert :

PushCuckoo(table,hash1);
table_check[hash1] = hash2;
table[hash1] = data;



PushCuckoo(table,hash1)
{
// I want to write at hash1; kick out whatever is there

if ( table[hash1] is empty ) return;

// move my entry from hash1 to hash2
hash2 = table_check[hash1];
PushCuckoo(hash2);

table[hash2] = table[hash1];
table_check[hash2] = hash1;

}

Now of course that's not quite right because this is a cache table, not a hash table. As written above you have a gauranteed infinite loop because cache tables are usually run with more unique insertions than slots, so PushCuckoo will keep trying to push things and never find an empty slot.

For cache tables you just want to do a small limited number of pushes (maybe 4?). Hopefully you find an empty slot to in that search, and if not you lose the entry that had the lowest "quality" in the sequence of steps you did. That is, remember the slot with lowest quality, and do all the cuckoo-pushes that precede that entry in the walk.

For example, if you have a sequence like :

I want to fill index A

hash2[A] = B
hash2[B] = C
hash2[C] = D
hash2[D] = E

none are empty

entry C has the lowest quality of A-E

Then push :

B -> C
A -> B
insert at A

That is,

table[C] = table[B]
hash2[C] = B
table[B] = table[A]
hash2[B] = A
table[A],hash2[A] = new entry

The idea is that if you have some very "high quality" entries in your cache table, they won't be destroyed by bad luck (some unimportant event which happens to have the same hash value and thus overwrites your high quality entry).

So, I have tried this and in my experiments it's not a win.

To test it I wrote a simple symbol-rank compressor. My SR is order-5-4-3-2-1 with only 4 symbols ranked in each context. (I chose an SR just because I've been working on SR for RAD recently; otherwise there's not much reason to pursue SR, it's generally not Pareto). Contexts are hashed and looked up in a cache table. I compressed enwik8. I tweaked the compressor just enough so that it's vaguely competitive with state of the art (for example, I use a very simple secondary statistics table for coding the SR rank), because otherwise it's not a legitimate test.

For Cuckoo Caching, the hash check value must be the same size as the hash table index, so that's what I've done for most fo the testing. (in all the other variants you are allowed to set the size of the check value freely). I also tested 8-bit check value for the single lookup case.

I'm interested in low memory use and really stressing the cache table, so most of the testing was at 18-bits of hash table index. Even at 20 bits the difference between Cuckoo and no-Cuckoo disappears.

The results :

18 bit hash :

Single hash ; no confirmation :
Compress : 100000000 -> 29409370 : 2.353

Single hash ; 8 bit confirmation :
Compress : 100000000 -> 25169283 : 2.014

Single hash ; hash_bits size confirmation :
Compress : 100000000 -> 25146207 : 2.012

Dual Hash ; hash_bits size confirmation :
Compress : 100000000 -> 24933453 : 1.995

Cuckoo : (max of 10 pushes)
Compress : 100000000 -> 24881931 : 1.991

Conclusion : Cuckoo Caching is not compelling for data compression. Having some confirmation hash is critical, but even 8 bits is plenty. Dual hashing is a good win over single hashing (and surprisingly there's very little speed penalty (with small cache table tables, anyway, where you are less likely to pay bad cache miss penalties)).

For the record :

variation of compression with hash table size :

two hashes, no cuckoo :

24 bit o5 hash : (24,22,20,16,8)
Compress : 100000000 -> 24532038 : 1.963
20 bit o5 hash : (20,19,18,16,8)
Compress : 100000000 -> 24622742 : 1.970
18 bit o5 hash : (18,17,17,16,8)
Compress : 100000000 -> 24933453 : 1.995

Also, unpublished result : noncuckoo-dual-hashing is almost as good with the 2nd hash kept within cache page range of the 1st hash. That is, the good thing to do is lookup at [hash1] and [hash1 + 1 + (hash2&0xF)] , or some other form of semi-random nearby probe (as opposed to doing [hash1] and [hash2] which can be quite far apart). Just doing [hash1] and [hash1+1] is not as good.

08-08-13 - Oodle Static LZP for MMO network compression

Followup to my post 05-20-13 - Thoughts on Data Compression for MMOs :

So I've tried a few things, and Oodle is now shipping with a static dictionary LZP compressor.

OodleStaticLZP uses a static dictionary and hash table which is const and shared by all network channels. The size is set by the user. There is an adaptive per-channel arithmetic coder so that the match length and literal statistics can adapt to the channel a bit (this was a big win vs. using any kind of static models).

What I found from working with MMO developers is that per-channel memory use is one of the most important issues. They want to run lots of connections on the same server, which means the limit for per-channel memory use is something like 512k. Even a zlib encoder at 400k is considered rather large. OodleStaticLZP has 182k of per-channel state.

On the server, a large static dictionary is no problem. They're running 16GB servers with 10,000 connections, they really don't care if the static dictionary is 64MB. However, that same static dictionary also has to be on the client, so the limit on how big a static dictionary you can use really comes from the client side. I suspect that something in the 8MB - 16MB range is reasonable. (and of course you can compress the static dictionary; it's only something like 2-4 MB that you have to distribute and load).

(BTW you don't necessarily need an adaptive compression state for every open channel. If some channels tend to go idle, you could drop their state. When the channel starts up again, grab a fresh state (and send a reset message to the client so it wipes its adaptive state). You could do something like have a few thousand compression states which you cycle in an LRU for an unbounded number of open channels. Of course the problem with that is if you actually get a higher number of simultaneous active connections you would be recycling states all the time, which is just the standard cache over-commit problem that causes nasty thrashing, so YMMV etc.)

This is all only for downstream traffic (server->client). The amount of upstream traffic is much less, and the packets are tiny, so it's not worth the memory cost of keeping any memory state per channel for the upstream traffic. For upstream traffic, I suggest using a static huffman encoder with a few different static huffman models; first send a byte selecting the huffman table (or uncompressed) and then the packet huffman coded.

I also tried a static dictionary / adaptive statistics LZA (LZA = LZ77+arith) (and a few other options, like a static O3 context coder and some static fixed-length string matchers, and static longer-word huffman coders, but all those were much worse than static LZA or LZP). The static dictionary LZA was much worse than the LZP.

I could conjecture that the LZP does better on static dictionaries than LZA because LZP works better when the dictionary mismatches the data. The reason being that LZP doesn't even try to code a match unless it finds a context, so it's not wasting code space for matches when they aren't useful. LZ77 is always trying to code matches, and will often find 3-byte matches just by coincidence, but the offsets will be large so they're barely a win vs literals.

But I don't think that's it. I believe the problem with static LZA is simply for an offset-coded LZ (as I was using), it's crucial to put the most useful data at low offset. That requires a very cleverly made static dictionary. You can't just put the most common short substrings at the end - you have to also be smart about how those substrings run together to make the concatenation of them also useful. That would be very interesting hard algorithm to work on, but without that work I find that static LZA is just not very good.

There are obvious alternatives to optimizing the LZA dictionary; for example you could take the static dictionary and build a suffix trie. Then instead of sending offsets into the window, forget about the original linear window and just send substring references in the suffix trie directly, ala the ancient Fiala & Green. This removes the ugly need to optimize the ordering of the linear window. But that's a big complex bowl of worms that I don't really want to go into.

Some results on some real packet data from a game developer :

downstream packets only
1605378 packets taking 595654217 bytes total
371.0 bytes per packet average


O0 static huff : 371.0 -> 233.5 average

zlib with Z_SYNC_FLUSH per packet (32k window)
zlib -z3 : 371.0 -> 121.8 average
zlib -z6 : 371.0 -> 111.8 average

OodleLZH has a 128k window
OodleLZH Fast :
371.0 -> 91.2 average

OodleLZNib Fast lznib_sw_bits=19 , lznib_ht_bits=19 : (= 512k window)
371.0 -> 90.6 average

OodleStaticLZP [mb of static dic|bits of hash]

LZP [ 4|18] : 371.0 -> 82.8 average
LZP [ 8|19] : 371.0 -> 77.6 average
LZP [16|20] : 371.0 -> 69.8 average
LZP [32|21] : 371.0 -> 59.6 average

Note of course that LZP would also benefit from dictionary optimization. Later occurances of a context replace earlier ones, so more useful strings should be later in the window. Also just getting the most useful data into the window will help compression. These results are without much effort to optimize the LZP dictionary. Clients can of course use domain-specific knowledge to help make a good dictionary.

TODOS : 1. optimization of LZP static dictionary selection. 2. mixed static-dynamic LZP with a small (32k?) per-channel sliding window.

06-18-13 - How to Work

Reminder to myself, because I've gotten out of the habit. In the months before baby I had developed a pretty good work pattern and I want it back.

There is only full-on hard work, and away-from-computer restorative time. Nothing in between.

1. When working, disable internet. No browsing around. If you have a long test run or something, usually it's not actually blocking and you can work on something else while it goes, but if it is blocking then just walk away from the computer, get your hands off the machine, do some stretching.

2. No "easing into it". This is a self-indulgence that I can easily fall into, letting myself start slowly in the morning, and before I know it it's close to noon. When you start you just fucking start.

3. If you're tired and can't keep good posture when working, stop working. Go sleep. Work again when you're fresh.

4. Whenever you aren't working, don't do anything that's similar to work. No computer time. Fuck computers, there's nothing good to see on there anyway. Just walk away. Avoid any activity that has your hands in front of your body. Try to spend time with your arms overhead and/or your hands behind your back.

5. When you feel like you need to work but can't really focus, don't substitute shitty work like paying bills or online shopping or fiddling around cleaning up code pointlessly, or whatever that makes you feel like you're doing something productive. You're not. Either fucking get over it and work anyway, or if you really can't then walk away.

6. Be defensive of your good productive time. For me it's first thing in the morning. Lots of forces will try to take this away from you; you need to hold baby, you need to commute to go to the office. No no no, this is the good work time, go work.

7. Never ever work at a laptop. Go to your workstation. If you feel your ergonomics are bad, do not spend one second working in the bad position. Fix it and then continue.

8. Set goals for the day; like "I'm going to get X done" not just "I'm going to work on X for a while" which can easily laze into just poking at X without making much progress.

9. When you decide to stop working for the day, be *done*. No more touching the computer. Don't extend your work hours into your evening with pointless trickles of super-low-productivity work. This is easier if you don't use any portable computing device, so just step away from the computer and that's it.

10. Avoid emotional disturbances. Something like checking email in the morning should be benign, but if there's a 10% chance of it makes you pissed off, that's a big negative because it lingers as a distraction for a while. I've basically stopped reading any news, and I think it's a big life +EV and certainly productivity +EV.

05-20-13 - Thoughts on Data Compression for MMOs

I've been thinking about this a bit and thought I'd scribble some ideas publicly. (MMO = not necessarily just MMOs but any central game server with a very large number of clients, that cares about total bandwidth).

The situation is roughly this : you have a server and many clients (let's say 10k clients per server just to be concrete). Data is mostly sent server->client , not very much is client->server. Let's say 10k bytes per second per channel from server->client, and only 1k bytes per second from client->server. So the total data rate from the server is high (100 MB/s) but the data rate on any one channel is low. The server must send packets more than once per second for latency reasons; let's say 10 times per second, so packets are only 1k on average; server sends 100k packets/second. You don't want the compressor to add any delay by buffering up packets.

I'm going to assume that you're using something like TCP so you have gauranteed packet order and no loss, so that you can use previous packets from any given channel as encoder history on that channel. If you do have an error in a connection you have to reset the encoder.

This is a rather unusual situation for data compression, and the standard LZ77 solutions don't work great. I'm going to talk only about the server->client transmission for now; you might use a completely different algorithm for the other direction. Some properties of this situation :

1. You care more about encode time than decode time. CPU time on the server is one of the primary limiting factors. The client machine has almost no compression work to do, so decode time could be quite slow.

2. Per-call encode time is very important (not just per-byte time). Packets are small and you're doing lots of them (100k packets/sec), so you can't afford long startup/shutdown times for the encoder. This is mostly just an annoyance for coding, it means you have to be really careful about your function setup code and such.

3. Memory use on the server is a bit limited. Say you allow 4 GB for encoder states; that's only 400k per client. (this is assuming that you're doing per-client encoder state, which is certainly not the only choice).

4. Cache misses are much worse than a normal compression encoder scenario. Say you have something like a 256k hash table to accelerate match finding. Normally when you're compressing you get that whole table into L2 so your hash lookups are in cache. In this scenario you're jumping from one state to another all the time, so you must assume that every memory lookup is a cache miss.

5. The standard LZ77 thing of not allowing matches at the beginning or end is rather more of a penalty. In general all those inefficiencies that you normally have on tiny buffers are more important than usual.

6. Because clients can be added at any time and connections can be reset, encoder init/reset time can't be very long. This is another reason aside from memory use that encoder state must be small.

7. The character of the data being sent doesn't really vary much from client to client. This is one way in which this scenario differs from a normal web server type of situation (in which case, different clients might be receiving vastly different types of data). The character of the data can change from packet to packet; there are sort of a few different modes of the data and the stream switches between then, but it's not like one client is usually receiving text and another one is receiving images. They're all generally receiving bit-packed 3d positions and the same type of thing.

And now some rambling about what encoder you might use that suits this scenario :

A. It's not clear that adaptive encoding is a win here. You have to do the comparison with CPU use held constant, if you just compare an encoder running adaptive vs the same encoder with a static model, that's not fair, because the static model can be so much faster you should use a more sophisticated encoder. The static model can also use vastly more memory. Maybe not a whole 4G, but a lot more than 400k.

B. LZ77 is not great here. The reason we love LZ77 is the fast, simple decoder. We don't really care about that here. An LZP or ROLZ variant would be better, that has a slightly slower and more memory-hungry decoder, but a simpler/faster encoder.

C. There are some semi-static options. Perhaps a static match dictionary with something like LZP, and then an adaptive simple context model per channel. That makes the per-channel adaptive part small in memory, but still allows some local adaptation for packets of different character. Another option would be a switching static-model scheme. Do something like train 4 different static models for different packet types, and send 2 bits to pick the model then encode the packet with that static model.

D. Static context mixing is kind of appealing. You can have static hash tables and a static mixing scheme, which eliminates a lot of the slowness of CM. Perhaps the order-0 model is adaptive per channel, and perhaps the secondary-statistics table is adaptive per channel. Hitting 100 MB/s might still be a challenge, but I think it's possible. One nice thing about CM here is that it can have the idea of packets of different character implicit in the model.

E. For static-dictionary LZ, the normal linear offset encoding doesn't really make a lot of sense. Sure, you could try to optimize a dictionary by laying out the data in it such that more common data is at lower offsets, but that seems like a nasty indirect way of getting at the solution. Off the top of my head, it seems like you could use something like an LZFG encoding. That is, make a Suffix Trie and then send match references as node or leaf indexes; leaves all have equal probability, nodes have a child count which is proportional to their probability (relative to siblings).

F. Surely the ideal solution is a blended static/dynamic coder. That is, you have some large trained static model (like a CM or PPM model, or a big static dictionary for LZ77) and then you also run a local adaptive model in a circular window for each channel. Then you compressing using a mix of the two models. There are various options on how to do this. For LZ77 you might send 0-64k offsets in the local adaptive window, and then 64k-4M offsets as indexes into the static dictionary. Or you could more explicitly code a selector bit to pick one of the two and then an offset. For CM it's most natural, you just mix the result of the static model and the local adaptive model.

G. What is not awesome is model preconditioning (and it's what most people do, because it's the only thing available with off-the-shelf compressors like zlib or whatever). Model precondition means taking an adaptive coder and initially loading its model (eg. an LZ dictionary) from some static data; then you encode packets adaptively. This might actually offer excellent compression, but it has bad channel startup time, and high memory use per channel, and it doesn't allow you to use more efficient algorithms that are possible with fully static models (such as different types of data structures that provide fast lookup but not fast update).

I believe if you're doing UDP or some other unreliable packet scheme, then static-model compression is the only way to go (rather than trying to track the different received and transmitted states to use for a dynamic model). Also if clients are very frequently joining and leaving or moving servers, then they will never build up much channel history, so static model is the way to go there as well. If streams vary vastly in size, like if they're usually less than 1k but occasionally you do large 1M+ transfers (like for content serving as opposed to updating game state) you would use a totally different scheme for the large transfers.

I'd like to do some tests. If you work on an MMO or similar game situation and can give me some real-world test data, please be in touch.

05-08-13 - A Lock Free Weak Reference Table

It's very easy (almost trivial (*)) to make the table-based {index/guid} style of weak reference lock free.

(* = obviously not trivial if you're trying to minimize the memory ordering constraints, as evidenced by the revisions to this post that were required; it is trivial if you just make everything seq_cst)

Previous writings on this topic :

Smart & Weak Pointers - valuable tools for games - 03-27-04
cbloom rants 03-22-08 - 6
cbloom rants 07-05-10 - Counterpoint 2
cbloom rants 08-01-11 - A game threading model
cbloom rants 03-05-12 - Oodle Handle Table

The primary ops conceptually are :

Add object to table; gives it a WeakRef id

WeakRef -> OwningRef  (might be null)

OwningRef -> naked pointer

OwningRef construct/destruct = ref count inc/dec

The full code is in here : cbliblf.zip , but you can get a taste for how it works from the ref count maintenance code :

    // IncRef looks up the weak reference; returns null if lost
    //   (this is the only way to resolve a weak reference)
    Referable * IncRef( handle_type h )
    {
        handle_type index = handle_get_index(h);
        LF_OS_ASSERT( index >= 0 && index < c_num_slots );
        Slot * s = &s_slots[index];

        handle_type guid = handle_get_guid(h);

        // this is just an atomic inc of state
        //  but checking guid each time to check that we haven't lost this slot
        handle_type state = s->m_state.load(mo_acquire);
        for(;;)
        {
            if ( state_get_guid(state) != guid )
                return NULL;
            // assert refcount isn't hitting max
            LF_OS_ASSERT( state_get_refcount(state) < state_max_refcount );
            handle_type incstate = state+1;
            if ( s->m_state.compare_exchange_weak(state,incstate,mo_acq_rel,mo_acquire) )
            {
                // did the ref inc
                return s->m_ptr;
            }
            // state was reloaded, loop
        }
    }

    // IncRefRelaxed can be used when you know a ref is held
    //  so there's no chance of the object being gone
    void IncRefRelaxed( handle_type h )
    {
        handle_type index = handle_get_index(h);
        LF_OS_ASSERT( index >= 0 && index < c_num_slots );
        Slot * s = &s_slots[index];
        
        handle_type state_prev = s->m_state.fetch_add(1,mo_relaxed);
        state_prev;
        // make sure we were used correctly :
        LF_OS_ASSERT( handle_get_guid(h) == state_get_guid(state_prev) );
        LF_OS_ASSERT( state_get_refcount(state_prev) >= 0 );
        LF_OS_ASSERT( state_get_refcount(state_prev) < state_max_refcount );
    }

    // DecRef
    void DecRef( handle_type h )
    {
        handle_type index = handle_get_index(h);
        LF_OS_ASSERT( index >= 0 && index < c_num_slots );
        Slot * s = &s_slots[index];
        
        // no need to check guid because I must own a ref
        handle_type state_prev = s->m_state.fetch_add((handle_type)-1,mo_release);
        LF_OS_ASSERT( handle_get_guid(h) == state_get_guid(state_prev) );
        LF_OS_ASSERT( state_get_refcount(state_prev) >= 1 );
        if ( state_get_refcount(state_prev) == 1 )
        {
            // I took refcount to 0
            //  slot is not actually freed yet; someone else could IncRef right now
            //  the slot becomes inaccessible to weak refs when I inc guid :
            // try to inc guid with refcount at 0 :
            handle_type old_guid = handle_get_guid(h);
            handle_type old_state = make_state(old_guid,0); // == state_prev-1
            handle_type new_state = make_state(old_guid+1,0); // == new_state + (1<<handle_guid_shift);
  
            if ( s->m_state($).compare_exchange_strong(old_state,new_state,mo_acq_rel,mo_relaxed) )
            {
                // I released the slot
                // cmpx provides the acquire barrier for the free :
                FreeSlot(s);
                return;
            }
            // somebody else mucked with me
        }
    }

The maintenance of ref counts only requires relaxed atomic increment & release atomic decrement (except when the pointed-at object is initially made and finally destroyed, then some more work is required). Even just the relaxed atomic incs could get expensive if you did a ton of them, but my philosophy for how to use this kind of system is that you inc & dec refs as rarely as possible. The key thing is that you don't write functions that take owning refs as arguments, like :

void bad_function( OwningRefT<Thingy> sptr )
{
    more_bad_funcs(sptr);
}

void Stuff::bad_caller()
{
    OwningRefT<thingy> sptr( m_weakRef );
    if ( sptr != NULL )
    {
        bad_function(sptr);
    }
}

hence doing lots of inc & decs on refs all over the code. Instead you write all your code with naked pointers, and only use the smart pointers where they are needed to ensure ownership for the lifetime of usage. eg. :

void good_function( Thing * ptr )
{
    more_good_funcs(ptr);
}

void Stuff::bad_caller()
{
    OwningRefT<thingy> sptr( m_weakRef );
    Thingy * ptr = sptr.GetPtr();
    if ( ptr != NULL )
    {
        good_function(ptr);
    }
}

If you like formal rules, they're something like this :

1. All stored variables are either OwningRef or WeakRef , depending on whether it's
an "I own this" or "I see this" relationship.  Never store a naked pointer.

2. All variables in function call args are naked pointers, as are variables on the
stack and temp work variables, when possible.

3. WeakRef to pointer resolution is only provided as WeakRef -> OwningRef.  Naked pointers
are only retrieved from OwningRefs.

And obviously there are lots of enchancements to the system that are possible. A major one that I recommend is to put more information in the reference table state word. If you use a 32-bit weak reference handle, and a 64-bit state word, then you have 32-bits of extra space that you can check for free with the weak reference resolution. You could put some mutex bits in there (or an rwlock) so that the state contains the lock for the object, but I'm not sure that is a big win (the only advantage of having the lock built into the state is that you could atomically get a lock and inc refcount in a single op). A better usage is to put some object information in there that can be retrieved without chasing the pointer and inc'ing the ref and so on.

For example in Oodle I store the status of the object in the state table. (Oodle status is a progression through Invalid->Pending->Done/Error). That way I can take a weak ref and query status in one atomic load. I also store some lock bits, and you aren't allowed to get back naked pointers unless you have a lock on them.

The code for the weak ref table is now in the cbliblf.zip that I made for the last post. Download : cbliblf.zip

( The old cblib has a non-LF weak reference table that's similar for comparison. It's also more developed with helpers and fancier templates and such that could be ported to this version. Download : cblib.zip )

ADDENDUM : alternative DecRef that uses CAS instead of atomic decrement. Removes the two-atomic free path. Platforms that implement atomic add as a CAS loop should probably just use this form. Platforms that have true atomic add should use the previously posted version.

    // DecRef
    void DecRef( handle_type h )
    {
        handle_type index = handle_get_index(h);
        LF_OS_ASSERT( index >= 0 && index < c_num_slots );
        Slot * s = &s_slots[index];
        
        // no need to check guid because I must own a ref
        handle_type state_prev = s->m_state($).load(mo_relaxed);
        
        handle_type old_guid  = handle_get_guid(h);

        for(;;)
        {
            // I haven't done my dec yet, guid must still match :
            LF_OS_ASSERT( state_get_guid(state_prev) == old_guid );
            // check current refcount :
            handle_type state_prev_rc = state_get_refcount(state_prev);
            LF_OS_ASSERT( state_prev_rc >= 1 );
            if ( state_prev_rc == 1 )
            {
                // I'm taking refcount to 0
                // also inc guid, which releases the slot :
                handle_type new_state = make_state(old_guid+1,0);

                if ( s->m_state($).compare_exchange_weak(state_prev,new_state,mo_acq_rel,mo_relaxed) )
                {
                    // I released the slot
                    // cmpx provides the acquire barrier for the free :
                    FreeSlot(s);
                    return;
                }
            }
            else
            {
                // this is just a decrement
                // but have to do it as a CAS to ensure state_prev_rc doesn't change on us
                handle_type new_state = state_prev-1;
                LF_OS_ASSERT( new_state == make_state(old_guid,  state_prev_rc-1) );
                
                if ( s->m_state($).compare_exchange_weak(state_prev,new_state,mo_release,mo_relaxed) )
                {
                    // I dec'ed a ref
                    return;
                }
            }
        }
    }

05-02-13 - Simple C++0x style LF structs and adapter for x86-Windows

I've seen a lot of lockfree libraries out there that are total crap. Really weird non-standard ways of doing things, or overly huge and complex.

I thought I'd make a super simple one in the correct modern style. Download : cbliblf.zip

(If you want a big fully functional much-more-complete library, Intel TBB is the best I've seen. The problem with TBB is that it's huge and entangled, and the license is not clearly free for all use).

There are two pieces here :

"cblibCpp0x.h" provides atomic and such in C++0x style for MSVC/Windows/x86 compilers that don't have real C++0x yet. I have made zero attempt to make this header syntatically identical to C++0x, there are various intentional and unintentional differences.

"cblibLF.h" provides some simple lockfree utilities (mostly queues) built on C++0x atomics.

"cblibCpp0x.h" is kind of by design not at all portable. "cblibLF.h" should be portable to any C++0x platform.

WARNING : this stuff is not super well tested because it's not what I use in Oodle. I've mostly copy-pasted this from my Relacy test code, so it should be pretty strong but there may have been some copy-paste errors.

ADDENDUM : In case it's not clear, you do not *want* to use "cblibCpp0x.h". You want to use real Cpp0x atomics provided by your compiler. This is a temporary band-aid so that people like me who use old compilers can get a cpp0x stand-in, so that they can do work using the modern syntax. If you're on a gcc platform that has the __atomic extensions but not C1X, use that.

You should be able to take any of the C++0x-style lockfree code I've posted over the years and use it with "cblibCpp0x.h" , perhaps with some minor syntactic fixes. eg. you could take the fastsemaphore wrapper and put the "semaphore" from "cblibCpp0x.h" in there as the base semaphore.

Here's an example of what the objects in "cblibLF.h" look like :

//=================================================================         
// spsc fifo
//  lock free for single producer, single consumer
//  requires an allocator
//  and a dummy node so the fifo is never empty
template <typename t_data>
struct lf_spsc_fifo_t
{
public:

    lf_spsc_fifo_t()
    {
        // initialize with one dummy node :
        node * dummy = new node;
        m_head = dummy;
        m_tail = dummy;
    }

    ~lf_spsc_fifo_t()
    {
        // should be one node left :
        LF_OS_ASSERT( m_head == m_tail );
        delete m_head;
    }

    void push(const t_data & data)
    {
        node * n = new node(data);
        // n->next == NULL from constructor
        m_head->next.store(n, memory_order_release); 
        m_head = n;
    }

    // returns true if a node was popped
    //  fills *pdata only if the return value is true
    bool pop(t_data * pdata)
    {
        // we're going to take the data from m_tail->next
        //  and free m_tail
        node* t = m_tail;
        node* n = t->next.load(memory_order_acquire);
        if ( n == NULL )
            return false;
        *pdata = n->data; // could be a swap
        m_tail = n;
        delete t;
        return true;
    }

private:

    struct node
    {
        atomic<node *>      next;
        nonatomic<t_data>   data;
        
        node() : next(NULL) { }
        node(const t_data & d) : next(NULL), data(d) { }
    };

    // head and tail are owned by separate threads,
    //  make sure there's no false sharing :
    nonatomic<node *>   m_head;
    char                m_pad[LF_OS_CACHE_LINE_SIZE];
    nonatomic<node *>   m_tail;
};

Download : cbliblf.zip

04-30-13 - Packing Values in Bits - Flat Codes

One of the very simplest forms of packing values in bits is simply to store a value with non-power-of-2 range and all values of equal probability.

You have a value that's in [0,N). Ideally all code lengths would be the same ( log2(N) ) which is fractional for N not a power of 2. With just bit output, we can't write fractional bits, so we will lose some efficiency. But how much exactly?

You can of course trivially write a symbol in [0,N) by using log2ceil(N) bits. That's just going up to the next integer bit count. But you're wasting values in there, so you can take each wasted value and use it to reduce the length of a code that you need. eg. for N = 5 , start with log2ceil(N) bits :

0 : 000
1 : 001
2 : 010
3 : 011
4 : 100
x : 101
x : 110
x : 111

The first five codes are used for our values, and the last three are wasted. Rearrange to interleave the wasted codewords :

0 : 000
x : 001
1 : 010
x : 011
2 : 100
x : 101
3 : 110
4 : 111

now since we have adjacent codes where one is used and one is not used, we can reduce the length of those codes and still have a prefix code. That is, if we see the two bits "00" we know that it must always be a value of 0, because "001" is wasted. So simply don't send the third bit in that case :

0 : 00
1 : 01
2 : 10
3 : 110
4 : 111

(this is a general way of constructing shorter prefix codes when you have wasted values). You can see that the number of wasted values we had at the top is the number of codes that can be shortened by one bit.

A flat code is written thusly :

void OutputFlat(int sym, int N)
{
    ASSERT( N >= 2 && sym >= 0 && sym < N );

    int B = intlog2ceil(N);
    int T = (1<<B) - N;
    // T is the number of "wasted values"
    if ( sym < T )
    {
        // write in B-1 bits
        PutBits(sym, B-1);
    }
    else
    {
        // write in B bits
        // push value up by T
        PutBits(sym+T, B);
    }
}

int InputFlat(int sym,int N)
{
    ASSERT( N >= 2 && sym >= 0 && sym < N );

    int B = intlog2ceil(N);
    int T = (1<<B) - N;

    int sym = GetBits(B-1);
    if ( sym < T )
    {
        return sym;
    }
    else
    {
        // need one more bit :
        int ret = (sym<<1) - T + GetBits(1);        
        return ret;
    }
}

That is, we write (T) values in (B-1) bits, and (N-T) in (B) bits. The intlog2ceil can be slow, so in practice you would want to precompute that or pass it in as a parameter.

So, what is the loss vs. ideal, and where does it occur? Let's work it out :

H = log2(N)  is the ideal (fractional) entropy

N is in (2^(B-1),2^B]
so H is in (B-1,B]

The number of bits written by the flat code is :

L = ( T * (B-1) + (N-T) * B ) / N

with T = 2^B - N

Let's set

N = f * 2^B

with f in (0.5,1] our fractional position in the range.

so T = 2^B * (1 - f)

At f = 0.5 and 1.0 there's no loss, so there must be a maximum in that interval.

Doing some simplifying :

L = (T * (B-1) + (N-T) * B)/N
L = (T * B - T + N*B - T * B)/N
L = ( N*B - T)/N = B - T/N
T/N = (1-f)/f = (1/f) - 1
L = B - (1/f) + 1

The excess bits is :

E = L - H

H = log2(N) = log2( f * 2^B ) = B + log2(f)

E = (B - (1/f) + 1) - (B + log2(f))
E = 1 - (1/f) - log2(f)

so find the maximum of E by taking a derivative :

d/df(E) = 0
d/df(E) = 1/f^2 - (1/f)/ln2
1/f^2 = (1/f)/ln2
1/f = 1/ln(2)
f = ln(2)
f = 0.6931472...

and at that spot the excess is :

E = 1 - (1/ln2) - ln(ln2)/ln2
E = 0.08607133...

The worst case is 8.6% of a bit per symbol excess. The worst case appears periodically, once for each power of two.

The actual excess bits output for some low N's :

The worst case actually occurs as N->large, because at higher N you can get f closer to that worst case fraction (ln(2)). At lower N, the integer steps mean you miss the worst case and so waste less. This is perhaps a bit surprising, you might think that the worst case would be at something like N = 3.

In fact for N = 3 :

H = l2(3) = 1.584962 ...

L = average length written by OutputFlat

L = (1+2+2)/3 = 1.66666...

E = L - H = 0.08170421...

(obviously if you measure the loss as a percentage of the output length, the worst case is at N=3, and there it's 5.155% of the entropy).