other little things

So it turned out i was quite wrong on the prefix sorted table thing, it can be done in less memory and more efficiently and there's a whole field of research newly reinvigorated by search engines and genome stitching and modern hardware capabilities. But for a casual observer most of it is a bit complex for a weekend hack and needs some pretty messy pointer-filled code so doesn't translate well to Java; I tried a few things but gave up on that idea since my naive approaches weren't much worse in speed to the code i could find on the sort of data i'm playing with. If it was that important I would just use some C, but it really isn't. But like most of this stuff its good to know it's out there should I actually need it some day. And the maven stuff everyone in java-land insists on now using was giving me the utter shits too; e.g. oh, lets just import a whole fecking platform just so we can use one trivial one-line function that just calls java.util.* anyway, ... once. Why why?

Then I got a bit side-tracked in trying to re-use the system primitive array sort to sort sub-strings by sorting them 4-bytes at a time packed into a long. The lower 31 bits are the offset into the array (i.e. base pointer) and the next 32 bits are 4 bytes to sort in order with truncation handled using 0 padding. As it only uses 63 bits I can use a signed long sort to sort 4 bytes of string at a time. This gets sorted then ranges with a common prefix are recursively sorted again, and so on. Managed about a 2x speedup over a straight memcmp sort; which is probably nothing to sneeze at but not really enough here. Then I tried 8-bit radix sorting the first pass: gains a little bit more. And then a 16-bit radix first pass which was over 2x speed-up again, although by this time I didn't feel like writing multiple whole sorts just to test ideas and they still have undesirable worst-case behaviour. Actually a 6x speedup (if the code is functionally correct, which i didn't get to checking) is pretty decent: but it's delving into territory where far better and more scalable algorithms for the problem exist and i already have one that works well enough for me as a (better than) "70% solution".

Sorting is something i poke at every now just for interests sake so i may still revisit it later. I can't even remember if i've done radix sorting before, but i probably should have given it is parallelisable in a massively-parallel sense.

I also had the headache of trying to troll through a big C++ library yesterday trying to understand something. Ugh, it's like reading through a whole C application written using pre-processor macros, one for every case imaginable but few actually ever realised. Apparently this is a desirable thing in C++. But yeah, abstraction isn't really about hiding so much detail you can't work out what something is doing without intimately knowing everything about it; that's pretty much the opposite. And those compile times. And those error messages. With all that i'm suprised how much work the language and compiler still forces on the developer, and yet it is trivial to write incorrect code. But I digress, I had enough of that yesterday.

Limits

I did have another idea for the string matcher either this morning or yesterday which I finally just remembered and tried: just truncate the maximum hash bucket length to some fixed maximum. It drops the match rate (particularly for popular symbols) and thus the compression rate but it drastically improves run-time speed and worst-case behaviour. Saves some memory too. Ok I guess everyone else does this already but I tried to get by without it; but alas could not. Because i'm using a bucket-based hash table i've got some more options on how i deal with it; i don't just have to throw them away.

Actually the way i implemented it I think it has some interesting side-effects together with the new delta format; common prefixes are updated more often and this more likely to be close by or in the exact-address table so the address compression works better. Initially I tried replacing a random record with the new entry: this is usually a good idea for mathematical reasons "I recognise but don't completely understand", but generating the random numbers proved to be too expensive for short files. So I just have a rolling index shared across all records which is super-cheap and should be relatively random in a local sense and merely practical in all others.

So here's some variations and times for my two current format encoders on the kjv text - on the smaller files it doesn't make much difference. The limit is (2^n - 1) because i store the chain length/insertion point in the first index and i double the size each time i grow it. I included one result when using random replacement: as suggested it does improve the compression - even if only very slightly! Here the cost is somewhat hidden by the string compares. The dez home page has the benchmarks of the other software i've tried; they are not even remotely close in terms of output size even related to the fastest and "worst" below.

                   time                  size
             dez-1      dez-2*      dez-1    dez-2
limit
3            0.232623   0.319473    2596997  1970223
7            0.334969   0.433130    2328817  1831470
15           0.429424   0.521525    2157175  1757288
15 (random)  0.572432   0.666268    2156093  1756776
31           0.545488   0.626991    2028280  1702969
63           0.732696   0.822705    1934709  1659212

unlimited    9.724143   9.853381    1731250  1539501

     empty string to KJV bible "delta" encode

* actually i'm going to just call dez-2 `dez-1'.

The unlimited case is a bit (well 70%!) faster than previous because I added a small optimisation to the string length matcher: it first checks to see if the next character after the current best length is a match, if not it doesn't bother scanning the rest of the string at all. But still, whether 10s or 17s, it's still pretty shit (the main issue with this text is it is indented, so 25K+ substrings begin with newline+several spaces and they all end up in the same hash bucket).

For a given limit both format encoders are being fed an identical list of edits, which shows just how much better the second format is and why the first will vanish next time I do a code-drop.