Saturday, September 27, 2014

Counting bytes fast - little trick from FSE

 An apparently trivial and uninteresting task nonetheless received some special optimization care within FSE : counting the bytes (or 2-bytes shorts when using the U16 variant).

It seems a trivial task, and could indeed be realized by a single-line function, such as this one (assuming table is properly allocated and reset to zero) :

while (ptr<end) count[*ptr++]++;

And it works. So what's the performance of such a small loop ?
Well, when counting some random data, the loop performs at 1560 MB/s on the test system. Not bad.
(Edit : Performance numbers are measured  on a Core i5-3340M @2.7GHz configuration. Benchmark program is also freely available within the FSE project)
But wait, data is typically not random, otherwise it wouldn't be compressible. Let's use a more typical compression scenario for FSE, with a distribution ratio of 20%. With this distribution, the counting algorithm works at 1470 MB/s. Not bad, but why does it run slower ? We are starting to notice a trend here.
So let's go to the other end of the spectrum, featuring highly compressible data with a distribution ratio of 90%. How fast does the counting algorithm run on such data ? As could be guessed, speed plummets, reaching a miserable 580 MB/s.

This is a 3x performance hit, and more importantly, it makes counting now a sizable portion of the overall time to compress a block of data (let's remind FSE targets speeds of 400 MB/s overall, so if just counting costs that much, it drags the entire compression process down).

What does happen ? This is where it becomes interesting. This is an example of CPU write commit delay.

Because the algorithm writes into a table, this data can't be cached within registers. Writing to a table cell means the result must necessarily be written to memory.
Of course, this data is probably cached into L1, and a clever CPU will not suffer any delay for this first write.
The situation becomes tricky for the following byte. In the 90% distribution example, it means we have a high probability to count the same byte twice. So, when the CPU wants to add +1 to the appropriate table cell, write commit delay gets into the way. +1 means CPU has to perform both a read and then a write at this memory address. If the previous +1 is still not entirely committed, cache will make the CPU wait a bit more before delivering the data. And the impact is sensible, as measured by the benchmark.

So, how to escape this side-effect ?
A first idea is, don't read&write to the same memory address twice in a row. A proposed solution can be observed in the FSE_count() function. The core loop is (once cleaned) as follows :


The burden of counting bytes is now distributed over 4 tables. This way, when counting 2 identical consecutive bytes, they get added into 2 different memory cells, escaping write commit delay. Of course, if we have to deal with 5 or more identical consecutive bytes, write commit delay will still be there, but at least, the latency has been used counting 3 other bytes, instead of wasted.

The function is overall more complex : more tables, hence more memory to init, special casing non-multiple-of-4 input sizes, regroup all results at the end, so intuitively there is a bit more work involved in this strategy. How does it compare with the naive implementation ?

When compressing random data, FSE_count() gets 1780 MB/s, which is already slightly better than the naive strategy. But obviously, that's not the target. This is when distribution gets squeezed that it makes the most difference, with 90% distribution being counted at 1700 MB/s. Indeed, it's still being hit, but much less, and prove overall much more stable.

With an average speed > 1700MB/s, it may seem that counting is a fast enough operation. But it is still nonetheless the second contributor to overall compression time, gobbling on its own approximately 15% of budget. That's perceptible, and still a tad too much if you ask me for such a simple task. But save another great find, it's the fastest solution I could come up with.

Edit :
Should you be willing to test some new ideas for the counting algorithm, you may find it handy to get the benchmark program which produced the speed results mentioned in this article. The program is part of the "test directory" within FSE project, as a single file named fullbench.c :

Edit 2 :
Thanks to recent comments, notably from gpdNathan, and Henry Wong, a new and better reason has been provided to explain the observed delay. Its name is store-to-load forwarding. I would like to suggest here the read of the detailed explanation from Nathan Kurz, backed by his cycle-exact Likwid analysis, and the excellent article from Henry on CPU microarchitecture.
In a nutshell, while write commit delay used to be a problem, it should now be properly handled by store-cache on modern CPU. However, it introduces some new issues, related to pipeline, serial dependency and prefetching, with remarkably similar consequences, save the number of lost cycles at stake, which is quite reduced.

Edit 3 :
Nathan Kurz provided an entry which beats the best speed so far, achieving 2010 MB/s on a Core i5-3340M @ 2.7 GHz. Its entry is provided within the fullbench program (as algorithm 202), alongside a simplified version which achieves the same speed but is shorter (algorithm 201).
It's more than 10% better than the initial entry suggested in this blog, and so is definitely measurable.
Unfortunately, these functions use SSE 4.1 intrinsic functions, and therefore offer limited portability perspectives.