jix

"In doing that they usually jump to the most uncharitable, horrible reasons they can imagine for why we might have done so."

So you do understand why one wouldn't want to deal with a significant part of the user base here given that they behave in such ways, and thus why one might want to avoid any traffic coming from here, but feel that it's not your job to deal with those users, because then their behavior would affect you? I really hope you'll reflect on that...

The paper where they introduce subsumption is "Michael Codish, Luís Cruz-Filipe, Michael Frank, and Peter Schneider-Kamp. 2016. Sorting nine inputs requires twenty-five comparisons. Journal of Computer and System Sciences 82, 3 (May 2016), 551–563." and I just realized that I lost the actual citation while editing my blog post, fixed that now.

Those are interesting questions! For example generating and looking at all networks of optimal size which have distinct circuits (assuming unlabeled inputs, so that rearranging those doesn't count as distinct) is something I still want to do at some point. Extending my search to produce this wouldn't be too complicated... but I haven't found the time for this so far.

I replied to your other comment :)

Interesting :)

Codish et al. have a background in SAT solving, which is somewhat related to logic programming. In SAT solving subsumption of clauses usually doesn't involve any substitutions. That's the notion of subsumption I was familiar with before reading Codish et al. Given that, extending subsumption to handle the symmetries inherent in the problem felt like a natural extension as it maintains all the relevant properties, but I also wouldn't be surprised if this was inspired by ILP.

Computing s(11) and s(12) together took just below 5 hours on a 24 core server, but it also required almost 200 GB of RAM. Verifying the computation took about 3 days in total on the same server.

Computing s(9) and s(10) with the same approach takes under a second and a few megabytes, so while this is much faster than the previous approach (the one I described in the blog post) it still grows very quickly.

I don't know exactly how much s(13) would take, but extrapolating from the number I have for smaller n, my estimate is that it would take over 20000 TB of RAM and take proportionally longer. Distributing the computation would also slow it down a lot as all cores are doing frequent random accesses to all the used memory.

So s(12) seems to be the end of what's possible with this exact approach, but I think some of the theory I developed might be usable beyond.

Author here, in case anyone has questions

I haven't read everything, but it does contain a section about something I'm quite familiar with:

The article says "We compute the hashcode of the entire graph by hashing the multiset of WL labels. With one round, we’re just comparing the degree histogram. The more rounds we add, the more likely we are to detect a symmetry-breaker:", which is not correct.

Repeatedly re-labeling a graph by assigning a unique label to each unique neighborhood histogram, until the corresponding partition reaches a fixpoint would compute the one-dimensional Weisfeiler-Lehman refinement. But there are many non-isomorphic graphs that you cannot tell apart with this! It cannot tell apart any two regular graphs of the same size and degree, and you can easily run into those in practice.

Even if the code would repeat this process until a fixpoint is reached, instead of hoping that 10 iterations suffice, non-isomorphic graphs that result in the same WL partition means that "The more rounds we add, the more likely we are to detect a symmetry-breaker" doesn't hold.

There are also more efficient ways of computing this.

Now apart from one-dimensional WL refinement, where you compute a label from the neighborhood of individual vertices, there is also k-dimensional WL refinement, which very roughly speaking looks at all length k sequences of vertices and computes statistics for those. Here it is true that as k reaches |V| you will be able to tell apart any two non-isomorphic graphs, but only because if k=|V| you're trying all permutations! There is no fixed k that will tell apart any two graphs.

If you want to perform graph isomorphism tests in practice, I'd recommend Traces: http://pallini.di.uniroma1.it/

It combines two-dimensional WL refinement with a recursive search to tell apart all graphs, while using computational group theory algorithms to efficiently prune the search space for graphs with many symmetries. It is very efficient in practice.

It is described in https://arxiv.org/abs/0804.4881 (also linked from the website) and also has references for everything I wrote (modulo any mistakes I made while summarizing).

That's just defining the term. AFAICT the law only says that an employee has a right to receive fair compensation for a technical improvement in some cases. It explicitly says that apart from that, procedures covering technical improvements are a matter of contracts: https://www.gesetze-im-internet.de/arbnerfg/__20.html

For this project I don't really have to say much about the rust side of it. There were no surprises. The only thing special I can think of is the excellent cross-compiling support. That came in handy as I had to produce windows binaries for the 3D artists.

I've never had a Mega Drive before working on this, so I wasn't really familiar with a lot of its games.

I took a quick look at F1 just now though. The way it makes use of the nametable and patterns is very similar to what I do. There are precomputed fully solid patterns at a fixed location and the non-solid patterns seem to be bump allocated.

It makes use of both layers though, drawing the street on one and everything else on the other. I think it uses per scanline scrolling to apply correct perspective to the street.

I can't say anything about how it actually renders into the tile map for now. That would require a lot more than looking at the VDP (graphics chip) debugger in an emulator.

Thanks for writing this. I didn't really expect that much attention, so I kind of assumed most people reading it are at least somewhat familiar with the graphics hardware of that area. I shouldn't have assumed that :)

There weren't really any dead ends. Mostly because I started with a very simple naive way to draw polygons and improved it incrementally. I didn't implement all those steps, but convinced myself that they would work. I started with a generic plot-individual-pixels-into-tilemap routine. Going by tile-rows and columns with special casing solid tiles came next. That required "convexity" in x direction but at that point I was only thinking of triangles. Then I noticed that avoiding overdraw and working with a tesselation of the screen is probably faster. A that point I also extended it from triangles to polygons. While fleshing out the details of everything I noticed that I don't have to be exact for right-side edges if I draw the polygons in the right order.

There actually was an extension I did, that was scrapped because it just didn't look good. At some point there was support for dithering. That helps with the low color precision of the Mega Drive (3-bit/channel). It only supported 50% checkerboard dither though, which looked odd when animated. I toyed with some ideas on how to improve upon that and discussed them within our demo group, but in the end the decision was to not use dithering.

For the Mega Drive/Genesis the framerate depends on the region, matching the local video standard. The European Mega Drive uses PAL with 50Hz.

As the biggest part (but not all) of the demoscene is based in Europe, most demos target PAL hardware. The same is true for our demo group. NTSC ports can be very difficult if not impossible as PAL often does have a slight advantage in CPU cycles per frame. This is also the case on the Mega Drive.

Porting the polygon renderer shouldn't be a problem as it renders in an off-screen CPU RAM buffer. In the worst case it would have to skip more frames, having a lower effective framerate.

A lot of the other effects have very critical timing though. I've been told that porting some of them to NTSC is just impossible.

Author here, happy to answer any questions you might have.

No. Apart from the mapper chip used to address 8MB of ROM this demo requires no additional chips on the cartridge. Everything is done by the 68k CPU (running the effects) and the z80 CPU (running the sound engine).

Not all everdrive flash carts support the mapper/rom size our demo uses (the SSF2 mapper with an 8MB rom). The included nfo file lists some supported flash carts.

I'm one of the coders who worked on the Overdrive 2 demo (although not on the reverse engineering that resulted in this document). We're going to release more follow-ups about the development of the demo.

I'm currently working on a write-up of the polygon to tile drawing routine used for the fullscreen 3D scenes.

I'm not sure about the time frame yet, but they will be posted at http://www.pouet.net/prod.php?which=69648 and/or http://www.pouet.net/topic.php?which=11035.

It does. It supports mingw on windows as well as cross-compiling from linux using cargo (rust's package manager and build tool). Installing mingw-w64 from my distribution's package manager and telling cargo where to find its linker and assembler was all I needed to cross compile stand alone windows binaries of some command line tools I wrote.

There is http://www.olegkikin.com/md5game/ on which I wasted some GPU cycles many years ago. It uses a very silly metric for progress though. Finding a longer substring that matches doesn't bring you closer to finding MD5(x) = x. It was a fun problem to try out some crypto bruteforcing on the GPU though.

I don't think any of the known weaknesses of MD5 would help you in finding MD5(x) = x.

BeRo did build a javascript engine from scratch on his own: https://github.com/BeRo1985/besen

From the copyright headers he worked on it starting in 2009 and had the first public release in 2014 (actually 2010, see comment below). He certainly worked on other stuff in between too. This is also not a toy implementation. While I have no idea how it compares to state of the art engines, it does feature a whole bunch of optimizations and a JIT compiler.

Starting in a corner seems to be a worst case choice for a random walk on a non-looped grid. I forked it to

a) use a random order for starting (and restarting) http://bl.ocks.org/jix/30e55ae16b99efe94bfc/ab5a84881174512a... and

b) start from the center and always restart with the innermost free cell http://bl.ocks.org/jix/30e55ae16b99efe94bfc/aeaced224b45a413...

Apparently it wasn't considered dead enough early enough: http://www.win.tue.nl/hashclash/rogue-ca/