ฝัง
- เผยแพร่เมื่อ 23 ก.ค. 2022
- media.ccc.de/v/mch2022-236-no...
We all know that the value of pi is a constant with a particular immutable value. Anyone who has done any graphical programming also knows that visual rendering relies not just on pi but trigonometry more broadly as well as other mathematical techniques. If we look into the source code of the first person shooter Doom we find that the value of pi used in the game is wrong. In this talk I will explore what happens when we subtly and not so subtly break math in the source.
Doom is a well known classic first person shooter game with source code released under the GPL in 1999. In this talk I will begin by exploring what happens to the game when we make the value of pi even more wrong. What about when we change other trigonometric functions and constants to incorrect values? How will our familiar understanding and ability to traverse this virtual world change when we do this. Are there any interesting gaming possibilities with non-Euclidean geometries? A brief segway will cover some optimization tricks made to enable the game to run well on hardware available at the time. At the end I will provide a link to other games and public source code repositories that also use an incorrect value of pi. Pointers will also be provided to allow the audience to compile their own incorrect math version of the game.
Luke Gotszling
program.mch2022.org/mch2022/t...
#mch2022 #MCH2022Curatedcontent
Pi = (Health + 1) / 201 * 3.1415...
The world becomes more and more unhinged as you loose health. You MUST find health bonuses, soul spheres, and mega spheres in order to have a normal experience. +1 so that PI is never 0.
I would've left out the +1 though
You die, the game dies as well 🤣
Sadly, PI is a const and cannot be changed during runtime.
But yeah, that would be hilarious.
@@markbloom7434 nothing stops you from defining PI as a variable
@@yusuf_kizilkaya The lookup tables do. Granted, it's simple enough to precompute them for all health values.
@@yusuf_kizilkayayou'd have to constantly recalculate lookup tables tho
Most important conclusion:
Rounding down pi to 3 is an acceptable practice in game development
More acceptable than whatever the fuck EA is doing
In general, it depends what level of accuracy and precision you need. The smaller the circle, the larger the difference.
@@AnnieC.1993 A dumpster fire is more acceptable
@@AnnieC.1993 "pi = 3 polygons"
Or just use lots of triangles instead.
Honestly i can't really think for what you would need pi, other then round objects.
Is there some magic optimization somewhere needing PI?
lets normalize a pi=e% speedrun
heh normalize... you're funny.
I read pi is on a spectrum
@@NoahtheEpicGuy Heh heh shut up
DOOM (Engineer Edition)
Let's normalise being a 30 year old virgin
As an engineer, I use the identity of pi=e=√g
And always get saved by sufficiently high safety factors
pi ≈ 1. it has the right number of digits
As a physicist I hate that I love this
Found the astronomer @@keiyakins
2=e=3=pi=sqrt(g)
It turns into LSDoom
DooMT
@@SonOfMeme KetaDoom
@@martybyrnemusic nah you ruined it
ShrooM
@@martybyrnemusic you don't understand how drugs work. At least, not ketamine. This is not how it feels to be in a k-hole. A K-Hole is weird, it's like you can't remember how you even got there, like that scene at the cafe in Inception where Di Caprio explains that you never remember the start of a dream, you never remember how you arrived there.
The main thing about being in a k-hole is that everything kinda starts feeling like you're in a world of bubble wrap, or that everything in the world is pixelated. But it's less that you're seeing the world like that and more like you're _FEELING_ it. Time itself stops being one smooth movement and instead becomes very jittery and only progresses in distinct pixelated chunks like that too. It becomes next to impossible to move, because every step feels like it takes an absolutely monumental amount of time to happen, and you feel so shaky and your legs weak that you don't wanna risk moving anyway and so if you do, then it'll be on your hands and knees crawling so that you don't fall over.
And sound becomes pixelated too, if that makes sense. It probably doesn't make sense, unless you've been in a k-hole before. You know like when you put your face up to a fan and start humming into it and it makes it sound weird? It's like that. Except you're the only person who can hear sound in that way, other people just hear you sounding normal.
It's nothing like non-euclidean Doom.
At university we scattered parts of a zip file for installing Doom across the generic logins used for night classes. A batch file would go and retrieve the parts, assemble them, and install, and delete itself after. To hide from the sysadmin...
Carmack is always right, it's circles that are wrong!
π = John Carmack
This sounds like a line from The Simpsons
of course the circles are wrong if they're coming up against supergenious alien in person suit John Carmack
psychic supersoldier prototype and brazilian jiu jitsu practitioner john carmack?
@@seltzer666 The same John Carmack who used chemlab thermite to break into his school so he could play with the school's Apple ][s.
It was my friend John Cash who discovered that Doom ran by using global broadcast packets, he saw that when he used a LanAlyzer to capture the traffic from their regular night-time deathmatches on the corporate IPX net.
When he told Carmack, Carmack replied by sending him the source code and told him to "fix it!" Cash did so and later joined Carmack and Abrash to make Quake...
what
@@asuka_the_void_witch What what?
The Man in Black
Very cool! But according to the Doom wiki, the guy was hired by Carmack for Quake 2. And he was the lead programmer there. And the man left id in 2000 and later worked on World of Warcraft at Blizzard. Talented guy. Worked as a software engineer and the passion for games led him to Carmack himself to get an offer to fix the bug in the code, all of which shaped his career in game development for years, lol
@@KeksimusMaximus The starting at Quake 2 quote is definitely wrong: John started well before the original quake architecture had settled down, something which caused a lot of issues when Carmack's very frequent rewrites caused Cash's bot code to stop working.
When he said "Pi=0 does it run?" and all the software developers in the audience confidently yell "NOOO!"
The "it doesn't compile" part is interesting, because calculating the LUTs is a build step and the program that does it crashes.
And the segfaults happen because it tries to look up a value for an angle that's not in the table, I assume
Yeah, I figured it would throw a divide by zero error or, because of the lookup table, an indexing error.
10:33 me trying to play doom after the lobotomy:
you should have two lobotomies, not only one.
???
@@xanderplayz3446sorry, let me explain it for you. It’s them trying to play doom after the lobotomy
Me trying to understand words after the lobotomy
#relatable
Now I want to make the lookup tables dynamic and make damage / healing cause the tables to regenerate with a value of pi with accuracy based on remaining health
Damn, that actually sounds really dope. Throw in some palette magic and maybe even texture shifting, sprite scaling or sound pitching as well while you're at it :D
or use dynamic tables that changes the value of pi to something between 2.5 and 3.3 every x seconds
@@thehellriddenBaron I saw this suggestion (linking pi to your health) in another comment and got nerd sniped by it. Long story short, I uploaded a video to my channel of me attempting to play nightmare with this change, and it's very cursed. In fact that's the title of the video. "Doom E1M1 Nightmare Difficulty but it's cursed". I also included the git diff in a gitlab snippet which is linked in the description.
It would probably be more balanced being normalized to a range other than 1-100. Right now it's clamped to 1 so dying doesn't crash the game, but by the time you're below 50 health, you've already lost because basic navigation becomes impossible. Like, I'm in E1M2 right now and I'm stuck in the east stair wing because I can't turn around to get to the door.
@@BradenBestWoooow that's awesome!
@@BradenBest real one
I love the Jpeg injection part. Now the question isn't "can it run doom ?", it is "can it run on doom ?"
"can doom load run doom?"
DoomOS
That was indeed very cool.
@@landspide I'm fairly certain I've seen that. But maybe I'm just remembering that time someone (technically) got it running in Minecraft via redstone.
@@JoshWinibergnew linux distro idea. based on arch to further solidify the meme value
The “I hope somebody got fired for that blunder” was a tongue-in-cheek Simpsons reference, lol
“Pi is equal to exactly three!!!”
imagine making a friend on acid play the 3π version while he thinks its just normal doom
probably will look normal to him and he will doubt acid kicked in
"these tabs were bunk, man. you got burned"
breathes really heavily into your ear "yeah"
it's yeah, pretty yeah, a little... yeah
"so now it starts to just be yeah it's uh it's yeah um a little yeah pretty pretty hard"
@@SkilledTadpole Boioioioioioing🍆
"I bet he's thinking about that hottie in front of us"
Him:
@@zelda_smilenothing hotter than my fridge running doom
Pi over 2: You have collapsed space-time into a smaller area. XD
ahhh fascinating
An issue with this is that the maps are still euclidean even though the rendering is not, so you get a clash between different geometries.
I am also sure ist Not an real non euclidea geometry. You need tensor calculations. Objects are warped and don't disappear
@@stefanhoffmann5281but the objects are 2D. Either visible or non visible.
@@RKroese nope : read Riemann
@@stefanhoffmann5281 read riemann what exactly? any specific theorems/results you could point to?
@@stefanhoffmann5281 If it breaks the rules of euclidean geometry, then that is not euclidean geometry. non-euclidean. it's not specifying what it is, just what it isn't.
8:37 when the shrooms hit
Things are a little off, the walls move in a way that you don't expect, amd things start to shift 🤣🤣🤣
Movies trying to show how a trip looks: *pink floating elephants everywhere*
Actually how a trip looks like: *Doom with Pi=e*
Shrooms will eat a slice of your pi
Shrooms hit in a nearby forrest once and I wanted to walk home as the mosquitos bugged me... normally a 15 min walk now felt like walking around in a maze. Everything further away than the tips of my shoes didn't make sense anymore... everything I focused on in front of me became an individual and isolated piece/snapshot of reality suspended in a void as if my brain lost the ability to "glue" the pieces together and turn everything in a coherent reality, which made navigating very challenging. A weak mind would've probably freaked out, I thought it was as interesting as it was annoying. The interesting part was having a direct experience on how bits and pieces of smaller realities become a coherent big reality.
kinda accurate actually huh
This is why all the cthulu mythos inhabitants go insane lol
Omg Carmack is Cthulu
wait. That timeline though? Doom was released in 92 but opensourced in 1997? Opensourcing a game after just 5 years of release is wild, considering modern aaa are still expecting players to purchase games made 10+ years ago for modern day, adjusted for inflation, full-price.
90s were a period of rapid technological breakthroughs, a game would look completely outdated after just a few years. Quake came out in 1996, and it had a fully 3D graphics engine with free look. At that point, a game like Doom had no market value.
@vytah indeed, indeed. It's such a trip seeing how quite much has changed in the intervening years. Such a shame we don't live in the timeline where this is still the norm (opensourcing older games, that is).
1993 actually. Doom released in December 1993 and became source code was released in December 1997. So just 4 years.
It's not the actual game (as in levels, graphics, sounds etc) that was made free, just the engine source code - unless you were going to pirate Doom then you would have been expected to pay for it
The Doom's distribution was initially a shareware. Meaning the Game Engine was free to share and use but not the contents of the game itself (maps, graphics, sounds...).
Elite had just released the source code of the game engine, by doing this, the game is technically playable and saleable on everything.
The question really is, between pi and 4, where exactly does it segfault. It clearly doesn't like pi=4 but likes pi=3.141952654 so where is the cutoff? Is 3.5 fine? 3.75? 3.25?
I thought about this too. Why didn't he put this in his talk??
And why would it segfault to begin with?!
Theres probably a bounding limit on the functions used , maybe they limited the domaine of definition to - pi to pi. And since the real pi is smaller by the the pi coded it works. Idk tho just a hypothesis
Maybe, but then that would require the function to have the correct definition of PI as well. More probably the maths result in a runtime error (division by zero or other illegal operation) at some value greater than pi.
It's also worth noting that carmack's wrong pi is technically larger than pi, by 0.0000000003 but still it *is* larger, so the precise cutoff would be interesting (and the effects thereof likely subtle since 4 crashes)
Anyway, it'd be trivial enough to test this myself but I don't actually care enough to do that. I just wish it was covered in the talk is all.
Hell, given a few minutes I could work through the code and figure out why it crashes too but again: not worth the effort.
More interesting questions than does it play at -1000000. The talk had the bones of a good concept but not properly explored.
I like how the slide spelled it “segway” instead of “segue” - the homophone-induced visual metaphor is so strong for me that they’re just the same word in my mind
someone make me a sign that says if you are here for euclidean doom you're in the wrong room 😂
pi=3 is basically Playstation 1 mode!
I know nothing about programming and I do math on my fingers but I find this absolutely fascinating.
I think for most of the history of trigonometry the fastest way to calculate trig functions was using pre-computed tables.
I wonder if you could use this for VR games. That way you can walk for miles without leaving your room. You'd probably get dizzy because you'd have to end up walking in cricles. However what if for every pi you used 2*pi that way you are trying to go left in the game but you actually walk in a circle. In order to walk slightly right you walk in a circle. Or maybe a straight line in the game requires you to walk in a circle. Maybe you could do it outside you walk in a large circle to go in a straight line. Turning left requires more turning than turning right. And going in a straight line requires turning.
This sounds like motion sickness: the game
Check out Hyperbolica.
It's been around for a while and wobbling your head changes direction. Motion Sickness: The Game it is!
This exists! It is called "Redirected Walking" in research papers, see Nilsson et al, IEEE 2015
Check out Hyperbolica! It's a VR game with noneuclidean spaces -- the main hub area has 5 squares to a corner so it has more space per space
I’d say “π = e” is the sweet spot 9:33 (aka DrunkDOOM) but ShroomDoom at 10:20 might be a little too high...
ShroomDoom
The next frontier isnt what can we run doom on, its what we can run in doom. Asteroids is just the first step.
9:20 but what aboit non-hitscan weapons? Those might be fkd
yeah I really wanted to see a rocket
BFG-9000!
@@makipri
I could be wrong but given that the only examples shown on his slides of the Doom splash-screen are those from the shareware doom1.wad, I think that's what he was using in this demonstration. If so, Plasma Rifle and BFG are unavailable even with cheats; the only non-hitscan weapon he could have shown was the Rocket Launcher.
@@ph0endTechnically enemies like imps fire non hitscan projectiles.
Speedrunners: "What's code injection? I've never heard about that before and don't know what you can do with it."
(and then they get told)
"Oh its arbitrary code execution? cool"
I just submitted a bug report to a Google project and a Starlink project that had this wrong value of pi present.
It makes me giggle like a little girl to know that even such large companies have replicated this discrepancy.
Heheh, imagine non-Euclidean geometry causing Musk's spaceships to explode...
Having spent way too much time in E1M1 in my life... this makes my skin absolutely crawl in a way I can't adequately explain.
Lovecraft would have loved that. He anticipated that in his famous story "The Call of Ctulhu": "... and twisted menace and suspense lurked leeringly in those crazily elusive angles of carven rock where a second glance shewed concavity after the first shewed convexity."
I think programmers should stop abusing the term "non-Euclidian". If you screw with the variables (or constants) in a program so it doesn't work properly anymore that isn't non-Euclidian it's just intentionally introducing bugs into a program which still uses Euclidian geometry only it doesn't produce the calculations you expect.
Yesn't
so you're telling me that making a euclidian world work in a way that breaks the euclidian part of it doesn't make it non-euclidian?
@@troyjohnson2137
It isn't breaking anything. It's just changing the formula.
If you swap 2 + 3 = 5 for 2.1 + 3 = 5.1 you haven't broken anything.
@@nowonmetube😂
Doesn't the change to pi make movement of the character non-euclidian? Well technically, the character doesn't move, the world moves around the character, but it does so relative to the player, so it is in essence a circle around the character. So by changing the value of pi, that circle now has a curvature stronger or weaker than it should have. Which makes it non-euclidian, yes?
Reminds me of MIT's "A Slower Speed of Light" for some reason
Let’s take it into the imaginary realm:
Pi = i
That was a very fun talk given that code is involved ! Its amazing to see that after 30 years since launched this game is still disscused and studied. What a technical breakthrough Doom was ! ❤🎉
not sure I've ever been nauseated by a tech talk before
code injection via jpg? so you could port pico-8 stuff to run on doom?
but will it run Doom?
to run Doom on Doom
@@abcpea someone did port doom to the pico-8, so it might be possible :3
@@champagnesupernova1839It could be, which makes it even more interesting
"...and smokes of assorted types." Nice, very subtle.
I wonder if you could find the limits, figure out a way for the values and tables to be recalculated every tick, and then modulate the base value of pi with a (limited) feedback loop of something else, like the player's health or the look vert angle or some combination of who-knows-what-else.
That would be so sick!
@@philipegoulet448 you could even make it so it wouldn't update if you didn't move location, so that you had a *chance* at gaining a bearing.
"I bet he's thinking about that hottie in front of us"
Him:
The largest value of pi I would assume is whatever value that the lookup table will no longer be able to compute.
“Hyperbolica” on Oculus Quest deserves special mention. Non-Euclidean vr is fun
well now I'm really curious what the highest value pi can be while keeping the game playable
same here. he had a whole gradient over numbers lower than pi, and none noticeably greater than pi
If the lookup table for tangents had 4096 slots, then it's probably π + (π / 4096) or something like that, which causes an additional value in the table to become infinity or switch sign.
*sporadic half-hearted clapping*
"Thank you for the warm welcome."
I used to play this a lot as a kid; it was fun but also a frightening experience
Software Engineer - Data Platforms here. Precomputing via LUTs is such a great strat. I use it all the time, especially when you don't need reactive concurrency for data retrieval.
Say you've got a PowerBI model (ugh IKR), selecting from data on that model takes compute, DAX on the query takes compute... Say, why don't we use a CTE to precompute the results for the semantic model? Then we can just create a holding table and truncate it and insert from the view every time we want to run this report.
Well that just removed a lot of compute time for end users!
And since we're inserting a whole dataset, we can then alias that against anything else we might want precomputed... How about a date slicer with historical values grouped by date? Dynamic, complex, historical queries. In PowerBI. Resolved to the end user in 0.001s
Powerful stuff LUTs.
Oh they also make LODs a lot easier in Game Design. Dame with lighting and reflection probes too actually.
You didn't try the Indiana Legal pi of 3.2 😢
Such an enjoyable presentation. Thanks for this!
I wish I could understand why anyone would think this. I'm trying to put myself in the shoes of a software engineer and still can't see how I would find this entertaining or even mildly interesting? If you can explain it, I'm curious?
@cichlisuite2 I randomly came across this. I have no idea about code or developing, neither am I good at maths. I clicked it out of pure curiosity expecting the game to look trippy with changed pi values, and it did. That was neat :) Hence me liking this.
@@nickkohlmann Thanks for the explanation. I also randomly came across it and watched hoping it might show something interesting. It wasn't that trippy to my eyes and the presentation style was about as drab as it could be. But good to know that for some the visuals alone were enough to generate enjoyment. I thought maybe you might have to understand coding or game mechanics.
@@cichlisuite2 You never think "what would the universe look lik e if the constants are different?" or "what would it be like to live in a two dimensional world?" If you would like to explore the second question, go read the book Flatland by A. Square.
Stuff like this makes math look cool. If I had lessons in high school that allowed me to slice open Doom and play around then maybe I wouldn't have had to take Algebra II three fucking times.
Guys... I really love you so much... thanks a lot! I was searching for an inspiration for describing not euclidean spaces in a Call of Cthulhu adventure. Now i have it
If you compute the circumference of Earth using the incorrect value, the result is 4 cm larger than using the correct value, so errors are negligible. However, it would be interesting to use the value 3.2 for pi in this simulation, since this was the value proposed in the Indiana pi bill of 1897, that sought to fix the value of pi once and for all. Using the Indiana value for pi, the calculation of Earth's circumference would be 742.6 km too large.
Lol, that was my idea for day of PI 14 of March, glad that somebody made this already and i don't have to recompile any doom port for that :)
This is what Lovecraft was talking about.
holy moly... PI being 3 is trippy as ballz man.
SO MANY firsts to my disbelief. I mean, this is a first person shooting game, and doesn’t even employ DirectX because it’s from a time before DirectX - probably 10 years before or more. I can recall a few of my very first encounters with l desktop computers where x86 machines required the user to type a few DOS commands to actually start up Doom. Reminds me of Sierra games. The guys who created Doom though - must be some awesome people - for giving Doom the open source licensing at a time when Napster would be the big media buzz for a couple years at least… what great and special times these software engineers helped bring to us!
I love those kind of talk
As one professor said "pi is close to 5, which is close to 2pi, so you can just use 10".
What would make this really weird is if the object hitboxes and the map were actually moving. I don't think they are, since they are determined by the map developer, without need for pi (they are simple co-ords)
Great talk
I think 3.5 would have been an interesting one to try, between pi and 4
I was missing pi=3.15 or something like that. Would have been interesting for what values of fake_pi > pi it still would have been playable.
I find comfort in the idea that a 30 year old code is still relevant and usable today. It's a hint that coding games is slowly becoming an art of its own.
“I hope someone got fired for that blunder” is a simpsons reference. They didn’t mean it I'm sure
I love how with this crowd the question "Why do anything like this?" is not asked, or even considered.
18:15 I would change the sine table to a triangle waveform, thus making the unit circle a diamond.
That was magnificent.
I wonder if pi=3.2 will work. If so, that needs to be released as "Indiana Doom"
as an engineer, put a highpass filter on that audio, holy shit that rumble... why?
As a mechanical engineer this really fucks with my audio engineering sensibilities, won't this in-person conference speaker think of the TH-cam sound quality?!
@@arenomusic can easily be done in post quickly before an upload. fuck, id do it for free
@@ZeMovinPixxle Wasn't watching with headphones but I get what you mean 😂 It's part of the IMMERSION
@@arenomusic i work events sometimes and we always put a highpass on every microphone.
It's for artistic effect
I like this video becasue im not knowledgeable enough to understand the JPEG injection part, but im delighted that the audeince did and it made them happy.
Very interesting
It seems kind of odd, but computing trigonometric functions in hardware has gotten so fast that on modern hardware it beats table-driven functions. Partly that's an accuracy issue, but if we don't mind weird visual artifacting, then I guess it doesn't matter, and clearly there are games now that use the effect intentionally.
Are there harmonic resonance points along the substituted value for pi?
Regards from a Tom :)
I'm not sure that this is actually non-euclidean, but I'm interested in what is actually going on under the surface here.
Pi = 3 - Biblically Accurate Doom
since computers are powerful enough, you could have some code that periodically changes the lookup table values based on new values of pi. That would be interesting to see
Or calculate them instead of looking up, if you're going to be updating the lookup tables anyway the performance boost from using lookup tables is gone.
That way you can put powerups in the map that change all sorts of constants.
This was pretty fun and interesting for me as a total non-programmer and non-hacker (except for some high school java)
Would be interesting to see what that actually do to the geometry of the space and how/if things change relative to player or camera movement and stuff like that.
The reason for lookup tables wasn't that there was no 3D acceleration. The reason was that you couldn't assume there was an FPU! The first Intel x86 chip with an integrated FPU was the Pentium (originally with its FDIV bug). 386 and 486 didn't have one. That's a bit of an egregious error to make in a presentation like this.
486 already had an integrated FPU. en.m.wikipedia.org/wiki/I486
So what's the convergence function for non-euclidean Doom playability?
That was so cool!
8:53 I ❤ this
It was also Quake that used the reciprocal square root hack. I think they have accepted certain inaccuracies.
I think this is the closest I will ever get to being a 4th dimensional being
This is how I perceive moving through higher dimensions with a 3D body
22/7 is where it's at...
this is funny. i just watched another conference which started with a discussion on pi and i think the lecturer used that same incorrect approximation as an icebreaker
That was brilliant
New difficulty for speed runners unlocked Pi=e enemies disappear if they turn sideways 🤣
Its not really non-euclidean geometry with a fixed value of pi, its just a bug. Value of pi would vary with position/size of circle in a euclidean geometry. It can't be fixed at 3.
Best TED Talk ever 😂😂
6:00 my guess is that fetching the value from memory takes way less clockcycles than doing the math.
Source: Slaping together a pseudo-sine signal generator from some 8-bit Amtel uC and a resistor DAC half a decade ago.
Half a decade? Or 0.4875 decade?
Even in these 93 terms, I may as well be a fly on the wall listening to some conversation in from some remote village in the Andes or could be an alien outpost on an unknow planet.
4:20 Did he not have a pocket calculator at his disposal?
The question is no longer can it play Doom, the question is weather you can.
Might have to speedrun this.
For the record, that's STILL the fast way to do trig functions.
>guitars
Hackers in 1993 were so much cooler.