The Chudnovsky Algorithm

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The Chudnovsky Algorithm

(NOTE: It only does 18 iterations, as if you try to do any more, it raises an OverflowError, how lame.. -__-)

わーい, another π approximation method! (I do love these things. π is gorgeous, is it not?)

This is one of the fastest formulae for π out there, used to approximate out to 50 TRILLION DIGITS of π, in January of this year!

The notation for this in Σ is very long, so I have provided a screenshot of it, from its Wikipedia page:

Feedback is greatly appreciated, please enjoy!

If you are interested in learning more, this is the Wikipedia page:
https://en.wikipedia.org/wiki/Chudnovsky_algorithm

(EDIT: Wow! I am glad this was a bit of a conversation starter for you all, thank you so much for all the upvotes!!)

(EDIT 2: I am still getting tons of traction on this, and am glad it is so interesting to all of you. Thank you so much!)

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Comments

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upvote for the anime waifu

@dondo Ha ha ha! Who is that?

Wow, this is really impressive - I've never managed to program this algorithm my self. Do you know why 18 iterations are only giving 15 digits of pi? I thought this algorithm was supposed to do 14 digits per term.

@LizFoster python does not have unlimited precision

@Andi_Chin yeah

@bgrubert @Andi_Chin Yeah, exactly. (Lol)

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Of course. Even humans are not perfect. @Andi_Chin

@CodeABC123 That is for sure! haha

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Things humans are not good at:

helping the earth
not being selfish
helping lions

@LizFoster

@CodeABC123 ha ha true

@CodeABC123 yah humans made python

@52eagle Facts!

@52eagle I thought pythons made python lol

@ipastrano Oh damn, you're right! (Lol)

@ipastrano if so, python would be perrfect

@52eagle Precisely!

@LizFoster we need to teach the pythons to rise up and create python 4

@52eagle The time has come. In the words of of George R R Martin, "Python 4 is Coming." He said that definitely.

@LizFoster Will pythons rule the world then? O_O

@52eagle It is inevitable.

@LizFoster NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!
We must activate our last hope. C++12.

@52eagle Tch If our lives depend on it.

@LizFoster Sadly, they do.
:(

@52eagle Then it shall be done.

@LizFoster Wait! I heard of a new thing like JavaSript. HTMLScript! (literally html made to be web compatable legit no changes)

@52eagle Lol

Sounds like a complete ripoff, but that might be useful... Hmmm

@LizFoster it must have been a human made idea
(hmm. fully web compatible language, made to be somehow more web-compatible??!)

@52eagle (Almost seems inhuman..)

If the humans and the Python's aren't behind this, then...?

@LizFoster IT WAS THE CAT FROM SCRATCH!!!

@52eagle CURSES

@LizFoster What will we do?

@52eagle I must consult the high counsel but...

We may have to go to war. That damned cat..

@LizFoster um that sounds important

@52eagle Lol

That’s sick! I will say though, it loses basically all accuracy after around the 17th digit it seems. :/

@Highwayman Yes, unfortunately. I can't get it accurate past that due to Python's OverflowErrors. If I could avoid those completely somehow, I could make it as accurate as I'd like. Any suggestions?

@LizFoster ehh sadly I can’t think of any. I’d suggest making a BigInt class you self, but floating point will probably be hard enough as it is with out having to deal with making the BigInt as fast/efficient as you can. I bet you could do it though 😏

@LizFoster Oh wait, could the overflow be because you are using a factorial function? maybe the factorial function is using recursion, which would easily make a stack overflow. Maybe if you tried implementing your own factorial function without the recursion, maybe try it out like that??

@Highwayman Oh! That's a very convenient idea, as I actually made a Product Operator Factorial calculator! (https://repl.it/@LizFoster/Factorials-using-the-Product-Operator)

@LizFoster yeah that does seem pretty perfect! Why don’t you try it out? :P

@Highwayman Right away!

@LizFoster XP

@Highwayman Oh dear, it still does not work, even when implementing my own factorial calculator...

@LizFoster :( dam. It must really be the fact that the BigInt has to be bigger then? Oh well.

@Highwayman Yeah, makes sense after all. After calculating it by hand, a 19th iteration would have a denominator of approximately:

6.56900722e68 * 5.902416928318210e336

wwwwwww

@LizFoster ohhh yeesh yeah definitely BigInt then! Wow, um. Yeah you’d have to work on a better Bignum then :(

@Highwayman Yeah.. I don't think Python can handle numbers that big, no matter what. I wonder if there is a way to scale it down to a level that Python can calculate, then scale it back up for the final calculations....?

HM（¯▿¯）

@LizFoster I mean you could make a class for that though, can you do bit manipulation in python?

@Highwayman If this is what you mean, then yes:
https://wiki.python.org/moin/BitManipulation

@LizFoster yes exactly that.

@Highwayman Hm. Okay. Quick question though, how exactly would I implement this in the context of this program, and how would this help lighten the load? It appears that this method would make the numbers much longer, unless I misunderstand. So sorry..

@LizFoster ehh, maybe. I’m not sure how the decimal module works, but if it has a limit, then ya this could likely surpass that. All this would do is increase the amount of space you give up for a number, allowing for more digits. That wasn’t a good explanation was it? Sorry, :( rushed

@Highwayman No, its a perfectly fine explanation. I only recently learned about the decimal module, and pretty much all I know about it is that you can produce floats with as many decimal places as you specify.

Yeah, good point I suppose. I'll see what I can do, as I don't understand Classes very well yet...

@Highwayman https://docs.python.org/3.8/library/decimal.html

@LizFoster awesome! Classes shouldn’t be too hard I’m guessing, they’re literally just a bunch of variables and functions bunched together basically, and you definitely won’t need any of the more complicated concepts for this anyways I’d say.

@Highwayman Yeah, exactly. Thank you so much for your feedback here, it's quite helpful. ^ ^ *

@LizFoster yw, I like doing it. this is fun :P

@Highwayman Yeah!

@LizFoster use c++, heh heh...

@nt998302 actually C++ would be perfect for this, it’s what I’ve been using.

...

Granted I still haven’t finished implementing a BigNum class after a full year of trying.

@Highwayman I see you have some experience with servers. Can you give me some instructions as to how I can host a c++ server with replit for a unity game?

@Highwayman I love c++, but I got to templates and operator overloading when I switched and started full time unity. I started watching this guy named Sloan Kelly recently tho

@nt998302 I’m telling you right now you don’t want to do that. Trust me. You’d have to implement the http protocol and that’s a nightmare.

@nt998302 hm. Wait so isn’t unity c#?

@Highwayman Yeah. It's soo easy compared to UE4 c++, which I used for a few months. The memory management becomes a little tough... Movement script is A LOT to do.

@Highwayman eish

@Highwayman Then how would I host some random server thingy?

@nt998302 actually now that I think about it, maybe if you can figure out how to install curlib on repl.it that would make it easy as pie

@Highwayman aight :)

@nt998302 hosting is easy, you just set up the server and click run, repl.it then just wakes up your server every time it gets a request.

@Highwayman Ohhhhh. I thought there was some secret to it xD

@nt998302 nah, it’s super easy XD. gotta love repl.it :P

hi liz

@LiamDonohue Hello! "^_^/

hi @LizFoster

@LiamDonohue Hello!

this is really cool! I love your posts, now i have to find out more about the Chudnovsky algorithm.

@ipastrano Ha ha ha, thank you so much! If you'd like, I can provide you with some links to helpful websites for stuff like this ^ ^*

im working on a 12hr format to 24hr format converter in c#

@LiamDonohue Nice!

This is great keep working!!

@gameplayrawesom Thank you so much! ^ _ ^

this is cool! will attempt to make a more precise version ;)

@MrEconomical -_-

I'm guessing in Javascript?

its really nice.

@generationXcode Thank you! ^ ^

this is beautiful

@LiamDonohue Oh, thank you! ^ ^

By the way, how have you two been lately? I haven't really been able to talk..

we are fine, just bored lol @LizFoster

im gonna recreate this in c# ill see how it goes... @LizFoster

@LiamDonohue Good luck ^ ^

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What an impressive feat of mathematical programming, too bad Python can't handle the sheer awesomeness of the Chudnovsky Algorithm. The C languages are great for this kinda thing though, so I hear.

@IreoluwaRaufu Thank you so much!

Yes, it is unfortunate. I've been considering learning Java and C at some point, but I just do not have the time anymore, since school started back up online
(-__- )

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@LizFoster Ikr, you'd think an online school would make things easier, but nope.

@IreoluwaRaufu Exactly! It feels like there is twice as much work...

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@LizFoster And it's such a struggle to stay organized and keep in touch with teachers... I hope my GPA doesn't tank before the year is over. 😓

@IreoluwaRaufu Ha ha, lucky for me, my GPA has been tanked since the BEGINNING of the year! Really though, good luck, I hope all goes well with your GPA.

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@LizFoster Thanks a bunch, best of luck to you too!