Calculating n digits of Pi

How is this done in practice?
Monte Carlo simulations?

What can be achieved on a regular computer?

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numberworld.org/y-cruncher/
crypto.stanford.edu/pbc/notes/pi/ramanujan.html
twitter.com/NSFWRedditGif

>(((tranny)))
>(((goolag)))
>(((kleinman)))
(((they))) are not even trying to hide it anymore

>emma

this isn't Jow Forums friendo

I don't know what the optimal method is, but Parseval's theorem can be used to prove that (π^4)/90 = Σ (n^-4), with n starting at 1 and extending to infinity. It would be simple to throw that into a loop and calculate π to your desired precision. There's probably simpler equations for π as well

reddit detected

How do you deal with rounding?

How do you check if those numbers are correct?

It says they used
numberworld.org/y-cruncher/
in this and the previous attempts.

I'd assume since the summation terms get progressively smaller, you could just keep adding them until the addition of another term has no affect on the nth digit. After that rounding shouldn't matter

read the rules, newfriend

64bit double format only gives 15-17 decimal digits of precision. You would need 7.65*10^13 bits to represent that many digits if I did my math right

Afaik it's down to finding an infinite series expansion of pi that's easy to compute.

I used the wrong log, it would be 1.76*10^14 bits

tan(pi/4) = 1

that's a man, baby

Right, I misunderstood what type of rounding was meant. You'd have to use some sort of arbitrary precision arithmetic software. I know C libraries exist for that

So pi = arctan(1)/4 ?

That many bits is equal to 22000 gb.

Now you need to compute arctan(1) to any arbitrary number of digits..

And that is why you need Google's hardware

*4 I mean lol

crypto.stanford.edu/pbc/notes/pi/ramanujan.html

I'm curious now, if you had a 22000gb fp number then how many iteration should you do to get to 53 trillion digits? Just enough to not overflow?

So basically Google gave some woman access to their computer to use someone else's software to calculate it fully automatically and now it's somehow her achievment? Oh boy the lengths SJWs have to go to put a woman as the hero of some tech-related news.

Since each partial sum of an alternating infinite series is smaller than the last partial sum, once your partial sums get below 53 trillionths in decimal form you're done.

But how do they know it's right if no one ever calculated this many digits before?

You ever do math?

There is the BBP formula, which calculates Pi a digit at a time, so there should be no problems with overflowing.
It is a spigot algorithm much like converting decimal to binary, where a number is shifted to the left and the integer is preserved I think. This is how you can peek at an arbitrarily small part of Pi.

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shut up nigger

translating.... done
>Stop spreading truth you afroamerican

weeeelll it fuckin isnt?

Can I put a pi calculator in AWS and let it scale up to utilize the whole of their infrastructure to calculate even more digits than Google?

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Wolfram alpha: N[Pi,large number]

exactly what I thought
All she did was press fucking GO button
she was a site reliability engineer initially and has been an "evangalist", basically low IQ jap/chink/mix, but she's a girl so we give her a pass
her employment history is new job every year which tell u a lot
she's a proper lezzer too, check her twitter, why u gotta announce they u gay?
i'd tap it tho

You don't. Because it's just a pointless meme

it's a guy, you blind faggots

Oh then he's my hero and he deserves all the praise he's getting

Of course nobody cares about the creator of y-cruncher