I was playing around with the calculator on my phone and I discovered I can see arbitrary numbers of digits of pi on there. I know double precision floats only have accuracy up to ~16 digits so I figured anything past then would be gibberish, right?
It turns out it's able to display way more digits than 16, I'm talking thousands of digits.
I went to a website claiming to have the first million digits of pi https://www.piday.org/million/ and I checked to see if they lined up and surprisingly they did. I checked up to 700+ digits (using ctrl+f to check if the sequence of digits exists) and they still matched which doesn't seem possible with normal data types.
What kind of black magic are they using to pull this off? I checked with multiple sites claiming to have the digits of pi and they all also lined up. How is this possible?
Amazon has numerous books that have the first million (or 5 million or 10 million) digits of pi.
According to https://www.livescience.com/record-number-of-pi-digits.html pi has been calculated to 62.8 trillion digits (presumably 2.pi.10^13). Don't try to buy that in book form.
To do these calculations you need an extended floating point representation. That might be using words of 64bit unsigned integers. You just need a lot of them, and to do all of the housekeeping to do stuff like carry propagation between the words.