Arbitrary precision arithmetic with GMP

Question

I\'m using the GMP library to make a Pi program, that will calculate about 7 trillion digits of Pi. Problem is, I can\'t figure out how many bits are needed to hold that many de

Answer 1

7 trillion digits can represent any of 10^(7 trillion) distinct numbers.

x bits can represent 2^x distinct numbers.

So you want to solve:

2^x = 10^7000000000000

Take the log-base-2 of both sides:

x = log2(10^7000000000000)

Recall that log(a^b) = b * log(a):

x = 7000000000000 * log2(10)

I get 23253496664212 bits. I would add one or two more just to be safe. Good luck finding the petabytes to hold them, though.

I suspect you are going to need a more interesting algorithm.