Dividing 1 by a huge integer [closed]

Question

I have to divide 1 by a number X of more than 4000 digits that I have stored in a string and obviously this is going to return a floating point number. I'm looking for algorithms to perform this division efficiently but I could not find anything that convinces me.

As a side note, I would like to implement the algorithm on my own without using a third-party library.

Anyone have any idea?

Thanks!

EDIT: The reason why I do not want to use a third-party library it's that I want to do this operation using openCL but without losing too much accuracy in the process. Therefore using one of those libraries is actually not possible in this case.

Answer 1

You are describing a special case of division, known as inverting a number. Here's a paper which gives a description of Picarte's Iteration method of inverting a large integer: http://www.dcc.uchile.cl/~cgutierr/ftp/picarte.pdf