How to calculate the terms of the continued fraction of pi?

Question

The other day, the Wolfram Blog published an article about a thirteen year old boy, Neil Bickford, who computed the first 458 million terms of the simple continued fraction representation of pi, beginning with [3; 7, 15, 1, 292, ...]. Bickford described his accomplishment on his blog, and even quoted Bill Gosper's algorithm, but I haven't been able to work out the algorithm.

One thing I do know is how to convert the decimal representation of pi to a continued fraction, using the method given at the Wikipedia article on continued fractions. But that requires a decimal representation of pi to a sufficient number of places, and certainly Bickford didn't have millions of digits of pi backing his calculation.

Can someone please explain -- in considerable detail -- the algorithm Bickford used to make his calculation?

Answer 1

Actually he DID have millions of digits of Pi to start with. He probably used either Mathematica or another pi-program to get the initial digits.

Here's the link to his previous record:

http://neilbickford.com/picf.htm

In this one, he said he used a program called y-cruncher to compute 500 million digits of Pi to start with.

EDIT:

As far as explaining exactly how the algorithm works: I'm not familiar with it myself. It's probably too localized for anyone on SO to be able to answer that.