如何计算圆周率的连分数项？
前几天，Wolfram 博客发表了一篇文章关于一个 13 岁的男孩 Neil Bickford，他计算了 pi 的简单连分数表示法的前 4.58 亿项，从 [3; 开始。 7、15、1、292、...]。 Bickford 在他的博客上描述了他的成就，甚至引用了Bill Gosper 的算法，但我还没能弄清楚该算法。
我确实知道的一件事是如何使用 关于连分数的维基百科文章。但这需要将圆周率用十进制表示到足够多的位数，而且比克福德当然没有数百万位数的圆周率支持他的计算。
有人可以非常详细地解释一下比克福德用来进行计算的算法吗？
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?
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事实上，他一开始确实有数百万位圆周率。他可能使用 Mathematica 或其他 pi 程序来获取初始数字。
以下是他之前唱片的链接：
http://neilbickford.com/picf.htm
在这张唱片中，他说他使用了一个名为 y-cruncher 的程序首先计算 Pi 的 5 亿位数字。
编辑：
至于准确解释该算法是如何工作的：我自己并不熟悉它。对于 SO 上的任何人来说，这可能太本地化了，无法回答这个问题。
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.