[NUMBERS-131] Re-write implementations of double approximation factory methods in BigFraction

[Schamschi]

[coveralls]

Coverage increased (+0.2%) to 94.471% when pulling cf54480eb238d9e3f722d9626842c864f7369d03 on Schamschi:NUMBERS-131 into 3eb540507a559b4c37a802c489b8c9218cf6bc9c on apache:master.

[ericbarnhill]

Thanks for the great contribution Heinrich! I can't figure out why it's giving you a conflict, looks like you just deleted that code to me :).

[Schamschi]

Hi Eric,

sorry for the late reply, I have a bit much to do right now, and I don't think I'll be able to have a look at it before Sunday. But thanks for taking the time to look at it. There are some other things that need to be changed besides those you mentioned, for example the Javadoc, as I've learned in the meantime that MathJax is preferred over HTML also in private and package-private elements.

And about the lengthy explanation of the algorithm: Do you have a specific suggestion? The essence of the algorithm is described in the Wikipedia article Continued Fraction, which is where I got it from, but I'm not sure if this is a suitable source to cite, because it doesn't contain any explanation as to why the algorithm works, and the references for the respective sections of the article were not very helpful either, as far as I remember. The book by A. Khinchin was the best source I could find, and the sections I cited are available on the free preview on Google Books, but I couldn't find a summary of the algorithm there (at least not in the free preview, I don't have the book, so I don't know if there is one somewhere in the rest of the book).

[aherbert]

This PR is out-of-date. The algorithm for BigFraction was rewritten since this PR was made. But IIUC this contains a method to extend beyond the long datatype for the numerator/denominator used in the current implementation.

If you care to rebase the code on the current master then I'll take a look.