implement better complex division algorithm

[JeffBezanson]

I discovered this through the LAPACK 3.5.0 release notes:

http://www.netlib.org/lapack/explore-html/df/d90/dladiv_8f_source.html

We are using a standard algorithm, but the one above is better.

[ggggggggg]

I can give this a shot. How do I do the equivalent of

  136       ov = dlamch( 'Overflow threshold' ) # realmax(Type)
  137       un = dlamch( 'Safe minimum' ) # realmin(Type)
  138       eps = dlamch( 'Epsilon' ) # this one is eps(Type)

edit: added my guesses

[ggggggggg]

The archive paper provides 10 example hard complex divisions with answers. It also provides an algorithm for measuring the accuracy of the result in "bits", which I have implemented. The robust cdiv algorithm is said to get 53 bits for all but num8 on the hard problems, where it gets 52 bits. I reproduce all of the results (also the default julia / reproduces results for smith's algorithm), except I get 0 bits on num5. I've tracked this down to the division of b/c returning zero inside robust_cdiv2, after r is also zero. But it's not clear how to fix it.

Link to gist with code and output: https://gist.github.com/ggggggggg/7904745

[ggggggggg]

I just had transcribed the answer to num5 incorrectly.