http://en.wikipedia.org/wiki/Binary_GCD_algorithm
This Wikipedia entry has a very dissatisfying implication: the Binary GCD algorithm was at one time as much as 60% more efficient than the standard Euclid Algorithm, but as late as 1998 Knuth concluded that there was only a 15% gain in efficiency on his contemporary computers.
Well another 15 years has passed... how do these two algorithms stack today with advances in hardware?
Does the Binary GCD continue to outperform the Euclidean Algorithm in low-level languages but languish behind due to its complexity in higher level languages like Java? Or is the difference moot in modern computing?
Why do I care you might ask? I just so happen to have to process like 100 billion of these today :) Here's a toast to living in an era of computing (poor Euclid).