Just a heads up--the mediant algorithm can be O(d) in the size of the denominator for fractions that are close to 0 or close to 1 (it's possible for the denomin

Just a heads up--the mediant algorithm can be O(d) in the size of the denominator for fractions that are close to 0 or close to 1 (it's possible for the denominator to increase by only 1 at each step). The Aberth algorithm (I hadn't heard it called that; nice to know) is much more efficient--it converges quadratically.