(02-08-2015 08:56 PM)rprosperi Wrote: I (and I suspect other lurkers) would like to know how it applies, and why such precision can have practical use or impact.

From a mathematical perspective the "algorithm designer" does not know how the algorithm will be used, or how accurate the requirements of it's application will be. So he strives to achieve the "Maximum Possible" accuracy given the limits of the floating point number system used in the implementation. Many algorithms exhibit strange behaviors when their results approach minimums, maximums, zero, or infinity, so it is a challenge to keep errors to a minimum over the algorithm's full operational range. Dieter was illustrating how his algorithm performed at the bottom end of this operational range (where the gamma function reaches its minimum value in the positive domain). He demonstrated how the algorithm

gracefully gave an error when it reached this lower limit. This is why he needed to show so many significant digits.