Algorithm accuracy vs calculator precision

[carey]

(11-12-2024 05:44 PM)dm319 Wrote:  I certainly share your view. I think Steve will hopefully chime in with a Prof Kahan quote about the algorithms of the HPs being superior even though the digits were less. I guess HP persisted with 10 digits for a while also when other manufacturers offered more, and maybe they felt that having better algorithms was more useful than digits.

From a user perspective I'd prefer less digits if better accuracy, especially if accuracy could be guaranteed.

Hidden precision is somewhat relevant though because it allows built-in functions to utilise more digits. That may or may not be beneficial to the accueacy though, and really hiding the precision means "I am not allowing you to use this precision in your calculations or your programs, just for my built-in functions". which is an odd stance.

When I went on my dive of TVM calculators I noticed very varied results depending on the algorithm. I plotted a 'digit efficiency' graph to show how well the calculators did for their precision. I'll dig out my latest graph and post it here later.

Thank you for your reply and your great point about preferring "less digits if better accuracy, especially if accuracy could be guaranteed." With the range of possible functions that algorithms can be applied to and in which accuracy can vary, it argues strongly for either: (i) robust algorithms even if other algorithms might be more accurate in special cases, or (ii) a choice of algorithms.

Yes, Professor Kahan quotes are always informative and posting your latest "digit efficiency" graph for TVM calculators would be of interest!