Error margins

[c3d]

(10-27-2024 01:45 PM)Maximilian Hohmann Wrote:  Hello,

over the last two days we have been treated to fascinating demonstations and insights into Christophe de Dinechin's ongoing development and refinement of his DB48X project. When you see the developer present his product you instinctively think: "This is the calculator that I want to have!", even if you don't really need it :-)

On my way home I thought about it and the arbitrary precision arithmetic implemented and how that relates to real life uses. During my study time we had to do eperiments / measurements, e.g. some wind-tunnel measurements, process the data and write a report about it. This always had to include an error analyis, which - for me at least - was the most difficult and tedious part.

I have no idea if that already exists somewhere (I guess it does but I don't have seen it yet), but a data type "Real World Number" that includes a value, an error margin, the unit (optional) and maybe the sensor designation so that you don't have to enter the data every time.
For example the datasheet of an arbitrarily selected digital laboratory thermometer for the range between -50°C and 250°C states a typical error of +/-0.648°C. So a real world measurement input of 33.5°C from that sensor might look like this: [33.5;-0.648;0.648;°C;"MCC USB-TC"]

Interesting. A related idea is "inverval arithmetic". The basic idea is to have arithmetic on intervals Low...High, where you do computations on Low rounding down, and on High rounding up.

Getting this right is quite difficult. Consider something as simple as the sin() function. Internally, this is implemented with a number of alternating additions and subtractions, and depending on the sign, figuring out how you need to setup your rounding is not a trivial problem. Also, since these functions are periodic, as soon as the input interval is wider than 2π, the only valid output is -1...1 which is not super useful. Digit cancellation is problematic. And so on.

There is a reason error analysis in real life is hard ;-)

Quote:Now wouldn't it be useful if the calculator could "propagate" that error through all the calculations done with data of this type and, combined with the other input data and their own error margins, give an end result that contains the total error margin? Again, this may already exist in some form, but I have yet so see it.

Regards
Max