Yes, real data is noisy but testing needs do be precise and repeatable. For example, if we need to test that a value is <=100, then it must pass at 100 and fail at 100.00000001. And yes, we use margins and fixed point numbers too but sometimes, we need to be precise with floating point numbers.
It also matters in some calculations, for example when doing GCD/LCM with periods and frequencies. For that, we eventually switched to rational numbers because precision of source data was all over the place.
We all know that parts per billion rarely make sense but where do we draw the line? Sometimes, it really matters (ex: GPS clocks), sometimes, PI=3 is fine. So in doubt, use the highest precision possible, you can relax later if you can characterize your error.
I didn't work in avionics but a field that used a lot of GPS bits. Depending on where your error is, it can be +/- 100 feet or more or less depending on what point the cut off is. Like you say you need to know what your target is.
Of course, the fact that the threshold has to be so precise is because that's the rules, not because of anything related to aviation. That's a human-enforced quality. A threshold at 100 probably has about one significant figure, sometimes less.
Well, not necessarily. The "and repeatable" can be quite a constraint.
Imagine three redundant systems on a plane that want to compute the same from the same input array (and then check whether they all agree). You want to implement this, and figure that (since there's a lot of data) it makes sense to parallelize the sum. Each thread sums some part and then in the end you accumulate the per-thread results. No race conditions, clean parallelization. And suddenly, warning lights go off, because the redundant systems computed different results. Why? Different thread team assignments may lead to different summation orders and different results, because floating point addition is not associative.
More generally, whenever you want fully reproducible results (like "the bits hash to the same value"), you need to take care of these kinds of "irrelevant" problems.
Yes, real data is noisy but testing needs do be precise and repeatable. For example, if we need to test that a value is <=100, then it must pass at 100 and fail at 100.00000001. And yes, we use margins and fixed point numbers too but sometimes, we need to be precise with floating point numbers.
It also matters in some calculations, for example when doing GCD/LCM with periods and frequencies. For that, we eventually switched to rational numbers because precision of source data was all over the place.
We all know that parts per billion rarely make sense but where do we draw the line? Sometimes, it really matters (ex: GPS clocks), sometimes, PI=3 is fine. So in doubt, use the highest precision possible, you can relax later if you can characterize your error.