Evaluating bitrounded results with metrics?

[observingClouds]

To ease the decision on specific keepbits for a simulation, it would be great to include some metrics into this package that can quantify the differences between bit-rounded and original values. The simplest being:

• mean
• standard deviation

These could also be enhanced by plotting routines that loop over possible keepbits.

[aaronspring]

do you mean temporal metrics, eg. temporal mean?

I would go for normalized error (ori - bitrounded)/ori and error normalized by temp std (ori - bitrounded)/ori.std("time").

we could use metrics from https://xskillscore.readthedocs.io/en/stable/api.html#distance-metrics

In general, I am not sure whether we can provide a general solution here. for simple metrics such as mean and std, the user can easily do this in xr. maybe what I lack is a short API proposal like compare(ori, rounded, metrics=[])->"xr.plot(col="metric",row='?")" I think this will be hard to generalize

see also milankl/BitInformation.jl#25 (comment)

I'm not sure I managed to get my point across: If you approach the compression of fgco2 with the prior knowledge that your error should not be higher than 1% then you don't need the bitinformation algorithm. You can directly infer that for a max 1% error you'll need 6 mantissa bits

[aaronspring]

lets definately have a notebook how to deal with this. or even integrate just one plot into the quick-start

[milankl]

Note that both mean and standard deviation are not particularly insightful metrics for assessing bitrounding. Following the IEEE-754 standard, bitrounding is bias-free with respect to 0 and also for absolute values. Having said that, this is true for any data, as long as the assumption of a uniform distribution within ulp is true. If, for example, for some weird reason all your data is just larger than ulp/2 (ulp=unit in the last place, the distance between two adjacent representable numbers after rounding) there'll be a bias as every value is rounded up. But in practice, a bias-free rounding mode will not affect the mean.

A similar argument holds for standard deviation: As long as the standard deviation is much larger than ulp then rounding will not affect it.