Addition and subtraction

[EricDarve]

floating-point-gui.de/content/errors/propagation.html

Line 13 in 3d2c97d

* Addition and subtraction are dangerous, because when numbers of different magnitudes are involved,

I don't think this line really represents what is happening. The typical problem is trying to subtract 2 numbers that are almost equal. An example is computing (exp(eps) - 1) / eps. For a small eps, exp(eps) - 1 may be computed with insufficient accuracy and the final result is typically inaccurate. Adding/subtracting numbers that have different magnitudes typically does not lead to issues in a computation.
See "Catastrophic cancellation" in your reference
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

[brazzy]

The problem I had in mind was the one solved by Kahan summation. But catastrophic cancellation is of course also important and not addressed by the line you cited. I have expanded this line to explain and give examples for both issues.

Thanks for bringing this to my attention!