No, but I'm out of ideas for how to explain it any more clearly. If you really think this is all correct behavior and IA is going to make your life better, start using it in production and you'll learn it the hard way.
> If you really think this is all correct behavior and IA is going to make your life better, start using it in production and you'll learn it the hard way.
Even if this may come out as a bit snarky, this is a very good, honest, and helpful answer. At least, it would be helpful to extremely skeptical people like me. I'm a bit like crazygringo, and I cannot be convinced of anything until I have tried it myself and dirtied my hands with it.
To crazygringo: for a concrete, real-world example, try to implement a Kalman filter (a very simple numerical algorithm) using interval arithmetic. It simply doesn't work. You'll see that you cannot extract any useful result from the output of the computation. The implementation of an "interval Kalman filtering" is a (niche) subject of current research, where various very complicated algorithms are being invented to try to reproduce the nice properties of Kalman filtering--even when using something obviously inappropriate like interval arithmetic. For an intuitive understanding, assume that the input data are quantized to integer values, so that the starting intervals are of length 1.
I guess I just don't see why it's worse than FP. I mean, you said:
> Contrast this with just leaving it as a float instead of an interval, where you would've gotten the correct answer.
But if I type into my console:
var a = 0.1; var b = a + 0.2; b -= 0.2; b == a;
I get false. That's not correct. Whereas if "==" checked for overlap between intervals, it would be true. Which would be correct.
Heck, to use your own division example:
(0.1 + 0.2 - 0.2) / 0.1 ==> 1.0000000000000002
That's not 1.0. So the FP you claim is so correct... just isn't at all. Again, while interval arithmetic would correctly detect overlap of intervals between that and 1.0.
Ah, thanks for that, I finally understand what you were getting at. I see now what you mean about intervals growing larger than they actually need to in formulas that use the same variable more than once, that is an unfortunate drawback.
Now you've got me learning about how affine arithmetic can help with the dependency problem but has its own drawbacks. Thanks for pointing me in that direction!
I think you run into the opposite issue, where equality is too likely and nonequal values return as equal. There might be a sweet spot with something like
Even if this may come out as a bit snarky, this is a very good, honest, and helpful answer. At least, it would be helpful to extremely skeptical people like me. I'm a bit like crazygringo, and I cannot be convinced of anything until I have tried it myself and dirtied my hands with it.
To crazygringo: for a concrete, real-world example, try to implement a Kalman filter (a very simple numerical algorithm) using interval arithmetic. It simply doesn't work. You'll see that you cannot extract any useful result from the output of the computation. The implementation of an "interval Kalman filtering" is a (niche) subject of current research, where various very complicated algorithms are being invented to try to reproduce the nice properties of Kalman filtering--even when using something obviously inappropriate like interval arithmetic. For an intuitive understanding, assume that the input data are quantized to integer values, so that the starting intervals are of length 1.