Author here. Outward rounding to combat precision issues is what interval arithmetic is most known for (try 0.1+0.2 with "full precision mode" enabled), but that's really a shame in my opinion. Outward rounding is cool, but the "inclusion property", as it's known in research papers, works at every scale! This is what enables things like:
50 * (10 + [-1, 1])
[450, 550]
which is lovely, I think. Adding the union layer to it enables even cooler things, like the true inverse of the square function. Did you know it's not sqrt? Try 'sqinv(64)'.
I made interval calculator actually mostly as a way to test my implementation of interval union arithmetic [0], which I needed for another project: a backwards updating spreadsheet [1][2].
Very nice, thanks for sharing!
Maybe show which upper or lower values are included in the intervals?
A notation I am familiar with uses outward facing brackets if the value is not included in the interval. That always applies to infinity.
Applied to the cases here:
]-∞, -1] U [0.5, +∞[
The excluded interval in between becomes ]-1, 0.5[ then.
That’s how min (and analogously max) works, right?
min(A, B) = [lo(A,B), lo (hi(A), hi(B))].
Edit: idea: copy a formula from the results section to the input field if the user clicks/taps on it.
It's possible to support that but it makes the code very very much more complicated. I've decided early on to not support it. Would be a cool addition though!
From reading the linked paper[0], It explains closed interval only. "An interval union is a set of closed and disjoint intervals where the bounds of the extreme interval can be ±∞".
Excellent!! I love interval arithmetic and also wrote a TS implementation for a graphing calculator project. Agree that it's very underrated, and I wish that directed rounding was exposed in more languages.
I made interval calculator actually mostly as a way to test my implementation of interval union arithmetic [0], which I needed for another project: a backwards updating spreadsheet [1][2].
[0] https://github.com/victorpoughon/not-so-float
[1] https://victorpoughon.github.io/bidicalc/
[2] https://news.ycombinator.com/item?id=46234734
https://youtu.be/UxGxsGnbyJ4?si=Oo6Lmc4ACaSr5Dk6&t=1006
Applied to the cases here:
]-∞, -1] U [0.5, +∞[
The excluded interval in between becomes ]-1, 0.5[ then.
That’s how min (and analogously max) works, right? min(A, B) = [lo(A,B), lo (hi(A), hi(B))].
Edit: idea: copy a formula from the results section to the input field if the user clicks/taps on it.
[0]: https://www.ime.usp.br/~montanhe/unions.pdf
https://memalign.github.io/m/formulagraph/index.html
Some detail on how this works, including links to the relevant interval math code:
https://memalign.github.io/p/formulagraph.html