How to get the modulus of two intervals or intervalsets?

[jyswjjgdwtdtj]

I'm interest in interval arithmetic. And thank for graphest, this wonderful mathematical function graph software gives me the ability to approach the beautiful world of mathematics and interval arithmetic. I have been looking for the implementation of interval arithmetic but i only find very few of them for "Rational", maybe "Rational" is a simplified version of interval?
I'd like to know how to get the modulus of two intervals or intervalsets. When I use i1-Floor(i1/i2)*i2 to calculate i1%i2 directly, I found it incorrect at the place where i2->0, like i1/i1 at i1->0. So what's the way that graphest do this? Or graphest use Subpixel test to get rid of all its incorrect?

[unageek]

Hi! Thank you for your encouraging words!

rug::Rational is used for constant folding during the AST transformation and does not involve interval arithmetic. Does that answer your question?

[unageek]

OK, that makes sense. Although it is different from what Graphest is doing, your method should give a valid interval as well. Anyway, you should be very careful when implementing interval algorithms/functions. It is also possible that the .NET's trigonometric functions do not always return the closest floating-point number, so do not rely on them.

[jyswjjgdwtdtj]

yes, i have done it in IntervalSetMath.cs.
And maybe it is not necessary to pursue the most accurate calculation results, but to fix the image by "subpixels"(marching squares uh?), because it can't be absolutely correct when calculate expressions like x-x or x/x in interval algorithms no matter how you refine the result. Actually I'm curious about how you use marching squares and branch cut in graphest😊. I have been trying to read your code but rust is a bit unreadable.

[jyswjjgdwtdtj]

Could you tell me more details about subpixel test? when i use marching squares merely, image drawn by my program may have some mistakes, which happen to programs using marching squares like desmos.
(+)--(+)
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marching squares can not find that a curve passes through a square like this. It's useless to divide the square into four part and do so again. How do you deal with the problem?😊

[unageek]

Please take a closer look at both my code and yours. I'd be happy to help if your question were more specific.

[jyswjjgdwtdtj]

you are right. but rust is really unreadable and i failed to configure the environment of rust in vscode.
i just want to know the steps of subpixel. i have read your comments in implicit.rs many times, but i can't understand them. they're a bit imprecise i think. and name of functions can't reflect its role visually.
i am sorry that i didn't get back to you in time. i'm in high school and you know, i cannot use phone in school.