Modulo operation for negative values

[ovk]

I noticed that A mod N (or mod(A, N)) operation in MathJS doesn't return expected values ("expected" in terms of modular arithmetic) for negative values of A. For example, -5 mod 3 returns -2 while the correct result should be 1 (example on wolframalpha).

In addition, mod also works for negative values of N while I think modulo operation is only defined for N > 1.

Here is an example of what MathJS returns (you can see it on clcalc that uses MathJS):

• 5 mod 3 = 2
• -5 mod 3 = -2
• 5 mod -3 = 2

My guess is that such behaviour is the result of how % operator behaves in Javascript (example).
However, while some programming languages like JS, or C/C++ (example) produce the same result
(although, my understanding is that for C/C++ the result in case of negative A is implementation defined), some others, like Python, give different answer (example).

I'm not sure what is the best way to address that. I think either MathJS mod operation should be fixed to behave like proper modulo operation, or the documentation/help should be changed to reflect the fact that it emulates what JavaScript % operator does, and is not proper modulo in terms of modular arithmetic.

[josdejong]

Thanks for your inputs.

If you try out those examples in the small demo calculator on https://mathjs.org/, it will return the outputs that you expect:

I'm not sure what is going on in clcalc, it seems to be using the latest version of mathjs. Maybe it has loaded the buildin JavaScript mod function instead or so?

[ovk]

Thanks for the pointers, @josdejong , I should've tried it myself before posting.

I tracked down what the differences are and here is a minimal reproducible example:

math.config({ 'number': 'BigNumber' });

// Prints: -2
console.log(math.evaluate('-5 mod 3').toString());

If you comment out the first line, then it returns the correct results (1). On clcalc I always use BigNumber which is why mod always appears "broken".

Looking at MathJS code for mod it looks like in the case of BigNumber it just invokes mod from the bignumber library. In the library itself there is MODULO_MODE (https://github.com/MikeMcl/bignumber.js/blob/master/bignumber.js#L144) which perhaps should be set to EUCLID to be consistent with MathJS mod when operating on Numbers?

[josdejong]

Ahhh, that makes sense. Yes, then we should change the MODULO_MODE of the library (I wasn't aware there was a setting for this).

Anyone interested in working this out in a PR and adding a few unit tests?

[ovk]

I also noticed the same issue with fractions:

mod(fraction("-5"), fraction("3")) 
-2/1

Unless somebody else volunteers, I'll work on a PR in a week or so (once I'm back to my computer).

[josdejong]

Thanks @ovk , would be great if you could pick this up 👍

[josdejong]

Fix is published now in v7.3.0 🎉