Added modMultiplicativeInverseNumber to the number arithmetic module

[ohpyupi]

Addressed #1744

So far, I added a function modMultiplicativeInverseNumber in the number arithmetic module. And I guess remaining task is to implement this function to the library. But before doing it, I wanted to open this PR to get feedbacks and comments in early steps.

[josdejong]

Thanks @ohpyupi , this is a nice start! Next step will indeed be to make an implementation that supports data types like BigNumber, and expose it in the library as a new function.

What would make most sense to return when there is no result? Currently you return null, but maybe NaN is more logic and consistent with the rest of the library. What do you think.

[ohpyupi]

@josdejong Totally agree. I will start implementing supporting other types and replace null with NaN. Thanks!

[josdejong]

Hi @ohpyupi, did you find some time already to work further on this PR?

[ohpyupi]

@josdejong Hi. I was busy for last few weeks. I will have time to work on it from next weekend.

[josdejong]

Thanks for the update! Take it easy :)

[ohpyupi]

@josdejong I think I cannot extend the argument type to both float and big number since xgcdNumber throws an error if the params are non-integer. I need to update this function's logic in a way it can handle non-integer as well.

[josdejong]

@ohpyupi The xgcd function indeed only works with integers.

To get a working solution for BigNumber, you can inject xgcd instead of using xgcdNumber, this works for number and BigNumber. Like:

const dependencies = ['typed', 'xgcd']
// ...
export const createModMultiplicativeInverse = /* #__PURE__ */ factory(name, dependencies, ({ typed, xgcd }) => {
  // ...
  const [div, m] = xgcd(a, b)
  // ...
}

[ohpyupi]

@josdejong Oh cool! But what about the float type? Does it work with the float type as well?

[josdejong]

The function xgcd does not support floats, only integer values. Function mod does support floats. If needed for modMultiplicativeInverseNumber I guess we have to extend xgcd?

[ohpyupi]

What about this? In this scope of PR, I ignore the float support for the modular inverse. And if the float support is requested, it can be implemented then. let me know if this approach works on your end.

[josdejong]

Yes that sounds like a pragmatic approach 👍

[gwhitney]

Was this superseded by #2368 and should be closed?

[josdejong]

I think so. Let's close this PR. Feel free to reopen if needed Hoseong Lee.