invmod(n::BitInteger): efficient native modular inverses

[StefanKarpinski]

Implement algorithm described in https://arxiv.org/pdf/2204.04342.pdf. The algorithm is pleasingly simple and efficient and the generic Julia implementation is also really enjoyable.

[oscardssmith]

I'm not sure this is invmod. I think this method should possibly be invmod(n::T, T) where T for consistency

[StefanKarpinski]

It's a modular inverse where the modulus is implied by the type. In an alternate history I could see having inv(n::T) mean this, but we've already defined that to mean 1/n which is not this operation.

I'm certainly ok with having an invmod(n::Integer, ::Type{T}) where {T<:Integer} method, but its definition would simply be invmod(n % T). I can add that method to the PR.

[oscardssmith]

my point is that I don't think invmod makes sense as a 1 argument function (because inv mod what?)

[StefanKarpinski]

because inv mod what?

Mod by the the modulus implied by type of the argument. It seems reasonable to have an abbreviation for invmod(n, typeof(n)). What other function would you add that method to? We could define a new modinv(n) function for that, but why? This seems like a very natural and convenient place for this functionality.

[oscardssmith]

fair enough.

[StefanKarpinski]

Failures look unrelated, this is a simple PR, and there's a decent spread of successes, so I'm gonna merge.