How do you implement complementary "A*(A*A) = A^3" operator overloads (I'm getting strange results)

[IchorDev]

On Monday, 19 August 2024 at 09:42:44 UTC, Daniel Donnelly, Jr. 
wrote:
> ```d
>    Type opBinary(string op="^")(int k)
>    in {
>       assert (k > 0);
>    }
>    do {
>       if (k == 1)
>          return this;
>
>       auto P = this;
>
>       while (k > 0)
>       {
>          k --;
>          P = this * P;
>       }
>
>       return P;
>    }
> ```

`^` should be a bitwise XOR, instead you can overload `^^` which 
is for exponentiation.

Also, your algorithm is a little bit flawed. To rework it, it 
would help if you consider cases like:
- `1^^n == 1`
- `n^^0 == sign(n)` (if `n` is 0, returns 1 or undefined)
- `0^^n == 0` (divide by zero if `n` is negative)

It’s cases like these which can help inform us how the algorithm 
should work. If you can’t think of how you’d make all those cases 
line up correctly, try looking at an existing integer 
exponentiation algorithm online. An algorithm written in another 
language will still be applicable in D.