[bArray]

> it’s strictly limited to only being able to compute x/y when |x|>|y|. Anything else, you get garbage, including in the y=x

I think it's literally just to keep the math circuit logic very simple, it'll be identical to MOD (just need to look at the remainder register) and |x| <= |y| will either require some hackery to convert it (with an appropriate test) or the machine having some idea of non-integer numbers.

For implementation of division, you could have the circuit equivalence of:

    uint div(x, y){
      uint t = x; //temporary (don't want to touch x)
      uint c = 0; //counter
      while(t >= y){
        t = t - y;
        c = c + 1;
      }
      return c; //remainder is in t
    }

Not sure about the x == y case though.

Of course there would be no checking, hence the garbage out when you misuse it. Your checking would be done manually.

[1] https://en.wikipedia.org/wiki/Ones%27_complement