Code or Algo for Modulo Division

Question

I need to find Res = (A / B) % P. (P is prime).

I have Num = A % P, and Den = B % P.

Is there any way to find Res just by using Num, Den and P?

I came across this :

(a / b) mod p = ((a mod p) * (b^(-1) mod p)) mod p 
i.e. Res = (Num * b ^ (p - 2) % p) % p

Now how can I find b^(p-2) % p using Den?

If you can provide me with a C++/C code, I would be more than happy, as I can then directly use it in my game, otherwise, please help me in finding a formula, so that I can obtain the Res on my own.

Answer 1

You can get the result of b^(p-2) % p using quick exponentiation.

int qexp (int b, int e) {
    if (e == 0) return 1;
    long long h = qexp(b, e/2); //long long to prevent overflow in next step
    h *= h;
    h %= p;
    if (e % 2 == 0) return h;
    else return (h*b)%p;
}

call using qexp(b, p-2);