Long Division when dividend and divisor are of same size (same number of digits)

I want to know if there is some optimized method (constant complexity preferred) to obtain the quotient when the dividend and the divisor contain the same number of digits. I know about algorithm D of “The Art of Computer Programming” but there Knuth describes how to find quotient digit when the dividend is $ n+1$ in length and divisor is $ n$ . Is there any method of finding the quotient digit when they both are of the same length? Obviously I can search linearly from $ 1$ to $ base$ or use Binary search for the same but I was looking for something more optimal as my Base is very large $ (\approx 10^{18})$