How to get the Nth digit of an integer with bit-wise operations?

Question

Example. 123456, and we want the third from the right (\'4\') out.

The idea in practise is to access each digit seperately (ie. 6 5 4 3 2 1).

C/C++/C# preferred.

Answer 1

This works for unsigned ints up to 451069, as explained here:

def hundreds_digit(u): return mod10(div100(u))

def div100(u): return div10(div10(u))
def mod10(u):  return u - mul10(div10(u))
def mul10(u):  return ((u << 2) + u) << 1

def div10(u):
    Q = ((u >> 1) + u) >> 1  # Q = u*0.11
    Q = ((Q >> 4) + Q)       # Q = u*0.110011
    Q = ((Q >> 8) + Q) >> 3  # Q = u*0.00011001100110011
    return Q

# Alternatively:
#   def div100(u): return (u * 0xa3d7) >> 22
# though that'd only work for 16-bit u values.
# Or you could construct shifts and adds along the lines of div10(),
# but I didn't go to the trouble.

Testing it out:

>>> hundreds_digit(123456)
4
>>> hundreds_digit(123956)
9

I'd be surprised if it's faster, though. Maybe you should reconsider your problem.