Also, with integers, a signed right shift is rounding down (towards negative infinity), whereas the division operator/instruction in many languages/hardware is rounding towards 0.

To adjust the rounding, you'd add the sign-bit to the first fractional bit before shifting the last step. Let's say that 'x' is a signed long, and a signed long has 64 bits, then:

result = ((x >> amount-1) + ((unsigned long)x >> 63)) >> 1;