1/2
gives
0
as it should. However,
-1/2
-1
Throwing my hat in with a few alternate ideas:
Multiple the sign of the number [abs(x)/x] by the abs(x)/2
(abs(x)/x)*(abs(x)/2)
Perform the addition, but if the number is less than zero add one to shift it closer to 0.
x/2 + int(x<0)