s1 = ((a / 2) / b) * 2;
[download]

Then, we use the approximation to build the exact solution as:

s = s1 + (a - s1 * b) / b
[download]

Well, actually, in order to do everything using bug-free operations, the code uses the following equivalence:

s2 = (a / 2) / b
s1 = s2 * 2
s = s1 + (a - s1 * b) / b
s = s2 * 2 + (a - (s2 * b) * 2) / b
[download]