Turn while loop into math equation?

Question

I have two simple while loops in my program that I feel ought to be math equations, but I'm struggling to convert them:

float a = someValue;
int b = someOtherValue;
int c = 0;

while (a <= -b / 2) {
    c--;
    a += b;
}
while (a >= b / 2) {
    c++;
    a -= b;
}

This code works as-is, but I feel it could be simplified into math equations. The idea here being that this code is taking an offset (someValue) and adjusting a coordinate (c) to minimize the distance from the center of a tile (of size someOtherValue). Any help would be appreciated.

Answer 1

I think you want something like this:

c = ((int) a + b / 2 * sign(a)) / b

That should match your loops except for certain cases where b is odd because the range from -b/2 to b/2 is smaller than b when b is odd.

Answer 2

Assuming b is positive, abs(c) = floor((abs(a) - b/2) / b). Then, apply sign of a to c.

Answer 3

c = (int)((a - (b / 2)) / b + 1);
a -= c * b;

Test case at http://pastebin.com/m1034e639