Question

Suppose I have some code such as:

float a, b = ...; // both positive
int s1 = ceil(sqrt(a/b));
int s2 = ceil(sqrt(a/b)) + 0.1;

Is it ever possible that s1 != s2? My concern is when a/b is a perfect square. For example, perhaps a=100.0 and b=4.0, then the output of ceil should be 5.00000 but what if instead it is 4.99999?

Similar question: is there a chance that 100.0/4.0 evaluates to say 5.00001 and then ceil will round it up to 6.00000?

I’d prefer to do this in integer math but the sqrt kinda screws that plan.

EDIT: suggestions on how to better implement this would be appreciated too! The a and b values are integer values, so actual code is more like: ceil(sqrt(float(a)/b))

EDIT: Based on levis501’s answer, I think I will do this:

float a, b = ...; // both positive
int s = sqrt(a/b);
while (s*s*b < a) ++s;

Thank you all!

Answer 1

You may want to write an explicit function for your case. e.g.:

/* return the smallest positive integer whose square is at least x */
int isqrt(double x) {
  int y1 = ceil(sqrt(x));
  int y2 = y1 - 1;
  if ((y2 * y2) >= x) return y2;
  return y1;
}

This will handle the odd case where the square root of your ratio a/b is within the precision of double.