Expressing relationship between two variables in pseudocode?

Question

I have some pseudocode I am trying to analyze:

public static void test(float z) {
  float y = 0;
  for (float i = 1; i <= z; i++) {
    if (y < z) {
      y = 4 * i * i + 6;
    }
  }
  return y;
}

From the function, I understand that y = 4i^2 + 6 whenever y < z . However, I am having trouble capturing the relationship between y and z in an equation. I feel that it could be captured as a floor function (step function) -- for a certain range of numbers in z, y will have that specified value.

Answer 1

y becomes greater than z (and stops changing) for the first i such that 2*i^2 + 3 > z . In other words, a minimal i > sqrt((z - 3) / 2) , which is floor(sqrt((z - 3)/2)) + 1 . Now as you know i , compute y .