Question

Is division by zero possible in the following case due to the floating point error in the subtraction?

float x, y, z;
...
if (y != 1.0)
    z = x / (y - 1.0);

In other words, is the following any safer?

float divisor = y - 1.0;
if (divisor != 0.0)
    z = x / divisor;

Answer 1

This will prevent you from dividing by exactly zero, however that does not mean still won’t end up with +/-inf as a result. The denominator could still be small enough so that the answer is not representable with a double and you will end up with an inf. For example:

#include <iostream>
#include <limits>

int main(int argc, char const *argv[])
{
    double small = std::numeric_limits<double>::epsilon();
    double large = std::numeric_limits<double>::max() / small;
    std::cout << "small: " << small << std::endl;
    std::cout << "large: " << large << std::endl;
    return 0;
}

In this program small is non-zero, but it is so small that large exceeds the range of double and is inf.