Comparing floating point number to zero

Question

The C++ FAQ lite "[29.17] Why doesn't my floating-point comparison work?" recommends this equality test:

#include <cmath>  /* for std::abs(double) */  inline bool isEqual(double x, double y) {   const double epsilon = /* some small number such as 1e-5 */;   return std::abs(x - y) <= epsilon * std::abs(x);   // see Knuth section 4.2.2 pages 217-218 } 

1. Is it correct, that this implies that the only numbers which are equal to zero are +0 and -0?
2. Should one use this function also when testing for zero or rather a test like |x| < epsilon?

Update

As pointed out by Daniel Daranas the function should probably better be called isNearlyEqual (which is the case I care about).

Someone pointed out "Comparing Floating Point Numbers", which I want to share more prominently.

Answer 1

You are correct with your observation.

If x == 0.0, then abs(x) * epsilon is zero and you're testing whether abs(y) <= 0.0.

If y == 0.0 then you're testing abs(x) <= abs(x) * epsilon which means either epsilon >= 1 (it isn't) or x == 0.0.

So either is_equal(val, 0.0) or is_equal(0.0, val) would be pointless, and you could just say val == 0.0. If you want to only accept exactly +0.0 and -0.0.

The FAQ's recommendation in this case is of limited utility. There is no "one size fits all" floating-point comparison. You have to think about the semantics of your variables, the acceptable range of values, and the magnitude of error introduced by your computations. Even the FAQ mentions a caveat, saying this function is not usually a problem "when the magnitudes of x and y are significantly larger than epsilon, but your mileage may vary".