c++ comparing two floating point values

Question

I\'m wondering what is the difference for comparing two double between this two manner :

double a1 = ...;
double a2 = ....;

1. fabs(a1-a

Answer 1

Personally, I'm using std::nextafter for comparing two double. This use the smallest epsilon on a value (or a factor of the smallest epsilon).

bool nearly_equal(double a, double b)
{
  return std::nextafter(a, std::numeric_limits::lowest()) <= b
    && std::nextafter(a, std::numeric_limits::max()) >= b;
}

bool nearly_equal(double a, double b, int factor /* a factor of epsilon */)
{
  double min_a = a - (a - std::nextafter(a, std::numeric_limits::lowest())) * factor;
  double max_a = a + (std::nextafter(a, std::numeric_limits::max()) - a) * factor;

  return min_a <= b && max_a >= b;
}