NaN and negative zero with == and equals

public class Main {
    public static void main(String[] args) {
        double nan = Double.NaN;
        System.out.println(nan == nan);
        System.out.println(Double.valueOf(nan).equals(nan));
        System.out.println(0.0 == -0.0);
        System.out.println(Double.valueOf(0.0).equals(-0.0));
    }
}