How to compare that sequence of doubles are all “approximately equal” in Java?

Question

I have a method in java that returns a double number and I want to compare every double number that is returned every time I call the method(say 5 times), so that I can conclude

Answer 1

It depends on what you mean by similar. If you want to compare two numbers within an absolute error e.g. 1e-6 you can use epsilon. If you want to compare two double regardless of scale. e.g. 1.1e-20 and 1.3e-20 are not similar but 1.1e20 and 1.1e20+1e5 are you can compare the raw value.

public static void main(String... args) throws IOException {
    test(1.1e-20, 1.3e-20);
    test(1.1e20, 1.1e20 + 1e5);
}

private static void test(double a, double b) {
    System.out.println(a + " and " + b + ", similar= " + similarUnscaled(a, b, 10));
}

public static boolean similarUnscaled(double a, double b, long representationDifference) {
    long a2 = Double.doubleToRawLongBits(a);
    long b2 = Double.doubleToRawLongBits(b);
    // avoid overflow in a2 - b2
    return ((a2 >= 0) == (b2 >= 0)) &&
            Math.abs(a2 - b2) <= representationDifference;
}

prints

1.1E-20 and 1.3E-20, similar= false
1.1E20 and 1.100000000000001E20, similar= true