Calculating nth root in Java using power method

Question

I was trying to get a cubic root in java using Math.pow(n, 1.0/3) but because it divides doubles, it doesn't return the exact answer. For example, with 125, this gives 4.9999999999. Is there a work-around for this? I know there is a cubic root function but I'd like to fix this so I can calculate higher roots.

I would not like to round because I want to know whether a number has an integer root by doing something like this: Math.pow(n, 1.0 / 3) % ((int) Math.pow(n, 1.0 / 3)).

Answer 1

Since it is not possible to have arbitrary-precision calculus with double, you have three choices:

1. Define a precision for which you decide whether a double value is an integer or not.
2. Test whether the rounded value of the double you have is a correct result.
3. Do calculus on a BigDecimal object, which supports arbitrary-precision double values.

Option 1

private static boolean isNthRoot(int value, int n, double precision) {
    double a = Math.pow(value, 1.0 / n);
    return Math.abs(a - Math.round(a)) < precision; // if a and round(a) are "close enough" then we're good
}

The problem with this approach is how to define "close enough". This is a subjective question and it depends on your requirements.

Option 2

private static boolean isNthRoot(int value, int n) {
    double a = Math.pow(value, 1.0 / n);
    return Math.pow(Math.round(a), n) == value;
}

The advantage of this method is that there is no need to define a precision. However, we need to perform another pow operation so this will affect performance.

Option 3

There is no built-in method to calculate a double power of a BigDecimal. This question will give you insight on how to do it.