Given two doubles, how to determine if their quotient is exact?

Given two double values, p and q, how can I determine if their quotient:

double result = p / q;

is an exact result in terms of the binary values of p and q?

That is, whether result is exactly equal to the mathematical division of p and q.

Clearly this is true for some values, such as 1.0 / 2.0 and false for others such as 1.0 / 5.0, so I'm looking for an idiomatic and accurate way to separate the cases.

It seems like the floating point modulus p % q == 0 might work, but I'm not sure!

You could use BigDecimal to see if the division is exact:

private static boolean canDivideExact(double p, double q) {
  double r = p / q;
  BigDecimal d = new BigDecimal(r);
  return d.multiply(new BigDecimal(q)).compareTo(new BigDecimal(p)) == 0;
}

For example:

System.out.println(canDivideExact(1, 2)); //true
System.out.println(canDivideExact(1, 3)); //false