Rounding Errors?

Question

In my course, I am told:

Continuous values are represented approximately in memory, and therefore computing with floats involves rounding errors. These are tiny discrepancies in bit patterns; thus the test e==f is unsafe if e and f are floats.

Referring to Java.

Is this true? I've used comparison statements with doubles and floats and have never had rounding issues. Never have I read in a textbook something similar. Surely the virtual machine accounts for this?

Answer 1

It is true.

It is an inherent limitation of how floating point values are represented in memory in a finite number of bits.

This program, for instance, prints "false":

public class Main {
  public static void main(String[] args) {
    double a = 0.7;
    double b = 0.9;
    double x = a + 0.1;
    double y = b - 0.1;
    System.out.println(x == y);
  }
}

Instead of exact comparison with '==' you usually decide on some level of precision and ask if the numbers are "close enough":

System.out.println(Math.abs(x - y) < 0.0001);