Double comparison precision loss in C#, accuracy loss happening when adding subtracting doubles

Question

Just started learning C#. I plan to use it for heavy math simulations, including numerical solving. The problem is I get precision loss when adding and subtracting double's, as well as when comparing. Code and what it returns (in comments) is below:

namespace ex3
{
    class Program
    {
        static void Main(string[] args)
        {

            double x = 1e-20, foo = 4.0;

            Console.WriteLine((x + foo)); // prints 4
            Console.WriteLine((x - foo)); // prints -4
            Console.WriteLine((x + foo)==foo); // prints True BUT THIS IS FALSE!!!
        }
    }
}

Would appreciate any help and clarifications!

What puzzles me is that (x + foo)==foo returns True.

Answer 1

Take a look at the MSDN reference for double: https://msdn.microsoft.com/en-AU/library/678hzkk9.aspx

It states that a double has a precision of 15 to 16 digits.

But the difference, in terms of digits, between 1e-20 and 4.0 is 20 digits. The mere act of trying to add or subtract 1e-20 to or from 4.0 simply means that the 1e-20 is lost because it cannot fit within the 15 to 16 digits of precision.

So, as far as double is concerned, 4.0 + 1e-20 == 4.0 and 4.0 - 1e-20 == 4.0.