Java: Why does "long" number get negative?

Question

I have this code:

    long i = 0;
    while (true) {  
        i += 10*i + 5;
        System.out.println(i);
        Thread.sleep(100);      
    }

Why does the long i get negative after a few prints? If the range is exceeded, shouldn't an error occur?

Answer 1

Java doesn't throw an error if you increase a number after its maximum value. If you wish to have this behaviour, you could use the Math.addExact(long x, long y) method from Java 8. This method will throw an ArithmeticException if you pass the Long.MAX_VALUE.

The reason why Java doesn't throw an exception and you receive negative numbers has to do with the way numbers are stored. For a long primitive the first byte is used for indicating the sign of the number (0 -> positive, 1 -> negative), while the rest are used for the numeric value. This means that Long.MAX_VALUE which is the biggest positive value will be stored as 01111...111 (0 followed by 63 bits of 1). Since you add a number to Long.MAX_VALUE you will start receiving negative integers since the sign byte changes to 1. This means you have an numeric overflow, but this error isn't thrown by Java.