Question

Here is a Java program that left shifts the short value of 2. I have two questions:

Why does num << i for values of i between 16 and 29 produce valid results? A short should only hold values from -32,768 to 32,767.

So I thought, maybe System.out.println interprets num << i as a value larger than a short. But then why does it start producing unexpected values at num << 30?

public class LeftShift {

    public static void main(String[] args)
    {
        short num = 2;
        for (int i = 0; i < 32; i++) {
            System.out.println("Left-shifting 2 by " + i + " places yields: " 
                                + (num << i));
        }
    }

}

The output:

Left-shifting 2 by 0 places yields: 2
Left-shifting 2 by 1 places yields: 4
Left-shifting 2 by 2 places yields: 8
Left-shifting 2 by 3 places yields: 16
Left-shifting 2 by 4 places yields: 32
Left-shifting 2 by 5 places yields: 64
Left-shifting 2 by 6 places yields: 128
Left-shifting 2 by 7 places yields: 256
Left-shifting 2 by 8 places yields: 512
Left-shifting 2 by 9 places yields: 1024
Left-shifting 2 by 10 places yields: 2048
Left-shifting 2 by 11 places yields: 4096
Left-shifting 2 by 12 places yields: 8192
Left-shifting 2 by 13 places yields: 16384
Left-shifting 2 by 14 places yields: 32768
Left-shifting 2 by 15 places yields: 65536
Left-shifting 2 by 16 places yields: 131072
Left-shifting 2 by 17 places yields: 262144
Left-shifting 2 by 18 places yields: 524288
Left-shifting 2 by 19 places yields: 1048576
Left-shifting 2 by 20 places yields: 2097152
Left-shifting 2 by 21 places yields: 4194304
Left-shifting 2 by 22 places yields: 8388608
Left-shifting 2 by 23 places yields: 16777216
Left-shifting 2 by 24 places yields: 33554432
Left-shifting 2 by 25 places yields: 67108864
Left-shifting 2 by 26 places yields: 134217728
Left-shifting 2 by 27 places yields: 268435456
Left-shifting 2 by 28 places yields: 536870912
Left-shifting 2 by 29 places yields: 1073741824
Left-shifting 2 by 30 places yields: -2147483648
Left-shifting 2 by 31 places yields: 0

Answer 1

Because arithmetic operations on shorts yield ints, unless you cast them back down. For example,

short value = 2;
short result = value << 31;

gives you a compile error that you need to cast it down to a short.

This is for a couple reasons, most notably

• the bytecode language doesn’t really deal with any types smaller than int
• otherwise operations on shorts overflow much more often.
• to better model most hardware, which usually doesn’t do operations on sub-32-bit values