Multiplication of Integer.MAX_VALUE in Java [duplicate]

Question

I was just playing around in Java. Wrote this small program:

public class MaxValue{
    public static void main(String[] args){
        int i  =  Integer.MAX_VALUE;
        for(int j = 1; j<=10;j++){
            System.out.println(i*j);
        }
    }
}

The output is as follows:

2147483647

-2

2147483645

-4

2147483643

-6

2147483641

-8

2147483639

-10

Now I got surprised. I do not know how to explain this output. I know I can use long instead for handling values more than the max limit of integer. However I am only interested to know how java calculates the this?

Answer 1

We need to analize binary content of the result:

Integer.MAX_VALUE * 1 = 0x7fffffff which is decimal 2147483647

Integer.MAX_VALUE * 2 = 0xfffffffe which is -2

Integer.MAX_VALUE * 3 = 0x17ffffffd but it is 33 bits, after truncation it is 0x7ffffffd which is 2147483645

and so on...

Answer 2

It is called an overflow. Since you are operating over the maximum possible value, any mathematical increasing operation can potentially end up in an overflow.

More info about overflows in Java: http://javapapers.com/core-java/java-overflow-and-underflow/