I'm pretty sure that most developers do not think about how to do right math with scalar types in Java. Experienced developers can say - "we do not use scalar types for business math, for this we use java.lang.BigDecimal."  And it is true, in Java world all business math operations used java.lang.BigDecimal or java.lang.BigInteger classes. But this article is not for business math.

Almost all Java developers know that the integer operators do not indicate overflow or underflow in any way (jls-4.2.2).

 For instance, we have to calculate half of the sum of variables a and b. Let's say that variables have type int and (a%2 ==0, b%2 == 0). Below we have the method doJob.

public int doJob(int a, int b) {
...
}

For this job (calculating half of the sum a and b) almost all developers will write code like this:

public int doJob(int a, int b) {
return (a + b)/2;
}

Even though they know about jls-4.2.2, but someone can say - "In my situation there is no possible way for a and b when the result of the doJob method will overflow or underflow." But when it somehow happens, there will be overflow or underflow. How can I rewrite the result in the doJob method to avoiding this? The answer is we must take care of expression. For any type of expression, you need to think how to write it more optimized to minimizing or even avoiding overflow or underflow.

We can rewrite this method:

public int doJob(int a, int b) {
return a/2 + b/2;
}

The current implementation avoids all collision of jls-4.2.2.

But ok, if we have expressions like this:

• a + b
• a * b
• etc.
  In Java 8 we have in class java.lang.Math additional methods for checking overflow and underflow:

public static int addExact(int x, int y)
public static long addExact(long x, long y)
public static int subtractExact(int x, int y)
public static long subtractExact(long x, long y)
public static int multiplyExact(int x, int y)
public static long multiplyExact(long x, long y)
public static int incrementExact(int a)
public static long incrementExact(long a)
public static int decrementExact(int a)
public static long decrementExact(long a)
// etc.

All these methods may throw ArithmeticException.

And now we do not need to check overflowing or underflowing by ourselves, we can use very helpful method like in this example:

public int doJobSum(int a, int b) {
return Math.addExact(a, b);
}

That's all, and if the result will overflow int type method addExact will throw ArithmeticException.

If you will check class java.lang.Math you can find many helpful methods since Java 8.