You need to handle integer numbers larger than Long.MAX_VALUE or floating-point values larger than Double.MAX_VALUE.

Use the BigInteger or BigDecimal values in package java.math :

// BigNums.java 
System.out.println("Here's Long.MAX_VALUE: " + Long.MAX_VALUE); 
BigInteger bInt = new BigInteger("3419229223372036854775807"); 
System.out.println("Here's a bigger number: " + bInt); 
System.out.println("Here it is as a double: " + bInt.doubleValue(  ));

Note that the constructor takes the number as a string. Obviously you couldn’t just type the numeric digits, since by definition these classes are designed to represent numbers larger than will fit in a Java long.

Both BigInteger and BigDecimal objects are immutable; that is, once constructed, they always represent a given number. That said, there are a number of methods that return new objects that are mutations of the original, such as negate( ) , which returns the negative of the given BigInteger or BigDecimal. There are also methods corresponding to most of the Java language built-in operators defined on the base types int/long and float/double. The division method makes you specify the rounding method; consult a book on numerical analysis for details. Here is a simple stack-based calculator using BigDecimal as its numeric data type:

import java.math.BigDecimal;
import java.util.Stack;

/** A trivial reverse-polish stack-based calculator for big numbers */
public class BigNumCalc {

    /** an array of Objects, simulating user input */
    public static Object[] input = {
        new BigDecimal("3419229223372036854775807.23343"),
        new BigDecimal("2.0"),
        "*",
        "=",
    };

    public static void main(String[] args) {
        Stack s = new Stack(  );
        for (int i = 0; i < input.length; i++) {
            Object o = input[i];
            if (o instanceof BigDecimal)
                s.push(o);
            else if (o instanceof String) {
                switch (((String)o).charAt(0)) {
                case '+':
                    s.push(((BigDecimal)s.pop()).add((BigDecimal)s.pop(  )));
                    break;
                case '-':
                    s.push(((BigDecimal)s.pop()).subtract((BigDecimal)s.pop(  )));
                    break;
                case '*':
                    s.push(((BigDecimal)s.pop()).multiply((BigDecimal)s.pop(  )));
                    break;
                case '/':
                    s.push(((BigDecimal)s.pop()).divide((BigDecimal)s.pop(  ),
                        BigDecimal.ROUND_UP));
                    break;
                case '=':
                    System.out.println(s.pop(  ));
                    break;
                default:
                    throw new IllegalStateException("Unknown OPERATOR popped");
                }
            } else {
                throw new IllegalStateException("Syntax error in input");
            }
        }
    }
}

Running this produces the expected (very large) value:

> jikes +E -d . BigNumCalc.java
> java BigNumCalc
6838458446744073709551614.466860
>

The current version has its inputs hardcoded, but in real life you can use regular expressions to extract words or operators from an input stream (as in Section 4.8) or use the StreamTokenizer approach of the simple calculator (Section 9.13). The stack of numbers is maintained using a java.util.Stack (Section 7.16).

BigInteger is mainly useful in cryptographic and security applications. Its method isProbablyPrime( ) can create prime pairs for public key cryptography. BigDecimal might also be useful in computing the size of the universe.