BigInteger

A more serious issue is that often arithmetic operations need to be exact. Recall that operations with floating point are often not exact. double is represented in 64 bits, so only some numbers in its range can be represented exactly. For number theory, cryptography, and other applications, exact calculations are needed.

The Advance Encryption Standard (the most commonly used cipher), uses keys up to 256 bits in length. Ordinary arithmetic with ints is not going to work.

You could write your own methods where an integer is represented with array of ints. Addition could be done by adding corresponding elements of two arrays. Logic would be needed to deal with overflow from one element into the next higher element. But, conveniently, the Java BigInteger class already has what you need.

BigInteger implements immutable integers of unlimited magnitude. They can be as big or as negative as you need. Here is an example program:

import java.math.BigInteger;

class BigIntAdd
{

  public static void main ( String[] args )
  {
    BigInteger a = new BigInteger( "1000000000" );  
    BigInteger b = new BigInteger( "2000000000" );

    System.out.println("The sum of " + a + " and " + b + " is " + a.add( b ) );
  }
}


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The sum of 1000000000 and 2000000000 is 3000000000 

Notes:

1. BigInteger is a class (not a primitive type). Big integers are represented as objects.

2. import java.math.BigInteger to use the class.

3. The BigInteger objects are immutable. The value of a BigInteger object does not change, although a BigInteger reference variable can point to different objects as needed.

4. Arithmetic operations (and other operations) are implemented as methods of the class.

5. The usual operators (+, -, *, /) will not work. Use methods add, subtract, multiply, divide.

6. The result of using add, subtract, multiply, divide methods is another BigInteger.

7. The constructor used here takes a String of decimal digits representing an integer of any size. The String is converted into the internal representation used by BigInteger.

8. The toString() method of BigInteger is invoked when needed (as in the last statement above.)