Arithmetic with IPv6 addresses (large integers)

I'm working with IPv6 addresses in the form:

FFFF:FFFF:FFFF:FFFF:FFFF:FFFF:FFFF:FFFF

Internally, I store them in an array:

TIp6Bytes = array [0..15] of Byte;

I need to manipulate the IPv6 addresses in a number of ways including adding, dividing, multiplying etc. Can anyone suggest a good way to do this?

I guess I should have mentioned that I'm working with Delphi 2009

After trying many of the suggestions I could not find a library that fulfilled all my needs and were bug free. I searched a little harder and found a relatively new library by Alex Ciobanu which does BigIntegers (and Big Cardinals) seamlessly allowing you to manipulate them in much the same way as you manipulate normal Integers, Cardinals etc.

As well as BigIntegers, the library also provides a number of very useful features. From the readme:

• A set of generic collections classes (List, Dictionary, HashSet, etc).
• Date/Time functionality all combined in a few structures (somehow equivalent to .NET's DateTime structure)
• Type Support concept that defines a set of default "support classes" for each built-in Delphi types (used as defaults in collections). Custom "type support" classes can be registered for your custom data types.
• BigCardinal and BigInteger data types.
• Smart pointers in Delphi

The library is being actively developed. In fact, the author fixed a small bug I found within a day.

You can read more about the library on Alex's blog and download DeHL from Google code.