Upon reaching a brick wall with the .Net framework's lack of a BigInteger class (yet), I've decided I'd like to develop my own as an exercise (I realize open source alternatives exist). What hoops do I need to jump through to be able to develop this? Is there any particuliar knowledge pieces that I probably wouldn't have?
edit: side question. Which data type would you use to represent the numbers inside of your new big integer class?
Arbitrary precision arithmetic?
Edit: To represent your numbers you will probably want a resizeable array of integers.
I would brush up on your basic math skills. When I wrote a Big Int class I had to remember how to add, multiply and divide by hand like in Elementary school.
Next if you are going to create a new class I would try to follow the standards that have been set up for the Framework. So it looks like any other .Net class.
I would follow TDD so you know your class works the way it is designed.
Maybe studying an already implemented BigInteger class might help?
You need to have a very good understanding of number systems. You could choose to represent the bignum in base 10, base 2 or any base x. This choice would affect your class performance a lot. You also have to choose the algorithms you want to implement. In general, great libraries like GMP for example, choose the algorithm based on the size of the operands. There are a lot of topics you have to be aware of, but in the end you should be convinced that you can't produce something really interesting. As a learning topic it is very valuable, but as producing something useful consider NOT reinventing the wheel!
If you want to dive really deep into the math of it, you need to read Donald Knuth.
.Net 3.5 has a BigInteger class, but it's scoped internal to the CLR. You can see the code using Reflector. Open System.Core.dll and look in the System.Numeric namespace. BigInteger is the only class in that namespace.
If you want to see the code for the F# BigInteger class, look in the [F# install folder]\source\fsharp\FSharp.Core\math\z.fs file.
If you use elementary algorithms, your BigInts will be unusable for very large integers, for example like Mersenne Primes.
If this is ok for you, use a simple 32 bit int as the basic data type. You need to handle 64 results in this case. If you don't care about speed at all, use some radix-10 number as base, lets say 10000, which will be very easy to implement.
This is mainly because the multiplication in a naive implementation has O(n^2) runtime. Advanced algorithms, based on fourier transforms, have O(n(log(n)) runtime. This requires some mathematical skills and knowledge.