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IntX Description

An arbitrary precision integers library written in pure C# 2.0 with fast - about O(N * log N)

It provides all the basic arithmetic operations on integers, comparing, bitwise shifting etc. It also allows parsing numbers in different bases and converting them to string, also in any base. The advantage of this library is fast multiplication, division and from base/to base conversion algorithms - all the fast versions of the algorithms are based on fast multiplication of big integers using Fast Hartley Transform which runs for O(N * log N * log log N) time instead of classic O(N^2).

Bits of History
I have written IntX basically because I like big numbers and had some free time. Initial implementation was standard - I was using standard big integers +, -, *, / algorithms from Khuth book. After library was written I've decided to participate in contest held by GotDotNet.ru and received some replies which were saying that my library is too ... usual. Well, it was true, so I've decided to implement some more interesting algorithms in it.

I've started with writing multiplication using Fast Hartley Transform so big integers multiplication time estimate became to be O(N * log N * log log N) (here N is amount of DWORDs in number representation) which was a bit better then O(N^2) with classic algorithm :) Then I saw fast algorithm for transforming from one base to another in Knuth book; it was based on fast multiplication so Parse()/ToString() started working faster - O(N * (log N)^2) instead of O(N^2). Finally division was also optimized (again, with the help of fast multiplication) - became as fast as multiplication.

All this happened in 2005 year and in 2008 I've decided to publish this library on CodePlex - maybe it will be useful for someone out there (well, there is not so many similar libraries under .NET; also System.Numeric.BigInteger from .NET FW 3.5 was cancelled). Before publishing it on CodePlex I also made some cosmetic changes in code - used new .NET 2.0 features like generics (to minimize code duplication) and rewritten unit tests to use NUnit (they were previously written for MbUnit which is almost unknown and not used by community).

Code Example
Here is the sample of code which uses IntX and calculates 42 in power 1048576 (which is 2^20):

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