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A Tour of NTL: NTL past, present, and future

### Some History

Work on NTL started around 1990, when I wanted to implement some new algorithms for factoring polynomials over finite fields. I found that none of the available software was adequate for this task, mainly because the code for polynomial arithmetic in the available software was too slow. So I wrote my own. My starting point was Arjen Lenstra's LIP package for long integer arithmetic, which was written in `C`. It soon became clear that using `C++` instead of `C` would be much more productive and less prone to errors, mainly because of `C++`'s constructors and destructors which allow memory management to be automated. Using `C++` has other benefits as well, like function and operator overloading, which makes for more readable code.

One of the basic design principles of LIP was portability. I adopted this principle for NTL as well, for a number of reasons, not the least of which was that my computing environment kept changing whenever I changed jobs. Achieving portability is getting easier as standards, like IEEE floating point, get widely adopted, and as the definition of and implementations of the `C++` language stabilize (which a few years ago was a huge headache, but is now only a big one, and in a few years will be a small one).

Since 1990, NTL has evolved in many ways, and it now provides a fairly polished and well-rounded programming interface.

When I started working on NTL, there really were not that many good, portable long integer packages around. Besides LIP, there was the BSD Unix MP library. The first version of GMP was released in the early 1990's. At that point in time, LIP seemed like the best starting point. LIP remains a reasonable long integer package, but in recent years, GMP has really become quite good: it seems well supported on many platforms, and is typically much faster than LIP.

I've now re-structured NTL so that one can use either 'traditional' LIP or GMP as the primary long integer package. Doing this introduced some (minor) backward incompatabilies in the programming interface, so there is also a 'third way' -- you can use GMP as a supplemental long integer package, getting many (but not all) of the performance benefits of GMP, while maintaining complete backward compatability with the traditional long integer package. This 'third way' is not highly recommended -- it is only intended as backward compatabilty hack.

### The Future of NTL

I hope that NTL remains stable in its current form. I plan to support NTL, fixing bugs and serious performance problems, but otherwise not to add significant new functionality or modify the programming interface.

I don't have time to add significant new functionality to NTL. However, there seems to be an ever-growing number of NTL users out there, and I encourage them to make their code available to others. These might be in the form of NTL "add ons", but there is the possibility of integrating new functionality or algorithmic improvements into NTL itself. One thing in particular that would be nice is support for bivariate polynomial arithmetic, including GCDs, resultants, and factoring, and for integer and all the various finite field coefficient rings. Another nice thing would be code for elliptic curves, including an elliptic curve point counting algorithm. Another nice thing would be something for factoring integers. Any one of these projects would be a nice master's thesis project, I think.

As you can well imagine, there is potentially no end to algorithms one could implement. That is why I have to stop somewhere. I think NTL has reached a point where it provides a reasonably well-rounded suite of algorithms for basic problems.