
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 wellrounded 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 restructured 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 evergrowing 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
wellrounded suite of algorithms for basic problems.
