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A Tour of NTL: Using NTL with the `GF2X` library

`gf2x` is a library for fast multiplication of polynomials over GF(2). The `gf2x` library was developed by Emmanuel Thomé, Paul Zimmermmann, Pierrick Gaudry, and Richard Brent. You can get more information about it, as well as the latest version from here.

Unlike NTL, which only imlements a version of Karatsuba multiplication, `gf2x` implements other algorithms that are faster for very large degree polynomials. If you use NTL if the `gf2x` library, then multiplication, division, GCD, and minimum polynomal calculations for the GF2X class will be faster for large degree polymials.

## Downloading and building `gf2x`

Download `gf2x` from here. You will get a file `gf2x-XXX.tar.gz`.

Now do the following:

       % gunzip gf2x-XXX.tar.gz
       % tar xf gf2x-XXX.tar
       % cd gf2x-XXX
       % ./configure --prefix=$HOME/sw
       % make
       % make check
       % make install

This will build, test, and install `gf2x` in `$HOME/sw`. Of course, change $HOME/sw to whatever you want (the default is `/usr/local`). You will find the `gf2x` header files in `$HOME/sw/include` and the compiled binaries in `$HOME/sw/lib`.

You can also supply the option `--disable-shared` to the `configure` script, if you only want static libraries. However, if you ultimately want to build NTL as a shared library, then you must also buld `gf2x` as a shared library.

You must ensure that NTL and `gf2x` have the same ABI. `gf2x`'s configuration script might need some help to select the right one. For example, you may have to pass

       ABI=64 CFLAGS="-m64 -O2"

to `gf2x`'s configure script to force a 64-bit ABI.

## Building and using NTL with `gf2x`

When building NTL with `gf2x`, you have to tell NTL that you want to use it. The easiest way to do this is by passing the argument `NTL_GF2X_LIB=on` to the NTL configuration script when you are installing NTL. Assuming you installed `gf2x` in `$HOME/sw` as above, and you also want to install NTL in `$HOME/sw`, you execute:

       % ./configure PREFIX=$HOME/sw NTL_GF2X_LIB=on  GF2X_PREFIX=$HOME/sw

You can write this more simply as

       % ./configure DEF_PREFIX=$HOME/sw NTL_GF2X_LIB=on

Here, `DEF_PREFIX` is a variable that is used to specify the location of all software, and it defaults to `/usr/local`.

If you installed `gf2x` in `/usr/local` (or some other standard system directory where your compiler will look by default) then simply

       % ./configure PREFIX=$HOME/sw NTL_GF2X_LIB=on

does the job. Moreover, if NTL is also to be installed in `/usr/local`, then

       % ./configure NTL_GF2X_LIB=on

does the job.

Instead of passing arguments to the configure script, you can also just edit the `config.h` and `makefile` by hand. The documentation in these files should be self-explanatory.

When compiling programs that use NTL with `gf2x`, you need to link with the `gf2x` library. If `gf2x` is installed as above in `$HOME/sw`, rather than in a standard system directory, this just means adding `-L$HOME/sw/lib -lgf2x` to the compilation command. If you installed `gf2x` in a standard system directory, then just `-lgf2x` does the job. Note that `-lgf2x` must come after `-lntl` on the command line. Finally, if NTL and `gf2x` are installed as shared libraries, then you don't even need `-lgf2x`.