A Tour of NTL: Using NTL with GMP

GMP is the GNU Multi-Precision library. You can get more information about it, as well as the latest version from here.

Briefly, GMP is a library for long integer arithmetic. It has hand-crafted assembly routines for a wide variety of architectures. For basic operations, like integer multiplication, it can be two to three (and sometimes bit more) times faster than NTL's traditional long integer package. The speedup is most dramatic on x86 machines.

As of version 9.6.3, NTL uses GMP by default. You can disable GMP by passing NTL_GMP_LIP=off as an option to NTL's configure script. If you disable the use of GMP, NTL uses a long integer package derived from Arjen Lenstra's LIP package. This is not recommended: GMP is much faster.

Even if you do not use GMP, you should still read the section below on backward compatabilty so that you can write portable code and avoid deprecated constructs.

Note: GMP is thread safe, so you should feel free to use it in a thread-safe build of NTL. However, the current version of GMP (v6.1) is not entirely exception friendly (it may abort a running program, but only in some very extreme and unusal circumstances).

Downloading and building GMP

Many unix distributions now include GMP by default. But if not, it is pretty easy to install it directly from source, as follows.

Download GMP from here. You will get a file gmp-XXX.tar.gz.

Now do the following:

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

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 GMP as a shared library.

You must ensure that NTL and GMP have the same ABI. Usually, GMP's configure script will automatically choose a 64-bit ABI if available.

Building and using NTL with GMP

When you are installing NTL, if you installed GMP in $HOME/sw as above, and you also want to install NTL in $HOME/sw, you execute:

   % ./configure PREFIX=$HOME/sw GMP_PREFIX=$HOME/sw

   % ./configure DEF_PREFIX=$HOME/sw 

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

   % ./configure PREFIX=$HOME/sw 

   % ./configure 

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

NTL has been tested and works correctly with GMP versions 3.1, 3.1.1, 4.1.4, 5.1, 6.0, and 6.1 (among others). It is not possible to use versions of GMP prior to 3.1 with NTL.

When using NTL with GMP, as a user of NTL, you do not need to know or understand anything about the the GMP library. So while there is detailed documentation available about how to use GMP, you do not have to read it. The programming interface to the long integer package completely hides implementation details.

Backward compatbility

With version 5.0 of NTL, some aspects of the programming interface are 'deprecated' so as to allow the use of another long integer package, such as GMP, as the long integer package.

Prior to version 5.0, the macro NTL_NBITS was defined, along with the macro NTL_RADIX defined to be (1L << NTL_NBITS). While these macros are still available when using NTL's traditional long integer package (i.e., when NTL_GMP_LIP is not set), they are not available when using the GMP as the long integer package (i.e., when NTL_GMP_LIP is set). Furthermore, when writing portable programs, one should avoid these macros.

Also, the static function long ZZ::digit(const ZZ &, long); is defined when using traditional long integer arithmetic, but is not available when using GMP as the long integer package, and in any case, its use should be avoided when writing portable programs.

Instead of the above macros, one should use the followng macros:

   NTL_ZZ_NBITS -- number of bits in a limb;
                   a ZZ is represented as a sequence of limbs.

   NTL_SP_NBITS -- max number of bits in a "single-precision" number

   NTL_WSP_NBITS -- max number of bits in a "wide single-precision" number

The following relations hold:

   NTL_SP_NBITS <= NTL_WSP_NBITS <= NTL_ZZ_NBITS
   26 <= NTL_SP_NBITS <= min(NTL_BITS_PER_LONG-2, NTL_DOUBLE_PRECISION-3)
   NTL_WSP_NBITS <= NTL_BITS_PER_LONG-2

Note that NTL_ZZ_NBITS may be less than, equal to, or greater than NTL_BITS_PER_LONG -- no particular relationship should be assumed to hold. In particular, expressions like (1L << NTL_ZZ_BITS) might overflow.

"single-precision" numbers are meant to be used in conjunction with the single-precision modular arithmetic routines.

"wide single-precision" numbers are meant to be used in conjunction with the ZZ arithmetic routines for optimal efficiency.

Note that when using traditional long integer arithmetic, we have

    NTL_ZZ_NBITS = NTL_SP_NBITS = NTL_WSP_NBITS = NTL_NBITS.

The following auxilliary macros are also defined:

NTL_FRADIX -- double-precision value of 2^NTL_ZZ_NBITS
NTL_SP_BOUND -- (1L << NTL_SP_NBITS)
NTL_WSP_BOUND -- (1L << NTL_WSP_NBITS)

Note that for a ZZ n, n.size() returns the number of "limbs" of n. This is supported with either traditional or GMP integer arithemtic. Note, however, that some old codes might write n.size() <= 1 as a way to test if NumBits(n) <= NTL_NBITS. This is no longer the right thing to do, if one wants portable code that works with either traditional or GMP long integer arithmetic. First, one has to decide whether one wants to test if NumBits(n) is bounded by NTL_ZZ_NBITS, NTL_SP_NBITS, or NTL_WSP_NBITS. In the first case, n.size() <= 1 is still the right way to test this. In the second case, write this as n.SinglePrecision(). In the third case, write this as n.WideSinglePrecision(). The routines SinglePrecision and WideSinglePrecision are new to NTL version 5.0.

Most "high level" applications that use NTL should not be affected by these changes to NTL's programming interface, and if they are, changing the programs should be quite easy.