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Available on Github
- Generated on Tue Jun 11 2019 15:21:27 for Lattice Tester Guide by
1.8.15
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Lattice Tester Guide
1.0-9
Software Package For Testing The Uniformity Of Integral Lattices In The Real Space
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If you intend on building LatticeTester from scratch, the following software will need to be installed on the system:
You will also need a compiler compliant with the C++14 standard.
This section won't go in depth and explain all the particularities of the build process. If you are a developper and wish to participate to this project, please look at the README for more details about the build system.
The prefered way of getting this software is by downloading it on github (either via git clone or with a .zip) and to compile it yourself (for now). The build process uses the waf metabuild system that greatly streamlines the process.
To build the project, you simply need to be in the root folder of LatticeTester and call:
or, on Windows,
If the build process fails, the README might offer you some insight as to what went wrong. Note that for the installation process to work, you will need the have administrative rights on the installation folder.
The previous command will fetch the environment variables specific to your system to prepare the compilation, compile the program in a local folder and place the binaries and header files in a default location depending on your OS. Depending on your installation path, you might need to specify a path to you compilier when using the LatticeTester library. After that, the library will be available under the lib folder in the installation path and the executable program under the bin folder as LatticeTester(.exe on Windows).
LatticeTester uses NTL's types and implementations of a few algorithms. If you ever happen to browse the code of LatticeTester, you will notice that many of the classes use templates. This is because the library is compiled to work on a variety of types with the same code. These types provide a variable precision in the representation of both integer numbers and floating point numbers.
It is possible to use integers represented as both ‘std::int64_t’ (integers of exactly 64 bits) and NTL::ZZ (NTL implementation of exact arbitrary length integers) and floating points as double and NTL::RR (NTL implementation of arbitrary precision floating point numbers). Obviously, standard types provide better performance, but can lead to errors in a few algorithms.
When using the library, you will have to consider which types you will want to use to represent numbers. While it is quite safe to assume floating point arithmetic should not cause problems and that doubles should be fine, this is not true for integers. This is because the computations performed on lattices basis need to be done exactly on integers. Using arbitrary precision integers is necessary when working with matrix entries that can get close to \(2^{63}\). This is the case, for example, in LatMRG when working with generators with modulus close to \(2^{64}\).
LatticeTester is built in order to analyse a Lattice based on a set of vectors called basis therefore it provides an executable that can be used directly to do so at a small scale. This executable is a small program that can read data from a file to perform tests as specified by the user. Through this program, all the problems LatticeTester aims at solving can be addressed, as well as the computation of figures of merit. Although, concerns for the efficiency of object instanciation when using LatticeTester are not needed (since it should not take a large proportion of the execution time), it is recommended that, if you want to perform tests or algorithms on numerous lattices, you make a C++ program using the library instead of sending multiple files to the executable.
Once the program is compiled, to use it, you simply have to call it from a command line with a filename argument. That file name must have a .dat extension that should not be included when calling the program like
in a POSIX shell. You can specify a directory relative to your current working directory for either of the program and the executable. LLDD, ZZDD and ZZRR are integer type specifiers. For more information on the type usage, please look into Types. For most use cases, ZZDD should do the trick, or will be needed since a few functions only need with ZZ integers.
The file must contain, in order:
The file format depends on the work you ask from LatticeTester. There is an example available for each case in the folder inputTestFiles in the repository. There are 5 computations possible when calling LatticeTester. In what follows, we present them and explain what each parameter is. Parameters are written in the format parameter <option1, option2, ...> if you need to choose from multiple options or in the format parameter [type] if it is a basic type. When writing a parameter, you just have to write the choosen option and not the parameter name.
This is the simplest case, where the file looks like this.
.res extension.NumRows \(\times\)NumCols matrix where each line represents a vector of the lattice. This matrix does not need to be non-singular or have full rank.In that case, the file will look like this :
.res extension.Dim \(\times\)Dim matrix where each line represents a vector of the lattice. This matrix must be invertible.In that case, the file will look like this :
.res extension.Dim \(\times\)Dim matrix where each line represents a vector of the lattice. This matrix must be invertible.In that case, the file will look like this :
true.true. This field is not needed if Reduction is false. Look at Lattice Reduction for more details..res extension.Dim \(\times\)Dim matrix where each line represents a vector of the lattice. This matrix must be invertible.In that case, the file will look like this :
true.true. This field is not needed if Reduction is false. Look at Lattice Reduction for more details..res extension.Dim \(\times\)Dim matrix where each line represents a vector of the lattice. This matrix must be invertible. 1.8.15