YalAA - Yet Another Library for Affine Arithmetic

Introduction

YalAA is an object-oriented C++ based template library for affine arithmetic (AA). Similarly to interval arithmetic (IA), this computation model allows us to derive bounds on a function's codomain. In contrast to IA, AA tracks first-order dependencies during the computation process resulting often in tighter bounds on the codomain at the price of an increased computational effort.

Installation

Requirements

YalAA supports both Microsoft Windows and Linux/Unix-like platforms You can choose one of the following supported compilers

• Microsoft Visual Studio 2010 (Windows only)
• GNU GCC >= 4.5 (Linux/Unix-like)
• CLANG++ (Linux/Unix-like)

Furthermore, YalAA requires the Boost libaries >= 1.4.7

In order to use YalAA an external library for interval arithmetic is required. The following libraries are currently supported

• C-XSC >= 2.5.0
• filib++ >= 3.0.2
• Profile/Bias >= 2.0.8

If you want to use another library, you have to provide a specialization of the interval_traits template class. Please refer to Usage of a custom interval library.

Microsoft Windows

• TODO

Linux/Unix-like

• Unpack the archive to your desired location (tar xfj yalaa.tar.bz2)
• Check the configure parameters (./configure --help)
• Run configure with desired parameters for your system
  (Example: ./configure --with-cxsc=<CXSC-PATH> --with-boost==<BOOST-PATH>)
• Build the library (make)
• Install the library (make install)
  If desired, use the prefix option of configure if to install YalAA in your $HOME directory

Documentation

For creating the documentation you need Doxygen.

• Select the output format by using the configure script
• Start the creation process (make doxygen-doc)
• The documentation is generated in the directory doc

Usage

To use the library you have to include the yalaa.hpp (or yalaa_fwd.hpp for forward declations) headers and link your program against the respective library libyalaa.so on Linux or libyalaa.lib on Windows.

You can use one of the predfined types described in the table below or you can defined your own type based on our templates. All of them are located in the namespace yalaa.ExactErrorFP If you use custom types, please note that YalAA uses an explicit template instantiation approach. To avoid linker errors you have to use explicit template instatiations like it is done for the predefined types in yalaa_fp_impl.cpp.

Name	Base type	Kernel	Policy	Error handling
aff_e_d	double	ExactErrorFP	AF0	Standard
aff_af1_e_d	double	ExactErrorFP	AF1	Standard
aff_af2_e_d	double	ExactErrorFP	AF2	Standard
aff_e_d_dec	double	ExactErrorFP	AF0	Decorations
aff_af1_e_d_dec	double	ExactErrorFP	AF1	Decorations
aff_af2_e_d_dec	double	ExactErrorFP	AF2	Decorations

The different error handling approaches and the policy types are explained in YalAA's implementation paper. Furthermore, the namespace yalaa::concepts contains templates for creating your own policies.

Examples

To illustrate the usage of YalAA in more detail we distribute some examples with the library.

Example	Description
function.cpp	Evaluates a function with YalAA
decorations.cpp	Shows the usage of decorations in YalAA
policies.cpp	Shows how the different policies alter the computation in YalAA

Further Documentation, References and Libraries

• Kiel, S.: YalAA: Yet Another Library for Affine Arithmetic, Presentation at SWIM'2011 Bourges, PDF
• Kiel, S.: YalAA: Yet Another Library for Affine Arithmetic, Reliable Computing, Submitted
• Jorge Stolfi's Homepage (Homepage of AA's inventor, most important publications and the reference implementation libaa are available on this site.)
• Messine F., A general reliable quadratic form: An extension of affine arithmetic, Reliable Computing, 2006 (Introduces AF1 and AF2)
• libaffa (Yet another) C++ library for AA

License

YalAA is free software and available under the terms of the GNU Lesser General Public License Version 3. For more details refer to the files COPYING and COPYING.LESSER, which are included in the distribution.

Download

Current version

• YalAA Version 0.92 (Preview version)

Old versions

• YalAA Version 0.91 (Preview version)
• YalAA Version 0.9 (Preview version)

Contact

If you have any questions, suggenstions or bug reports regarding YalAA do not hesitate to write me an email.