Here, you find a collection of useful programs in C-XSC and some additional headerfiles for C-XSC:
 

• C++ Toolbox for Verified Computing (C-XSC)
• One- and multidimensional interval taylor arithmetic
• One- and multidimensional (interval) slope arithmetic
• Complex interval standard functions library (CoStLy)
• Automatic Computation of Estimates for Taylor Coefficients of Analytic Functions (ACETAF)
• Classes for Verified Integration over Singularities (CLAVIS)
• Verified Fredholm Integral Equation Solver (VFIS)
• Elementary Functions of High Accuracy (additional headerfiles)
• Selfverifying Solvers for Dense Systems of Linear Equations
• Fast verified parallel solvers for dense linear (interval-)systems (FastPILSS)
• Verified Solvers for sparse linear (interval-) systems (SparseLinSys)
• Solving Parametric Interval Linear Systems (ParLinSys)
• MPI Extension for the Use of C-XSC in Parallel Environments
• Modified staggered correction arithmetic with enhanced accuracy and very wide exponent range (Prerelease lx_interval)
• Arbitrary precision arithmetics in C-XSC

(Authors: R. Hammer, M. Hocks, U. Kulisch, D. Ratz; Universität Karlsruhe)

Content:

1. One-Dimensional Problems:
   • Evaluation of Polynomials (Module rpoly, Module rpeval)
   • Automatic Differentiation (Module ddf_ari)
   • Nonlinear Equations in One Variable (Module xi_ari, Module nlfzero)
   • Global Optimization (Module lst1_ari, Module gop1)
   • Evaluation of Arithmetic Expressions (Module expreval)
   • Zeros of Complex Polynomials (Module cpoly, Module cipoly, Module cpzero)
2. Multi-Dimensional Problems:
   • Linear Systems of Equations (Module matinv, Module linsys)
   • Linear Optimization (Module set_ari, Module lop_ari, Module rev_simp, Module lop)
   • Automatic Differentiation for Gradients, Jacobians, and Hessians (Module hess_ari, Module grad_ari)
   • Nonlinear Systems of Equations (Module nlinsys)
   • Global Optimization (Module lst_ari, Module gop)
3. Utility Modules:
   • (Modules r_util, i_util, ci_util, mv_util, mvi_util)

Documentation:
R. Hammer, M. Hocks, U. Kulisch, D. Ratz: "C++ Toolbox for Verified Computing", Springer Verlag, Berlin, Heidelberg (1995).

Download: Since C-XSC Version 2.0 the C-XSC library and the toolbox are in one archiv: C-XSC Download

(Authors: F. Blomquist, M. Bräuer, M. Grimmer, W. Hofschuster, W. Krämer; Universität Wuppertal)

Content: Classes for one- and multidimensional interval taylor arithmetic. Some sample programs illustrate how to use the software package.

Documentation:

• Blomquist, F.; Hofschuster, W.; Krämer, W.: Real and Complex Taylor Arithmetic in C-XSC
  Preprint 2005/4, Universität Wuppertal, 2005 (PDF (254 KB)).

Download:

• One-dimensional interval taylor arithmetic
  itaylor.hpp, itaylor.cpp, itayl_ex1.cpp, itayl_ex2.cpp
• One-dimensional multiple-precision interval taylor arithmetic
  litaylor.hpp, litaylor.cpp, litayl_ex1.cpp, litayl_ex2.cpp
• Complex one-dimensional interval taylor arithmetic
  citaylor.hpp, citaylor.cpp, citayl_ex1.cpp
• Two-dimensional interval taylor arithmetic
  dim2taylor.hpp, dim2taylor.cpp, dim2tayl_ex1.cpp, dim2tayl_ex2.cpp
• Two-dimensional multiple-precision interval taylor arithmetic
  ldim2taylor.hpp, ldim2taylor.cpp, ldim2tayl_ex1.cpp, ldim2tayl_ex2.cpp

• All files in one archiv: taylor.tgz (Update September 2012)

(Authors: M. Bräuer, W. Hofschuster, W. Krämer; Universität Wuppertal)

Content: Classes for one- and multidimensional (interval) slope arithmetic in forward and reverse mode. Sample programs illustrate how to use the software package.

Documentation:

• Bräuer, M.; Hofschuster, W.; Krämer, W.: Steigungsarithmetiken in C-XSC
  Preprint 2001/3, Universität Wuppertal, 2001 (PDF (390 KB)).
• Ratz, D.: An Optimized Interval Slope Arithmetic and its Application
  Bericht 4/1996 aus dem Forschungsschwerpunkt "Computerarithmetik, Intervallrechnung und Numerische Algorithmen mit Ergebnisverifikation (CAVN)" an der Universität Karlsruhe, 1996 (PDF (426 KB)).

Download:

• Slope arithmetic in forward mode (includes: slope_ari.h, slope.h, multi_dim_slope.h, helpfuncs.h, ...)
  README, slope_for.tar.gz (32 KB)
• Slope arithmetic in reverse mode (includes: s_reverse.h, helpfuncs.h, ...)
  README, slope_rev.tar.gz (23 KB)

(Authors: M. Neher, I. Eble; KIT/Universität Karlsruhe; original Pascal-XSC version: W. Krämer, A. Westphal)

Content: CoStLy is a free alternative to any expensive commercial library of complex interval standard functions. It is distributed under the terms of the GNU general public license.

Documentation:
The mathematical foundations of CoStLy are discussed in the following paper:

• K. Braune and W. Krämer: High--accuracy standard functions for real and complex intervals.
  In: Computerarithmetic: Scientific computation and programming languages
  (E. Kaucher, U. Kulisch and Ch. Ullrich, eds.), 81--114, Teubner, Stuttgart, 1987.
  
• G. Bühler: Standardfunktionen für komplexe Intervalle im 64 Bit IEEE Datenformat.
  Diploma thesis, Universität Karlsruhe, 1993.
• M. Neher: Complex standard functions and their implementation in the CoStLy library.
  Preprint 04/18, Fakultät für Mathematik, Universität Karlsruhe, 2004. (PDF)

Download:
There's a README file for the installation.

• CoStLy 2.0.5 for C-XSC (released 080918).
• Archive: CoStLy 2.0.4 for C-XSC and filib++ (released 051017).

Alternative Download (KIT): CoStLy

(Authors: M. Neher, I. Eble; KIT/Universität Karlsruhe)

Content: ACETAF is a powerful program for the validated computation of bounds for Taylor coefficients and for Taylor remainder series of analytic functions. It is distributed under the terms of the GNU general public license.

Documentation:
The mathematical foundations of ACETAF are discussed in the following papers:

• M. Neher: Validated bounds for Taylor coefficients of analytic functions.
  Reliable Computing 7 (2001), 307-319. (PDF)
  
• M. Neher: Improved validated bounds for Taylor coefficients and for Taylor remainder series.
  J. Comput. Appl. Math. 152 (2003), 393-404. (PDF)
  
• I. Eble and M. Neher: ACETAF: A Software Package for Computing Validated Bounds for Taylor Coefficients of Analytic Functions.
  ACM TOMS 29 (2003), 263-286. (PDF)

Download:

• README
• ACETAF 3.0.1 for C-XSC (released 080918)
• Archive: ACETAF 3.0 for C-XSC and filib++ (released 040930)

Alternative Download (KIT): ACETAF

(Author: S. Wedner)

Content: Classes for Verified Integration over Singularities with example programs in C-XSC.

Documentation:

• Wedner, S.: Verifizierte Bestimmung singulärer Integrale - Quadratur und Kubatur
  Dissertation, Universität Karlsruhe, 2000 (UB Karlsruhe: Online-Version, Postscript (gnuzipped 586 KB)).

Download:

• README, clavis-1-1.tar.gz (89 KB)

(Author: M. Grimmer)

Content: Verified Fredholm Integral Equation Solver for linear Fredholm Integral Equations of the second kind

Documentation:

• Grimmer, Markus: Selbstverifizierende mathematische Softwarewerkzeuge im High Performance Computing
  Dissertation, Universität Wuppertal, 2007 (Abstract, (2070 KB))

Download:

• Einzel-FIGL-Loeser.tgz (Single Version)
• System-FIGL-Loeser.tgz (Serial System Version)
• System-FIGL-Loeser-par.tgz (Parallel System Version, Update September 2012)

(Author: W. Hofschuster; Universität Wuppertal)

Content: The headerfiles ha_rmath.hpp and ha_imath.hpp are additional headerfiles for the C-XSC 2.0 - Library. They are an interface for mathematical standard functions (elementary functions) of high accuracy for real and interval arguments (see README).

Download:

• README, ha_rmath.hpp, ha_imath.hpp, example.cpp

(Authors: C. Hölbig, PPGC at UFRGS and Universidade de Passo Fundo, Brazil; W. Krämer, Universität Wuppertal)

Documentation:

• BUW-WRSWT 2003/1
  Hölbig, C.; Krämer, W.:
  Selfverifying Solvers for Dense Systems of Linear Equations Realized in C-XSC
  Preprint 2003/1, Universität Wuppertal, 2003 (PDF (196 KB))

Download:

• ilss.hpp, ilss.cpp, lss_aprx.hpp, lss_aprx.cpp

(Author: M. Zimmer, Universität Wuppertal)

Note:
The serial solvers have been moved directly into the C-XSC library and are no longer a part of this package.

Documentation:

• Zimmer, M.:
  Laufzeiteffiziente, parallele Löser für lineare Intervallgleichungssysteme in C-XSC
  Master-Thesis, Universität Wuppertal, 2007
• Krämer, W.; Zimmer, M.:
  Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS
  To appear: LNCS Dagstuhl Seminar 08021 Postproceedings (219 KB)

Download:

• FastPILSS-0-4-2.tar.gz (Version 0.4.2, released 06.06.12, for C-XSC 2.5.2 and newer)

(Author: M. Zimmer, Universität Wuppertal)

Content:
The SparseLinSys package contains the following verified solvers:

1. A solver (slss) based on the modified Krawczyk operator with 3 methods to solve the occurring triangular systems with interval right hand side: simple forward/backward substitution (only applicable for matrices with special structure, especially M-matrices), inversion of the triangular matrices (very costly in most cases) and forward/backward substitution using parallel epipeds (works well for very small bandwidth b<10).
2. A solver (slssn) based on a normwise error estimation. For point systems and interval systems with small width this solver works best in general, especially for symmetric positive definite systems. However, for general system with condition >10^8 it will often fail.

Solver 1 gives better enclosures for interval systems, but is somewhat slower and applicable to a smaller class of systems. Solver 2 will be faster in general and gives good enclosures for point systems and interval systems with small width. Both can profit a lot from multithreading, especially for larger systems. OpenMP should be activated if available.

Requirement:

• C-XSC version 2.5.4 or higher
• SuiteSparse, version 4.0.2 or higher (tested with version 4.0.2) using Metis 4.0
• C++ Compiler with OpenMP capabilities recommended
• Optimized BLAS and LAPACK libraries recommended (also for the installation of SuiteSparse)

Download:

• SparseLinSys.tar.gz (Version March 2013)

Optimized solver for real or complex parametric linear systems with dense or sparse coefficient matrices
(Author: M. Zimmer, Universität Wuppertal, based on older ParLinSys version from E. Popova and W. Krämer)

Requirement:

• C-XSC version 2.5.4 or higher
• C++ Compiler with OpenMP capabilities recommended
• Optimized BLAS and LAPACK libraries recommended

Download:

• ParLinSys_optimized.tar.gz (Version March 2013)
• Archive: ParLinSys_beta.tar.gz (Beta-Version December 2010, version for talk at SCAN 2010)

---

Solving Parametric Interval Linear Systems (ParLinSys)

(Authors: E. Popova, Inst. of Maths & Informatics at BAS, Sofia; W. Krämer, Universität Wuppertal)

Content: ParLinSys is a free module that supplements the library C++-Toolbox. ParLinSys computes verified enclosure of the solution set of parametric interval linear systems and an inner approximation of the solution enclosure. Current download version is ParLinSys 0.1 (released 011203). ParLinSys 0.1 is distributed under the terms of the GNU general public license. See the included file COPYING.txt. ParLinSys 0.1 requires the GNU C++ compiler gcc 2.95.2 and the libraries C-XSC and CToolbox (Release 2.0 beta and above).

Documentation:
The mathematics behind ParLinSys is discussed in the following paper which can be also used as a user guide:

• Popova, E.; Krämer, W.: Parametric Fixed-Point Iteration Implemented in C-XSC
  Preprint BUW-WRSWT 2003/3, Univ. Wuppertal, 2003 (Update May 2004) (PDF (325 KB)).

Download:

• README, ParLinSys.tgz (Update May 2008)

(Author: M. Grimmer, M. Zimmer, Universität Wuppertal)

Documentation:

• BUW-WRSWT 2005/3
  Grimmer, M.:
  An MPI Extension for the Use of C-XSC in Parallel Environments
  Preprint 2005/3, Universität Wuppertal, 2005 (PDF (89 KB))

Download:

• cxscmpi.tar.gz (for C-XSC 2.4.0 and newer, updated 18.11.2015)

Archive (original version from preprint BUW-WRSWT 2005/3; only for C-XSC 2.3.1 and older versions):

• cxsc_mpicomm.h, cxsc_mpicomm.cpp, cxsc_mpi_example_real.cpp
• cxsc_mpicomm_templ.h, cxsc_mpicomm_templ.cpp

(Authors: F. Blomquist, W. Hofschuster, W. Krämer, Universität Wuppertal)

Documentation:

• BUW-WRSWT 2007/8
  Blomquist, F.; Hofschuster, W.; Krämer, W.:
  Vermeidung von Über- und Unterlauf und Verbesserung der Genauigkeit bei reeller und komplexer staggered Intervall-Arithmetik mit Hilfe der C-XSC Klassen L_interval, L_cinterval
  Preprint 2007/8, Universität Wuppertal, 2007 (to appear) ()
  Talk at Dagstuhl-Seminar: Slides ()
• BUW-WRSWT 2008/1
  Blomquist, F.; Hofschuster, W.; Krämer, W.:
  Real and Complex Staggered (Interval) Arithmetics with Wide Exponent Range (in German)
  Preprint 2008/1, Universität Wuppertal, 2008 ( (1.2 MB))

Download:

• lx_interval-0-8-0.tgz (Prerelease Version 0.8.0 for C-XSC 2.2.3)
• lx_interval-0-9-0.tgz   README (Prerelease Version 0.9.0 for C-XSC 2.2.4 (!) or higher)

(Authors: F. Blomquist, H. S. Brand, W. Hofschuster, W. Krämer, Universität Wuppertal)

Content: Arbitrary precision real and complex and corresponding interval arithmetics in C-XSC (based on the libraries MPFR and MPRI).

Documentation:

• BUW-WRSWT 2007/8
  Blomquist, F.; Hofschuster, W.; Krämer, W.:
  C-XSC-Langzahlarithmetiken füer reelle und komplexe Intervalle basierend auf den Bibliotheken MPFR und MPFI
  Preprint 2011/1, Universität Wuppertal, 2011 (in german) ()

Download:

• MPFR-MPFI.tar.gz   README (Prerelease Version 0.10.0 for C-XSC 2.5.0 or higher)

How can I get the C-XSC library?

http://www.math.uni-wuppertal.de/wrswt/xsc/cxsc_new.html
or
http://www.xsc.de