Interval and Related Software
Interval and Verified Software
 ACETAF,
a CXSC library for the verified
automatic computation of estimates for Taylor
coefficients of analytic functions.
 AERN, Approximating Exact Real Numbers,
a Haskell library for rigorous and exact real number and real function computation
 ALIAS
Library, Algorithms Library of Interval Analysis for Systems; see
also this
link
 AQCS,
a free software package for Approximate Quantified Constraint Solving
 computes box approximations of the solution set of formulae of
the firstorder predicate language over the reals.
 Ariadne,
a package for verified reachability analysis of hybrid systems that
includes a library for verified setbased computation
 AWA,
a software package for verified solution of ordinary
differential equations.
 BARON,
Global Optimization Software.
Purely continuous, purely integer, and
mixedinteger nonlinear problems can be solved with the
software.
 BOOST
interval C++ library
implemented within the popular BOOST project
 CAPD, ComputerAssisted Proofs in Dynamics (also available at
this website),
a C++
package for rigorous numerics for dynamical systems, oriented mostly
for computer assisted proofs in dynamics.
This library provides provides rigorous
solvers for ODEs, variational equations for ODEs, differential
inclusions, automatic computation of Poincare maps and their
derivatives, computation of homology of spaces, maps and many other
features.
 CGAL,
Computational Geometry Algorithms Library, written in C++,
uses interval computations to make geometric computations
robust and efficient; the related part of CGAL manual can be found at
the
following site
the CLIP
 CLIP
Among other applications, it allows rigorous modeling of hybrid systems

CLP(BNR), a Constraint IntervalArithmetic
Package
This package is actually
a language for Constraint Logic Programming based on
Interval Arithmetic.
 CoStLy,
a library of complex interval standard functions.
 COSY.
This software package is based on Taylor model and interval
methods. It is intended
for verified solution of such problems as ordinary differential
equations, quadrature, range bounding, etc. It
can either be used as a standalone program or via C++ and Fortran
90/95 frontends.
 DAEPACK,
MITproduced symbolic and numeric library for general numerical
calculations which uses interval computations.
 FADBAD/TADIFF,
an automatic differentiation package, with applications to verified
solution of ordinary differential equations.
 filib++,
Fast Interval LIRrary, a C++ library on extended interval arithmetic.
 Interval arithmetic library for
a special programming language Frink (implemented in Java)
 General
Interval Arithmetic package for
manipulating finite sets of (possibly unbounded) intervals; there is
an applet
interface
 GlobSol
 software for global solutions; downloading instructions
 HSolver
This package allows analysis of hybrid systems with
nonlinear ODEs over an unbounded time horizon, uses intervals as its main
workhorse
 HySAT,
A bounded model checker for hybrid systems
The package allows boundedtime analysis of hybrid
systems with complex discrete structure, also uses intervals for reasoning about
numerical constraints
 ICE,
Interval Calculator for Engineers
Intervals are to be entered like
min_max or mean%tol, for example: 1_2, 4_3, 4%2.
The help section of this ICE is full of examples and
explanations to use properly the syntax which looks like Mathlab.
 ICOS,
Interval COnstraints Solver
 InC++
libraries for interval computations and constraint satisfaction.
 INTBLAS: C++
Implementation
An implementation of
INTerval Basic Linear Algebra Software.
 Interval
arithmetic for ADA
 Interval
arithmetic in Sun's Forte C++ compiler
 Interval
arithmetic in Sun's Forte Fortran 95 compiler
 Interval library is a part of Intel
Math Kernel Library (MKL).
It includes
interval arithmetic (standard and two complex) and
interval linear solvers that compute enclosures (sharp or fast) of
the solution set to interval linear systems of equations,
check properties of interval matrices; some part of the solvers works
with complex intervals. Questions and suggestions are welcome at
MKL
forum

Interval
Software in Fortran77

Interval Software in Fortran90
This Fortran90 module is actually a
language for interval computations
 Interval based Java applets:
 Karlsruhe
and Wuppertal interval software
 Libaffa; a
C++ affine arithmetic library for GNU/Linux
 Maple: Interval Software in Maple and its clones:
 Mathematica based
web site
supports dynamic interval web computations and visualization.
 Matlab: Interval Software in Matlab:
 MISO, a software
package containing a set of solvers based on Modal Interval Analysis.
These solvers are:
 FSTAR solver: Allows doing computations with Modal Intervals.
 QRCS solver: Allows proving the satisfiability of a class of quantified
real constraints.
 QSI solver: Allows obtaining inner and outer approximations of the solution
set of a class of quantified real constrains.
 MINIMAX solver: Allows solving constrained minimax optimization problems.
 SQUALTRACK solver: Allows detecting faults in dynamic systems.
 MPFI,
Multiple Precision FloatingPoint Interval Library
 MuPAD,
integrates interval computation in its kernel;
both Maple and MuPad are integrated into Scientific Workplace
 GNU Octave
interval package
The package conforms to IEEE Interval
Standard 1788
 ParaGlobSol
Parallel/distributed implementations of the
interval global optimization FORTRAN
90 package GlobSol, which solves global optimization problems with the
interval branchandbound algorithm together with interval
Newton/generalized bisection method.

ParLinSys, software for solving parametric interval linear systems
 PROFIL/BIAS
A fast C++ library for interval
arithmetic.
Speed and comparisons can be found in:
O. Knueppel: PROFIL/BIAS  A Fast Interval Library,
COMPUTING, Vol. 53, No. 34, p. 277287.
 Pytaylor, a Python package
implementing Taylor models and associated guaranteed ODE solvers.
Pytaylor uses mpmath
for interval arithmetic and sympy for symbolic manipulation.
 RealPaver
Interval software implementing constraint
satisfaction techniques for solving nonlinear systems.

Range software of Oliver Aberth
A suite of demonstration programs, using variable precision interval arithmetic, that can solve the typical problems of elementary numerical analysis to desired accuracy.
 SMMS
 Rsolver
solves quantified inequality
constraints
 smathlib
A library of C routines for interval
arithmetic and constraint narrowing
 Interface
between the
interval and constraint propagation library smathlib
and a functional programming language
Objective Caml
 Statool
Software for intervalbased arithmetic on
random variables.

SvLis
a free C++ geometric
modeller that is substantially based on interval arithmetic
 UniCalc
A solver based on interval constraint propagation. It
allows to tackle nonlinear algebraic systems with real
and/or integer variables.
 VALENCIAIVP
software for VALidation of state ENClosures using
Interval Arithmetic for Initial Value Problems
 VNODELP
A C++ based Interval Solver for Initial Value
Problems in Ordinary Differential Equations
 XSC software (for more detailed
information about XSC languages, see
the following page)
XSC
languages and fi_lib
Related Software
CBDO: A Matlab toolbox for Cloud Based Design Optimization
Software for uncertainty modeling by clouds,
by Martin Fuchs
 CADNA,
Control of Accuracy and Debugging for Numerical Appplications
Software for estimating propagation of
roundoff errors.
 DALSolution,
Innovative software for the analysis of questionnaire
surveys, public polls, medical records, etc.; uses intervalvalued
probabilities and other intervalrelated types of partial information
about probabilities.
 PDV,
Software that extends operations with intervals
to operations with probability distributions.
 RealRoots,
A free app for iPhone/iPod/iPad, performs
real root isolation
and a few other polynomial functions.
 RiskCalc,
Software for Risk Assessment with Uncertain Numbers,
including operations with interval, probabilitistic, and fuzzy
uncertainties, and their combination.
See also Languages for Interval Analysis.
See also MathTools.net, a
free portal covering computing tools for science and
engineering. This portal contains over
20,000 useful links, covering software in
Matlab, Java, Excel, C/C+, Fortran, etc.
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