Results 1  10
of
19
Enhanced Dynamic Queries via Movable Filters
, 1995
"... Traditional database query systems allow users to construct complicated database queries from specialized database language primitives. While powerful and expressive, such systems are not easy to use, especially for browsing or exploring the data. Information visualization systems address this probl ..."
Abstract

Cited by 78 (0 self)
 Add to MetaCart
Traditional database query systems allow users to construct complicated database queries from specialized database language primitives. While powerful and expressive, such systems are not easy to use, especially for browsing or exploring the data. Information visualization systems address this problem by providing graphical presentations of the data and direct manipulation tools for exploring the data. Recent work in this area has reported the value of dynamic queries coupled with twodimensional data representations for progressive refinement of user queries. However, the queries generated by these systems are limited to conjunctions of global ranges of parameter values. In this paper, we extend dynamic queries by encoding each operand of the query as a Magic Lens filter. Compound queries can be constructed by overlapping the lenses. Each lens includes a slider and a set of buttons to control the value of the filter function and to define the compostion operation generated by overlapp...
MPFR: A multipleprecision binary floatingpoint library with correct rounding
 ACM Trans. Math. Softw
, 2007
"... This paper presents a multipleprecision binary floatingpoint library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitraryprecision ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these stron ..."
Abstract

Cited by 70 (14 self)
 Add to MetaCart
This paper presents a multipleprecision binary floatingpoint library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitraryprecision ideas from the IEEE 754 standard, by providing correct rounding and exceptions. We demonstrate how these strong semantics are achieved — with no significant slowdown with respect to other arbitraryprecision tools — and discuss a few applications where such a library can be useful. Categories and Subject Descriptors: D.3.0 [Programming Languages]: General—Standards; G.1.0 [Numerical Analysis]: General—computer arithmetic, multiple precision arithmetic; G.1.2 [Numerical Analysis]: Approximation—elementary and special function approximation; G 4 [Mathematics of Computing]: Mathematical Software—algorithm design, efficiency, portability
Universally Quantified Interval Constraints
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decompo ..."
Abstract

Cited by 46 (0 self)
 Add to MetaCart
Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of innerapproximation of real relations.
FloatingPoint LLL Revisited
, 2005
"... The LenstraLenstraLovász lattice basis reduction algorithm (LLL or L³) is a very popular tool in publickey cryptanalysis and in many other fields. Given an integer ddimensional lattice basis with vectors of norm less than B in an ndimensional space, L³ outputs a socalled L³reduced basis in po ..."
Abstract

Cited by 37 (6 self)
 Add to MetaCart
The LenstraLenstraLovász lattice basis reduction algorithm (LLL or L³) is a very popular tool in publickey cryptanalysis and in many other fields. Given an integer ddimensional lattice basis with vectors of norm less than B in an ndimensional space, L³ outputs a socalled L³reduced basis in polynomial time O(d 5 n log³ B), using arithmetic operations on integers of bitlength O(d log B). This worstcase complexity is problematic for lattices arising in cryptanalysis where d or/and log B are often large. As a result, the original L³ is almost never used in practice. Instead, one applies floatingpoint variants of L³, where the longinteger arithmetic required by GramSchmidt orthogonalisation (central in L³) is replaced by floatingpoint arithmetic. Unfortunately, this is known to be unstable in the worstcase: the usual floatingpoint L³ is not even guaranteed to terminate, and the output basis may not be L³reduced at all. In this article, we introduce the L² algorithm, a new and natural floatingpoint variant of L³ which provably outputs L 3reduced bases in polynomial time O(d 4 n(d + log B) log B). This is the first L³ algorithm whose running time (without fast integer arithmetic) provably grows only quadratically with respect to log B, like the wellknown Euclidean and Gaussian algorithms, which it generalizes.
Defining the IEEE854 FloatingPoint Standard in PVS
 in PVS. Technical Memorandum 110167, NASA, Langley Research
, 1995
"... A significant portion of the ANSI/IEEE854 Standard for RadixIndependent FloatingPoint Arithmetic is defined in PVS (Prototype Verification System). Since IEEE854 is a generalization of the ANSI/IEEE754 Standard for Binary FloatingPoint Arithmetic, the definition of IEEE854 in PVS also formall ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
A significant portion of the ANSI/IEEE854 Standard for RadixIndependent FloatingPoint Arithmetic is defined in PVS (Prototype Verification System). Since IEEE854 is a generalization of the ANSI/IEEE754 Standard for Binary FloatingPoint Arithmetic, the definition of IEEE854 in PVS also formally defines much of IEEE754. This collection of PVS theories provides a basis for machine checked verification of floatingpoint systems. This formal definition illustrates that formal specification techniques are sufficiently advanced that it is reasonable to consider their use in the development of future standards. keywords: Floatingpoint arithmetic, Formal Methods, Specification, Verification. 1 Introduction This document describes a definition of the ANSI/IEEE854 [3] Standard for RadixIndependent FloatingPoint Arithmetic in the PVS verification system (developed at SRI International) [4]. IEEE854 is a generalization of the ANSI/IEEE754 [2] Standard for Binary FloatingPoint Ari...
Handling FloatingPoint Exceptions in Numeric Programs
 ACM Transactions on Programming Languages and Systems
, 1996
"... Language Constructs Termination exception mechanisms like in Ada and C++ are supposed to terminate an unsuccessful computation as soon as possible after an exception occurs. However, none of the examples of numeric exception handling presented earlier depends ACM Transactions on Programming Languag ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
Language Constructs Termination exception mechanisms like in Ada and C++ are supposed to terminate an unsuccessful computation as soon as possible after an exception occurs. However, none of the examples of numeric exception handling presented earlier depends ACM Transactions on Programming Languages and Systems, Vol. 18, No. 2, March 1996. Handling FloatingPoint Exceptions 167 on the immediate termination of a calculation signaling an exception. The IEEE exception flags scheme actually takes advantage of the fact that an immediate jump is not necessary; by raising a flag, making a substitution, and continuing, the IEEE Standard supports both an attempted/alternate form and a default substitution with a single, simple reponse to exceptions. A detraction of the IEEE flag solution, though, is its obvious lack of structure. Instead of being forced to set and reset flags, one would ideally have available a language construct that more directly reflected the attempted/alternate algorit...
RealPaver: An Interval Solver using Constraint Satisfaction Techniques
 ACM TRANS. ON MATHEMATICAL SOFTWARE
, 2006
"... RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed, using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreove ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed, using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or non square, sparse or dense, linear, polynomial or involving transcendental functions. The modeling language permits stating constraint models and tuning parameters of solving algorithms, which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, 3B) are implemented. The distribution includes C sources, executables for different machine architectures, documentation and benchmarks. The portability is ensured by the GNU C compiler.
Automatic Generation of Staged Geometric Predicates
, 2002
"... Algorithms in Computational Geometry and Computer Aided Design are often developed for the Real RAM model of computation, which assumes exactness of all the input arguments and operations. In practice, however, the exactness imposes tremendous limitations on the algorithms – even the basic operation ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Algorithms in Computational Geometry and Computer Aided Design are often developed for the Real RAM model of computation, which assumes exactness of all the input arguments and operations. In practice, however, the exactness imposes tremendous limitations on the algorithms – even the basic operations become uncomputable, or prohibitively slow. In some important cases, however, the computations of interest are limited to determining the sign of polynomial expressions. In such circumstances, a faster approach is available: one can evaluate the polynomial in floating point first, together with some estimate of the rounding error, and fall back to exact arithmetic only if this error is too big to determine the sign reliably. A particularly efficient variation on this approach has been used by Shewchuk in his robust implementations of Orient and InSphere geometric predicates. We extend Shewchuk’s method to arbitrary polynomial expressions. The expressions are given as programs in a suitable source language featuring basic arithmetic operations of addition, subtraction, multiplication and squaring, which are to be perceived by the programmer as exact. The source language also allows for anonymous
Is Your Model Susceptible to FloatingPoint Errors?
"... For information about citing this article, click here ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
For information about citing this article, click here
Formal Methods: Why Should I Care?  The development of the T800 transputer floatingpoint unit
 In Proc. 13th New Zealand Computer Society Conference
, 1993
"... The term `formal methods' is a general term for precise mathematicallybased techniques used in the development of computer systems, both hardware and software. This paper discusses formal methods in general, and in particular describes their successful role in specifying, constructing and proving c ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The term `formal methods' is a general term for precise mathematicallybased techniques used in the development of computer systems, both hardware and software. This paper discusses formal methods in general, and in particular describes their successful role in specifying, constructing and proving correct the floatingpoint unit of the Inmos T800 transputer chip. 1. Introduction The need for reliable computer systems is increasing rapidly, in step with our growing dependence on computers in daily life. This need can only be met by developing more rigorous methods for constructing these systems. The term `formal methods' is a blanket term for such precise, mathematicallybased techniques for the development of computer systems. In this paper, we aim to give an introduction to formal methods in general, and to discuss how they helped in constructing the floatingpoint unit of the Inmos T800 transputer chip. The transputer [Inmos Ltd 1988b] is a microprocessor chip designed specificall...