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94
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 ..."
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Cited by 109 (16 self)
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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
Uniform Random Generation of Decomposable Structures Using FloatingPoint Arithmetic
 THEORETICAL COMPUTER SCIENCE
, 1997
"... The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, ..."
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Cited by 36 (3 self)
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The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, in expected O(n 1+ffl ) time and space, after a preprocessing phase of O(n 2+ffl ) time, which reduces to O(n 1+ffl ) for contextfree grammars.
FALCON: A MATLAB Interactive Restructuring Compiler
 IN LANGUAGES AND COMPILERS FOR PARALLEL COMPUTING
, 1995
"... The development of efficient numerical programs and library routines for highperformance parallel computers is a complex task requiring not only an understanding of the algorithms to be implemented, but also detailed knowledge of the target machine and the software environment. In this paper, w ..."
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Cited by 35 (10 self)
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The development of efficient numerical programs and library routines for highperformance parallel computers is a complex task requiring not only an understanding of the algorithms to be implemented, but also detailed knowledge of the target machine and the software environment. In this paper, we describe a programming environment that can utilize such knowledge for the development of highperformance numerical programs and libraries. This environment uses an existing highlevel array language (MATLAB) as source language and performs static, dynamic, and interactive analysis to generate Fortran 90 programs with directives for parallelism. It includes capabilities for interactive and automatic transformations at both the operationlevel and the functional or algorithmlevel. Preliminary experiments, comparing interpreted MATLAB programs with their compiled versions, show that compiled programs can perform up to 48 times faster on a serial machine, and up to 140 times fas...
Multivariate Statistical Techniques for Parallel Performance Prediction
 IN PROC. 28TH HAWAII INT. CONF. ON SYSTEM SCIENCES, VOL. II, IEEE
, 1995
"... Performance prediction can play an important role in improving the efficiency of multicomputers in executing scalable parallel applications. An accurate model of program execution time must include detailed algorithmic and architectural characterizations. The exact values for critical model paramete ..."
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Cited by 26 (4 self)
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Performance prediction can play an important role in improving the efficiency of multicomputers in executing scalable parallel applications. An accurate model of program execution time must include detailed algorithmic and architectural characterizations. The exact values for critical model parameters such as message latency and cache miss penalty can often be difficult to determine. This research uses multivariate data analysis to estimate the values of these coefficients in an analytical model. Representing the coefficients as random variables with a specified mean and variance improves the utility of a performance model. Confidence intervals for predicted execution time can be generated using the standard error values for model parameters. Improvements in the model can also be made by investigating the cause of large variance values for a particular architecture.
Implementing NonLinear Constraints With Cooperative Solvers
, 1995
"... We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of nonlinear polynomial constraints. Instead of using a general and often inefficient decision procedure we propose a new approach for handling these constraints by cooperat ..."
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Cited by 24 (12 self)
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We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of nonlinear polynomial constraints. Instead of using a general and often inefficient decision procedure we propose a new approach for handling these constraints by cooperating specialised solvers. Our approach requires the design of a client/server architecture to enable communication between the various components. The main modules are a linear solver, a nonlinear solver, a constraint manager, a communication protocol component and an answer processor module. This work is motivated by the need for a declarative system for robot motion planning and geometric problem solving. We have implemented a prototype called CoSAc (Constraint System Architecture) to validate our approach using cooperating solvers for nonlinear constraints over the real numbers. Our language is illustrated by an example that also shows the advantages of cooperation.
Automatic construction of accurate models of physical systems
 IN PROC . 8TH INTERNATIONAL WORKSHOP ON QUALITATIVE REASONING, NARA
, 1994
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Computer algebra meets automated theorem proving: Integrating Maple and pvs
 Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS
, 2001
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Convex Distance Functions in 3Space are Different
 Fundam. Inform
, 1994
"... The bisector systems of convex distance functions in 3space are investigated and it is shown that there is a substantial difference to the Euclidean metric which cannot be observed in 2space. This disproves the general belief that Voronoi diagrams in convex distance functions are, in any dimension ..."
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Cited by 16 (6 self)
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The bisector systems of convex distance functions in 3space are investigated and it is shown that there is a substantial difference to the Euclidean metric which cannot be observed in 2space. This disproves the general belief that Voronoi diagrams in convex distance functions are, in any dimension, analogous to Euclidean Voronoi diagrams. The fact is that more spheres than one can pass through four points in general position. In the L 4 metric, there exist quadrupels of points that lie on the surface of three L 4 spheres. Moreover, for each n # 0 one can construct a smooth and symmetric convex distance function d and four points that are contained in the surface of exactly 2n +1 dspheres, and this number does not decrease if the four points are disturbed independently within 3dimensional neighborhoods. This result implies that there is no general upper bound to the complexity of the Voronoi diagram of four sites based on a convex distance function in 3space.