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XDR: External Data Representation Standard
, 1995
"... This document describes the External Data Representation Standard (XDR) protocol as it is currently deployed and accepted. TABLE OF CONTENTS 1. ..."
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Cited by 92 (1 self)
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This document describes the External Data Representation Standard (XDR) protocol as it is currently deployed and accepted. TABLE OF CONTENTS 1.
Affine Arithmetic and its Applications to Computer Graphics
, 1993
"... We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations betw ..."
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Cited by 66 (6 self)
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We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and subformulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.
Interval constraint logic programming
 CONSTRAINT PROGRAMMING: BASICS AND TRENDS, VOLUME 910 OF LNCS
, 1995
"... Abstract. In this paper, we present anoverview on the use of interval arithmetic to process numerical constraints in Constraint Logic Programming. The main principle is to approximate nary relations over IR with Cartesian products of intervals whose bounds are taken in a nite subset of I R.Variabl ..."
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Cited by 47 (5 self)
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Abstract. In this paper, we present anoverview on the use of interval arithmetic to process numerical constraints in Constraint Logic Programming. The main principle is to approximate nary relations over IR with Cartesian products of intervals whose bounds are taken in a nite subset of I R.Variables represent real values whose domains are intervals de ned in the same manner. Narrowing operators are de ned from approximations. These operators compute, from an interval and a relation, aset included in the initial interval. Sets of constraints are then processed thanks to a local consistency algorithm pruning at each stepvalues from initial intervals. This algorithm is shown to be correct and to terminate, on the basis of a certain number of properties of narrowing operators. We focus here on the description of the general framework based on approximations, on its application to interval constraint solving over continuous and discrete quantities, we establish a strong link between approximations and local consistency notions and show that arcconsistency is an instance of the approximation framework. We nally describe recentwork on di erent variants of the initial algorithm proposed by John Cleary and developed by W. Older and A. Vellino which havebeen proposed in this context. These variants address four particular points: generalization of the constraint language, improvement of domain reductions, e ciency of the computation and nally, cooperation with other solvers. Some open questions are also identi ed. 1
An industrially effective environment for formal hardware verification
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2005
"... This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyrig ..."
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Cited by 32 (5 self)
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This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Integer Priority Queues with Decrease Key in . . .
 STOC'03
, 2003
"... We consider Fibonacci heap style integer priority queues supporting insert and decrease key operations in constant time. We present a deterministic linear space solution that with n integer keys support delete in O(log log n) time. If the integers are in the range [0,N), we can also support delete i ..."
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Cited by 27 (2 self)
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We consider Fibonacci heap style integer priority queues supporting insert and decrease key operations in constant time. We present a deterministic linear space solution that with n integer keys support delete in O(log log n) time. If the integers are in the range [0,N), we can also support delete in O(log log N) time. Even for the special case of monotone priority queues, where the minimum has to be nondecreasing, the best previous bounds on delete were O((log n) 1/(3−ε) ) and O((log N) 1/(4−ε)). These previous bounds used both randomization and amortization. Our new bounds a deterministic, worstcase, with no restriction to monotonicity, and exponentially faster. As a classical application, for a directed graph with n nodes and m edges with nonnegative integer weights, we get single source shortest paths in O(m + n log log n) time, or O(m + n log log C) ifC is the maximal edge weight. The later solves an open problem of Ahuja, Mehlhorn, Orlin, and
A tool for unbiased comparison between logarithmic and floatingpoint arithmetic
 LIP, École Normale Supérieure de
, 2004
"... arithmetic ..."
A library of parameterizable floatingpoint cores for FPGAs and their application to scientific computing
 In Proc. of International Conference on Engineering Reconfigurable Systems and Algorithms
, 2005
"... Abstract — Advances in field programmable gate arrays (FPGAs), which are the platform of choice for reconfigurable computing, have made it possible to use FPGAs in increasingly many areas of computing, including complex scientific applications. These applications demand high performance and highpr ..."
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Cited by 21 (9 self)
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Abstract — Advances in field programmable gate arrays (FPGAs), which are the platform of choice for reconfigurable computing, have made it possible to use FPGAs in increasingly many areas of computing, including complex scientific applications. These applications demand high performance and highprecision, floatingpoint arithmetic. Until now, most of the research has not focussed on compliance with IEEE standard 754, focusing instead upon custom formats and bitwidths. In this paper, we present doubleprecision floatingpoint cores that are parameterized by their degree of pipelining and the features of IEEE standard 754 that they implement. We then analyze the effects of supporting the standard when these cores are used in an FPGAbased accelerator for LennardJones force and potential calculations that are part of molecular dynamics (MD) simulations. I.
Double bubbles minimize
 Ann. of Math
"... The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a sin ..."
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Cited by 21 (1 self)
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The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 ◦. 1.
SelfIntersection of Composite Curves and Surfaces
 Computer Aided Geometric Design
, 1997
"... This paper provides computationally tractable conditions to determine whether a composite spline curve or patch selfintersects, according to a definition that includes the important limiting cases of cusps, singularities, and tangential intersections of adjacent components. These results follow upo ..."
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Cited by 19 (13 self)
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This paper provides computationally tractable conditions to determine whether a composite spline curve or patch selfintersects, according to a definition that includes the important limiting cases of cusps, singularities, and tangential intersections of adjacent components. These results follow upon our exposition of necessary and sufficient conditions to preclude such selfintersections. The paper includes a numerical example illustrating the results, and discusses an important application, namely, guaranteeing that a finite curvilinear simplicial complex in R 3 , made up of properlyjoined parametric patches, will retain its original topological form when its control points are perturbed. 1 Introduction In this paper we give conditions permitting avoidance of selfintersections of composite spline curves and patches [1]. We also give limits on the size of controlpoint perturbations so that the perturbed curve or patch has no selfintersection. The results are formulated in term...
A proven correctly rounded logarithm in doubleprecision
 In Real Numbers and Computers, Schloss Dagstuhl
, 2004
"... Abstract. This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in doubleprecision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the pr ..."
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Cited by 19 (9 self)
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Abstract. This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in doubleprecision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processorspecific optimization to get performance equivalent to the best current mathematical libraries, while trying to minimize the proof work. The implementation of the natural logarithm is detailed to illustrate these questions. Mathematics Subject Classification. 2604, 65D15, 65Y99. 1.