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This paper presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision 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 arbitrary-precision 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

In the k-median problem we are given a set N of n points in a metric space and a positive integer k: The objective is to locate k medians among the points so that the sum of the distances from each point in N to its closest median is minimized. The k-median problem is a well-studied, NP-hard, basic clustering problem, which is closely related to facility location. Obtaining constant-factor approximations for this problem, even for the 2-dimensional Euclidean metric, had long been an elusive goal. First Arora, Raghavan and Rao gave a randomized polynomial-time approximation scheme by extending techniques introduced originally by Arora for the Euclidean TSP. For any xed " > 0; their algorithm outputs a (1 + ")-approximation in O(nkn log n) time.

The development of efficient numerical programs and library routines for high-performance 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 high-performance 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 operation-level and the functional- or algorithm-level. 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...

The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floating-point 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 context-free grammars.

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.

We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of non-linear 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 non-linear 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 non-linear constraints over the real numbers. Our language is illustrated by an example that also shows the advantages of cooperation.

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An algorithm is described for multiplying multiprecision floating point numbers. The returned result is equal to the floating point number obtained by rounding the exact product. Software implementations of multiprecision floating point multiplication can reduce the computing time by a factor of two if they do not compute the low order digits of the product of the two mantissas. However, these algorithms do not necessarily provide exactly rounded results. The algorithm described in this paper is guaranteed to produce exactly rounded results and typically obtains the same savings. 1 Introduction We present an algorithm for multiplying multiprecision floating point numbers. The returned result is equal to the floating point number obtained by rounding the exact product. A rounding operation which satisfies this requirement is called exact rounding. Exact rounding provides a well defined, implementation independent semantics for floating point arithmetic. For this reason, floating point ...