by
Mark Sofroniou
,
Giulia Spaletta
,
Dedicated Jerry
,
B. Keiper
,
Nicholas C. Metropolis
Journal of Logic and Algebraic Programming. Special Issue on Practical Development of Exact Real Number Computation
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Abstract:
this article we will describe a model known as significance arithmetic. We will give details of the implementation in Mathematica along with several examples that illustrate the design goals and differences over conventional fixed precision floating point systems. Wolfram Research Inc, Champaign, Illinois, U. S. A. Department of Mathematics, University of Bologna, Italy Introduction Knuth has expressed a desiderata of floating point arithmetic as follows [Knuth 1998]: It would be nice if we could give our input data for each problem in an unnormalized form which expresses how much precision is assumed, and if the output would indicate just how much precision is known in the answer. This enhancement would assist those who do not wish to undertake a rigorous analysis of computational error. Significance arithmetic is one approach for providing such a facility. It provides local error monitoring. The computati
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