
Accession Number : ADA311439
Title : Adaptive Precision FloatingPoint Arithmetic and Fast Robust Geometric Predicates,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Shewchuk, Jonathan R.
PDF Url : ADA311439
Report Date : 17 MAY 1996
Pagination or Media Count : 57
Abstract : Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast softwarelevel algorithms for exact addition and multiplication of arbitrary precision floatingpoint values. The second is to propose a technique for adaptiveprecision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floatingpoint arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floatingpoint numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness.
Descriptors : *ALGORITHMS, *FLOATING POINT OPERATION, SOFTWARE ENGINEERING, OPTIMIZATION, COMPUTATIONS, ACCURACY, INPUT OUTPUT PROCESSING, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, PRECISION, ADAPTIVE SYSTEMS, SYSTEMS ANALYSIS, COMPILERS, ARITHMETIC, BINARY ARITHMETIC, TRIANGULATION, ADDITION, C PROGRAMMING LANGUAGE.
Subject Categories : Computer Programming and Software
Distribution Statement : APPROVED FOR PUBLIC RELEASE