Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates,
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TLDR
This article offers fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values and proposes a technique for adaptive precision arithmetic that can often speed these algorithms when they are used to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound.Abstract:
Exact computer arithmetic has a variety of uses, including the robust implementation of geometric algorithms. This article has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive precision arithmetic that can often speed these algorithms when they are used to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to use these techniques to develop 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.read more
Citations
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A BSP-based algorithm for dimensionally nonhomogeneous planar implicit curves with topological guarantees
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On the computation of the reciprocal of floating point expansions using an adapted Newton-Raphson iteration
TL;DR: This article presents a new algorithm for computing the reciprocal FP expansion a-1 of aFP expansion a, based on an adapted Newton-Raphson iteration where “truncated” operations (additions, multiplications) involving FP expansions are used.
References
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
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Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
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