Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates,
Reads0
Chats0
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
More filters
Journal ArticleDOI
One machine, one minute, three billion tetrahedra
TL;DR: In this paper, a scalable parallelization scheme is presented to generate the 3D Delaunay triangulation of a given set of points, where the Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads.
Posted Content
Combined Integer and Variable Precision (CIVP) Floating Point Multiplication Architecture for FPGAs
TL;DR: In this article, the authors proposed an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication, which will be of great importance in applications which require variable precision multipliers such as multi-media processing applications.
Journal ArticleDOI
Robustness and efficiency of geometric programs
TL;DR: A system to automatically generate C++ code for robust predicates from their formulas, and a companion open-source implementation of a toolset (PCK: Predicate Construction Kit) that makes it reasonably easy to design geometric programs free of numerical errors.
Journal ArticleDOI
Master-field simulations of O(a)-improved lattice QCD: Algorithms, stability and exactness
TL;DR: In this paper, the O( a )-improved Wilson formulation of lattice QCD and the viability of the proposed measures is then checked in extensive simulations of the theory with 2 + 1 flavours of quarks.
Implementation of float-float operators on graphics hardware
Guillaume da Graçca,David Defour +1 more
TL;DR: In this paper, the emulation of a 44-bit floating-point number format and its corresponding operations is presented along with performance and accuracy results, along with an implementation of an FPGA.
References
More filters
Book
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.
Book ChapterDOI
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.
Related Papers (5)
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
Primitives for the manipulation of general subdivisions and the computation of Voronoi
Leonidas J. Guibas,Jorge Stolfi +1 more