• Corpus ID: 237532311

Computing the exact sign of sums of products with floating point arithmetic

  title={Computing the exact sign of sums of products with floating point arithmetic},
  author={Walter F. Mascarenhas},
  • W. Mascarenhas
  • Published 16 September 2021
  • Computer Science, Mathematics
  • ArXiv
In computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed for the exact solution of linear programming problems and systems of linear inequalities. Computing these signs exactly with inexact floating point arithmetic is challenging, and we present yet another algorithm for this task. Our algorithm is efficient and… 

Figures from this paper

Solving systems of inequalities in two variables with floating point arithmetic
The data structure and algorithm were developed as a building block for the rigorous solution of relevant practical problems and were implemented in C++ and the code was carefully tested.


A note on Dekker’s FastTwoSum algorithm
The original assumptions for an error-free transformation via the FastTwoSum algorithm are reminded, the conditions for arbitrary bases are generalized and a possible modification of the algorithm is discussed to extend its applicability even further.
Interval Arithmetic in C++20
  • Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science,
  • 2018
Floating point numbers are real numbers
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction,
A robust algorithm for geometric predicate by errorfree determinant transformation, Information and Computation
  • 2012
Error estimation of floating-point summation and dot product
We improve the well-known Wilkinson-type estimates for the error of standard floating-point recursive summation and dot product by up to a factor 2. The bounds are valid when computed in rounding to
Algorithm 908
A novel, online algorithm for exact summation of a stream of floating-point numbers that is the fastest, most accurate, and most memory efficient among known algorithms.
Accurate Sum and Dot Product
Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed
Applications of fast and accurate summation in computational geometry
In this paper, we present a recent algorithm given by Ogita, Rump and Oishi [39] for accurately computing the sum of n floating point numbers. They also give a computational error bound for the
Fast and Accurate Floating Point Summation with Application to Computational Geometry
The results show that in the absence of massive cancellation (the most common case) the cost of guaranteed accuracy is about 30–40% more than the straightforward summation, and the accurate summation algorithm improves the existing algorithm by a factor of two on a nearly coplanar set of points.