# Applications of fast and accurate summation in computational geometry

@inproceedings{Graillat2005ApplicationsOF, title={Applications of fast and accurate summation in computational geometry}, author={Stef Graillat}, year={2005} }

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 computed result. We apply this algorithm in computing determinant and more particularly in computing robust geometric predicates used in computational geometry. We improve existing results that use either a multiprecision libraries or extended large accumulators.

## 7 Citations

On the Design and Performance of Reliable Geometric Predicates using Error-free Transformations and Exact Sign of Sum Algorithms

- Computer ScienceCCCG
- 2007

In a case study, several implementations of planar orientation test and incircle tests that make use of utilities for exact computation of the sign of a sum of floating-point numbers are compared.

Ultimately Fast Accurate Summation

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2009

Two new algorithms to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in $K$-fold precision, which are the fastest known in terms of flops.

Floating-point filters towards floating-point exceptions

- 2013

This talk is concerned with robustness problems in computational geometry. Floating-point numbers and floating-point arithmetic are widely used on recent computational environments due to their high…

Compensated Algorithm for Evaluating the Derivative of Bézier Tensor Product Surface

- Mathematics2012 Fourth International Conference on Computational and Information Sciences
- 2012

We present a compensated algorithm to evaluate the first derivative of B'ezier tensor product surface in floating arithmetic. The algorithm based on error-free transformation is fast in terms of…

An efficient software implementation of correctly rounded operations extending FMA: A + b + c and a × b + c × d

- Computer Science2017 51st Asilomar Conference on Signals, Systems, and Computers
- 2017

This work proposes an efficient software implementation of two additional operations of the Fused-Multiply-Twice-And-Add operation, guaranteeing correct rounding in all rounding modes and IEEE754 compliant signaling.

Fiabilité des algorithmes numériques : pseudosolutions structurées et précisions

- Physics
- 2005

Les travaux presentes dans cette these portent sur la stabilite et la precision de certains algorithmes numeriques. Les contributions de cette these se situent a quatre niveaux : 1) Amelioration de…

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

- Computer ScienceArXiv
- 2021

The algorithm is efficient and uses only of floating point arithmetic, which is much faster than exact arithmetic, and it is proved that the algorithm is correct and the efficient and tested C++ code for it is correct.

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