scholarly journals Certifying the Floating-Point Implementation of an Elementary Function Using Gappa

2011 ◽  
Vol 60 (2) ◽  
pp. 242-253 ◽  
Author(s):  
Florent de Dinechin ◽  
Christoph Lauter ◽  
Guillaume Melquiond
Keyword(s):  
Elementary Function ◽  
Floating Point ◽  
Floating Point Implementation

NUMERICAL STABILITY OF ALGORITHMS FOR 2D DELAUNAY TRIANGULATIONS

1995 ◽  
Vol 05 (01n02) ◽  
pp. 193-213 ◽  
Author(s):  
STEVEN FORTUNE
Keyword(s):  
Delaunay Triangulation ◽  
Floating Point ◽  
Worst Case ◽  
Delaunay Triangulations ◽  
Floating Point Arithmetic ◽  
Circular Arcs ◽  
Stability Of Algorithms ◽  
Forming Angle ◽  
Point Arithmetic ◽  
Floating Point Implementation

We consider the correctness of 2-d Delaunay triangulation algorithms implemented using floating-point arithmetic. The α-pseudocircle through points a, b, c consists of three circular arcs connecting ab, bc, and ac, each arc inside the circumcircle of a, b, c and forming angle α with the circumcircle; a triangulation is α-empty if the α-pseudocircle through the vertices of each triangle is empty. We show that a simple Delaunay triangulation algorithm—the flipping algorithm—can be implemented to produce O(n∈)-empty triangulations, where n is the number of point sites and ∈ is the relative error of floating-point arithmetic; its worst-case running time is O(n2). We also discuss floating-point implementation of other 2-d Delaunay triangulation algorithms.

scholarly journals Efficient Calculation of the Genomic Relationship Matrix

2020 ◽  
Author(s):  
Martin Schlather
Keyword(s):  
Floating Point ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Double Precision ◽  
Genomic Relationship ◽  
Arithmetic Operations ◽  
Efficient Calculation ◽  
Floating Point Implementation

Since the calculation of a genomic relationship matrix needs a large number of arithmetic operations, fast implementations are of interest. Our fastest algorithm is more accurate and 25× faster than a AVX double precision floating-point implementation.

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