scholarly journals A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
M. Romera ◽  
G. Pastor ◽  
A. B. Orue ◽  
A. Martin ◽  
M.-F. Danca ◽  
...  
Keyword(s):  
Computer Programs ◽  
Mandelbrot Set ◽  
Floating Point ◽  
Drawing Tool ◽  
Floating Point Arithmetic ◽  
External Rays ◽  
External Ray ◽  
Floating Point Computation ◽  
Point Arithmetic ◽  
Drawing Program

The external rays of the Mandelbrot set are a valuable graphic tool in order to study this set. They are drawn using computer programs starting from the Böttcher coordinate. However, the drawing of an external ray cannot be completed because it reaches a point from which the drawing tool cannot continue drawing. This point is influenced by the resolution of the standard for floating-point computation used by the drawing program. The IEEE 754 Standard for Floating-Point Arithmetic is the most widely used standard for floating-point computation, and we analyze the possibilities of the quadruple 128 bits format of the current IEEE 754-2008 Standard in order to draw external rays. When the drawing is not possible, due to a lack of resolution of this standard, we introduce a method to draw external rays based on the escape lines and Bézier curves.

scholarly journals Numerical algorithms for high-performance computational science

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190066 ◽  
Author(s):  
Jack Dongarra ◽  
Laura Grigori ◽  
Nicholas J. Higham
Keyword(s):  
High Performance ◽  
Numerical Algorithms ◽  
Computational Science ◽  
Floating Point ◽  
Important Criterion ◽  
Data Movement ◽  
Floating Point Arithmetic ◽  
High Performance Computers ◽  
Point Arithmetic ◽  
Speed And Accuracy

A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

Fast and robust mesh arrangements using floating-point arithmetic

2020 ◽  
Vol 39 (6) ◽  
pp. 1-16
Author(s):  
Gianmarco Cherchi ◽  
Marco Livesu ◽  
Riccardo Scateni ◽  
Marco Attene
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

Floating-point arithmetic with 84-bit numbers

1964 ◽  
Vol 7 (1) ◽  
pp. 10-13 ◽  
Author(s):  
Robert T. Gregory ◽  
James L. Raney
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

Reducing power by optimizing the necessary precision/range of floating-point arithmetic

2000 ◽  
Vol 8 (3) ◽  
pp. 273-286 ◽  
Author(s):  
J.Y.F. Tong ◽  
D. Nagle ◽  
R.A. Rutenbar
Keyword(s):  
Reducing Power ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

scholarly journals An Automatable Formal Semantics for IEEE-754 Floating-Point Arithmetic

2015 ◽  
Author(s):  
Martin Brain ◽  
Cesare Tinelli ◽  
Philipp Ruemmer ◽  
Thomas Wahl
Keyword(s):  
Formal Semantics ◽  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

scholarly journals Secure floating point arithmetic and private satellite collision analysis

2014 ◽  
Vol 14 (6) ◽  
pp. 531-548 ◽  
Author(s):  
Liina Kamm ◽  
Jan Willemson
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic
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