Corpus ID: 14809551

# Fast Algorithms for High-Precision Computation of Elementary Functions

@inproceedings{Brent2006FastAF,
title={Fast Algorithms for High-Precision Computation of Elementary Functions},
author={Richard P. Brent},
year={2006}
}
Open problem: Is γ or exp(γ) rational ? Since the regular continued fraction gives best rational approximations, continued fraction computations can give theorems of the form: If x is rational, say x = p/q, then |q| > B for some (very large) bound B. To obtain a result like this with given bound B, we need to compute x with absolute error O(1/B2). Using this method we know that, if γ or exp(γ) is rational, say p/q, then |q| must be very large. Thus, in some sense these numbers are “unlikely” to… Expand
9 Citations
Modern Computer Arithmetic
• Computer Science
• 2010
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topicsExpand
Modern Computer Arithmetic (version 0.5.1)
• Computer Science, Mathematics
• ArXiv
• 2010
This book focuses on algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Expand
Matters Computational: Ideas, Algorithms, Source Code
This book provides algorithms and ideas for computationalists on low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Expand
Sampling from Arbitrary Centered Discrete Gaussians for Lattice-Based Cryptography
• Computer Science
• ACNS
• 2017
This work study how to reduce the number of centers for which the authors have to precompute tables and propose a non-centered CDT algorithm with practicable size of precomputed tables as fast as its centered variant. Expand
Efficient evaluation methods of elementary functions suitable for SIMD computation
• N. Shibata
• Computer Science
• Computer Science - Research and Development
• 2010
Efficient methods are proposed for evaluating the sine, cosine, arc tangent, exponential and logarithmic functions in double precision without table look-ups, scattering from, or gathering into SIMD registers, or conditional branches. Expand
978-0-521-19469-3-Modern Computer Arithmetic
• Computer Science
• 2008
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad. Expand
Time-Bounded Reachability for Initialized Hybrid Automata with Linear Differential Inclusions and Rectangular Constraints
• Mathematics, Computer Science
• FORMATS
• 2014
The main result is that while the control state reachability problem for such automata is undecidable, the time-bounded reachable problem is decidable. Expand
An ECMA-55 Minimal BASIC Compiler for x86-64 Linux
This compiler is designed to be small, simple, and easy to understand for people who want to study a compiler that actually implements full error checking on floating point on x86-64 CPUs even if those people have little programming experience. Expand
Contents / Preface
• Journal of Inherited Metabolic Disease
• 2004
grouping The abstracts have been grouped according to their subject matter. This has not always been easy, since there is often a degree of overlap. If authors feel they have been misallocated,Expand

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