The Mathematical-Function Computation Handbook

@inproceedings{Beebe2017TheMC,
  title={The Mathematical-Function Computation Handbook},
  author={Nelson H. F. Beebe},
  booktitle={Springer International Publishing},
  year={2017}
}
  • N. H. Beebe
  • Published in
    Springer International…
    2017
  • Mathematics
Pade Series Approximation of Static Nondifferentiable Nonlinearities
  • K. Perev
  • Proceedings of the Technical University of Sofia
  • 2022
Drawing Random Floating-point Numbers from an Interval
  • F. Goualard
  • Computer Science
    ACM Transactions on Modeling and Computer Simulation
  • 2022
TLDR
This work investigates and quantify precisely the shortcomings of floating-point arithmetic's location-scale transformation while reviewing the actual implementations of the method in major programming languages and libraries, and proposes a simple algorithm to avoid these shortcomings without compromising performances.
Multiple-Valued Logic Modelling for Agents Controlled via Optical Networks
TLDR
Multiple-valued logic functions defined within discrete k-valued Allen–Givone algebra are proposed for the logically linked list of entries and the distributed ledger, which can be used for distant data verification and breakdown restoration in mobile agents with the help of partner network nodes.
Efficient computation of some special functions
We introduce a new algorithm to efficiently compute the functions belonging to a suitable set F defined as follows: 5 ∈ Fmeans that 5 (B, G), B ∈ ⊂ R being fixed and G > 0, has a power series
Multiple-Valued Logic and Neural Network in the Position-Based Cryptography Scheme
  • A. Y. Bykovsky
  • Computer Science, Mathematics
    Journal of Russian Laser Research
  • 2021
TLDR
The design of position-based cryptography schemes for network mobile robots can be simplified by means of multiple-valued logic used both for modeling of the position- based cryptography protocol by Unruh and the neural network to enlarge the variety of verification schemes.
Arbitrary-precision computation of the gamma function
TLDR
The best methods available for computing the gamma function Γ(z) in arbitrary-precision arithmetic with rigorous error bounds are discussed and some new formulas, estimates, bounds and algorithmic improvements are presented.
Algorithmic Determination of a Large Integer in the Two-Term Machin-like Formula for π
In our earlier publication we have shown how to compute by iteration a rational number u2,k in the two-term Machin-like formula for π of the kind π4=2k−1arctan1u1,k+arctan1u2,k,k∈Z,k≥1, where u1,k
Generating Random Floating-Point Numbers by Dividing Integers: A Case Study
A method widely used to obtain IEEE 754 binary floating-point numbers with a standard uniform distribution involves drawing an integer uniformly at random and dividing it by another larger integer.
Design and Implementation Hardware Architecture for Four–Quadratic Arctangent
TLDR
An FPGA based architecture design and the implementation of the Four-Quadratic Arctangent function, used in transformation from Cartesian to polar coordinates is presented.

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