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Mathematical proof of functionality, of a highly efficient pseudo-random number generator: The Ziggurat Method
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README.md

This repo. contains the results from my 3 month summer internship at the University of Toronto under the supervision of Prof. Frank Kschischang in 2014.

A Report on the Ziggurat Method

How to reference this repo.

@misc{Severo2014,
  author = {Severo, D.},
  title = {A Report on the Ziggurat Method},
  year = {2014},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/dsevero/A-Report-on-the-Ziggurat-Method}},
  commit = {master}
}

Files

Compile LaTeX

Run make report or make slides to compile the respective files from tex/ to build/. You will need the following:

apt install texlive latexmk texlive-fonts-extra texlive-pictures

Abstract

Pseudo-random number generators (PRNG's) are crucial in the context of simulating noise in communication channels. We present a report on an efficient method for generating pseudo-random samples from any decreasing probability distribution called the Ziggurat Method. The initial idea was developed by [1], but has been enhanced by Marsaglia, Tsang [3] and others. Specifically, we will show the latest and most efficient version presented by McFarland [4]. In the latter paper, the method shows a speedup of over 3 times compared to traditional algorithms such as Marsaglia's Polar Method [2]. We present a speed comparison in C implemented on an Intel i7-4790 clocked at 3.60 GHz. McFarland [4] provides all the necessary code to implement an ad hoc version of the algorithm, as well as a ready-to-use C code for a univariate Gaussian. A proof that the samples from this method are truly Gaussian is also provided.

Related Work

References

[1] George Marsaglia, ”A convenient method for generating normal variables.”, SIAM Rev. 6, 260-264,1964.

[2] George Marsaglia, Wai Wan Tsang, ”A fast, easily implemented method for sampling from de-creasing or symmetric unimodal density functions”, SIAM Journ. Scient. and Statis. Computing,5, 349-359, 1984.

[3] George Marsaglia, Wai Wan Tsang, ”The Ziggurat Method for Generating Random Variables”,Journal of Statistical Software, 2000.

[4] Christopher D. McFarland, ”A modified ziggurat algorithm for generating exponentially- andnormally-distributed pseudorandom numbers.”, Apr. 2014.

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