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A modified ziggurat algorithm for generating exponentially- and normally-distributed pseudorandom numbers.

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This study introduces an improved Ziggurat Algorithm for faster PseudoRandom Number (PRN) generation. The enhanced method reduces runtime for statistical distributions, offering significant speedups.

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Area of Science:

  • Computational statistics
  • Numerical analysis
  • Algorithm development

Background:

  • Rejection sampling methods are widely used for generating PseudoRandom Numbers (PRNs) from statistical distributions.
  • The Ziggurat Algorithm is a known fast method, but involves rejection tests within sampling layers.

Purpose of the Study:

  • To present a novel implementation of the Ziggurat Algorithm that eliminates rejection tests within its core layers.
  • To improve the efficiency of PseudoRandom Number generation for statistical distributions.

Main Methods:

  • Developed a Ziggurat Algorithm variant where sampling layers are fully contained beneath the probability density function.
  • Incorporated triangularly-shaped sampling domains to efficiently sample remaining probability density segments.
  • Implemented the algorithm in C, with extensions for Python and MATLAB/Octave.

Main Results:

  • Median runtimes for generating exponential variates were reduced to 58% of the original.
  • Median runtimes for generating normal variates were reduced to 53% of the original.
  • Observed overall runtime reductions in the range of 41-93% across tested distributions.

Conclusions:

  • The modified Ziggurat Algorithm offers a significant performance improvement for PseudoRandom Number generation.
  • The elimination of rejection tests and use of specialized sampling domains contribute to increased efficiency.
  • The provided C library and extensions facilitate the adoption of this faster algorithm in various computational environments.