Implementing Sobol's Quasirandom Sequence Generator

Implementing Sobol's Quasirandom Sequence Generator

March 1988 | PAUL BRATLEY and BENNETT L. FOX
This paper presents an implementation of Sobol's quasirandom sequence generator and compares it with the Faure generator. The authors discuss the theoretical foundations of Sobol's method and provide an informal description of the necessary computations. They describe how to generate quasirandom sequences using primitive polynomials and direction numbers. The Sobol generator is implemented using integer arithmetic and is shown to be faster than the original method. The paper also discusses the computational complexity of the generator and the choice of initial values. The authors compare the performance of the Sobol and Faure generators in terms of accuracy and speed. They find that the Sobol generator is roughly as accurate as the Faure generator but is much faster when implemented with a nonstandard exclusive-or function. The paper concludes that the Sobol generator is recommended for dimensions 2 to 6, while the Faure generator is recommended for higher dimensions. The authors also provide a detailed description of the implementation of the Sobol generator and the associated subroutines. The paper includes test results comparing the performance of the Sobol and Faure generators.This paper presents an implementation of Sobol's quasirandom sequence generator and compares it with the Faure generator. The authors discuss the theoretical foundations of Sobol's method and provide an informal description of the necessary computations. They describe how to generate quasirandom sequences using primitive polynomials and direction numbers. The Sobol generator is implemented using integer arithmetic and is shown to be faster than the original method. The paper also discusses the computational complexity of the generator and the choice of initial values. The authors compare the performance of the Sobol and Faure generators in terms of accuracy and speed. They find that the Sobol generator is roughly as accurate as the Faure generator but is much faster when implemented with a nonstandard exclusive-or function. The paper concludes that the Sobol generator is recommended for dimensions 2 to 6, while the Faure generator is recommended for higher dimensions. The authors also provide a detailed description of the implementation of the Sobol generator and the associated subroutines. The paper includes test results comparing the performance of the Sobol and Faure generators.
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[slides and audio] Algorithm 659%3A Implementing Sobol's quasirandom sequence generator