Keywords
LCG
CLCG
Simulation
Performance analysis
How to Cite
Abstract
The generation of high-quality randomness is a fundamental prerequisite for the integrity of stochastic modeling and numerical simulations across various scientific disciplines. As the complexity of computational experiments grows, the robustness of the underlying Pseudo-Random Number Generators (PRNGs) becomes a decisive factor in preventing systematic biases. This study examines the performance and reliability of PRNGs, focusing on the widely utilized Linear Congruential Generator (LCG) and the Combined Linear Congruential Generator (CLCG), which was developed to address the inherent limitations of the former. Using a simulation environment implemented in Python, both algorithms were evaluated based on visual distribution analysis (histograms and 2D/3D scatter plots), statistical fitness (Chi-Square and autocorrelation tests), and computational efficiency (execution speed). The empirical findings demonstrate that while the LCG operates approximately 2.1 times faster than the CLCG, it exhibits a distinct "lattice structure" in multi-dimensional space, leading to significant structural correlation errors. In contrast, the CLCG method, despite its higher computational overhead, achieved a high p-value of 0.92 in the Chi-Square goodness-of-fit test, indicating near-perfect alignment with the theoretical uniform distribution and minimized sequential dependency. Consequently, this study concludes that CLCG is a more reliable choice for high-precision simulations, whereas LCG remains viable for simple applications where computational speed is the primary constraint.
References
AbdELHaleem, S. H., S. K. Abd-El-Hafiz, and A. G. Radwan, 2024. Analysis and guidelines for different designs of pseudo random number generators. IEEE Access, 12: 115697–115715.
Banks, J., 1998. Handbook of simulation: Principles, methodology, advances, applications, and practice. John Wiley & Sons.
Banks, J., 2005. Discrete event system simulation. Pearson Education India.
Bhattacharjee, K. and S. Das, 2022. A search for good pseudorandom number generators: Survey and empirical studies. Computer Science Review, 45: 100471.
Gentle, J. E., 2003. Random number generation and Monte Carlo methods. Springer.
Hamming, R., 1952. Mathematical methods in large-scale computing units. Math Rev, 13: 495.
Johnston, D., 2018. Random Number Generators—Principles and Practices: A Guide for Engineers and Programmers. Walter de Gruyter GmbH & Co KG.
Knuth, D. E., 2014. The art of computer programming: Seminumerical algorithms, Volume 2. Addison-Wesley Professional.
Kroese, D. P. and R. Y. Rubinstein, 2012. Monte Carlo methods. Wiley Interdisciplinary Reviews: Computational Statistics, 4: 48–58.
Law, A. M., W. D. Kelton, and W. D. Kelton, 2007. Simulation modeling and analysis, Volume 3. McGraw-Hill, New York.
L’Ecuyer, P., 1988. Efficient and portable combined random number generators. Communications of the ACM, 31: 742–751.
L’Ecuyer, P. and R. Simard, 2007. TestU01: A C library for empirical testing of random number generators. ACM Transactions on Mathematical Software (TOMS), 33: 1–40.
L’Ecuyer, P., 2011. Random number generation. In Handbook of Computational Statistics: Concepts and Methods, pp. 35–71, Springer.
Marsaglia, G., 1996. Diehard: A battery of tests of randomness. https://cir.nii.ac.jp/crid/1571698600935841152
Marsaglia, G., 2003. Xorshift RNGs. Journal of Statistical Software, 8: 1–6.
Matsumoto, M. and T. Nishimura, 1998. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation (TOMACS), 8: 3–30.
O’Neill, M. E., 2014. PCG: A family of simple fast space-efficient statistically good algorithms for random number generation. ACM Transactions on Mathematical Software, 204: 1–46.
Park, S. K. and K. W. Miller, 1988. Random number generators: Good ones are hard to find. Communications of the ACM, 31: 1192–1201.
Rukhin, A., J. Soto, J. Nechvatal, M. Smid, and E. Barker, 2001. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical Report, NIST SP-800-02.
Zio, E., 2012. Monte Carlo simulation: The method. In The Monte Carlo Simulation Method for System Reliability and Risk Analysis, pp. 19–58, Springer.
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