Comparison of Random Number Generator Algorithms: What Makes Them 'Better'?

When it comes to evaluating random number generator (RNG) algorithms, the quest for the best generator becomes a bit of a paradox. Gerry Rzeppa's first sentence succinctly captures the essence: "It depends on what you mean by ‘better.’"

Indeed, there are numerous criteria that can indicate the quality of an RNG. Some people prioritize a longer period, others focus on unpredictability, and still others require a specific distribution that the numbers must match. Some might look for algorithms that pass rigorous tests listed by Knuth, while others opt for speed or simplicity in code implementation. The absence of a universal "best" algorithm underscores the inherent contradictions in the criteria.

Marsaglia’s XorShift and My FRand Package

Marsaglia's XorShift RNG and my FRand package are both noteworthy for their robust performance. Marsaglia's XorShift is known for its simplicity and efficiency, while my FRand package offers a range of options tailored to specific needs. While the Mersenne Twister is well-regarded for a combination of performance and randomness, it can be notably slower than other alternatives.

Historical Issues with Random Number Generators

Historically, some RNGs, particularly those used in FORTRAN programs, had significant flaws. A notable example was the predictability of the low-order bit, leading to a basic pattern of alternating even and odd numbers. Nowadays, RNGs usually come with detailed descriptions of their algorithms, providing users with insights into potential issues. The "Mersenne Twister" remains a preferred choice due to its good performance and randomness.

Subjectivity in the Evaluation of Randomness

Another aspect that adds complexity to the comparison is the subjective nature of the desired outcome. In practice, what many people need are numbers that are uniformly spread across a specified range in an arbitrary order, rather than truly random numbers. This is highlighted by a simple Plain English program that demonstrates this idea. The program fills boxes with random spots, stopping at different values, and shows how such numbers might be more uniformly distributed than truly random numbers.

Conclusion: Beyond True Randomness

In conclusion, while the concept of a 'better' random number generator might seem straightforward, it is anything but. The choice of an RNG should be based on specific needs and requirements. Understanding the underlying algorithms and their characteristics is crucial to making informed decisions. For most practical applications, finding an RNG that meets the desired criteria for uniformity and spread is often more relevant than striving for true randomness.

By choosing an RNG that aligns with your specific requirements, you can achieve more predictable and reliable results, enhancing the accuracy and efficiency of your simulations and applications.