The post "Perfect Random Floating-Point Numbers" explores generating uniformly distributed random floating-point numbers within a specific range, addressing the subtle biases that can arise with naive approaches. It highlights how simply casting random integers to floats leads to uneven distribution and proposes a solution involving carefully constructing integers within a scaled representation of the desired floating-point range before converting them. This method ensures a true uniform distribution across the representable floating-point numbers within the specified bounds. The post also provides optimized implementations for specific floating-point formats, demonstrating a focus on efficiency.
The blog post "Perfect Random Floating-Point Numbers" delves into the intricacies of generating random floating-point numbers within a specified range, focusing on achieving true uniformity and addressing the subtle biases that can arise from naive approaches. The author begins by highlighting the common pitfall of simply scaling a random integer to the desired range. This method, while seemingly straightforward, introduces non-uniformity due to the uneven distribution of floating-point numbers across the real number line. Floating-point numbers are denser near zero and become sparser as magnitude increases, meaning that scaling an integer effectively oversamples certain regions of the target range while undersampling others.
The post then introduces the concept of generating random floats uniformly within a power-of-two range. This approach leverages the fact that floating-point numbers are uniformly spaced within such ranges. By randomly generating both the significand (mantissa) and exponent within appropriate bounds, a perfectly uniform distribution can be achieved within this power-of-two interval. The author describes the implementation details of this method, emphasizing the need to carefully handle exponent biases and special floating-point values like infinity and NaN (Not a Number). Code examples demonstrating the generation process in C++ are provided, along with explanations of the bit manipulation techniques involved.
The core of the post lies in extending this power-of-two range generation to arbitrary ranges. The author presents an algorithm that effectively partitions the desired range into a series of overlapping power-of-two intervals. A random float is then generated within one of these intervals, selected with probability proportional to its size. This ensures that the overall distribution across the entire target range is uniform. The post provides a detailed breakdown of the algorithm's logic, accompanied by C++ code implementation.
The author concludes by discussing potential optimizations and performance considerations, highlighting the trade-off between simplicity and efficiency. They also address the nuances of handling open intervals (excluding endpoints) and offer insights into generating random numbers from other distributions, such as the normal distribution, by applying transformations to the uniformly distributed floats generated by the presented algorithm. Ultimately, the post serves as a comprehensive guide to generating truly uniform random floating-point numbers, offering both theoretical understanding and practical implementation details.
Summary of Comments ( 3 )
https://news.ycombinator.com/item?id=43887068
Hacker News users discuss the practicality and nuances of generating "perfect" random floating-point numbers. Some question the value of such precision, arguing that typical applications don't require it and that the performance cost outweighs the benefits. Others delve into the mathematical intricacies, discussing the distribution of floating-point numbers and how to properly generate random values within a specific range. Several commenters highlight the importance of considering the underlying representation of floating-points and potential biases when striving for true randomness. The discussion also touches on the limitations of pseudorandom number generators and the desire for more robust solutions. One user even proposes using a library function that addresses many of these concerns.
The Hacker News post titled "Perfect Random Floating-Point Numbers" (linking to an article on specbranch.com about generating random floating-point numbers) generated several comments discussing various aspects of random number generation, particularly within the context of floating-point representation and its limitations.
One commenter pointed out that the premise of "perfect" randomness is misleading when dealing with floating-point numbers. They argue that due to the discrete nature of floating-point representation, achieving true uniform distribution across the entire range of representable values is mathematically impossible with standard pseudo-random number generators (PRNGs). They suggest that the article might be more accurately framed around generating random floats with specific distributional properties suitable for particular applications.
Another comment thread delves into the complexities of representing irrational numbers, which are inherently non-repeating and infinite, within the finite precision of floating-point formats. This discussion highlights the inherent limitations of representing continuous probability distributions with discrete numerical representations.
A separate comment focuses on the practical implications of using PRNGs in simulations. They emphasize the importance of seeding PRNGs correctly, especially when reproducibility is crucial for validating scientific computations. This comment also touches upon the trade-off between performance and the quality of randomness provided by different PRNG algorithms.
Several commenters question the necessity of achieving perfectly uniform distributions for most practical use cases. They argue that for many applications, a "good enough" level of randomness is sufficient, and that striving for theoretical perfection can be computationally expensive with diminishing returns. They suggest alternative approaches like using quasirandom sequences (like Sobol sequences) when specific distribution properties are desired.
One commenter highlights the limitations of generating uniformly distributed random floats within a specific range, particularly when the range is very small. They point out that the spacing between representable floating-point values becomes increasingly sparse at higher magnitudes, leading to potential biases if not handled carefully.
Another thread discusses the subtleties of different PRNG algorithms, such as the Mersenne Twister, and their suitability for various tasks. The discussion touches on the period length of these generators and their impact on the perceived randomness of the generated sequences.
Finally, a few comments mention libraries and tools for generating random numbers in different programming languages, offering practical advice for readers looking to implement random number generation in their own projects. One such comment specifically suggests using the
randcrate in Rust for its robust and efficient random number generation capabilities.