Algorithm 488: A Gaussian pseudo-random number generator

  title={Algorithm 488: A Gaussian pseudo-random number generator},
  author={Richard P. Brent},
  journal={Commun. ACM},
  • R. Brent
  • Published 1 December 1974
  • Mathematics, Computer Science
  • Commun. ACM
The algorithm calculates the exact cumulative distribution of the two-sided Kolmogorov-Smirnov statistic for samples with few observations. The general problem for which the formula is needed is to assess the probability that a particular sample comes from a proposed distribution. The problem arises specifically in data sampling and in discrete system simulation. Typically, some finite number of observations are available, and some underlying distribution is being considered as characterizing… 

A fast normal random number generator

A method is presented for generating pseudorandom numbers with a normal distribution using the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves and can be implemented in 15 lines of FORTRAN.

Computer Generation of Random Variables Using the Ratio of Uniform Deviates

The ratio-of-uniforms method for generating random variables having continuous nonuniform distributions is presented and can be used for generating short and often as fast algorithms as well as longer algorithms.

Gaussian random number generators

The algorithms underlying various GRNGs are described, their computational requirements are compared, and the quality of the random numbers are examined with emphasis on the behaviour in the tail region of the Gaussian probability density function.

Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm

Algorithms to generate samples from the normal probability distribution were analyzed in a technology-independent empirical Knuth type A algorithm analysis, finding no conclusion of the best algorithm, but scrutiny of results would lead to selection of thebest algorithm for a specific implementation.

Sampling Exactly from the Normal Distribution

An algorithm for sampling exactly from the normal distribution that reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same base with mean cost that scales linearly in the precision.

Uniform Random Number Generators for Vector and Parallel Computers

  • R. Brent
  • Computer Science, Mathematics
  • 1992
A proposal for a class of random number generators which have good statistical properties and can be implemented eciently on vector processors and parallel machines is made.

Some Comments on C. S. Wallace's Random Number Generators

This work considers Chris Wallace’s recent idea for generating normally distributed variates without relying on a source of uniform random numbers, and compares it with more conventional methods for generating normal random numbers.

Uniform random number generators for supercomputers

A class of random number generators which have good statistical properties and can be implemented eciently on vector processors and parallel machines is proposed.

Fast normal random number generators on vector processors

  • R. Brent
  • Computer Science, Mathematics
  • 2010
We consider pseudo-random number generators suitable for vector processors. In particular, we describe vectorised implementations of the Box-Muller and Polar methods, and show that they give good



Von Neumann''s comparison method for random sampling from the normal and other distributions.

The author presents a generalization he worked out in 1950 of von Neumann''s method of generating random samples from the exponential distribution by comparisons of uniform random numbers on (0,1).

Algorithm 334: Normal random deviates

This algorithm is one of a class of normal deviate generators, which the authors shall call "chi-squared projections" by using van Neumann rejection to generate sin (¢) and cos (¢), without generating ¢ explicitly [3], which significantly enhances speed by eliminating the calls to the sin and cos functions.

Computer methods for sampling from the exponential and normal distributions

The authors' primary conwiba~ion is the rise of polynomiaI sampling (as ex~ p/tiffed in Section 2) to eliminate any dependency on standard&ruction programs.

Merge sort algorithm [M1]

This ALGOL 60 procedure demonstrates that, using recursion, an elegant and efficient algorithm can be designed, the correctness of which is easily proved.

The Traveling Salesman Problem: A Survey

A survey and synthesis of research on the traveling salesman problem is given and a general classification of the solution techniques and a detailed description of some of the proven methods are given.

An Algorithm for Path Connections and Its Applications

  • C. Y. Lee
  • Computer Science, Mathematics
    IRE Trans. Electron. Comput.
  • 1961
The algorithm described in this paper is the outcome of an endeavor to answer the following question: Is it possible to find procedures which would enable a computer to solve efficiently

The theory of graphs and its applications

This book on the theory of graphs provides the reader with a mathematical tool which can be used in the behavioral sciences, in the theory of information, cybernetics, games, transport networks, as

The Art of Computer Programming

The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.

A Modification of Lee's Path Connection Algorithm

  • S. Akers
  • Computer Science
    IEEE Trans. Electron. Comput.
  • 1967
It is shown that a set of diagnostic tests designed for a redundant circuit under the single-fault assumption is not necessarily a valid test set if a fault occurrence is preceded by the occurrence

Various techniques used in connection with random digits

  • Collected Works
  • 1963