Linear recurrences with carry as uniform random number generators

1995 ◽  
Author(s):  
Raymond Couture ◽  
Pierre L'Ecuyer
Keyword(s):  
Random Number ◽  
Random Number Generators ◽  
Linear Recurrences ◽  
Uniform Random Number

A General-Purpose Uniform Random Number Package

2021 ◽  
pp. 164-176
Author(s):  
E. Jack Chen
Keyword(s):  
Computer Simulation ◽  
Random Number ◽  
General Purpose ◽  
Random Numbers ◽  
Pseudorandom Generator ◽  
Random Number Generators ◽  
Uniform Random Number ◽  
Modeling And Analysis ◽  
Generating Sequences ◽  
Simulation Systems

As computer capacities and simulation technologies advance, simulation has become the method of choice for modeling and analysis. The fundamental advantage of simulation is that it can tolerate far less restrictive modeling assumptions, leading to an underlying model that is more reflective of reality and thus more valid, leading to better decisions. Simulation studies are typically preceded by transforming in a more or less complicated way of a sequence of numbers between 0 and 1 produced by a pseudorandom generator into an observation of the measure of interest. Random numbers are a fundamental resource in science and technology. A facility for generating sequences of pseudorandom numbers is a fundamental part of computer simulation systems. Furthermore, random number generators also play an important role in cryptography and in the blockchain ecosystem. All samples of the sequence are generated independently of each other, and the value of the next sample in the sequence cannot be predicted, regardless of how many samples have already been produced.

Uniform Random Number Generation With Jumping Facilities

2018 ◽  
pp. 1297-1306
Author(s):  
E. Jack Chen
Keyword(s):  
Variance Reduction ◽  
Random Number ◽  
Simple Procedure ◽  
Random Number Generation ◽  
Random Numbers ◽  
Random Number Generators ◽  
Uniform Random Number ◽  
Number Generation ◽  
Multiple Recursive Generator ◽  
Generating Sequences

A facility for generating sequences of pseudorandom numbers is a fundamental part of computer simulation systems. Furthermore, multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform random-number generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. Simple procedure calls allow the user to make any generator “jump” ahead/back v steps (random numbers). Implementation issues are discussed. An efficient and portable code is also provided to implement the package. The basic underlying generator CMRG (combined Multiple Recursive Generator) combines two multiple recursive random number generators with a period length of approximately 2191 (˜ 3.1× 1057), good speed, and excellent theoretical properties.

Fourier Analysis of Uniform Random Number Generators

1967 ◽  
Vol 14 (1) ◽  
pp. 100-119 ◽  
Author(s):  
R. R. Coveyou ◽  
R. D. Macpherson
Keyword(s):  
Fourier Analysis ◽  
Random Number ◽  
Random Number Generators ◽  
Uniform Random Number
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