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August, 1991 A New Class of Random Number Generators
George Marsaglia, Arif Zaman
Ann. Appl. Probab. 1(3): 462-480 (August, 1991). DOI: 10.1214/aoap/1177005878


We introduce a new class of generators of two types: add-with-carry and subtract-with-borrow. Related to lagged-Fibonacci generators, the new class has interesting underlying theory, astonishingly long periods and provable uniformity for full sequences. Among several that we mention, we recommend particularly promising ones that will generate a sequence of $2^{1751}$ bits, or a sequence of $2^{1376}$ 32-bit integers, or a sequence of $2^{931}$ reals with 24-bit fractions--all using simple computer arithmetic (subtraction) and a few memory locations.


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George Marsaglia. Arif Zaman. "A New Class of Random Number Generators." Ann. Appl. Probab. 1 (3) 462 - 480, August, 1991.


Published: August, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0733.65005
MathSciNet: MR1111529
Digital Object Identifier: 10.1214/aoap/1177005878

Primary: 65C10
Secondary: 10A30

Keywords: add-with-carry , lagged-Fibonacci , Monte Carlo , Random number generators , subtract-with-borrow

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 3 • August, 1991
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