A Pseudo-Random Number Generator Based on Normal Numbers

Technical Report · Fri Dec 31 04:00:00 EST 2004

DOI:https://doi.org/10.2172/860344· OSTI ID:860344

Bailey, David H

In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.

• Research Organization: Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Advanced ScientificComputing Research
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 860344
• Report Number(s): LBNL--57489; BnR: KJ0101030
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPUTER CODES
MATHEMATICS
RANDOMNESS
pseudo-random number generation normal numbers