Note on Marsaglia's xorshift random number generators

Richard P. Brent

doi:10.18637/jss.v011.i05

Note on Marsaglia's xorshift random number generators

Richard P. Brent^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

Marsaglia, (2003) has described a class of "xorshift" random number generators (RNGs) with periods 2ⁿ - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.

Original language	English
Journal	Journal of Statistical Software
Volume	11
DOIs	https://doi.org/10.18637/jss.v011.i05
Publication status	Published - 7 Jul 2004
Externally published	Yes

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abstract = "Marsaglia, (2003) has described a class of {"}xorshift{"} random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using {"}exclusive or{"} (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.",

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N2 - Marsaglia, (2003) has described a class of "xorshift" random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.

AB - Marsaglia, (2003) has described a class of "xorshift" random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.

KW - LFSR sequences

KW - Linear feedback shift registers

KW - Primitive polynomials

KW - Random number generators

KW - Xorshift RNGs

UR - https://www.scopus.com/pages/publications/27344453719

U2 - 10.18637/jss.v011.i05

DO - 10.18637/jss.v011.i05

M3 - Article

SN - 1548-7660

VL - 11

JO - Journal of Statistical Software

JF - Journal of Statistical Software

ER -

Note on Marsaglia's xorshift random number generators

Abstract

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