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abstract = {xorshift\sup{*} generators are a variant of Marsaglia's xorshift generators that eliminate linear artifacts typical of generators based on \\(Z/2Z\\)-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift\sup{*} generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in \\(Z/2^{32}Z\\), leading to the XSadd generator. Starting from the observation that the lower bits of XSadd are very weak, as its reverse fails systematically several statistical tests, we explore xorshift+, a variant of XSadd using 64-bit operations, which leads, in small dimension, to extremely fast high-quality generators.},
title = {{Further scramblings of Marsaglia's xorshift generators}},
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url = {https://arxiv.org/abs/1404.0390},
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volume = {abs/1404.0390},
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year = {2014},
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}
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@unpublished{marsaglia:2003,
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abstract = {Description of a class of simple, extremely fast random number generators (RNGs) with periods \\(2^k −1\\) for \\(k = 32, 64, 96, 128, 160, 192\\). These RNGs seem to pass tests of randomness very well.},
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