  xorshift* generators are a variant of Marsaglia's xorshift generators that
eliminate linear artifacts typical of generators based on $\mathbf Z/2\mathbf
Z$-linear operations using multiplication by a suitable constant. Shortly after
high-dimensional xorshift* generators were introduced, Saito and Matsumoto
suggested a different way to eliminate linear artifacts based on addition in
$\mathbf Z/2^{32}\mathbf Z$, 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.
