There's a paper by Panneton and l'Ecuyer (linked from the Wikipedia article about Xorshift) that seems to indicate that simple Xorshift generators fail some statistical tests very badly. (Not the ones in Marsaglia's Diehard suite -- he tested them with those -- but others.)
I think a better approach is another recommended by Marsaglia: take a few different RNGs working on different principles, and just combine them by (say) adding them up.
Or, of course, just use something like the Mersenne Twister, which is more complicated than (e.g.) Marsaglia's KISS but there are enough good implementations out there that it doesn't really matter.
I think a better approach is another recommended by Marsaglia: take a few different RNGs working on different principles, and just combine them by (say) adding them up.
Or, of course, just use something like the Mersenne Twister, which is more complicated than (e.g.) Marsaglia's KISS but there are enough good implementations out there that it doesn't really matter.