Thanks! It appears that Wikipedia has led me astray. The article in the top-level comment states, "if the generator is modified to return only the high 32 bits, then it passes BigCrush with zero failures."
Following through to the document Wikipedia cites, I'm unable to find the original source for that claim. I suppose I'll look again after I have my coffee.
Ah. Found it. From the PCG paper, "also of note, RanQ1[42] and XorShift* 64/32 are essentially the exact same generator,
yet the former fails the test suite and the latter passes. The difference is that the
former markets itself as a 64-bit generator and fails because its low-order bits are
weak, whereas the latter only returns the top 32 bits." The claim of zero Big Crush failures also appears in Figure 2. http://www.pcg-random.org/pdf/hmc-cs-2014-0905.pdf
I suppose the next question is if the claim is wrong or I screwed up the implementation.
It looks like https://de.wikipedia.org/wiki/Benutzer:Megatherium edited the German article to add Vigna's public domain multiplicative xorshift variants, and he misattributed xorshift64star to Marsaglia. https://github.com/jj1bdx/xorshiftplus/blob/5b345e2a2f32f1c5... Vigna obviously knows better than to multiply and not shift but that's not going to be obvious to an anonymous wikipedia editor since you really have to dig through the gpl framework code to find where he does that: https://github.com/jj1bdx/xorshiftplus/blob/1425aae20cd42324... The xorshift variant section should be deleted because if it's multiplying it's not a xorshift. The Lehmer generators show that multiplication alone with a 128-bit word size is enough to confound all the randomness tests experts wrote the last century on 32-bit computers. The value of something like xorshift is on a microcontroller that isn't good at multiplying.
Following through to the document Wikipedia cites, I'm unable to find the original source for that claim. I suppose I'll look again after I have my coffee.
Ah. Found it. From the PCG paper, "also of note, RanQ1[42] and XorShift* 64/32 are essentially the exact same generator, yet the former fails the test suite and the latter passes. The difference is that the former markets itself as a 64-bit generator and fails because its low-order bits are weak, whereas the latter only returns the top 32 bits." The claim of zero Big Crush failures also appears in Figure 2. http://www.pcg-random.org/pdf/hmc-cs-2014-0905.pdf
I suppose the next question is if the claim is wrong or I screwed up the implementation.