Re: Marsaglia's XOR-Shift (not conditional) PRNG was Marsaglia's XOR-Shift PRNG

David Sexton wrote:
> 

> I have done some more testing.
> 
> I find that when a generator shown by Berlekamp-Massey to have low
> linear complexity is XORed with a generator that has high complexity,
> the result has high complexity. I also found that XORing two
> generators with low linear complexity produced a sequence with low
> complexity, though higher than each generator alone.
> 
> I XORed a few weak generators with the Mersenne Twister (which still
> appears random no matter which tests I try, and no matter which bits
> of the output I test), and the results looked as random as the
> Mersenne Twister alone.
> 
> When I XORed generators that fail many tests (e.g. LCGs) with the
> XORshift generator, the results did as well as XORShift alone. What's
> more, generators with high linear complexity but poor statistics
> otherwise, when XORed with XORShift (which has low complexity), the
> results had high complexity.

Thanks for the experimental results. Another issue that
could be of similar interest is shuffling PRNG output
through a buffer. A well-known scheme due to Marsaglia 
uses one PRNG to process the output of another, while
a variant due to Bays and Durham (Knuth vol. 2)
uses the PRNG to process its own output. It would
be very fine, if you could sometime find the time
to do some experiments on these schemes with your (I 
suppose rather extensive) test software as well.

M. K. Shen