I just came across Random123 [1]: portable, parallel, high-quality pseudorandom 
number generators.  It's developed by DE Shaw, but the license [2] looks to me 
like we should be able to make a repo for it and use it as a PetscRandom 
implementation.  Does anyone savvier than me want to look at the license and 
see if I'm missing something?

Cheers,
  Toby

[1]: https://doi.org/10.1145/2063384.2063405
[2]: 
http://www.deshawresearch.com/downloads/download_random123.cgi/Random123_License.txt

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