[FabHK]

A few notes:

The author writes "Meanwhile, at least one influential researcher (whose work I respect) had harsh words publicly for her result", and then quotes some of these words:

   Note that (smartly enough) the PCG author avoids
   carefully to compare with xorshift128+ or xorshift1024*.
 

However, the author fails to note that said "influential researcher", Sebastiano Vigna, is the author of xorshift128+ and related PRNG.

In the linked test [2] by John D. Cook (who uses PactRand, a test similar to the (obsolete) DIEHARD), xorshift128+ and xoroshir0128+ fail within 3 seconds, while PCG ran 16 hours producing 2 TB of pseudo-random numbers without any suspicious p-value detected.

On the other hand, Vigna claims that the xoroshiro family does "pass" PactRand.

I've submitted an answer to StackOverflow a while ago [1], recommending xoroshiro and PCG, thus I'd be concerned if PCG turns out to be flawed. It's actually quite hard to get academics in the field to give an authoritative recommendation (I've tried) - their response is typically along the line "It's complicated"...

[1] https://stackoverflow.com/questions/4720822/best-pseudo-rand...

[2] https://www.johndcook.com/blog/2017/08/14/testing-rngs-with-...

Edit: remove italics due to asterisk in PRNG name, & add link to John. D Cook's test.

[MiceWithYaffle]

I think Vigna's claim is that if you ignore the PractRand tests that fail, it passes. (Really!)

O'Neill has instructions on how to test with PractRand and with TestU01 on her blog (http://www.pcg-random.org/blog/). I had a go with TestU01 on Vigna's generators, and when you test the low 32 bits reversed (for 64-bit PRNGs, you have to test the high 32, the low 32, both forwards and reversed), I found that all Vigna's generators fail.

Given the PractRand results it makes sense, I guess, but I had read that Vigna's generators were supposed to pass TestU01.

Does anyone else wants to have a go at testing so I can know if I screwed up somehow?

[rockdoe]

I think Vigna's claim is that if you ignore the PractRand tests that fail, it passes. (Really!)

The code does explain exactly what the issue is, i.e. that the last bit isn't random:

   This generator passes the PractRand test suite
   up to (and included) 16TB, with the exception of binary rank tests,
   which fail due to the lowest bit being an LFSR; all other bits pass all
   tests. We suggest to use a sign test to extract a random Boolean value.

But I'm tempted to agree this isn't a desirable property for a generic RNG.

How many users of JavaScript know about this property? (it's the default RNG for most browser engines) Or does it not matter because they return 53-bit floats?

[FabHK]

In the comment section to the V8 JavaScript blog post [1], Vigna writes:

  - Technically, it would be better if you used the upper
  52 bits, rather than the lower 52 bits, to generate a
  double. The lowest bit of a xorshift128+ generator is an
  LSFR, and while people has been happy using LSFR for
  decades, it is slightly inferior in quality to all other
  bits. This is really OCD, as computational errors makes
  the lowest bit almost irrelevant, but now you know.

I don't know whether that's been implemented, but the maintainer replied:

  Thanks for the suggestions! I will definitely revisit the 
  current implementation with your tips in mind.

[1] https://v8project.blogspot.nl/2015/12/theres-mathrandom-and-...