Cerian Knight

The short answer is that if you limit the statistical tests to those in PractRand with mostly default options, then 'yes', Xorshift cannot be said to be nonrandom up to 2^15 bytes. The point I was trying to make is that 'Xorshift cannot be said to be nonrandom up to 2^15 bytes' is true even if I run no randomness tests at all. This is as opposed to running all (easily available) randomness tests, which show Xorshift32 is not random up to 2^15 bytes.

For Windows, I typically already have (usually several version of free) Visual Studio installed, or just download and install the required runtime package. I've only just recently learned Linux and C over the last few years on my own for working with random numbers, as otherwise I am more competent on Windows using either Visual Basic or assembly language (so I probably should keep my opinions on Linux and C to myself).

A few critical points with your example (yes, I ramble): 1. To access the full power of PractRand in the sense you are looking for, in theory you should use additional command line switches. 2. The specific additional switches I use are '-tf 2 -te 1' (and 'stdin', instead of 'stdin32' might provide some additional benefit, but not sure about it with Xorshift). 3. However, doing so exposes issues with statistical calibration at ~64KB and lower. 4. Therefore, PractRand is not optimal for in-depth study...

TestU01: A C Library for Empirical Testing of Random Number Generators Page 5

P-values in TestU01 (and PractRand) are non-standard, so 0.5 (on average) is most likely. Values very close to 1 are 'too uniform' (i.e. a potential indication of a 'low-discrepancy sequence' and/or a PRNG run near its full period). From the TestU01 documentation: "Classical statistical textbooks usually say that when applying a test of hypothesis, one must select beforehand a rejection area R whose probability under H0 equals the target test level (e.g., 0.05 or 0.01), and reject H0 if and only...

P-values in TestU01 are non-standard, so 0.5 (on average) is most likely. Values very close to 1 are 'too uniform' (i.e. a potential indication of a 'low-discrepancy sequence' and/or a PRNG run near its full period). From the TestU01 documentation: "Classical statistical textbooks usually say that when applying a test of hypothesis, one must select beforehand a rejection area R whose probability under H0 equals the target test level (e.g., 0.05 or 0.01), and reject H0 if and only if Y ∈ R. This procedure...

TestU01 simply wants to draw your attention to anything statistically unlikely. I typically run the same PRNG on anywhere from a few dozen to a few thousand different seeds and perform meta-analysis of the set of results. In my experience, over hundreds of thousands of results, you should never see a p-value of less than 1.0e-08, or greater than 1 - 1.0e-08, from a good PRNG. If you do, then a single occurance (except perhaps, debatably, outside of perhaps 1.0e-15) is still not noteworthy unless...

I recommend compiling 0.94 first, since it should be fairly trouble free for .NET. Then try to merge pre0.95 into it, following some info here: https://sourceforge.net/p/pracrand/discussion/366935/thread/35c96c218d/ I actually run both GNU and Windows binaries of TestU01 (STDIN version compiled originally with Cygwin), PractRand and gjrand interchangably under WSL (sometimes piping output from a Windows exe PRNG source/graphical visualization tool to a GNU exe of one of those three).