I was messing around with this stuff some more and can now report this:

(noted in the web page comments -- I think I'm officially done testing)

A more vigorous (real) test was added called the Frequency (Monobit)

Test. The new algorithm passes this test similarly to the JavaScript

random() function, which additionally suggests that the Unsigned

8-Bit XOR-Shift PRNG Algorithm is most-probably a valid and usable

PRNG. For additional information, see the NIST Special Publication

800-22 Revision 1a document, "A Statistical Test Suite for Random

and Pseudorandom Number Generators for Cryptographic Applications",

Section 2.1 from the Computer Security Division, Computer Security

Resource Center website. Most of the tests described in that

document are fairly difficult to implement, so only Monobit was chosen.

A (separate) periodicity test suggests (barring error, etc.) that the

Unsigned 8-Bit XOR-Shift PRNG Algorithm repeats on (or approximately,

or after?) 1,032,056,991 iterations. (over 1 billion, a little over

41 million less than 2^30) If this is true, then this is additional

proof that the algorithm is valid (-ish) and pretty good. (probably)

The only question at this point is how to properly seed the PRNG.

(so the same sequence of random numbers is not produced every time (from initial use))