I took over because I wrote the RNG and to be fair the OP shouldn't have posted it because he knew none of the theory behind it so I came in to answer and clarify things for some of the posters.

As for the period as you said it is 2^64 - 1 (Maximal) which is why I chose these numbers. As for the statistical properties, I didn't realise that different choices in numbers could effect it. I will have to read up and better understand all these properties. As for now, I will change the values to your last suggested ones and have the OP correct it in the code.

Edit: I'm not having a go at the OP there he is trying to do the right thing by the community and provide you guys with some working code =)

It's an XORShift RNG (A subset of a Linear Feedback Shift Register [LFSR]) . The system is extremely fast at generating pseudo-random numbers and has been in use for a long time. The numbers that are being used for the shifts aren't just off the top of your head. They are picked to create a maximal 64 bits shift register (63 bits are caused from the absolute function, effectively doubling up the numbers that can be returned therefore halving the actual variation in numbers returned).

With LFSRs the sequence of numbers will eventually repeat. To be maximal means every single combination of bits (apart from the all zeroes) will appear before the sequence repeats. This means there are a total 9,223,372,036,854,775,808 numbers in a 64-bit LFSR that will appear before the sequence repeats itself when using a maximal sequence.

This system can be "cracked" with a given sample size so you wouldn't use it alone in a security system but there are security algorithms based off it.

However for the sake of games programming, 99 times out of 100 your random number generator doesn't need to be secure.

If you want more information there is plenty of information on the topic all over Google.

I hope this enlightens some of you who haven't seen this type of RNG before.

Matt.