Question

I use random numbers in several places and usually construct a random number generator whenever I need it. Currently I use the Marsaglia Xorshift algorithm seeding it with the current system time.
Now I have some doubts about this strategy:
If I use several generators the independence (randomness) of the numbers between the generators depends on the seed (same seed same number). Since I use the time (ns) as seed and since this time changes this works but I am wondering whether it would not be better to use only one singular generator and e.g. to make it available as a singleton. Would this increase the random number quality ?

Edit: Unfortunately c++11 is not an option yet

Edit: To be more specific: I am not suggesting that the singleton could increase the random number quality but the fact that only one generator is used and seeded. Otherwise I have to be sure that the seeds of the different generators are independent (random) from another.
Extreme example: I seed two generators with exactly the same number -> no randomness between them

Answer 1

Suppose you have several variables, each of which needs to be random, independent from the others, and will be regularly reassigned with a new random value from some random generator. This happens quite often with Monte Carlo analysis, and games (although the rigor for games is much less than it is for Monte Carlo). If a perfect random number generator existed, it would be fine to use a single instantiation of it. Assign the n^th pseudo random number from the generator to variable x₁, the next random number to variable x₂, the next to x₃, and so on, eventually coming back to variable x₁ on the next cycle. around. There’s a problem here: Far too many PRNGs fail the independence test fail the independence test when used this way, some even fail randomness tests on individual sequences.

My approach is to use a single PRNG generator as a seed generator for a set of N instances of self-contained PRNGs. Each instance of these latter PRNGs feeds a single variable. By self-contained, I mean that the PRNG is an object, with state maintained in instance members rather than in static members or global variables. The seed generator doesn’t even need to be from the same family as those other N PRNGs. It just needs to be reentrant in the case that multiple threads are simultaneously trying to use the seed generator. However, In my uses I find that it is best to set up the PRNGs before threading starts so as to guarantee repeatability. That’s one run, one execution. Monte Carlo techniques typically need thousands of executions, maybe more, maybe a lot more. With Monte Carlo, repeatability is essential. So yet another a random seed generator is needed. This one seeds the seed generator used to generate the N generators for the variables.

Repeatability is important, at least in the Monte Carlo world. Suppose run number 10234 of a long Monte Carlo simulation results in some massive failure. It would be nice to see what in the world happened. It might have been a statistical fluke, it might have been a problem. The problem is that in a typical MC setup, only the bare minimum of data are recorded, just enough for computing statistics. To see what happened in run number 10234, one needs to repeat that particular case but now record everything.