Having multiple streams of pseudo-random numbers known to be independent and with a uniform distribution I want to do Monte Carlo simulations in parallel.
In other words, one thread will have a full-period independent and uniformly distributed stream of pseudo-random numbers. Each thread will consume these numbers in four different functions (a,b,c,d).
My concern is about the distribution across threads for each function. Thread.1 func_a.1, thread.2 func_a.2... and so on. Do I still need to make sure this distribution is indeed uniform across func_a1, func_a2, etc? Failing to do so can make my simulation have flaws?
In summary,if I start using the pseudo-random numbers in a "random" fashion, rejection sampling. Can I still be sure of the uniform distribution among the different parts?