C++ super fast thread-safe rand function

Problem is that seedp variable (and its memory location) is shared among several threads. Processor cores must synchronize their caches each time they access this ever changing value, which hampers performance. The solution is that all threads work with their own seedp, and so avoid cache synchronization.

It depends on how good the statistical randomness needs to be. For high quality, the Mersenne twister, or its SIMD variant, is a good choice. You can generate and buffer a large block of pseudo-random numbers at a time, and each thread can have its own state vector. The Park-Miller-Carta PRNG is extremely simple - these guys even implemented it as a CUDA kernel.

Marsaglia's xor-shift generator is the probably fastest "reasonable quality" generator that you can use. It does not quite have the same "quality" as MT19937 or WELL, but honestly these differences are academic sophistries.
For all real, practical uses, there is no observable difference, except 1-2 orders of magnitude difference in execution speed, and 3 orders of magnitude of difference in memory consumption.

The xor-shift generator is also naturally thread-safe (in the sense that it will produce non-deterministic, pseudorandom results, and it will not crash) without anything special, and it can be trivially made thread-safe in another sense (in the sense that it will generate per-thread independent, deterministic, pseudorandom numbers) by having one instance per thread.
It could also be made threadsafe in yet another sense (generate a deterministic, pseudorandom sequence handed out to threads as they come) using atomic compare-exchange, but I don't think that's very useful.

The only three notable issues with the xor-shift generator are:

• It is not k-distributed for up to 623 dimensions, but honestly who cares. I can't think in more than 4 dimensions (and even that's a lie!), and can't imagine many applications where more than 10 or 20 dimensions could possibly matter. That would have to be some quite esoteric simulation.
• It passes most, but not ever pedantic statistic test. Again, who cares. Most people use a random generator that does not even pass a single test and never notice.
• A zero seed will produce a zero sequence. This is trivially fixed by adding a non-zero constant to one of the temporaries (I wonder why Marsaglia never thought of that?). Having said that, MT19937 also behaves extremely badly given a zero seed, and does not recover nearly as well.