Pseudo Random Number Generators (PRNGs) on the GPU

For RAYX we found a good and performant pseudo random number generator after some research. We cannot use default C++ options as they are not supported by our Shader code. We decided to use Squares RNG, which is counter based and utilizes a version of the Middle Square Weyl Sequence. We tested the method with the TestU01 bigcrush test with different seeds and it passed all of them.

We added a few more methods for creating random numbers with more variety. These methods are:

• uint64_t squares64RNG(inout uint64_t ctr), which generates 64-Bit random integers from two 32-Bit random integers
• double squaresDoubleRNG(inout uint64_t ctr), which generates uniformly distributed doubles between 0 and 1 from one 64-Bit random integer
• double squaresNormalRNG(inout uint64_t ctr, double mu, double sigma), which creates (via the Box-Muller transform) a normal distributed double with mean mu and standard deviation sigma. This takes three random doulbes, which takes six 32-Bit integers.

Links

• Squares: A Fast Counter-Based RNG
• TestU01: A C Library for Empirical Testing of Random Number Generators
• Box–Muller transform