These generators must meet the conflicting goals of being extremely fast while also providing random number streams that are indistinguishable from a true random number source.
However, a key component within Monte Carlo simulations is the random number generators (RNGs) that provide the independent stochastic input to each trial. The independent trials are inherently parallelizable, and they typically consist of dense numeric operations, so GPUs provide an almost ideal platform for Monte Carlo simulations. The results of the independent trials are then combined to extract the average answer, relying on the Law of Large Numbers, which states that as more trials are combined, the average answer will converge on the true answer. The defining characteristic of Monte Carlo simulations is the use of multiple independent trials, each driven by some stochastic (random) process. Monte Carlo methods provide approximate numerical solutions to problems that would be difficult or impossible to solve exactly. Efficient Random Number Generation and Application Using CUDA You can also subscribe to our Developer News Feed to get notifications of new material on the site.Ĭhapter 37. The CD content, including demos and content, is available on the web and for download.
#Best random generator algorithm for free#
If you'd like to use the PCG generation scheme, head to the download page.GPU Gems 3 GPU Gems 3 is now available for free online! The PCG paper describes permutation functions on tuples in depth, as well as the output functions used by different members of the PCG family. PCG's output functions are what gives it its excellent statistical performance and makes it hard predict from its output (and thus more secure). PCG's Output Function PCG uses a new technique called permutation functions on tuples to produce output that is much more random than the RNG's internal state.
Moreover, LCGs have number of very useful properties that make them a good choice. Linear congruential generators are known to be statistically weak, but PCG's state transition function only does half the work, so it doesn't need to be perfect. PCG's State-Transition Function The PCG family uses a linear congruential generator as the state-transition function-the “CG” of PCG stands for “congruential generator”. The PCG family takes a more balanced approach. The observation that underlies the PCG family is that these approaches are unbalanced, they put too much weight on one side or the other. For example, the Fortuna RNG has a trivial state transition function (it just increments a counter), but uses a cryptographic block cypher as the output function. Again, this is a very simple output function.Ī few RNGs adopt the opposite approach.
Some RNGs combine multiple simple RNGs and thus have an output function that just merges them together (e.g., with addition or xor). Many RNGs just use the identity function! They just return the state as is (making them easily predicted). Most RNGs use a very simple output function. We can see them as two functions: The State-Transition Function Governs how the RNG's internal state changes every time you ask for a random number The Output Function Turns the RNG's internal state into the actual random number There are two parts to a random number generator. To explain why the PCG family is better, we need to get a little bit technical.