Resource efficient generators for the floating-point uniform and exponential distributions

Monte-Carlo simulations and many other stochastic algorithms are almost ideal applications for FPGAs, as the huge amount of available parallelism allows deep pipelining without loop-carried dependencies and spatial scaling across large devices without shared resource bottlenecks. Another key advantage is that random number generation is very cheap (when compared to software), and can be tailored to meet the performance and quality needs of each application. However, in many cases this advantage is not exploited, either because an inefficient but simple to implement generator is chosen, or because a generator with properties that far exceed the needs of the application is used. This paper describes generators for the floating-point uniform and exponential distributions, which provide efficient resource usage, while remaining sufficiently simple to make them attractive to users.