Sampling from the exponential distribution using independent Bernoulli variates

The exponential distribution is a key distribution in many event-driven Monte-Carlo simulations, where it is used to model the time between random events in the system. This paper shows that each bit of a fixed-point exponential random variate is an independent Bernoulli variate, allowing the bits to be generated in parallel. This parallelism is of little interest in software, but is particularly well suited to FPGA generators, where huge numbers of independent uniform bits can be cheaply generated per cycle. Two generation architectures are developed using this approach, one using only logic elements to generate individual bits, and another using block-RAMs to group multiple bits together. The two methods are evaluated at three different quality-resource trade-offs, and when compared to existing methods have both higher performance and better resource utilisation. The method is particularly useful for very high performance applications, as extremely high-quality 36-bit exponential variates can be generated at 600MHz in the Virtex-4 architecture, using just 880 slices and no block-RAMs or embedded DSP blocks.