Defense Date


Document Type


Degree Name

Master of Science


Electrical Engineering

First Advisor

McCollum James


Many physical, biological, ecological and behavioral events occur at times and rates that are exponentially distributed. Modeling these systems requires simulators that can accurately generate a large quantity of exponentially distributed random numbers, which is a computationally intensive task. To improve the performance of these simulators, one approach is to move portions of the computationally inefficient simulation tasks from software to custom hardware implemented in Field Programmable Gate Arrays (FPGAs). In this work, we study efficient FPGA implementations of exponentially distributed random number generators to improve simulator performance. Our approach is to generate uniformly distributed random numbers using standard techniques and scale them using the inverse cumulative distribution function (CDF). Scaling is implemented by curve fitting piecewise linear, quadratic, cubic, and higher order functions to solve for the inverse CDF. As the complexity of the scaling function increases (in terms of order and the number of pieces), number accuracy increases and additional FPGA resources (logic cells and block RAMs) are consumed. We analyze these tradeoffs and show how a designer with particular accuracy requirements and FPGA resource constraints can implement an accurate and efficient exponentially distributed random number generator.


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Date of Submission

May 2010