Elke Korn

A New Hardware Efficient Inversion Based Random Number Generator for Non-uniform Distributions

For numerous computationally complex applications, like financial modelling and Monte Carlo simulations, the fast generation of high quality non-uniform random numbers (RNs) is essential. The implementation of such generators in FPGA-based accelerators has therefore become a very active research field. In this paper we present a novel approach to create RNs for different distributions based on an efficient transformation of floating-point inputs. For the Gaussian distribution we can reduce the number of slices needed by up to 48\% compared to the state-of-the-art while achieving a higher output precision in the tail region. Our architecture produces samples up to

A hardware efficient random number generator for nonuniform distributions with arbitrary precision

8.37\sigma

Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics

and achieves 381MHz. We also present a comprehensive testing methodology based on stochastic analysis and verification in practical applications.

Optionsbewertung und Portfolio-Optimierung

Nonuniform random numbers are key for many technical applications, and designing efficient hardware implementations of nonuniform random number generators is a very active research field. However, most state-of-the-art architectures are either tailored to specific distributions or use up a lot of hardware resources. At ReConFig 2010, we have presented a new design that saves up to 48% of area compared to state-of-the-art inversion-based implementation, usable for arbitrary distributions and precision. In this paper, we introduce a more flexible version together with a refined segmentation scheme that allows to further reduce the approximation error significantly. We provide a free software tool allowing users to implement their own distributions easily, and we have tested our random number generator thoroughly by statistic analysis and two application tests.