Efficient Floating-Point Implementation of the Probit Function on FPGAs

Non-uniform random number generators are key components in Monte Carlo simulations. The inverse cumulative distribution function (ICDF) technique provides a viable solution for generating random variables from various distributions. Thus, the ICDF of the standard normal distribution, or probit function for short, is of particular interest. The goal of this article is to revisit and improve a floating-point (FP) implementation of probit, from the perspective of modern hardware resources available on FPGAs. Beside reexamining the classical Wichura's algorithm, we propose: (1) a single-precision implementation using the embedded FP DSP Blocks available in recent FPGA families; (2) generic custom-precision architectures that scale up to double-precision. These present a user-selectable trade-off between tail accuracy and resource utilization. Our proposed cores outperform existing single-precision FPGA implementations in area, latency and accuracy, and also set benchmarks for new custom and double-precision FP implementations.