Abstract

Recently, fast computers have led to more complex scientific computations involving more and more arithmetic operations. Due to the use of finite precision arithmetic for Floating Point (FP) numbers, each elementary FP operation may induce a rounding error. Consequently, the computed results are affected by the rounding error propagation. The final result can be completely different from that which is expected.

Numerical accuracy analysis with respect to rounding error propagations is a general concern in both scientific and engineering applications. The Discrete Stochastic Arithmetic (DSA) is a powerful numerical accuracy analysis method that enables one to estimate the number of exact significant digits of any computed result. DSA is based on a probabilistic approach for round-off error analysis. Stochastic arithmetic operations are computed on a Stochastic Floating Point Unit (SFPU), where the rounding of the results is randomly chosen. However, software implementation of this method suffers from computational bottlenecks, while hardware alternative would accelerate the computation.

The purpose of this work is to develop a single-precision SFPU and to use it as the basis of the DSA method. The SFPU is then connected to the MicroBlaze processor via the Processor Local Bus (PLB). Virtex-5 Field-Programmable Gate Array (FPGA) is used to synthesis the system. In addition, The SFPU and the system have been verified to show the correctness, reliability as well as the performance of the system.