Development of an Automatic Numerical Stability Analyser Based on a Hardware Implementation of Discrete Stochastic Arithmetic

Computers usually represent numbers with finite precision arithmetic. Most real numbers can not be exactly represented. Results of assignment and computations have then to be approximated, and rounding errors are induced. Several approaches have been developed to study the rounding errors. Among these methods, the numerical accuracy analysis based on the discrete stochastic arithmetic is able to provide a tight and accurate estimation of the rounding errors. It have been proven to be effective and reliable in many publications. A hardware platform has been developed in a previous project to use the principles of discrete stochastic arithmetic. On this hardware platform, multiple processing blocks can execute the same program in parallel with random rounding. Adapted floating point units provide the necessary values to compute an estimation of the accuracy.

Based on the dedicated hardware platform, a numerical stability analyser is investigated in this work. The proposed numerical stability analyser is able to gather information from the dedicated hardware platform and provide the numerical accuracy information to the user. The interface to the user is kept the same as a state-of-the-art debugger, while providing additional commands that allows the accuracy estimation of intermediate results. The mechanisms involved in the numerical stability analyser is exposed and its usage is explained.