Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization

Precision analysis and optimization is very important when transforming a floating-point algorithm into fixed-point hardware implementations. The core analysis techniques are either based on dynamic analysis or static analysis. We believe in static error analysis, as it is the only technique that can guarantee the desired worst-case accuracy. In this paper we study various underlying arithmetic candidates that can be used in static error analysis and compare their computed sensitivities. The approaches studied include Affine Arithmetic(AA), General Interval Arithmetic (GIA) and Automatic Differentiation (Symbolic Arithmetic). Our study shows that symbolic method is preferred for expressions with higher order cancellation. For programs without strong cancellation, any method works fairly well and GIA slightly outperforms others. We also study the impact of program transformations on these arithmetics.