Efficient Static Analysis of Fixed-Point Error in DSP Applications via Affine Arithmetic Modeling

Translating digital signal processing (DSP) software into its finite-precision hardware implementation is often a timeconsuming task. We describe a new static analysis technique that can accurately analyze finite-precision e#ects arising from fixed-point implementations of DSP algorithms. The technique is based on recent interval representation methods from a#ne arithmetic, and the use of new probabilistic bounds. The resulting numerical error estimates are comparable to detailed statistical simulation, but achieve speedups of four to five orders of magnitude by avoiding actual bittrue simulation. We show error analysis results on several common DSP kernals