Saturation Arithmetic

Summary

This chapter has presented a novel technique for design automation of saturation arithmetic systems. An analytic saturation noise estimation method has been presented, based on the introduction of the saturated Gaussian distribution and a linearization of the saturation nonlinearities. In contrast to truncation and rounding, auto- and cross-correlations between linearized saturation nonlinearities have been accounted for using a bound derived through the Cauchy-Schwartz inequality. Techniques have been presented to reduce the slackness associated with such a bound.

The heuristic presented in Section 4.4 has been extended to incorporate combined scaling and word-length optimization. The results of such an optimization have been discussed for real examples of DSP systems and contrasted with more traditional approaches to scaling optimization. It has been shown that allowing rare saturation errors can result in fast and small implementations of IIR filters when the poles of the filter are close to the unit circle. Improvements have been achieved of up to 8% in area and 24% in speed over and above the improvements generated through the techniques of Chapter 4.