On the distribution of exponent differences during floating point addition

The paper addresses the characterization of exponent differences during floating point accumulate and multiply accumulate (MAC) operations. Our investigations suggest the existence of a class of probability density functions (pdfs) that exhibit non zero modes, describing the behavior of exponent differences. The distributions also support the hypothesis that the power consumption of floating point adders can be reduced by bypassing the adder during certain situations, that are characterized by an apriori knowledge of the final result.