PEMACx: A Probabilistic Error Analysis Methodology for Adders with Cascaded Approximate Units

In this paper, we propose a novel methodology for efficiently computing the Probability Mass Function (PMF) of error at the output of a major class of approximate adders that comprise of a cascade of multiple stages of smaller approximate adder units. The proposed methodology utilizes the carry-out probability of the previous stage along with the input probabilities of the current stage to recursively computes the PMF of error of the current stage. The proposed methodology eliminates the need for exhaustive simulations and, therefore, can be used for efficiently analyzing error distribution of a wide variety of low-power large bit-width adders with cascaded approximate adder units. Experimental results demonstrate that the proposed methodology provides error estimates that commensurate with exhaustive simulations, while offering a speedup of at least 2958x for 8-bit (or larger) approximate adder configurations.