An Improved Logarithmic Multiplier for Energy-Efficient Neural Computing

Multiplication is the most resource-hungry operation in neural networks (NNs). Logarithmic multipliers (LMs) simplify multiplication to shift and addition operations and thus reduce the energy consumption. Since implementing the logarithm in a compact circuit often introduces approximation, some accuracy loss is inevitable in LMs. However, this inaccuracy accords with the inherent error tolerance of NNs and their associated applications. This article proposes an improved logarithmic multiplier (ILM) that, unlike existing designs, rounds both inputs to their nearest powers of two by using a proposed nearest-one detector (NOD) circuit. Considering that the output of the NOD uses a one-hot representation, some entries in the truth table of a conventional adder cannot occur. Hence, a compact adder is designed for the reduced truth table. The 8×8 ILM achieves up to 17.48 percent saving in power consumption compared to a recent LM in the literature while being almost 8 percent more accurate. Moreover, the evaluation of the ILM for two benchmark NN workloads shows up to 21.85 percent reduction in energy consumption compared to the NNs implemented with other LMs. Interestingly, using the ILM increases the classification accuracy of the considered NNs by up to 1.4 percent compared to a NN implementation that uses exact multipliers.