Efficient approximate adders for fpga-based data-paths

Approximate computing represents a powerful technique to reduce energy consumption and computational delay in error-resilient applications, such as multimedia processing, machine learning, and many others. In these contexts, designing efficient digital data-paths is a crucial concern. For this reason, the addition operation has received a great deal of attention. However, most of the approximate adders proposed in the literature are oriented to Application Specific Integrated Circuits (ASICs), and their deployment on different devices, such as Field Programmable Gate Arrays (FPGAs), appears to be unfeasible (or at least ineffective). This paper presents a novel approximate addition technique thought to efficiently exploit the configurable resources available within an FPGA device. The proposed approximation strategy sums the k least significant bits two-by-two by using 4-input Look-up-Tables (LUTs), each performing a precise 2-bit addition with the zeroed carry-in. In comparison with several FPGA-based approximate adders in the existing literature, the novel adder achieves markedly improved error characteristics without compromising either the power consumption or the delay. As an example, when implemented within the Artix-7 xc7a100tcsg324-3 chip, the 32-bit adder designed as proposed here with k = 8 performs as fast as its competitors and reduces the Mean Error Distance (MED) by up to 72% over the state-of-the-art approximate adders, with an energy penalty of just 8% in the worst scenario. The integration of the new approximate adder within a more complex application, such as the 2D digital image filtering, has shown even better results. In such a case, the MED is reduced by up to 97% with respect to the FPGA-based counterparts proposed in the literature.