Comparative Study of Approximate Multipliers

Approximate multipliers are widely being advocated for energy-efficient computing in applications that exhibit an inherent tolerance to inaccuracy. However, the inclusion of accuracy as a key design parameter, besides the performance, area and power, makes the identification of the most suitable approximate multiplier quite challenging. In this paper, we identify three major decision making factors for the selection of an approximate multipliers circuit: (1) the type of approximate full adder (FA) used to construct the multiplier, (2) the architecture, i.e., array or tree, of the multiplier and (3) the placement of sub-modules of approximate and exact multipliers in the main multiplier module. Based on these factors, we explored the design space for circuit level implementations of approximate multipliers. We used circuit level implementations of some of the most widely used approximate full adders, i.e., approximate mirror adders, XOR/XNOR based approximate full adders and Inexact adder cell. These FA cells are then used to develop circuits for the approximate high order compressors as building blocks for 8x8 array and tree multipliers. We then develop various implementations of higher bit multipliers by using a combination of exact and inaccurate 8x8 multiplier cells. All these implementations have been done using the Cadence's Spectre tool with the TSMC65nm technology. The design space of these multipliers is explored based on their power, area, delay and error and the best approximate multiplier designs are identified. The report also presents the validation of our results using an image blending application. An open source library of implemented cells and multiplier circuits are available online.