Title: Small Logic-based Multipliers with Incomplete Sub-Multipliers for FPGAs

Abstract: There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for efficient small multipliers. The large DSP blocks have limitations implementing many small multipliers efficiently. Hence, this work proposes a solution for better logic-based multipliers that is especially beneficial for small multipliers. Our work is based on the multiplier tiling method in which a multiplier is designed out of several sub-multiplier tiles. The key observation we made is that these sub-multipliers do not necessarily have to perform a complete (rectangular) NxK multiplication and more efficient sub-multipliers are possible that are incomplete (non-rectangular). This proposal first seeks to identify efficient incomplete irregular sub-multipliers and then demonstrates improvements over state-of-the-art designs. It is shown that optimal solutions can be found using integer linear programming (ILP), which are evaluated in FPGA synthesis experiments.