Optimal Shift Reassignment in Reconfigurable Constant Multiplication Circuits

This paper presents a new method called optimal shift reassignment (OSR), used for reconfigurable multiplication circuits. These circuits consist of adders, subtractors, shifts, and multiplexers (MUXs). They calculate the multiplication of an input number by one out of several constants which can be selected dynamically during run-time. The OSR method is based on the idea that shifts can be placed at different positions along the circuit, while the calculated output constant stays the same. This differs from previous approaches, which were limited by the fact that all constants within the constant multiplier were forced to be odd. The OSR method subsequently releases this restriction. As a result, the number of required MUXs in the circuit can be reduced. This happens when the shift reassignment aligns the shift values of different inputs of an MUX. Experimental results show MUX savings of up to 50% and average savings between 11% and 16% using the OSR method compared to previous approaches.