OPTIMUS: a new program for OPTIMizing linear circuits with number-splitting and shift-and-add decompositions

Most behavioral synthesis tools perform limited architectural transformations to optimize hardware and power. Previously, researchers have proposed decomposition of multiplications into shifts and adds to achieve average savings of 2.5 times in hardware. In this paper, we propose a new program called OPTIMUS and related algorithms, that combine an architectural transformation procedure called number-splitting with shift-and-add decomposition to obtain up to an additional 2 fold savings, giving a factor of up to 5 savings in overall hardware. The number-splitting transformation changes the circuit interconnections and the descriptions of constant multipliers. The scheme is based on numerical matrix transformation algorithms that allow a given matrix to be expressed as the product of several matrices while maintaining numerical accuracy.