Truncated Multiple Constant Multiplication with Minimal Number of Full Adders

Many algorithms from digital signal processing, including digital filters or discrete transforms, require the multiplications with several constants. These can be efficiently implemented multiplierless by using additions, subtractions, and bit-shifts. Finding a multiplierless solution with minimal cost is known as the multiple constant multiplication (MCM) problem. Usually, not the full precision is required at the output. The state-of-the-art approaches consist in finding an MCM solution first, and truncating it in a second step. In this work, we solve the MCM problem with minimal number of full adders for truncated outputs. By combining the two steps into a global optimization problem, modeled through mixed-integer linear programming, we are able to reduce the number of full adders by 60% in best cases and by 12% on average. Our method has shown its efficiency on more than 80 instances from literature and permits a fast improvement of state-of-the-art results in most of the cases.