Truncated Multiple Constant Multiplication with Minimal Number of Full Adders

Rémi Garcia (1, 2) , Anastasia Volkova (1, 2) , Martin Kumm (3)

1 UN - Université de Nantes
2 LS2N - Laboratoire des Sciences du Numérique de Nantes
3 University of Applied Sciences [Fulda]

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.

Mots clés: Multiple constant multiplication; digital arithmetic; circuit optimization; full adders

Domaines: Informatique [cs]; Recherche opérationnelle [math.OC]; Systèmes embarqués; Architectures Matérielles [cs.AR]

Rémi Garcia, Anastasia Volkova, Martin Kumm. Truncated Multiple Constant Multiplication with Minimal Number of Full Adders. ISCAS 2022, May 2022, Austin, Texas, United States. pp.263-267, ⟨10.1109/ISCAS48785.2022.9937441⟩. ⟨hal-03582935⟩