Synthesis for mixed arithmetic

The primary goal of this paper is to show that a clever use of redundant nu mber systems in some parts of designs can significantly increase their spee d, without noticeably increasing their area and power consumption. This can be achieved by automatically using, in the same design, redundant (e.g., c arry save or borrow save) as well as non-redundant (i.e., conventional) num ber systems: this approach can be called mixed arithmetic. This implies spe cific constraints in the scheduling process. We propose an integer linear p rogramming (ILP) formulation. It finds an optimal solution for examples of reasonable sizes. In some cases, the ILP computational delay may become hug e. To solve this problem, we introduce a general solution, based on a const raint graph partitioning. This leads to an ILP formulation partitioning. Th is partitioning approach can be used for other similar problems in synthesi s, also formulated as ILPs.