Multiple constant multiplication with ternary adders

The scaling operation, i. e., the multiplication with a single constant is a frequently used operation in many kinds of numeric algorithms. The multiple constant multiplication (MCM) is a generalization where a variable is multiplied by several constants. This kind of operation is heavily used, e. g., in digital filters or discrete transforms. It was shown in recent work that small, fast and power efficient MCM implementations can be realized by using the fast carry chains of FPGAs rather than wasting specialized embedded multipliers. However, in the work so far, only common two-input adders were used. As FPGAs today support ternary adders, i. e., adders with three inputs, this work investigates the optimization of pipelined MCM circuits which include ternary adders. It is shown experimentally that 27% less operations are needed on average by using ternary adders, resulting in 15% slice (Xilinx) and 10% ALM (Altera) reductions, respectively.